### "New tools for precision phase measurements with atoms in cavities"

Atoms and atom-like systems have become attractive platforms for precision measurements, finding numerous applications such as clocks, magnetometers and gravimeters. Many such applications rely on the dynamics of pseudospin-1/2 systems with two long-lived states, with the signal encoded in the relative phase of the two states. Atoms provide several degrees of freedom such as internal electronic states and external motional states in which pseudospin-1/2 systems can be encoded with different advantages. Improving quantum metrology with atoms requires the development of techniques to efficiently and precisely measure the relative phase of the spin superposition. In this talk, I will describe two proposals to improve such phase measurements. In the first part, I will present a scheme using atoms in cavities to continuously track the relative phase in real-time [1]. Unlike the Ramsey sequence, the scheme directly probes the phase of the collective atomic spin without converting it into a population difference. As a bonus, spin squeezed states develop naturally, providing real-time phase estimation significantly more precise than what is possible with uncorrelated atoms. In the second part, I will describe a scheme to directly squeeze on pseudospins encoded in atomic center-of-mass momentum states, for use in a Bragg interferometer [2]. In this scheme, spin squeezed states develop as a result of cavity-mediated spin exchange between pairs of atoms. I will discuss the unique issues that arise with momentum pseudospins, such as non-zero temperature and the unavoidable coupling to states outside the pseudospin-1/2 manifold, and their impact on squeezing. In spite of these complications, I will show how this scheme can be used to demonstrate appreciable levels of spin squeezing in realistic parameter regimes.

**References**

- Shankar, A., Greve, G. P., Wu, B., Thompson, J. K. & Holland, M. Continuous Real-Time Tracking of a Quantum Phase Below the Standard Quantum Limit. Phys. Rev. Lett. 122, 233602 (June 2019).
- Shankar, A., Salvi, L., Chiofalo, M. L., Poli, N. & Holland, M. J. Squeezed state metrology with Bragg interferometers operating in a cavity. Quantum Science and Technology 4, 045010 (Oct. 2019).