Interfacing Atomic Spins with Photons for Quantum Metrology, Simulation and Computation

TL;DR

This work surveys how atom-light interfaces in cavities enable nonlocal spin interactions for quantum metrology, simulation, and computation. It builds from vacuum Jaynes-Cummings dynamics to cooperativity-limited coherence, then details QND measurements that generate squeezed and non-Gaussian entangled states, and finally analyzes photon-mediated interactions that produce Ising, XY, and Heisenberg spin models. The text emphasizes engineering programmable, nonlocal interaction graphs via multimode cavities and Floquet control, and it highlights metrological gains from entanglement (squeezed clocks, time-reversal readout) and graph-state resources for quantum information tasks. It also explores quantum-simulation directions, including nonlocal spin dynamics, spin glasses, holographic duality, and topological phases, while candidly addressing current cooperativity limits and pathways toward higher-coherence regimes using Rydberg and advanced cavity technologies.

Abstract

These lecture notes discuss applications of atom-light interactions in cavities to quantum metrology, simulation, and computation. A focus is on nonlocally interacting spin systems realized by coupling many atoms to a delocalized mode of light. We will build up from the fundamentals: understanding how a cavity enables light to coherently imprint information on atoms and atoms to imprint information on the light, enabling quantum non-demolition measurements that constitute a powerful means of engineering nonclassical states. By extension, letting the intracavity light act back on the atoms enables coherent photon-mediated interactions. I start by discussing collective spin models, emphasizing applications in entanglement-enhanced metrology, before proceeding to richer many-body physics enabled by incorporating spatiotemporal control or employing multiple cavity modes. I will highlight opportunities for leveraging these tools for quantum simulations inspired by problems in condensed matter and quantum gravity. Along the way, I provide a pedagogical introduction to criteria for strong atom-light coupling, illustrate how the corresponding figure of merit -- the cooperativity -- sets fundamental limits on the coherence of atom-light interactions, and discuss prospects for harnessing high-cooperativity cavity QED in quantum simulation and computation.

Figures (20)

• Figure 1: A two-level atom (spin) coupled to a cavity (oscillator), as described by the Jaynes-Cummings model of Eq. \ref{['eq:Hjc']}. Bottom left: vacuum Rabi splitting in the transmission spectrum for cavity tuned on resonance with the atomic transition ($\omega_c = \omega_0$). Bottom right: energy spectrum vs cavity-atom detuning $\Delta$.
• Figure 2: Adapted from Yan et al. yan2023superradiant. Super- and sub-radiant scattering observed by positioning atoms in optical tweezers with subwavelength precision within the standing-wave mode of a Fabry-Perot cavity. Left: schematic of the experimental setup. Right: dependence of cavity photon number on atom number $N$ for tweezers spaced by integer (red circles) and half-integer (red squares) wavelengths.
• Figure 3: Cavities come in many forms: examples of cavity types for achieving strong coupling $\eta> 1$. (a) Optical cavities formed by macroscopic super polished mirrors, including near-concentric davis2020engineering and near-planar northup2008coherent Fabry-Perot cavities and ring cavity clark2020observation. (b) Optical fiber cavities hunger2010fiber. (c) Nanophotonic cavities and waveguides dhordjevic2021entanglementgoban2015superradiance. (c) Millimeter-wave cavities, including Fabry-Perot cavity kuhr2007ultrahigh and three-dimensional cavity suleymanzade2020tunable.
• Figure 4: Quantum non-demolition (QND) measurements enabled by dispersive atom-light interactions. (a) QND measurement of light using atoms. Left: schematic, adapted from Ref. hinds2012manipulating, of microwave cavity probed by a beam of Rydberg atoms. To probe the photon number parity, the transit time of an atom through a cavity is tuned to so that a single photon imparts a $\pi$ phase shift to the atom. The backaction on the light is phase shift that depends on the atomic state, converting an initial coherent state of the light into a Schrödinger cat state. (b) QND measurement of atoms using light: the phase of light passing through the cavity becomes entangled with the collective spin component $S_z$, such that detecting the light enables a non-destructive measurement of $S_z$, projecting the atomic system into a state with squeezed quantum fluctuations. The backaction is an ac Stark shift that increases the uncertainty in $S_y$ due to photon shot noise in the light.
• Figure 5: Spin squeezing by quantum nondemolition measurement. Left (adapted from Hosten et al. hosten2016measurement): experimental setup used to achieve 20 dB of spin squeezing by cavity-aided QND measurement, with histograms of $S_z$ in the initial coherent spin state (blue) and in the squeezed state prepared by measurement, shown before and after the spin rotation indicated by the white arrow. Right (adapted from Bohnet et al. bohnet2014reduced): spin squeezing on a cycling transition, where the Raman scattering process shown in blue is absent, yielding an angular sensitivity with Heisenberg scaling $(\Delta\phi)^2 \propto 1/N^2$.