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arXiv:2301.11258

Quantum Test of the Local Position Invariance with Internal Clock Interferometry

Zhifan Zhou

Published Jan 26, 2023• 0 citations
arXivHTMLPDF

Abstract

Current attempts to test local position invariance (LPI) compare different clock transition rates with classically exchanged signals. We propose an experimental scheme for the quantum test of LPI: an internal atomic clock interferometer comprising two interfering clocks within one atom. We prepare the atom in a superposition of two clock states and one ground state, which evolves coherently along two quantum clock oscillations into stable internal Ramsey interference patterns. The interference pattern with the shared ground state shows a visibility modulation, which can be interpreted as the beating of the individual clock oscillations and a direct consequence of complementarity. Upon the interferometer experiencing a different gravitational potential, LPI predicts that both clock tick rates will change proportionally, while quantum complementarity indicates that the visibility modulation should modify accordingly. This change is deemed insignificant for the first period of visibility modulation but can be stacked up until the limit of the system coherence time. Since no splitting or recombining is involved, the system coherence time can be as long as the trap lifetime or the clock state lifetime. The required resolution to observe the visibility modulation is within reach of the state-of-art optical clocks' sensitivities. This experimental scheme is feasible in different scenarios, still or with speed, and may shed new light on studying the quantum effect of time and general relativity.

DOI
10.48550/arxiv.2301.11258

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Current attempts to test local position invariance (LPI) compare different clock transition rates with classically exchanged signals. We propose an experimental scheme for the quantum test of LPI: an internal atomic clock interferometer comprising two interfering clocks within one atom. We prepare the atom in a superposition of two clock states and one ground state, which evolves coherently along two quantum clock oscillations into stable internal Ramsey interference patterns. The interference pattern with the shared ground state shows a visibility modulation, which can be interpreted as the beating of the individual clock oscillations and a direct consequence of complementarity. Upon the interferometer experiencing a different gravitational potential, LPI predicts that both clock tick rates will change proportionally, while quantum complementarity indicates that the visibility modulation should modify accordingly. This change is deemed insignificant for the first period of visibility modulation but can be stacked up until the limit of the system coherence time. Since no splitting or recombining is involved, the system coherence time can be as long as the trap lifetime or the clock state lifetime. The required resolution to observe the visibility modulation is within reach of the state-of-art optical clocks' sensitivities. This experimental scheme is feasible in different scenarios, still or with speed, and may shed new light on studying the quantum effect of time and general relativity.
In Einstein's general theory of relativity, time depends locally on gravity; in standard quantum theory, time is global-all clocks "tick" uniformly. We demonstrate a new tool for investigating time in the overlap of these two theories: a self-interfering clock, comprising two atomic spin states. We prepare the clock in a spatial superposition of quantum wave packets, which evolve coherently along two paths into a stable interference pattern. If we make the clock wave packets "tick" at different rates, to simulate a gravitational time lag, the clock time along each path yields "which path" information, degrading the pattern's visibility. In contrast, in standard interferometry, time cannot yield "which path" information. This proof-of-principle experiment may have implications for the study of time and general relativity and their impact on fundamental effects such as decoherence and the emergence of a classical world.
The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics.This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined.Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field.All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times.This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available.Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations.Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the effects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed.It can describe freely falling atoms as well as the effects of external forces and guiding potentials, and it can be applied to a very wide range of situations.As an important ingredient for quantum-clock interferometry, suitable diffraction mechanisms for atoms in internal-state superpositions are investigated too.Finally, the relation of the proposed doubly differential measurement scheme to other experimental approaches and to tests of the universality of free fall is discussed in detail.
Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all atomic degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii) Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests. However, modified configurations, for example by relaunching the atoms, can mimic such tests under certain conditions and may constitute a competitive alternative. (iii) Guided atom interferometers are comparable to atomic clocks. (iv) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations.
This thesis examines how atomic quantum systems can be utilized to probe spacetime effects in regimes where quantum mechanics and general relativity intersect, and how gravitational phenomena imprint on experimentally accessible observables. The work is based on two complementary studies. In Article I, we propose an experimental scheme that combines trapped-atom interferometry with Ramsey interrogation to realize a clock held in a spatial superposition at two heights in Earth’s gravitational field. Using a path-integral treatment of interferometric phases and incorporating the internal-energy contribution to mass, we derive leading relativistic corrections and identify two signatures of proper-time superposition: (i) oscillations of interferometric visibility and (ii) an effective shift of the clock transition frequency. We argue that this frequency-shift signature may be within reach of current or near-term technology, even when visibility changes are too small to resolve. In Article II, we develop a general framework for spontaneous emission in curved spacetime and apply it to a gravitational-wave background. We demonstrate that gravitational waves can induce spectral sidebands and directional modulations in the emitted radiation, and formulate parameter estimation via Fisher-information-based sensitivity bounds, yielding order-of-magnitude requirements for detectability under idealized measurement conditions.
Remarkable advances in atom interferometry have enabled the creation of macroscopically delocalized quantum superpositions with atomic wave packets separated up to half a meter. Nevertheless, in all cases realized so far the differences in the dynamics of the two wave packets of the superposition can be entirely described in terms of Newtonian mechanics. Therefore, the creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. After explaining the major challenges that quantum-clock interferometry based on light-pulse atom interferometers is confronted with (including their insensitivity to gravitational redshift in a uniform field), I will present a promising scheme capable of measuring the effects of gravitational time dilation in interfering quantum clocks. Its experimental implementation should be within reach of the 10-meter atomic fountains of Sr and Yb atoms that will soon become available in Stanford and HITec (Hanover) respectively.
Clock interferometry refers to the coherent splitting of a clock into two different paths and recombining in a way that reveals the proper-time difference between them. Unlike the comparison of two separate clocks, this approach allows testing how nonflat space-time influences quantum coherence. Atomic clocks are currently the most accurate timekeeping devices. Here we propose using optical tweezers to implement clock interferometry. Our proposed clock interferometer employs an alkaline-earth-like atom held in an optical trap at the magic wavelength. Through a combination of adiabatic, tweezer-based splitting and recombining schemes and a modified Ramsey sequence of the clock states, we achieve linear sensitivity to the gravitational time dilation. Moreover, the measurement of the time dilation is insensitive to relative fluctuations in the intensity of the tweezer beams. We analyze the tweezer clock interferometer and show that it is feasible with current technological capabilities. The proposed interferometer could test the effect of gravitational redshift on quantum coherence and implement the quantum twin paradox.