Dirac states of an electron in a circular intense magnetic field [HEAP]


Neutron-star magnetospheres are structured by very intense magnetic fields extending from 100 to 10 5 km traveled by very energetic electrons and positrons with Lorentz factors up to $\sim$ 10 7. In this context, particles are forced to travel almost along the magnetic field with very small gyro-motion, potentially reaching the quantified regime. We describe the state of Dirac particles in a locally uniform, constant and curved magnetic field in the approximation that the Larmor radius is very small compared to the radius of curvature of the magnetic field lines. We obtain a result that admits the usual relativistic Landau states as a limit of null curvature. We will describe the radiation of these states, that we call quantum curvature or synchro-curvature radiation, in an upcoming paper.

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G. Voisin, S. Bonazzola and F. Mottez
Thu, 16 Mar 17

Comments: N/A


Non-cyclic geometric phases and helicity transitions for neutrino oscillations in magnetic field [CL]


We show that neutrino spin and spin-flavor transitions involve non-vanishing geometric phases. Analytical expressions are derived for non-cyclic geometric phases arising due to neutrino oscillations in magnetic fields and matter. Several calculations are performed for different cases of rotating and non-rotating magnetic fields in the context of solar neutrinos and neutrinos produced inside neutron stars. It is shown that the neutrino eigenstates carry non-vanishing geometric phases even at large distances from their original point of production. Also the effects of critical magnetic fields and cross boundary effects in case of neutrinos emanating out of neutron stars are analyzed.

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S. Joshi and S. Jain
Thu, 16 Mar 17

Comments: 12 pages, 7 figures

Cosmic Quantum Optical Probing of Quantum Gravity Through a Gravitational Lens [CL]


We consider the nonunitary quantum dynamics of neutral massless scalar particles used to model photons around a massive gravitational lens. The gravitational interaction between the lensing mass and asymptotically free particles is described by their second-quantized scattering wavefunctions. Remarkably, the zero-point spacetime fluctuations can induce significant decoherence of the scattered states with spontaneous emission of gravitons, thereby reducing the particles’ coherence as well as energy. This new effect suggests that, when photon polarizations are negligible, such quantum gravity phenomena could lead to measurable anomalous redshift of recently studied astrophysical lasers through a gravitational lens in the range of black holes and galaxy clusters.

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T. Oniga, E. Mansfield and C. Wang
Mon, 6 Mar 17

Comments: 4 pages, 2 figures

Topological Origin of Geophysical Waves [CL]


Symmetries and topology are central to an understanding of physics. Topology explains the precise quantization of the Hall effect and the protection of surface states in topological insulators against scattering by non-magnetic impurities or bumps. Subsequent to the discovery of the quantum spin Hall effect, states of matter with different topological properties were classified according to the discrete symmetries of the system. Recently topologically protected edge excitations have been found in artificial lattice structures that support classical waves of various types. The interplay between discrete symmetries and the topology of fluid waves has so far played no role in the study of the dynamics of oceans and atmospheres. Here we show that, as a consequence of the rotation of the Earth that breaks time reversal symmetry, equatorially trapped Kelvin and Yanai waves have a topological origin, manifesting as equatorial edge modes in the rotating shallow water model. These unidirectional edge modes are guaranteed to exist by the non-trivial global structure of the bulk Poincar\’e modes encoded through the first Chern number of value $\pm2$, in agreement with the correspondence between behavior deep in the bulk and edge excitations of a physical system. Thus the oceans and atmospheres of Earth and other rotating planets naturally share fundamental properties with topological insulators, despite the absence of an underlying lattice. As equatorially trapped Kelvin waves are an important component of El Ni\~no Southern Oscillation, and Madden-Julian Oscillation, our results demonstrate the topology plays an unexpected role in Earth’s climate system. These and other geophysical waves of topological origin are protected against static perturbations by time scale separation from other modes that inhibits scattering.

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P. Delplace, J. Marston and A. Venaille
Mon, 27 Feb 17

Comments: N/A

Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit [CL]


We consider cosmological evolution from the perspective of quantum information. We present a quantum circuit model for the expansion of a comoving region of space, in which initially-unentangled ancilla qubits become entangled as expansion proceeds. We apply this model to the comoving region that now coincides with our Hubble volume, taking the number of entangled degrees of freedom in this region to be proportional to the de Sitter entropy. The quantum circuit model is applicable for at most 140 $e$-folds of inflationary and post-inflationary expansion: we argue that no geometric description was possible before the time $t_1$ when our comoving region was one Planck length across, and contained one pair of entangled degrees of freedom. This approach could provide a framework for modeling the initial state of inflationary perturbations.

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N. Bao, C. Cao, S. Carroll, et. al.
Fri, 24 Feb 17

Comments: 12 pages, 1 figure. Including appendix

Quantum correlation measurements in interferometric gravitational wave detectors [CL]


Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational wave detectors, such as the Advanced Laser Interferometer Gravitational wave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer for the first time.

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D. Martynov, V. Frolov, S. Kandhasamy, et. al.
Tue, 14 Feb 17

Comments: N/A

Quantum principle of sensing gravitational waves: From the zero-point fluctuations to the cosmological stochastic background of spacetime [CL]


We carry out a theoretical investigation on the collective dynamics of an ensemble of correlated atoms, subject to both vacuum fluctuations of spacetime and stochastic gravitational waves. A general approach is taken with the derivation of a quantum master equation capable of describing arbitrary confined nonrelativistic matter systems in an open quantum gravitational environment. It enables us to relate the spectral function for gravitational waves and the distribution function for quantum gravitational fluctuations and to indeed introduce a new spectral function for the zero-point fluctuations of spacetime. The formulation is applied to two-level Rydberg-like identical bosonic atoms in a cavity, leading to a gravitational transition mechanism through certain quadrupole moment operators. For a large number $N$ of such atoms, we find their equilibrium state to satisfy the Boltzmann distribution. The overall relaxation rate before reaching equilibrium is found to scale collectively with $N$. However, we are able to identify certain states whose decay and excitation rates with stochastic gravitational waves and vacuum spacetime fluctuations amplify more significantly with a factor of $N^2$. Using such favourable states as a means of measuring both conventional stochastic gravitational waves and novel zero-point spacetime fluctuations, we determine the theoretical lower bounds for the respective spectral functions. Finally, we discuss the implications of our findings on future observations of gravitational waves of a wider spectral window than currently accessible. Especially, the possible sensing of the zero-point fluctuations of spacetime could provide an opportunity to generate initial evidence and further guidance of quantum gravity.

