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Optics Express

Effects of gravitational time dilation on multi-photon interference

Yiquan Yang

Published Oct 16, 2025• 0 citations
Publisher

Abstract

The unification of quantum mechanics and general relativity remains elusive due to the lack of experimental signatures. To explore the parameter regimes where both theories are relevant, growing attention is being paid to investigating the general relativistic effects on low-energy quantum systems. Such research offers valuable insights into the connection between the two pillars of modern physics. Entanglement and gravitational time dilation capture key aspects of quantum mechanics and general relativity, respectively. Thus, the dynamical evolution of entangled systems in curved space unambiguously reflects the interplay between quantum mechanics and general relativity. Specifically, we investigate the interference visibility reduction of entangled N00N states and quadrature entanglement in gravitational fields. The interference visibility reduction induced by gravitational time dilation differs significantly between N00N states and quadrature entanglement, owing to their distinct gravitational phase encoding mechanisms. For N00N states, the gravitational phase is encoded as a relative phase between the H and V polarization modes, and the visibility reduction is enhanced by a factor of N compared to the single-photon case, rendering them highly sensitive to observing the gravitational effect. In contrast, quadrature entanglement encodes the gravitational phase across its full Gaussian spectrum, leading to vanishing interference visibility in large-scale interferometers spanning from geostationary orbit to ground level.

DOI
10.1364/oe.574667

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The unification of quantum mechanics and general relativity remains elusive due to the lack of experimental signatures. To explore the parameter regimes where both theories are relevant, growing attention is being paid to investigating the general relativistic effects on low-energy quantum systems. Such research offers valuable insights into the connection between the two pillars of modern physics. Entanglement and gravitational time dilation capture key aspects of quantum mechanics and general relativity, respectively. Thus, the dynamical evolution of entangled systems in curved space unambiguously reflects the interplay between quantum mechanics and general relativity. Specifically, we investigate the interference visibility reduction of entangled N00N states and quadrature entanglement in gravitational fields. The interference visibility reduction induced by gravitational time dilation differs significantly between N00N states and quadrature entanglement, owing to their distinct gravitational phase encoding mechanisms. For N00N states, the gravitational phase is encoded as a relative phase between the H and V polarization modes, and the visibility reduction is enhanced by a factor of N compared to the single-photon case, rendering them highly sensitive to observing the gravitational effect. In contrast, quadrature entanglement encodes the gravitational phase across its full Gaussian spectrum, leading to vanishing interference visibility in large-scale interferometers spanning from geostationary orbit to ground level.
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 traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
Abstract 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 plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.
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.
Gravitational time dilation implies that clocks held at different heights accumulate different proper times. We analyze a memory-assisted quantum clock interferometer in which a frequency-bin photonic clock is stored in two vertically separated quantum memories for a controllable duration, such that the joint state evolves in a quantum superposition of two proper times. After retrieval, the photonic modes interfere in a Hong-Ou-Mandel (HOM) interferometer, for which we derive analytic expressions for the resulting multiphoton detection statistics. Extending this HOM-based scheme from entangled photon pairs to frequency-entangled 2N-photon inputs, we show that the proper-time dependent phase is amplified by a factor N, leading to an N-times faster collapse and revival of the interference signal compared with the two-photon case. Incorporating finite memory efficiency and lifetime, we identify regimes where this modulation remains observable. For parameters compatible with demonstrated Rb and Cs memories and achievable optical frequency separations, the first collapse occurs for height differences in the order of 10-100 m with subsecond to few-second storage times, while suitable rare-earth ion and alkali memory combinations can reduce the required height to the few-metre scale. These results establish near-term laboratory conditions for observing entanglement dynamics driven by gravitational time dilation in a photonic platform.
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.
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. In the theory of general relativity time flows at different rates depending on the space–time geometry. Here, a drop in the visibility of a quantum 'clock' interference in a gravitational potential is predicted, which cannot be explained without the general relativistic notion of time.