We study the loss of quantumness caused by time dilation [1] for a Schrödinger cat state. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decoherence times due to classical noise originating from the unavoidable statistical fluctuations in the characteristic parameters of the system [21]. We show that the experimental observation of decoherence due to time dilation imposes severe limitations on the allowed levels of classical noise in the experiments.
We investigate decoherence of quantum superpositions induced by gravitational time dilation and spontaneous emission between two atomic levels. It has been shown that gravitational time dilation can be an universal decoherence source. Here, we consider decoherence induced by gravitational time dilation only in the situation of spontaneous emission. Then, we obtain that the coherence of particle's position state depends on reference frame due to the time dilation changing the distinguishability of emission photon from two positions of particle. Changing the direction of light field can also res…
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).
Recently, a static gravitational field, such as that of the Earth, was proposed as a new source of decoherence [1]. We study the conditions under which it becomes the dominant decoherence effect in typical interferometric experiments. The following competing sources are considered: spontaneous emission of light, absorption, scattering with the thermal photons and collisions with the residual gas. We quantify all these effects. As we will see, current experiments are off by several orders of magnitude. New ideas are needed in order to achieve the necessary requirements: having as large as syste…
Atomic clock interferometers are a valuable tool to test the interface between quantum theory and gravity, in particular via the measurement of gravitational time dilation in the quantum regime. Here, we investigate whether gravitational time dilation may be also used as a resource in quantum information theory. In particular, we show that for a freely falling interferometer and for a Mach-Zehnder interferometer, the gravitational time dilation may enhance the precision in estimating the gravitational acceleration for long interferometric times. To this aim, the interferometric measurements sh…
We present a gravitationally rigorous and clear answer, in the negative, to the question whether gravimetry with atom interferometers is equivalent to the the measurement of the relative gravitational time dilation of two clocks separated in space. Though matter and light waves, quantum states and oscillator clocks are quantum synonymous through the Planck-Einstein-de Broglie relations and the equivalence principle, there are crucial differences in the context of tests of gravitation theories.
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…
Gravitational time dilation in quantum clock interferometry with entangled multi-photon states and quantum memories
Humboldt-Universität zu Berlin（柏林洪堡大学）；ZARM, Unversität Bremen（不来梅大学ZARM中心）；Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心，原子物理研究所，维也纳工业大学）
Interplays between quantum physics and gravity have long inspired exciting studies, which reveal subtle connections between quantum laws and the general notion of curved spacetime. One important example is the uniqueness of free-falling motions in both quantum and gravitational physics. In this work, we re-investigate the free-falling motions of quantum test wave packets that are distributed over weakly curved spacetime backgrounds. Except for the de Broglie relations, no assumption of priori given Hamiltonians or least actions satisfied by the quantum system is made. We find that the mean mot…
Atomic clocks can measure the gravitational redshift predicted by general relativity with great accuracy and for height differences as little as 1 cm. All existing experiments, however, involve the comparison of two independent clocks at different locations rather than a single clock in a delocalized quantum superposition. Here we present an interferometry scheme employing group-II-type atoms, such as Sr or Yb, capable of measuring the gravitational time dilation in a coherent superposition of atomic wave packets at two different heights. In contrast to other recent proposals, there is no need…
We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational potential. A crucial ingredient in our argument is that ideal classical mechanical motion occurs at const…
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum algorithm to model a many-body system of Dirac particles in a gauge field with Lorentz invariance down to the grid scale (Planck scale)--the lattice-based model neither suffers the Fermi-sign problem nor breaks Lorentz invariance. Yet, for the Dirac Hamiltonian to generate the unitary evolution of the 4-spinor field at the Planck scale, there is time dilation betw…
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.…
The Hong-Ou-Mandel (HOM) effect is analyzed for photons in a modified Mach-Zehnder setup with two particles experiencing different gravitational potentials, which are later recombined using a beam-splitter. It is found that the HOM effect depends directly on the relativistic time dilation between the arms of the setup. This temporal dilation can be used to estimate the $γ$ and $β$ parameters of the parameterized post-Newtonian formalism. The uncertainty in the parameters $γ$ and $β$ are of the order $ 10^{-8}-10^{-12}$, depending on the quantum state employed.