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D. Quinones, T. Oniga, B. Varcoe, et. al.
Tue, 14 Feb 17

Comments: 13 pages; 4 figures

Mitigating radiation damage of single photon detectors for space applications [CL]


Single-photon detectors in space must retain useful performance characteristics despite being bombarded with sub-atomic particles. Mitigating the effects of this space radiation is vital to enabling new space applications which require high-fidelity single-photon detection. To this end, we conducted proton radiation tests of various models of avalanche photodiodes (APDs) and one model of photomultiplier tube potentially suitable for satellite-based quantum communications. The samples were irradiated with 106 MeV protons at doses equivalent to lifetimes of 0.6 months, 6 months, 12 months and 24 months in a low-Earth polar orbit. Although most detection properties were preserved, including effciency, timing jitter and afterpulsing probability, all APD samples demonstrated significant increases in dark count rate (DCR) due to radiation-induced damage, many orders of magnitude higher than the 200 counts per second (cps) required for ground-tosatellite quantum communications. We then successfully demonstrated the mitigation of this DCR degradation through the use of deep cooling, to as low as -86 degrees C. This achieved DCR below the required 200 cps over the 24 months orbit duration. DCR was further reduced by thermal annealing at temperatures of +50 to +100 degrees C.

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E. Anisimova, B. Higgins, J. Bourgoin, et. al.
Tue, 7 Feb 17

Comments: N/A

The Anomalous Magnetic Moment of a photon propagating in a magnetic field [CL]


We analyze the spectrum of the Hamiltonian of a photon propagating in a strong magnetic field $B\sim B_{\rm{cr}}$, where $B_{\rm cr}= \frac{m^2}{e} \simeq 4.4 \times 10^{13}$ Gauss is the Schwinger critical field . We show that the expected value of the Hamiltonian of a quantized photon for a perpendicular mode is a concave function of the magnetic field $B$. We show by a partially analytic and numerical method that the anomalous magnetic moment of a photon in the one loop approximation is a non – decreasing function of the magnetic field $B$ in the range $0\leq B \leq 30 \, B_{\rm cr}$ We provide a numerical representation of the expression for the anomalous magnetic moment in terms of special functions. We find that the anomalous magnetic moment $\mu_\gamma$ of a photon for $B=30\, B_{\rm cr }$ is $8/3$ of the anomalous magnetic moment of a photon for $B = 1/2 ~ B_{\rm cr}$.

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J. Mielniczuk, D. Lamm, S. Auddy, et. al.
Fri, 3 Feb 17

Comments: arXiv admin note: text overlap with arXiv:1503.00532 by other authors

Quantum Break-Time of de Sitter [CL]


The quantum break-time of a system is the time-scale after which its true quantum evolution departs from the classical mean field evolution. For capturing it, a quantum resolution of the classical background – e.g., in terms of a coherent state – is required. In this paper, we first consider a simple scalar model with anharmonic oscillations and derive its quantum break-time. Next, we apply these ideas to de Sitter space. We formulate a simple model of a spin-2 field, which for some time reproduces the de Sitter metric and simultaneously allows for its well-defined representation as quantum coherent state of gravitons. The mean occupation number $N$ of background gravitons turns out to be equal to the de Sitter horizon area in Planck units, while their frequency is given by the de Sitter Hubble parameter. In the semi-classical limit, we show that the model reproduces all the known properties of de Sitter, such as the redshift of probe particles and thermal Gibbons-Hawking radiation, all in the language of quantum $S$-matrix scatterings and decays of coherent state gravitons. Most importantly, this framework allows to capture the $1/N$-effects to which the usual semi-classical treatment is blind. They violate the de Sitter symmetry and lead to a finite quantum break-time of the de Sitter state equal to the de Sitter radius times $N$. We also point out that the quantum-break time is inversely proportional to the number of particle species in the theory. Thus, the quantum break-time imposes the following consistency condition: Older and species-richer universes must have smaller cosmological constants. For the maximal, phenomenologically acceptable number of species, the observed cosmological constant would saturate this bound if our Universe were $10^{100}$ years old in its entire classical history.

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G. Dvali, C. Gomez and S. Zell
Wed, 1 Feb 17

Comments: 52 pages, 5 figures

Quantum coherence, radiance, and resistance of gravitational systems [CL]


We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A systematic approach to the generation of gravitational waves in the quantum domain is presented that recovers known classical limits in terms of the quadrupole radiation formula and back-reaction dissipation. Classical gravitational emission and absorption relations are quantized into their quantum field theoretical counterparts in terms of the corresponding operators and quantum ensemble averages. Certain arising consistency issues related to factor ordering have been addressed and resolved. Using the theoretical formulation established here with numerical simulations in the quantum regime, we demonstrate new predictions including decoherence through the spontaneous emission of gravitons and collectively amplified “superradiance” of gravitational waves by a highly coherent state of identical particles.

