Quantum-clock interferometry has been suggested as a quantum probe to test the universality of free fall and the universality of gravitational redshift. In typical experimental schemes, it seems advantageous to employ Doppler-free E1–M1 transitions which have so far been investigated in quantum gases at rest. Here, we consider the fully quantized atomic degrees of freedom and study the interplay of the quantum center-of-mass (COM)—that can become delocalized—together with the internal clock transitions. In particular, we derive a model for finite-time E1–M1 transitions with atomic intern–extern coupling and arbitrary position-dependent laser intensities. We further provide generalizations to the ideal expressions for perturbed recoilless clock pulses. Finally, we show, at the example of a Gaussian laser beam, that the proposed quantum-clock interferometers are stable against perturbations from varying optical fields for a sufficiently small quantum delocalization of the atomic COM.
Quantum-clock interferometry has been suggested as a quantum probe to test the universality of free fall and the universality of gravitational redshift. In typical experimental schemes, it seems advantageous to employ Doppler-free E1–M1 transitions which have so far been investigated in quantum gases at rest. Here, we consider the fully quantized atomic degrees of freedom and study the interplay of the quantum center-of-mass (COM)—that can become delocalized—together with the internal clock transitions. In particular, we derive a model for finite-time E1–M1 transitions with atomic intern–extern coupling and arbitrary position-dependent laser intensities. We further provide generalizations to the ideal expressions for perturbed recoilless clock pulses. Finally, we show, at the example of a Gaussian laser beam, that the proposed quantum-clock interferometers are stable against perturbations from varying optical fields for a sufficiently small quantum delocalization of the atomic COM.
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.
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)
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.
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.
Introducing internal-state transitions simultaneously on each branch of a light-pulse atom interferometer, we propose a scheme that is concurrently sensitive to both violations of the universality of free fall and gravitational redshift, two premises of general relativity. In contrast to redshift tests with quantum clocks, a superposition of internal states is not necessary but merely transitions between them, leading to a generalized concept of clocks in this context. The experimental realization seems feasible with already demonstrated techniques.
Introducing internal-state transitions simultaneously on each branch of a light-pulse atom interferometer, we propose a scheme that is concurrently sensitive to both violations of the universality of free fall and gravitational redshift, two premises of general relativity.In contrast to redshift tests with quantum clocks, a superposition of internal states is not necessary but merely transitions between them, leading to a generalized concept of clocks in this context.The experimental realization seems feasible with already demonstrated techniques.