Marc-Thierry Jaekel, Brahim Lamine, Astrid Lambrecht, Serge Reynaud, Paulo Maia Neto
备注：
7 pages
发表信息：
in Beyond the Quantum, Proceedings Leiden 2006, Eds. Th.M. Nieuwenhuizen, V. Spicka, B. Mehmani, M.J. Aghdami, A.Yu. Khrennikov, World Scientific, Singapore (2007) 125-134
The quite different behaviors exhibited by microscopic and macroscopic systems with respect to quantum interferences suggest the existence of a borderline beyond which quantum systems loose their coherences and can be described classically. Gravitational waves, generated within our galaxy or during the cosmic expansion, constitute a universal environment susceptible to lead to such a quantum decoherence mechanism. We assess this idea by studying the quantum decoherence due to gravitational waves on typical microscopic and macoscopic systems, namely an atom interferometer (HYPER) and the Earth-Moon system. We show that quantum interferences remain unaffected in the former case and that they disappear extremely rapidly in the latter case. We obtain the relevant parameters which, besides the ratio of the system's mass to Planck mass, characterize the loss of quantum coherences.
We show that, by treating the gravitational interaction between two mechanical resonators as a classical measurement channel, a gravitational decoherence model results that is equivalent to a model first proposed by Diosi. The resulting decoherence model implies that the classically mediated gravitational interaction between two gravitationally coupled resonators cannot create entanglement. The gravitational decoherence rate ( and the complementary heating rate) is of the order of the gravitationally induced normal mode splitting of the two resonators.
We present a series of arguments against the results of the paper "Universal decoherence due to gravitational time dilation" by Pikovski et al. (arXiv:1311.1095).
Models of gravitational decoherence are not commonly applied to ultra-relativistic systems, including photons. As a result, few quantum optical tests of gravitational decoherence have been developed. In this paper, we generalize the gravitational decoherence model of Anastopoulos and Hu (arXiv:1305.5231) to photons. In this model, decoherence originates from a bath of stochastic gravitational perturbations, possibly of fundamental origin. We derive a master equation for general states of the electromagnetic (EM) field; the only free parameter is a noise temperature $Θ$ of the gravitational flu…
We study the decoherence process associated with the scattering of stochastic backgrounds of gravitational waves. We show that it has a negligible influence on HYPER-like atomic interferometers although it may dominate decoherence of macroscopic motions, such as the planetary motion of the Moon around the Earth.
We study the effect of the scattering of gravitational waves on planetary motions, say the motion of the Moon around the Earth. Though this effect has a negligible influence on dissipation, it dominates fluctuations and the associated decoherence mechanism, due to the very high effective temperature of the background of gravitational waves in our galactic environment.
A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.
We discuss a mechanism of spin decoherence in gravitation within the framework of general relativity. The spin state of a particle moving in a gravitational field is shown to decohere due to the curvature of spacetime. As an example, we analyze a particle going around a static spherically-symmetric object.
We present a general master equation for the quantum dynamics of a scalar bosonic particle interacting with an external weak and stochastic gravitational field. The dynamics predicts decoherence in position as well as in momentum. We show how the master equation reproduces the results present in the literature by taking appropriate limits, thus explaining the apparent contradiction in their dynamical description. We apply our model to a matter wave experiment, providing a practical formula for determining of the magnitude of gravitational decoherence. We compare it with the standard experiment…
We present a simple calculation leading to the quantum gravitationally-induced decoherence of a spatial superposition of a massive object in the linear coupling regime. The point of this calculation is to illustrate that the gravitationally-induced collapse could be of the same origin as any other collapse, i.e. due to the entanglement between the system (here a massive object) and its environment (in this case gravity, but it could well be the electromagnetic or any other field). We then point out that, in some cases, one has to be careful when concluding that matter-wave interference of larg…
We discuss decrease of coherence in a massive system due to the emission of gravitational waves. In particular we investigate environmental gravitational decoherence in the context of an interference experiment. The time-evolution of the reduced density matrix is solved analytically using the path-integral formalism. Furthermore, we study the impact of a tensor noise onto the coherence properties of massive systems. We discuss that a particular choice of tensor noise shows similarities to a mechanism proposed by Diosi and Penrose.
We derive a general quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical external gravitational field. The dynamics predicts decoherence in position, momentum and energy. We show how our master equation reproduces the results present in the literature by taking appropriate limits, thus explaining the apparent contradiction in their dynamical description. Our result is relevant in light of the increasing interest in the low energy quantum-gravity regime.
We consider the possibility to measure the quantum decoherence using gravitational wave interferometers. Gravitational wave interferometers create the superposition state of photons and measure the interference of the photon state. If the decoherence occurs, the interference of the photon state vanishes and it can be measured by the interferometers. As examples of decoherence mechanisms, we consider 1) decoherence by spontaneous localization, 2) gravitational decoherence and 3) decoherence by extra-dimensional gravity.
Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms of energy and matter causing decoherence. This may have subtle implications on precision laboratory experiments and astronomical observations and could limit the ultimate capacities for quantum technologies prone to decoherence. To establish the essential physical mechanism of decoherence under weak spacetime fluctuations, we carry out a sequence of analytica…
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We poi…
We investigate the dynamics of two quantum mechanical oscillator system-bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar QED. The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence…
We study the decoherence process associated with the scattering of stochastic gravitational waves. We discuss the case of macroscopic systems, such as the planetary motion of the Moon around the Earth, for which gravitational scattering is found to dominate decoherence though it has a negligible influence on damping. This contrast is due to the very high effective temperature of the background of gravitational waves in our galactic environment.
We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be accessible by relatively inexpensive table-top experiments, way before the scales where true quantum gravity effects become important. Therefore, they can provide a first experimental view on gravity in the quantum regime. We will survey models of decoherence induced both by classical and quantum gravitational fluctuations; it will be manifest that a clear unders…
Recently Pikovski et al. have proposed in [ Pikovski I et al. 2015 Nature Phys. 11, 668] an intriguing universal decoherence mechanism, suggesting that gravitation may play a conceptually important role in the quantum-to-classical transition, albeit vanishingly small in everyday situations. Here we analyze information transfer induced by this mechanism. We show that generically on short time-scales, gravitational decoherence leads to a redundant information encoding, which results in a form of objectivization of the center-of-mass position in the gravitational field. We derive the relevant tim…
We investigate the effect of quantum metric fluctuations on qubits that are gravitationally coupled to a background spacetime. In our first example, we study the propagation of a qubit in flat spacetime whose metric is subject to flat quantum fluctuations with a Gaussian spectrum. We find that these fluctuations cause two changes in the state of the qubit: they lead to a phase drift, as well as the expected exponential suppression (decoherence) of the off-diagonal terms in the density matrix. Secondly, we calculate the decoherence of a qubit in a circular orbit around a Schwarzschild black hol…
The physics of low-energy quantum systems is usually studied without explicit consideration of the background spacetime. Phenomena inherent to quantum theory on curved space-time, such as Hawking radiation, are typically assumed to be only relevant at extreme physical conditions: at high energies and in strong gravitational fields. Here we consider low-energy quantum mechanics in the presence of gravitational time dilation and show that the latter leads to decoherence of quantum superpositions. Time dilation induces a universal coupling between internal degrees of freedom and the centre-of-mas…
Quantum mechanics and the theory of gravity are presently not compatible. A particular question is whether gravity causes decoherence - an unavoidable source of noise. Several models for gravitational decoherence have been proposed, not all of which can be described quantum mechanically. In parallel, several experiments have been proposed to test some of these models, where the data obtained by such experiments is analyzed assuming quantum mechanics. Since we may need to modify quantum mechanics to account for gravity, however, one may question the validity of using quantum mechanics as a calc…
We study the decoherence of atomic interferometers due to the scattering of stochastic gravitational waves. We evaluate the `direct' gravitational effect registered by the phase of the matter waves as well as the `indirect' effect registered by the light waves used as beam-splitters and mirrors for the matter waves. Considering as an example the space project HYPER, we show that both effects are negligible for the presently studied interferometers.
A new heuristic model of interaction of an atomic system with a gravitational wave is proposed. In it, the gravitational wave alters the local electromagnetic field of the atomic nucleus, as perceived by the electron, which changes the energy of the system. The spectral decomposition of the wave function is calculated, from which the energy of the system can be obtained. The results suggest a shift in the energy difference of the atomic energy levels, which will induce a small detuning to any given resonant transition. The detuning increases with the quantum numbers of the levels, making the e…
In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity; 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not; 3) Gravitational Decoherence: Derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) M…
The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the correlation between a system and a clock, where an idealized clock can be modelled as a two level systems. We investigate the dynamics of clocks interacting gravitationally by treating the gravitational interaction as a classical information channel. In particular, we focus on the decoherence rates and temporal resolution of arrays of $N$ clocks showing how the…
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling fact…
We consider a wave packet of a spin-1/2 particle in a gravitational field, the effect of which can be described in terms of a succession of local inertial frames. It is shown that integrating out of the momentum yields a spin mixed state, with the entropy dependent on the deviation of metric from the flat spacetime. The decoherence occurs even if the particle is static in the gravitational field.
Among the many worthwhile quantum experiments taking advantage of long baselines in space, this white paper points to the far-reaching significance of gravitational decoherence experiments. These experiments can provide clues as to whether gravity is of a fundamental or an effective nature. They can also discriminate between the predictions of quantum field theory in curved spacetime, our default theory for quantum phenomena in background gravitational fields, and other popular alternative quantum theories.