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T. Oniga and C. Wang
Tue, 17 Jan 17

Comments: 10 pages, 3 figures

Towards Searching for Entangled Photons in the CMB Sky [CL]


We explore the possibility of detecting an entangled pair of cosmic microwave background (CMB) photons from casually disconnected patches of the sky or other cosmological sources. The measurement uses the standard HBT intensity interferometer with the polarizer orientations for the two detectors chosen as in a Bell inequality experiment. However, unless the angle between the two sources is large such that entanglement is less likely, the entanglement signal is contaminated with un-entangled background which makes it hard to isolate the signal.

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J. Chen, S. Dai, D. Maity, et. al.
Fri, 13 Jan 17

Comments: 4 pages, 1 figure

Decoherence, discord and the quantum master equation for cosmological perturbations [CL]


We consider a model for the interaction between the cosmological perturbations and another environmental field during inflation, in order to study decoherence, the quantum to classical transition and the impact on quantum correlations. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. Our master equation reveals many important features characteristic of the quantum to classical transition which are not captured by an isolated pure state. In particular, we find that decoherence grows in strength as modes exit the horizon, and memory effects are negligible, implying that the Langevin description involves white noise. In contrast to pure states, entropy and the spread of the Wigner function increase in time due to environmental interactions, with their evolution determined by the relative strength of squeezing and decoherence. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord, but that these corrections are perturbatively small in the coupling. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.

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T. Hollowood and J. McDonald
Tue, 10 Jan 17

Comments: 22 pages, 12 figures

Bell violation in primordial cosmology [CL]


In this paper, we have worked on the possibility of setting up an Bell’s inequality violating experiment in the context of primordial cosmology following the fundamental principles of quantum mechanics. To set up this proposal we have introduced a model independent theoretical framework using which we have studied the creation of new massive particles for the scalar fluctuations in the presence of additional time dependent mass parameter. Next we explicitly computed the one point and two point correlation functions from this setup. Then we comment on the measurement techniques of isospin breaking interactions of newly introduced massive particles and its further prospects. After that, we give an example of string theory originated axion monodromy model in this context. Finally, we provide a bound on the heavy particle mass parameter for any arbitrary spin field.

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S. Choudhury, S. Panda and R. Singh
Mon, 2 Jan 17

Comments: 8 pages, 6 figures, 1 table, Shorter version of arXiv:1607.00237, “Talk presented at Varying Constants and Fundamental Cosmology-VARCOSMOFUN’16. To appear in a special issue of Universe.”. arXiv admin note: text overlap with arXiv:1508.01082 by other authors

On signatures of spontaneous collapse dynamics modified single field inflation [CEA]


The observed classicality of primordial perturbations, despite their quantum origin during inflation, calls for a mechanism for quantum-to-classical transition of these initial fluctuations. As literature suggests a number of plausible mechanisms which try to address this issue, it is of importance to seek for concrete observational signatures of these several approaches in order to have a better understanding of the early universe dynamics. Among these several approaches, it is the spontaneous collapse dynamics of Quantum Mechanics which is most viable of leaving discrete observational signatures as collapse mechanism inherently changes the generic Quantum dynamics. We observe in this study that the observables from the scalar sector, i.e. scalar tilt $n_s$, running of scalar tilt $\alpha_s$ and running of running of scalar tilt $\beta_s$, can not potentially distinguish a collapse modified inflationary dynamics in the realm of canonical scalar field and $k-$inflationary scenarios. The only distinguishable imprint of collapse mechanism lies in the observables of tensor sector in the form of modified consistency relation and a blue-tilted tensor spectrum only when the collapse parameter $\delta$ is non-zero and positive.

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S. Banerjee, S. Das, K. Kumar, et. al.
Fri, 30 Dec 16

Comments: 14 pg, 2 tables, 0 figs

Massive Fermi Gas in the Expanding Universe [CEA]


The behavior of a decoupled ideal Fermi gas in a homogeneously expanding three-dimensional volume is investigated, starting from an equilibrium spectrum. In case the gas is massless and/or completely degenerate, the spectrum of the gas can be described by an effective temperature and/or an effective chemical potential, both of which scale down with the volume expansion. In contrast, the spectrum of a decoupled massive and non-degenerate gas can only be described by an effective temperature if there are strong enough self-interactions such as to maintain an equilibrium distribution. Assuming perpetual equilibration, we study a decoupled gas which is relativistic at decoupling and then is red-shifted until it becomes non-relativistic. We find expressions for the effective temperature and effective chemical potential which allow us to calculate the final spectrum for arbitrary initial conditions. This calculation is enabled by a new expansion of the Fermi-Dirac integral, which is for our purpose superior to the well-known Sommerfeld expansion. We also compute the behavior of the phase space density under expansion and compare it to the case of real temperature and real chemical potential. Using our results for the degenerate case, we also obtain the mean relic velocity of the recently proposed non-thermal cosmic neutrino background.

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A. Trautner
Thu, 22 Dec 16

Comments: 19 pages, 16 figures

Geometric phases in neutrino oscillations with nonlinear refraction [CL]


Neutrinos propagating in dense astrophysical environments sustain nonlinear refractive effects due to neutrino-neutrino forward scattering. We study geometric phases in neutrino oscillations that arise out of cyclic evolution of the potential generated by these forward-scattering processes. We perform several calculations, exact and perturbative, that illustrate the robustness of such phases, and of geometric effects more broadly, in the flavor evolution of neutrinos. The scenarios we consider are highly idealized in order to make them analytically tractable, but they suggest the possible presence of complicated geometric effects in realistic astrophysical settings. We also point out that in the limit of extremely high neutrino densities, the nonlinear potential in three flavors naturally gives rise to non-Abelian geometric phases. This paper is intended to be accessible to neutrino experts and non-specialists alike.

