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arXiv:2402.14412 · Physical Review A

Atomic clock interferometry using optical tweezers

Ilan Meltzer, Yoav Sagi

Published Sep 3, 2024• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.110.032602

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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.
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 interferometers measure forces and acceleration with exceptional precision. The conventional approach to atomic interferometry is to launch an atomic cloud into a ballistic trajectory and perform the wave-packet splitting in momentum space by Raman transitions. This places severe constraints on the possible atomic trajectory, positioning accuracy, and probing duration. Here, we propose and analyze an alternative atomic interferometer that uses micro-optical traps (optical tweezers) to manipulate and control the motion of atoms. This interferometer allows long probing time, submicrometer positioning accuracy, and utmost flexibility in the shaping of the atomic trajectory. The cornerstone of the tweezer interferometer consists of the coherent atomic splitting and combining schemes. We present two adiabatic schemes with two or three tweezers that are robust in the presence of experimental imperfections and work simultaneously with many vibrational states. The latter property allows for multiatom interferometry in a single run. We also highlight the advantage of using fermionic atoms to obtain single-atom occupation of vibrational states and to eliminate mean-field shifts. We examine the impact of tweezer intensity noise and demonstrate that, when constrained by shot noise, the interferometer can achieve a relative accuracy better than ${10}^{\ensuremath{-}11}$ in measuring Earth's gravitational acceleration. The submicrometer resolution and extended measurement duration offer promising opportunities for exploring fundamental physical laws in new regimes. We discuss two applications well suited for the unique capabilities of the tweezer interferometer: the measurement of gravitational forces and the study of Casimir-Polder forces between atoms and surfaces. Crucially, our proposed tweezer interferometer is within the reach of current technological capabilities.
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 phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that (i) closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii) They can constitute a quantum version of the special-relativistic twin paradox. (iii) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.
The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that (i) closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii) They can constitute a quantum version of the special-relativistic twin paradox. (iii) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.