Quantum mechanical interference of wave functions leads to some difficulties if a probability density is considered as a source of gravity. We show that an introduction of a quantum energy-momentum tensor as a source term in Einstein equations can be consistent with general relativity if the gravitational waves are quantized.
The present work can be regarded as a corollary to the paper titled "Neutrino decoherence in presence of strong gravitational fields". Specifically, we investigate the gravitationally-induced decoherence on neutrino oscillation from the point of view of a locally inertial observer at rest with neutrino propagation. In so doing, we observe that in the aforementioned reference frame the effects of gravity can become manifest in a non-trivial manner with respect to an observer placed at infinity.
Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared t…
As laser interferometer gravitational wave (GW) detectors become quantum noise dominated, understanding the fundamental limit on measurement sensitivity imposed by quantum uncertainty is crucial to guide the search for further noise reduction. Recent efforts have included applying ideas from quantum information theory to GW detection -- specifically the quantum Cramer Rao bound, which is a minimum bound on error in parameter estimation using a quantum state and is determined by the state's quantum Fisher information (QFI) with respect to the parameter. Identifying the QFI requires knowing the …
Gravitationally Induced Quantum Decoherence of Macroscopic Objects
The Hakubi Center for Advanced Research, Kyoto University（京都大学白川中心）；Department of Physics, Kyoto University（京都大学物理系）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation $ζ$ due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state $Ψ$ in the Schrödinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorterwavelength) modes of $ζ$ as an environment. We show that inflation produces phas…
In many theories of quantum gravity quantum fluctuations of spacetime may serve as an environment for decoherence. Here we study quantum-gravitational decoherence of high energy astrophysical neutrinos in the presence of fermionic dark sectors and for a realistic three neutrino scenario. We show how violation of global symmetries expected to arise in quantum gravitational interactions provides a possibility to pin down the number of dark matter fermions in the universe. Furthermore, we predict the expected total neutrino flux and flavor ratios at experiments depending on the flavor composition…
We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer [1]. The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell's position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space.…
We discuss the interplay of wave packet decoherence and decoherence induced by quantum gravity via interactions with spacetime foam for high energy astrophysical neutrinos. In this context we point out a compelling consequence of the expectation that quantum gravity should break global symmetries, namely that quantum-gravity induced decoherence may not only be the most sensitive probe for quantum properties of spacetime, but also can provide both a powerful tool for the search for new particles, including totally decoupled backgrounds interacting only gravitationally, and at the same time a wi…
We study how quantum correlations survive at large scales in spite of their exposition to stochastic backgrounds of gravitational waves. We consider Einstein-Podolski-Rosen (EPR) correlations built up on the polarizations of photon pairs and evaluate how they are affected by the cosmic gravitational wave background (CGWB). We evaluate the quantum decoherence of the EPR correlations in terms of a reduction of the violation of the Bell inequality as written by Clauser, Horne, Shimony and Holt (CHSH). We show that this decoherence remains small and that EPR correlations can in principle survive u…
In Nature Phys. 11, 668 (2015) (Ref. [1]), a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field is shown to undergo a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's Equivalence Principle to be valid, we demonstrate, first in a Lorentz frame with accelerating detectors, and then directly in the Lab frame with uniform gravity, that the dephasing between the different internal states arise not from gravity but rather from differences in their rest mass, and the mass dependence of the de Br…
We investigate the squeezing of primordial gravitational waves (PGWs) in terms of quantum discord. We construct a classical state of PGWs without quantum discord and compare it with the Bunch-Davies vacuum. Then it is shown that the oscillatory behavior of the angular-power spectrum of the cosmic microwave background (CMB) fluctuations induced by PGWs can be the signature of the quantum discord of PGWs. In addition, we discuss the effect of quantum decoherence on the entanglement and the quantum discord of PGWs for super-horizon modes. For the state of PGWs with decoherence effect, we examine …
Graviton emission decoheres superpositions of matter states. We write the decoherence rate in terms of a "differential Bondi news" function, and show that this function can be written as an overlap integral between different asymptotic radiative states given by Ashtekar. This result - while derived in the linearized theory - is ultimately expressed for asymptotically flat space-times in terms of variables with unambiguous geometric meaning in the full theory. We treat a simple two-path experiment, and compute the differential news, the purity, the entanglement entropy, and the fidelity, to mak…
We review the difference between standard environmental decoherence and 'intrinsic decoherence', which is taken to be an ineluctable process of Nature. Environmental decoherence is typically modeled by spin bath or oscillator modes - we review some of the unanswered questions not captured by these models, and also the application of them to experiments. Finally, a sketch is given of a new theoretical approach to intrinsic decoherence, and this scheme is applied to the discussion of gravitational decoherence.