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L. Johns and G. Fuller
Thu, 22 Dec 16

Comments: 17 pages, 3 figures

Physical Effects of the Gravitational $Θ$-Parameter [CL]


We describe the effect of the gravitational $\Theta$-parameter on the behavior of the stretched horizon of a black hole in $(3+1)$-dimensions. The gravitational $\Theta$-term is a total derivative, however, it affects the transport properties of the horizon. In particular, the horizon acquires a third order parity violating, dimensionless transport coefficient which affects the way localized perturbations scramble on the horizon. In the context of the gauge/gravity duality, the $\Theta$-term induces a non-trivial contact term in the energy-momentum tensor of a $(2+1)-$dimensional large-N gauge theory, which admits a dual gravity description. As a consequence, the dual gauge theory in the presence of the $\Theta$-term acquires the same third order parity violating transport coefficient.

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W. Fischler and S. Kundu
Tue, 20 Dec 16

Comments: 4 pages. arXiv admin note: substantial text overlap with arXiv:1512.01238

How Decoherence Affects the Probability of Slow-Roll Eternal Inflation [CL]


Slow-roll inflation can become eternal if the quantum variance of the inflaton field around its slowly rolling classical trajectory is converted into a distribution of classical spacetimes inflating at different rates, and if the variance is large enough compared to the rate of classical rolling that the probability of an increased rate of expansion is sufficiently high. Both of these criteria depend sensitively on whether and how perturbation modes of the inflaton interact and decohere. Decoherence is inevitable as a result of gravitationally-sourced interactions whose strength are proportional to the slow-roll parameters. However, the weakness of these interactions means that decoherence is typically delayed until several Hubble times after modes pass the Hubble scale. We show how to modify the standard picture of eternal inflation to reflect this delayed decoherence. An increased time until decoherence, which gives more time for the quantum variance to grow larger, allows inflation to be eternal at smaller field values than previously realized. Near the maxima of hilltop models, the opposite is true: decoherence happens almost instantaneously before the variance can grow large, making eternal inflation impossible.

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K. Boddy, S. Carroll and J. Pollack
Fri, 16 Dec 16

Comments: 27 pages, 4 figures

Theoretical foundations of the Schrödinger method for LSS formation [CL]


It has been shown that the formation of large scale structures (LSS) in the universe can be described in terms of a Schr$\ddot{o}$dinger-Poisson system. This procedure, known as Schr$\ddot{o}$dinger method, has no theoretical basis, but it is intended as a mere tool to model the N-body dynamics of dark matter halos which form LSS. Furthermore, in this approach the “Planck constant” $\hbar$ in the Schr$\ddot{o}$dinger equation is just a free parameter. In this paper we give a theoretical foundation of the Schr$\ddot{o}$dinger method based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. The order of magnitude of the effective Planck constant is estimated as $\hbar \sim m^{5/3} G^{1/2} (N/<\rho>)^{1/6}$, where $N$ and $m$ are the number and the mass of the dark matter halos, $<\rho_0>$ is their average density, and $G$ the gravitational constant. The relevance of this finding for the study of LSS is discussed.

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F. Briscese
Thu, 15 Dec 16

Comments: N/A

Time Dependent Rindler Hamiltonian Eigen States in Momentum Space [CL]


We have developed a formalism to get the time evolution of the eigen states of Rindler Hamiltonian in momentum space. We have shown the difficulties with characteristic curves, and re-cast the time evolution equations in the form of two-dimensional Laplace equation. The solutions are obtain both in polar coordinates as well as in the Cartesian form.

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S. Mitra, S. Das and S. Chakrabarty
Mon, 12 Dec 16

Comments: Six pages REVTEX file with five .eps figures (included)

A Cosmic Bell Test with Measurement Settings from Astronomical Sources [CL]


Bell’s theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell’s inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this “freedom of choice” was addressed by ensuring that selection of measurement settings via conventional “quantum random number generators” (QRNGs) was space-like separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell’s inequality that, for the first time, uses distant astronomical sources as “cosmic setting generators.” In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. We observe statistically significant $\gtrsim 11.7 \sigma$ and $\gtrsim 13.8 \sigma$ violations of Bell’s inequality with estimated $p$-values of $ \lesssim 7.4 \times 10^{-32}$ and $\lesssim 1.1 \times 10^{-43}$, respectively, thereby pushing back by $\sim$600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.

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J. Handsteiner, A. Friedman, D. Rauch, et. al.
Tue, 22 Nov 16

Comments: 24 pages, 12 figures (including Supplemental Material)

A blueprint for a simultaneous test of quantum mechanics and general relativity in a space-based quantum optics experiment [IMA]


In this paper we propose an experiment designed to observe a general-relativistic effect on single photon interference. The experiment consists of a folded Mach-Zehnder interferometer, with the arms distributed between a single Earth orbiter and a ground station. By compensating for other degrees of freedom and the motion of the orbiter, this setup aims to detect the influence of general relativistic time dilation on a spatially superposed single photon. The proposal details a payload to measure the required effect, along with an extensive feasibility analysis given current technological capabilities.

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S. Pallister, S. Coop, V. Formichella, et. al.
Mon, 7 Nov 16

Comments: 21 pages, 9 figures

Schrödinger field theory in curved spacetime: In-In formalism and three-point function for inflationary background [CL]


We review the Schr\”odinger picture of field theory in curved spacetime and using this formalism, the power spectrum of massive non-interacting, minimally coupled scalars in a fixed de Sitter background is obtained. To calculate the N-point function in Schr\”odinger field theory, the “in-in” formalism is extended in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. We compute the three-point function for primordial scalar field fluctuation in the single field inflation by this in-in formalism. The results are the same as the three-point function in the Heisenberg picture.