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational poten…
The recently proposed centre of mass decoherence of composite objects due to gravitational time-dilation [Pikovski et al., Nat.Phys. 15. June (2015); arXiv:1311.1095] is confronted with the principle of equivalence between gravity and observer's acceleration. In the laboratory frame, a positional superposition $\vert x_1\rangle+\vert x_2\rangle$ can quickly decohere whereas in the free-falling frame, as I argue, the superposition can survive for almost arbitrary long times. The paradoxical result is explained by the so far unappreciated feature of the proposed model: the centre of mass canonic…
Exploring Einstein's theories of relativity in quantum systems, for example by using atomic clocks at high speeds can deepen our knowledge in physics. However, many challenges still remain on finding novel methods for detecting effects of gravity and of special relativity and their roles in light-matter interaction. Here we introduce a scheme of x-ray quantum optics that allows for a millimeter scale investigation of the relativistic redshift by directly probing a fixed nuclear crystal in Earth's gravitational field with x-rays. Alternatively, a compact rotating crystal can be used to force in…
There are discernible and fundamental differences between clocks, waves and physical states in classical physics. These fundamental concepts find a common expression in the context of quantum physics in gravitational fields; matter and light waves, quantum states and oscillator clocks become quantum synonymous through the Planck-Einstein-de Broglie relations and the equivalence principle. With this insight, gravitational effects on quantum systems can be simply and accurately analyzed. Apart from providing a transparent framework for conceptual and quantitative thinking on matter waves and qua…
We propose an experiment in which an entangled pair of optical pulses are propagated through non-uniform gravitational fields. A field operator calculation of this situation predicts decoherence of the optical entanglement under experimentally realistic conditions.
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon travelling in superposition…
Good clocks are of importance both to fundamental physics and for applications in astronomy, metrology and global positioning systems. In a recent technological breakthrough, researchers at NIST have been able to achieve a stability of 1 part in $10^{18}$ using an Ytterbium clock. This naturally raises the question of whether there are fundamental limits to the stability of clocks. In this paper we point out that gravity and quantum mechanics set a fundamental limit on the stability of clocks. This limit comes from a combination of the uncertainty relation, the gravitational redshift and the r…
We investigate the Hong-Ou-Mandel (HOM) effect $-$ a two-photon quantum-interference effect $-$ in the space-time of a rotating spherical mass. In particular, we analyze a common-path HOM setup restricted to the surface of the earth and show that, in principle, general-relativistic frame-dragging induces observable shifts in the HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time-dilation effects in HOM interference, for a dual-arm configuration. The formalism thus presented establishes a basis for encoding general-relativis…
In this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm-Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity …
We explore, in the framework of linearized quantum gravity, the induced gravitational interaction between two gravitationally polarizable objects in their ground states in the presence of an external quantized gravitational radiation field. The interaction energy decreases as $r^{-5}$ in the near regime, and oscillates with a decreasing amplitude proportional to $r^{-1}$ in the far regime, where $r$ is the distance between the two objects. The interaction can be either attractive or repulsive depending on the propagation direction, polarization and frequency of the external gravitational field…
We show that the gravitational modification of the phase of a neutron beam (the COW experiment) has a classical origin, being due to the time delay which classical particles experience in traversing a background gravitational field. Similarly, we show that classical light waves also undergo a phase shift in traversing a gravitational field. We show that the COW experiment respects the equivalence principle even in the presence of quantum mechanics.
The formal structure of Penrose's gravitationally induced reduction of the wave function mechanism is analyzed. It is shown that pushing Penrose's argument forward leads to the interpretation of quantum coherence in microscopic systems as an observable signature violation of general covariance. We discuss potential avenues to avoid this conclusion, among them emergent quantum mechanics and super-determinism.
Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States
University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；NYU Tandon School of Engineering（纽约大学坦登工程学院）；Vector Institute（向量研究所）
I present the exact solution of a toy model for gravitationally induced decoherence. The toy model has Hamiltonian resembling optomechanical systems. It is an oscillator system coupled through its energy to an oscillator heat bath. I find the decoherence effect of vacuum fluctuations at zero temperature. Also for a finite bath I show that the decoherence is in general present and the system does not return to its initial coherence unless the fundamental frequencies of the bath have rational ratios.
