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 a universal decoherence source by Pikovski et al. Here, we consider the decoherence induced by the gravitational time dilation only in the situation of spontaneous emission. We obtain the analytical results of the coherence of particle’s position state. Then, we obtain that the coherence of particle’s position state depends on reference frame because the time dilation changes the distinguishability of emitted photons from two positions of particle in different reference frames. For observing the decoherence effect induced by the gravitational time dilation, time-delayed feedback can be utilized to increase the decoherence of particle’s superposition state.
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 a universal decoherence source by Pikovski et al. Here, we consider the decoherence induced by the gravitational time dilation only in the situation of spontaneous emission. We obtain the analytical results of the coherence of particle’s position state. Then, we obtain that the coherence of particle’s position state depends on reference frame because the time dilation changes the distinguishability of emitted photons from two positions of particle in different reference frames. For observing the decoherence effect induced by the gravitational time dilation, time-delayed feedback can be utilized to increase the decoherence of particle’s superposition state.
According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom's emission spectrum.
Here we discuss an effect of gravitational decoherence due to time dilation on the collective radiation dynamics of atomic system in timed single-photon Dicke states. We show that a photon absorbed by the stationary system of randomly placed stationary atoms is no more spontaneously emitted in the direction of the impinging photon. Time-dilation effect leads to broadening of the angular distribution of the emitted photon. Even for the spherically symmetric gravitational field, the broadening has specific non-symmetrical character.
Both quantum mechanics and general relativity are based on principles that defy our daily intuitions, such as time dilation, quantum interference and entanglement. Because the regimes where the two theories are typically tested are widely separated, their foundational principles are rarely jointly studied. Recent works have found that novel phenomena appear for quantum particles with an internal structure in the presence of time dilation, which can take place at low energies and in weak gravitational fields. Here we briefly review the effects of time dilation on quantum interference and generalize the results to a variety of systems. In addition, we provide an extended study of the basic principles of quantum theory and relativity that are of relevance for the effects and also address several questions that have been raised, such as the description in different reference frames, the role of the equivalence principle and the effective irreversibility of the decoherence. The manuscript clarifies some of the counterintuitive aspects arising when quantum phenomena and general relativistic effects are jointly considered.
We study the loss of quantumness caused by time dilation [I. Pikovski, M. Zych, F. Costa, and \ifmmode \check{C}\else \v{C}\fi{}. Brukner, Nat. Phys. 11, 668 (2015)] for a Schr\"odinger 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 [J. Trapani, M. Bina, S. Maniscalco, and M. G. A. Paris, Phys. Rev. A 91, 022113 (2015)]. 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.
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.
The recently proposed centre-of-mass decoherence of composite objects due to gravitational time-dilation [Pikovski et al , Nat.Phys. 11, 668 (2015)] is confronted with the principle of equivalence between gravity and observer's acceleration. In the laboratory frame, a positional superposition | x 1 〉 + | x 2 〉 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 canonical subsystem is ambiguous, it is di˙erent in the laboratory and the free-falling frames, respectively. As long as the centre-of-mass motion of the composite object is non-relativistic, a simple Galilean-covariant Hamiltonian represents the Pikovski et al theory with exactly the same physical predictions. We emphasize the power of this Hamiltonian to understand essential features of the Pikovski et al theory and to moderate a few divergent statements in recent works.