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A. Rostami and J. Firouzjaee
Tue, 18 Oct 16

Comments: 20 pages

Properties of the false vacuum as the quantum unstable state [CL]


We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival probability has a non-exponential form. At asymptotically late times the survival probability as a function of time $t$ has an inverse power–like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. This means that the energy density in the unstable vacuum state should have analogous properties and hence the cosmological constant $\Lambda = \Lambda (t)$ too. The conclusion is that $\Lambda$ in the Universe with the unstable vacuum should have a form of the sum of the “bare” cosmological constant and of the term of a type $1/t^{2}$: $\Lambda(t) \equiv \Lambda_{bare} + d/ t^{2}$ (where $\Lambda_{bare}$ is the cosmological constant for the Universe with the true vacuum).

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K. Urbanowski
Tue, 4 Oct 16

Comments: 14 pages, 2 figures, accepted for Theoretical and Mathematical Physics. arXiv admin note: substantial text overlap with arXiv:1304.2796

Constraining symmetron fields with atom interferometry [CEA]


We apply the new constraints from atom-interferometry searches for screening mechanisms to the symmetron model, finding that these experiments exclude a previously unexplored region of parameter space. We discuss the possibility of networks of domain walls forming in the vacuum chamber, and how this could be used to discriminate between models of screening.

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C. Burrage, A. Kuribayashi-Coleman, J. Stevenson, et. al.
Fri, 30 Sep 16

Comments: 12 pages, 2 figures

Atomic Interferometry Test of Dark Energy [CEA]


Atomic interferometry can be used to probe dark energy models coupled to matter. We consider the constraints coming from recent experimental results on models generalising the inverse power law chameleons such as $f(R)$ gravity in the large curvature regime, the environmentally dependent dilaton and symmetrons. Using the tomographic description of these models, we find that only symmetrons with masses smaller than the dark energy scale can be efficiently tested. In this regime, the resulting constraints complement the bounds from the E\”otwash experiment and exclude small values of the symmetron self-coupling.

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P. Brax and A. Davis
Fri, 30 Sep 16

Comments: 26 pages, 3 figures

Perturbations and quantum relaxation [CL]


We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.

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A. Kandhadai and A. Valentini
Fri, 16 Sep 16

Comments: 23 pages, 12 figures

Anomalous spectral lines and relic quantum nonequilibrium [CL]


We describe general features that might be observed in the line spectra of relic cosmological particles should quantum nonequilibrium be preserved in their statistics. According to our arguments, these features would represent a significant departure from those of a conventional origin. Among other features, we find a possible spectral broadening (for incident photons) that is proportional to the energy resolution of the recording telescope (and so could be orders of magnitude larger than any intrinsic broadening). Notably, for a range of possible initial conditions we find the possibility of spectral line `narrowing’ whereby a telescope could observe a spectral line which is narrower than it should conventionally be able to resolve. We briefly discuss implications for the indirect search for dark matter.

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N. Underwood and A. Valentini
Fri, 16 Sep 16

Comments: 15 pages, 5 figures

Decoherence as a way to measure extremely soft collisions with Dark Matter [CL]


A new frontier in the search for dark matter (DM) is based on the idea of detecting the decoherence caused by DM scattering against a mesoscopic superposition of normal matter. Such superpositions are uniquely sensitive to very small momentum transfers from new particles and forces, especially DM with a mass below 100 MeV. Here we investigate what sorts of dark sectors are inaccessible with existing methods but would induce noticeable decoherence in the next generation of matter interferometers. We show that very soft, but medium range (0.1 nm – 1 {\mu}m) elastic interactions between matter and DM are particularly suitable. We construct toy models for such interactions, discuss existing constraints, and delineate the expected sensitivity of forthcoming experiments. The first hints of DM in these devices would appear as small variations in the anomalous decoherence rate with a period of one sidereal day. This is a generic signature of interstellar sources of decoherence, clearly distinguishing it from terrestrial backgrounds. The OTIMA experiment under development in Vienna will begin to probe Earth-thermalizing DM once sidereal variations in the background decoherence rate are pushed below one part in a hundred for superposed 5-nm gold nanoparticles. The proposals by Bateman et al. and Geraci et al. could be similarly sensitive, although they would require at least a month of data taking. DM that is absorbed or elastically reflected by the Earth, and so avoids a greenhouse density enhancement, would not be detectable by those three experiment. On the other hand, aggressive proposals of the MAQRO collaboration and Pino et al. would immediately open up many orders of magnitude in DM mass, interaction range, and coupling strength, regardless of how DM behaves in bulk matter.

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C. Riedel and I. Yavin
Thu, 15 Sep 16

Comments: 13 pages main text, 5 figures, 13 pages of appendices and references

Quantum and Classical Behavior in Interacting Bosonic Systems [CL]


It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by the corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, the classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.

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M. Hertzberg
Wed, 7 Sep 16

Comments: 7 pages, 4 plots

Entanglement Growth after a Global Quench in Free Scalar Field Theory [CL]


We compute the entanglement and R\’enyi entropy growth after a global quench in various dimensions in free scalar field theory. We study two types of quenches: a boundary state quench and a global mass quench. Both of these quenches are investigated for a strip geometry in 1, 2, and 3 spatial dimensions, and for a spherical geometry in 2 and 3 spatial dimensions. We compare the numerical results for massless free scalars in these geometries with the predictions of the analytical quasiparticle model based on EPR pairs, and find excellent agreement in the limit of large region sizes. At subleading order in the region size, we observe an anomalous logarithmic growth of entanglement coming from the zero mode of the scalar.

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J. Cotler, M. Hertzberg, M. Mezei, et. al.
Tue, 6 Sep 16

Comments: 32 pages, 9 figures

Is the quilted multiverse consistent with a thermodynamic arrow of time? [CL]


Theoretical achievements, as well as much controversy surround multiverse theory. Various types of multiverses, with an increasing amount of complexity, were suggested and thoroughly discussed by now. While these types are very different, they all share the same basic idea – our physical reality consists of more than just one universe. Each universe within a possibly huge multiverse might be slightly or even very different from the others. The quilted multiverse is one of these types, whose uniqueness arises from the postulate that every possible event will occur infinitely many times in infinitely many universes. In this paper we show that the quilted multiverse is not self-consistent due to the instability of entropy decrease under small perturbations. We therefore propose a modified version of the quilted multiverse which might overcome this shortcoming. It includes only those universes where the minimal entropy occurs at the same instant of (cosmological) time.

