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Frontiers in Optics

Photon-mediated Three- and Four-Body Interactions Between Atomic Momentum States in a High-Finesse Optical Cavity

Eliot A. Bohr, Chengyi Luo, Chitose Maruko, Leah Huzjak, Haoqing Zhang, James K. Thompson

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We demonstrate photon-mediated three- and four-body interactions between atomic momentum states using laser-dressed atoms in a high-finesse optical cavity. The resulting all-to-all interactions are relevant for quantum simulation and future entanglement-enhanced metrology.
DOI
10.1364/fio.2025.jtu5a.39

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Spin Hamiltonians in condensed matter and quantum sensing typically utilize pairwise or two-body interactions between constituents in the material or ensemble. However, there is growing interest in exploring more general n -body interactions for n > 2. In this study, we realized an effective n = 3-body Hamiltonian interaction using an ensemble of laser-cooled atoms in a high-finesse optical cavity with the pseudospin 1 / 2 encoded by two atomic momentum states. We applied two dressing tones that induce the atoms to exchange photons via the cavity to realize a virtual six-photon process; lower-order interactions destructively interfered. We also observed signatures of a n = 4-body interaction mediated by a virtual eight-photon process. Our approach may be extensible to three-body interactions in multilevel systems or to even higher-order interactions.
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.
Quantum simulation and sensing hold great promise for providing new insights into nature, from understanding complex interacting systems to searching for undiscovered physics. Large ensembles of laser-cooled atoms interacting via infinite-range photon mediated interactions are a powerful platform for both endeavours. Here, we realize for the first time momentum-exchange interactions in which atoms exchange their momentum states via collective emission and absorption of photons from a common cavity mode. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer, which is useful for entanglement generation. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing, akin to Mössbauer spectroscopy. The tunable momentum-exchange interaction provides a new capability for quantum interaction-enhanced matter-wave interferometry and for realizing exotic behaviors including simulations of superconductors and dynamical gauge fields.
Abstract An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit 1–3 set by projections of individual atoms. Large amounts of entanglement 4–6 involving the internal degrees of freedom of laser-cooled atomic ensembles 4–16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity 3 . 4−0.9+1.13\,.\,{4}_{-0.9}^{+1.1}3.4−0.9+1.1​ 3 . 4 − 0.9 + 1.1 dB and 2 . 5−0.6+0.62\,.\,{5}_{-0.6}^{+0.6}2.5−0.6+0.6​ 2 . 5 − 0.6 + 0.6 dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity 1 . 7−0.5+0.51\,.\,{7}_{-0.5}^{+0.5}1.7−0.5+0.5​ 1 . 7 − 0.5 + 0.5 dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors 17,18 , searches for new physics, particles and fields 19–23 , future advanced gravitational wave detectors 24,25 and accessing beyond mean-field quantum many-body physics 26–30 .
The controlled interaction between a single, trapped, laser-driven atom and the mode of a high-finesse optical cavity allows for the generation of temporally separated, entangled light pulses. Entanglement between the photon-number fluctuations of the pulses is created and mediated via the atomic center-of-mass motion, which is interfaced with light through the mechanical effect of atom–photon interaction. By means of a quantum noise analysis we determine the correlation matrix which characterizes the entanglement as a function of the system parameters. The scheme is feasible in experimentally accessible parameter regimes. It may be easily extended to the generation of entangled pulses at different frequencies, even at vastly different wavelengths.