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arXiv:2010.11156 · Physical review. D/Physical review. D.

Measuring gravitational time dilation with delocalized quantum superpositions

Albert Roura, Christian Schubert, Dennis Schlippert, Ernst Maria Rasel

Published Oct 1, 2021• 35 citations
arXivHTMLPDF

Abstract

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 for pulses that can efficiently diffract both internal states. Instead, the scheme relies on very simple atom optics for which high diffraction efficiencies can be achieved with rather mild requirements on laser power. Furthermore, the effects of vibration noise are subtracted by employing a simultaneous Rb interferometer that acts as an inertial reference. Remarkably, the recently commissioned VLBAI facility in Hannover, a 10-m atomic fountain that can simultaneously operate Yb and Rb atoms and enables up to 2.8 s of free evolution time, meets all the requirements for a successful experimental implementation.

DOI
10.1103/physrevd.104.084001

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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 for pulses that can efficiently diffract both internal states. Instead, the scheme relies on very simple atom optics for which high diffraction efficiencies can be achieved with rather mild requirements on laser power. Furthermore, the effects of vibration noise are subtracted by employing a simultaneous Rb interferometer that acts as an inertial reference. Remarkably, the recently commissioned VLBAI facility in Hannover, a 10-m atomic fountain that can simultaneously operate Yb and Rb atoms and enables up to 2.8 s of free evolution time, meets all the requirements for a successful experimental implementation.
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.
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.
The creation of delocalized coherent superpositions of quantum systems experiencing di erent relativistic e ects 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 di erent 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 su ers from major challenges including its insensitivity to the gravitational redshift in a uniform eld. All these di- culties can be overcome with a 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 di erential phase shift between the two internal states is compared for di erent initialization times. This can be exploited to test the universality of the gravitational redshift (UGR) 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 o ers signi cant advantages for more compact set-ups based on guided interferometry or hybrid con gurations. Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the e ects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed. It can deal with freely falling atoms, but also include the e ects of external forces and guiding potentials, and can be applied to a very wide range of situations. As an important ingredient for quantum-clock interferometry, suitable difraction mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of the proposed doubly-di erential measurement scheme to other experimental approaches and to tests of the universality of free fall (UFF) is discussed in detail.
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.
Atom interferometers are excellent tools for measuring inertial forces. Their high accuracy and sensitivity allow them to test fundamental physics, e.g., Einstein’s equivalence principle (EEP). One of the main assumptions of EEP is the universality of gravitational redshift (UGR), which states that the ticking rate measured by two idealised clocks at different points in a gravitational field is independent of their internal composition [1]. Although UGR has been successfully tested with two independent atomic clocks, the same effect on a single clock in a delocalised superposition of states has not been observed yet [2]. A promising approach for a delocalised test of UGR is quantum clock interferometry (QCI), which uses a sequence of light pulses to split, redirect, and recombine coherent wave packets and drive transitions between the internal states of the atoms to measure differences in proper time imprinted in the interferometer’s phase shift [3]. An experimental realisation of such schemes requires atomic species with large internal transitions. In this work, we propose an interferometry sensitive to gravitational redshift. By performing a double differential measurement in a single shot, this configuration benefits from a common-mode rejection of spurious effects in the interferometer’s phase. The feasibility of QCI experiments measuring gravitational redshift depends on the availability of long-lived internal states with large energy differences, making the ytterbium (Yb) optical transition an ideal candidate. The clock transition is excited through a two-photon Doppler-free E1-M1 mechanism [4]. This process requires a narrow linewidth, 1 kHz, and a high-power, 20 W, light source. We present our frequency stabilisation scheme and power amplification of an 1156 nm laser to drive the clock transition on a cold Yb cloud. [1] F. Di Pumpo et al., Phys. Rev. D 107, 064007 (2023). [2] A. Roura et al., Phys. Rev. D 104 084001 (2021). [3] C. Ufrecht et al., Phys. Rev. Research 2 043240 (2020). [4] E. A. Alden et al., Phys. Rev. A 90, 012523 (2014)
Abstract Light-pulse atom interferometers based on single-photon transitions are a promising tool for gravitational-wave detection in the mid-frequency band and the search for ultralight dark-matter fields. Here we present a novel measurement scheme that enables their use as freely falling clocks directly measuring relativistic time-dilation effects. The proposal is particularly timely because it can be implemented with no additional requirements in Fermilab’s MAGIS-100 experiment or even in the 10 m prototypes that are expected to start operating very soon. This will allow the unprecedented measurement of gravitational time dilation in a local experiment with freely falling atoms, which is beyond reach even for the best atomic-fountain clocks based on microwave transitions. The results are supported by a comprehensive treatment of relativistic effects in this kind of interferometer as well as a detailed analysis of the main systematic effects. Furthermore, the theoretical methods developed here constitute a valuable tool for modelling light-pulse atom interferometers based on single-photon transitions in general.