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Y. Aharonov, E. Cohen and T. Shushi
Thu, 1 Sep 16

Comments: 11 pages, 1 figure. Comments are welcome

Cosmic Decoherence: Massive Fields [CL]


We study the decoherence of massive fields during inflation based on the Zurek’s density matrix approach. With the cubic interaction between inflaton and massive fields, the reduced density matrix for the massive fields can be calculated in the Schr\”odinger picture which is related to the variance of the non-Gaussian exponent in the wave functional. The decoherence rate is computed in the one-loop form from functional integration. For heavy fields with $m\gtrsim \mathcal{O}(H)$, quantum fluctuations will easily stay in the quantum state and decoherence is unlikely. While for light fields with mass smaller than $\mathcal{O}(H)$, quantum fluctuations are easily decohered within $5\sim10$ e-folds after Hubble crossing. Thus heavy fields can play a key role in studying problems involving inflationary quantum information.

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J. Liu, C. Sou and Y. Wang
Tue, 30 Aug 16

Comments: 26 pages, 3 figures

Glauber theory and the quantum coherence of curvature inhomogeneities [CL]


The curvature inhomogeneities are systematically scrutinized in the framework of the Glauber approach. The amplified quantum fluctuations of the scalar and tensor modes of the geometry are shown to be first-order coherent while the interference of the corresponding intensities is larger than in the case of Bose-Einstein correlations. After showing that the degree of second-order coherence does not suffice to characterize unambiguously the curvature inhomogeneities, we argue that direct analyses of the degrees of third and fourth-order coherence are necessary to discriminate between different correlated states and to infer more reliably the statistical properties of the large-scale fluctuations. We speculate that the moments of the multiplicity distributions of the relic phonons might be observationally accessible thanks to new generations of instruments able to count the single photons of the Cosmic Microwave Background in the THz region.

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M. Giovannini
Tue, 23 Aug 16

Comments: 35 pages

Characterization of very narrow spectral lines with temporal intensity interferometry [IMA]


Context: Some stellar objects exhibit very narrow spectral lines in the visible range additional to their blackbody radiation. Natural lasing has been suggested as a mechanism to explain narrow lines in Wolf-Rayet stars. However, the spectral resolution of conventional astronomical spectrographs is still about two orders of magnitude too low to test this hypothesis. Aims: We want to resolve the linewidth of narrow spectral emissions in starlight. Methods: A combination of spectral filtering with single-photon-level temporal correlation measurements breaks the resolution limit of wavelength-dispersing spectrographs by moving the linewidth measurement into the time domain. Results: We demonstrate in a laboratory experiment that temporal intensity interferometry can determine a 20 MHz wide linewidth of Doppler-broadened laser light, and identify a coherent laser light contribution in a blackbody radiation background.

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P. Tan and C. Kurtsiefer
Thu, 21 Jul 16

Comments: 4 pages, 4 figures

Magneto-optic effects of the Cosmic Microwave Background [CEA]


Generation of magneto-optic effects by the cosmic microwave background (CMB) in the presence of cosmic magnetic fields is studied. Four mechanisms which generate polarization of the CMB such as the Cotton-Mouton effect, the vacuum polarization in external magnetic field, the photon-pseudoscalar mixing in external magnetic field and the Faraday effect are studied. Considering the CMB linearly polarized at decoupling time due to Thomson scattering, it is shown that second order effects in the magnetic field amplitude such as the Cotton-Mouton effect in plasma and the vacuum polarization (Euler-Heisenberg term) in cosmic magnetic field, would generate elliptic polarization of the CMB at post decoupling time depending on the photon frequency and magnetic field strength. The Cotton-Mouton effect in plasma turns out to be the dominant effect in the generation of CMB elliptic polarization in the low frequency part while the vacuum polarization in magnetic field is the dominant process in the high frequency part. The effect of pseudoscalar particles (axions and axion-like particles) on the CMB polarization is also studied. It is shown that photon-pseudoscalar particle mixing in cosmic magnetic field generates elliptic polarization of the CMB as well, depending on the circumstances and even in the case of initially unpolarized CMB. New limits on the pseudoscalar parameter space are set. Prior decoupling CMB polarization due to pseudoscalar particles is also discussed.

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D. Ejlli
Fri, 8 Jul 16

Comments: 45 pages, 2 figures

Quantum Walks as simulators of neutrino oscillations in vacuum and matter [CL]


We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to explore these effects in extreme conditions, such as the solar interior or supernovae, in a complementary way to existing experiments.

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G. Molfetta and A. Perez
Tue, 5 Jul 16

Comments: 3 figures, 6 pages

Bell violation in the Sky [CL]


In this work, we have studied the possibility of setting up Bell’s inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell’s inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in presence of additional time dependent mass contribution. Next using the background scalar fluctuation in presence of new time dependent mass contribution, we explicitly compute the expression for the one point and two point correlation functions. Furthermore, using the results for one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a future theoretical probe to break the degeneracy amongst various models of inflation. Additionally, we also fix the scale of inflation in a model independent way without any prior knowledge of primordial gravitational waves. Next, we also comment on the technicalities of measurements from isospin breaking interactions and the future prospects of newly introduced massive particles in cosmological Bell violating test experiment. Further, we cite a precise example of this set up applicable in the context of string theory motivated axion monodromy model. Then we comment on the explicit role of decoherence effect and high spin on cosmological Bell violating test experiment. In fine, we provide a theoretical bound on the heavy particle mass parameter for scalar fields, graviton and other high spin fields from our proposed setup.

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S. Choudhury, S. Panda and R. Singh
Mon, 4 Jul 16

Comments: 202 pages, 16 figures, 1 table

Hot dense magnetized ultrarelativistic spinor matter in a slab [CL]


Properties of hot dense ultrarelativistic spinor matter in a slab of finite width, placed in a transverse uniform magnetic field, are studied. The admissible set of boundary conditions is determined by the requirement that spinor matter be confined inside the slab. In thermal equilibrium, the chiral separation effect in the slab is shown to depend both on temperature and chemical potential; this is distinct from the unrealistic case of the magnetic field filling the unbounded (infinite) medium, when the effect is temperature-independent. In the realistic case of the slab, a stepwise behaviour of the axial current density at zero temperature is smoothed out as temperature increases, turning into a linear behaviour at infinitely large temperature. A choice of boundary conditions can facilitate either augmentation or attenuation of the chiral separation effect; in particular, the effect can persist even at zero chemical potential, if temperature is nonzero. Thus the boundary condition can serve as a source that is additional to the spinor matter density.

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Y. Sitenko
Tue, 28 Jun 16

Comments: 27 pages, 5 figures. arXiv admin note: text overlap with arXiv:1603.09268

Exact Solution for Chameleon Field, Self-Coupled Through the Ratra-Peebles Potential with n = 1 and Confined Between Two Parallel Plates [CL]


We calculate the chameleon field profile, confined between two parallel plates, in the chameleon field theory with Ratra-Peebles self-interaction potential with index n = 1. We give the exact analytical solution in terms of Jacobian elliptic functions, depending on the mass density of the ambient matter. The obtained analytical solution can be used in qBounce experiments, measuring transition frequencies between quantum gravitational states of ultracold neutrons and also for the calculation of the chameleon field induced Casimir force for the CANNEX experiment. We show that the chameleon-matter interactions with coupling constants beta < 10^4 can be probed by qBounce experiments with sensitivities Delta E < 10^(-18)eV.

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A. Ivanov, G. Cronenberg, R. Hollwieser, et. al.
Thu, 23 Jun 16

Comments: 1 figure, 6 pages

Detecting continuous gravitational waves with superfluid $^4$He [CL]


Direct detection of gravitational waves is opening a new window onto our universe. Here, we study the sensitivity to continuous-wave strain fields of a kg-scale optomechanical system formed by the acoustic motion of superfluid helium-4 parametrically coupled to a superconducting microwave cavity. This narrowband detection scheme can operate at very high $Q$-factors, while the resonant frequency is tunable through pressurization of the helium in the 0.1-1.5 kHz range. The detector can therefore be tuned to a variety of astrophysical sources and can remain sensitive to a particular source over a long period of time. For reasonable experimental parameters, we find that strain fields on the order of $h\sim 10^{-23} /\sqrt{\rm Hz}$ are detectable. We show that the proposed system can significantly improve the limits on gravitational wave strain from nearby pulsars within a few months of integration time.

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S. Singh, L. Lorenzo, I. Pikovski, et. al.
Fri, 17 Jun 16

Comments: N/A

Gravitational wave detection with optical lattice atomic clocks [CL]


We propose a space-based gravitational wave detector consisting of two spatially separated, drag-free satellites sharing ultra-stable optical laser light over a single baseline. Each satellite contains an optical lattice atomic clock, which serves as a sensitive, narrowband detector of the local frequency of the shared laser light. A synchronized two-clock comparison between the satellites will be sensitive to the effective Doppler shifts induced by incident gravitational waves (GWs) at a level competitive with other proposed space-based GW detectors, while providing complementary features. The detected signal is a differential frequency shift of the shared laser light due to the relative velocity of the satellites, rather than a phase shift arising from the relative satellite positions, and the detection window can be tuned through the control sequence applied to the atoms’ internal states. This scheme enables the detection of GWs from continuous, spectrally narrow sources, such as compact binary inspirals, with frequencies ranging from ~3 mHz – 10 Hz without loss of sensitivity, thereby bridging the detection gap between space-based and terrestrial GW detectors. Our proposed GW detector employs just two satellites, is compatible with integration with an optical interferometric detector, and requires only realistic improvements to existing ground-based clock and laser technologies.

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S. Kolkowitz, I. Pikovski, N. Langellier, et. al.
Tue, 7 Jun 16

Comments: 8 pages, 2 figures, and supplemental material

Bell's Inequalities for Continuous-Variable Systems in Generic Squeezed States [CL]


Bell’s inequality for continuous-variable bipartite systems is studied. The inequality is expressed in terms of pseudo-spin operators and quantum expectation values are calculated for generic two-mode squeezed states characterized by a squeezing parameter $r$ and a squeezing angle $\varphi$. Allowing for generic values of the squeezing angle is especially relevant when $\varphi$ is not under experimental control, such as in cosmic inflation, where small quantum fluctuations in the early Universe are responsible for structures formation. Compared to previous studies restricted to $\varphi=0$ and to a fixed orientation of the pseudo-spin operators, allowing for $\varphi\neq 0$ and optimizing the angular configuration leads to a completely new and rich phenomenology. Two dual schemes of approximation are designed that allow for comprehensive exploration of the squeezing parameters space. In particular, it is found that Bell’s inequality can be violated when the squeezing parameter $r$ is large enough, $r\gtrsim 1.12$, and the squeezing angle $\varphi$ is small enough, $\varphi\lesssim 0.34\,e^{-r}$.

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J. Martin and V. Vennin
Thu, 12 May 16

Comments: 9 pages without appendices (38 pages total), 16 figures, to be published in Physical Review A

Classical and quantum cosmology of the little rip abrupt event [CL]


We analyze from a classical and quantum point of view the behavior of the universe close to a little rip, which can be interpreted as a big rip sent towards the infinite future. Like a big rip singularity, a little rip implies the destruction of all bounded structure in the Universe and is thus an event where quantum effects could be important. We present here a new phantom scalar field model for the little rip. The quantum analysis is performed in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We find that the little rip can be avoided in the sense of the DeWitt criterion, that is, by having a vanishing wave function at the place of the little rip. Therefore our analysis completes the answer to the question: can quantum cosmology smoothen or avoid the divergent behavior genuinely caused by phantom matter? We show that this can indeed happen for the little rip, similar to the avoidance of a big rip and a little sibling of the big rip.

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I. Albarran, M. Bouhmadi-Lopez, C. Kiefer, et. al.
Fri, 29 Apr 16

Comments: 14 pages, 3 figures, RevTex4-1

Photon Bubble Turbulence in Cold Atomic Gases [CL]


Turbulent radiation flow is ubiquitous in many physical systems where light-matter interaction becomes relevant. Photon bubbling, in particular, has been identified as the main source of turbulent radiation transport in many astrophysical objects, such as stars and accretion disks. This mechanism takes place when radiation trapping in optically dense media becomes unstable, leading to the energy dissipation from the larger to the smaller bubbles. Here, we report on the observation of photon bubble turbulence in cold atomic gases in the presence of multiple scattering of light. The instability is theoretically explained by a fluid description for the atom density coupled to a diffusive transport equation for the photons, which is known to be accurate in the multiple scattering regime investigated here. We determine the power spectrum of the atom density fluctuations, which displays an unusual $\sim k^{-4}$ scaling, and entails a complex underlying turbulent dynamics resulting from the formation of dynamical bubble-like structures. We derive a power spectrum from the theoretical photon bubble model which, to a high level of accuracy, explains the observations. The experimental results reported here, along with the theoretical model we developed may shed light on the analogue photon bubble instabilities in astrophysical scenarios.

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J. Rodrigues, J. Rodrigues, A. Ferreira, et. al.
Thu, 28 Apr 16

Comments: 5 pages

Dark energy from non-unitarity in quantum theory [CL]


We consider a scheme whereby it is possible to reconcile semi-classical Einstein’s equation with the violation of the conservation of the expectation value of energy-momentum that is associated with dynamical reduction theories of the quantum state for matter. The very interesting out-shot of the formulation is the appearance of a nontrivial contribution to an effective cosmological constant (which is not strictly constant). This opens the possibility of using models for dynamical collapse of the wave function to compute its value. Another interesting implication of our analysis is that tiny violations of energy-momentum conservation with negligible local effects can become very important on cosmological scales at late times.

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T. Josset, A. Perez and D. Sudarsky
Fri, 15 Apr 16

Comments: 8 pages, 2 figures

One Bubble to Rule Them All [CL]


We apply the principles of quantum mechanics and quantum cosmology to predict probabilities for our local observations of a universe undergoing false vacuum eternal inflation. At a sufficiently fine-grained level, histories of the universe describe a mosaic of bubble universes separated by inflationary regions. We show that predictions for local observations can be obtained directly from sets of much coarser grained histories which only follow a single bubble. These coarse-grained histories contain neither information about our unobservable location nor about the unobservable large-scale structure outside our own bubble. Applied to a landscape of false vacua in the no-boundary state we predict our local universe emerged from the dominant decay channel of the lowest energy false vacuum. We compare and contrast this framework for prediction based on quantum cosmology with traditional approaches to the measure problem in cosmology.

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J. Hartle and T. Hertog
Thu, 14 Apr 16

Comments: 33 pages, 5 figures, revtex

Control of a velocity-sensitive audio-band quantum non-demolition interferometer [CL]


The Sagnac speed meter interferometer topology can potentially provide enhanced sensitivity to gravitational waves in the audio-band compared to equivalent Michelson interferometers. A challenge with the Sagnac speed meter interferometer arises from the intrinsic lack of sensitivity at low frequencies where the velocity-proportional signal is smaller than the noise associated with the sensing of the signal. Using as an example the on-going proof-of-concept Sagnac speed meter experiment in Glasgow, we quantify the problem and present a solution involving the extraction of a small displacement-proportional signal. This displacement signal can be combined with the existing velocity signal to enhance low frequency sensitivity, and we derive optimal filters to accomplish this for different signal strengths. We show that the extraction of the displacement signal for low frequency control purposes can be performed without reducing significantly the quantum non-demolition character of this type of interferometer.

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S. Leavey, S. Danilishin, A. Glafke, et. al.
Mon, 28 Mar 16

Comments: N/A

Limits of time in cosmology [CL]


We provide a discussion of some main ideas in our project about the physical foundation of the time concept in cosmology. It is standard to point to the Planck scale (located at $\sim 10^{-43}$ seconds after a fictitious “Big Bang” point) as a limit for how far back we may extrapolate the standard cosmological model. In our work we have suggested that there are several other (physically motivated) interesting limits — located at least thirty orders of magnitude before the Planck time — where the physical basis of the cosmological model and its time concept is progressively weakened. Some of these limits are connected to phase transitions in the early universe which gradually undermine the notion of ‘standard clocks’ widely employed in cosmology. Such considerations lead to a ‘scale problem’ for time which becomes particularly acute above the electroweak phase transition (before $\sim 10^{-11}$ seconds). Other limits are due to problems of building up a cosmological reference frame, or even contemplating a sensible notion of proper time, if the early universe constituents become too quantum. This ‘quantum problem’ for time arises e.g. if a pure quantum phase is contemplated at the beginning of inflation at, say, $\sim 10^{-34}$ seconds.

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S. Rugh and H. Zinkernagel
Fri, 18 Mar 16

Comments: 20 pages, 1 figure. To appear in “The Philosophy of Cosmology”; edited by K. Chamcham, J. Silk, J. Barrow and S. Saunders. Cambridge University Press, 2016