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arXiv:2410.12132

Realization of three and four-body interactions between momentum states in a cavity through optical dressing

Chengyi Luo, Haoqing Zhang, Chitose Maruko, Eliot A. Bohr, Anjun Chu, Ana María Rey, James K. Thompson

Published Oct 16, 2024• 0 citations
arXivHTMLPDF

Abstract

Paradigmatic spin Hamiltonians in condensed matter and quantum sensing typically utilize pair-wise or 2-body interactions between constituents in the material or ensemble. However, there is growing interest in exploring more general $n$-body interactions for $n >2$, with examples including more efficient quantum gates or the realization of exotic many-body fracton states. Here we realize an effective $n=3$-body Hamiltonian interaction using an ensemble of laser-cooled atoms in a high finesse optical cavity with the pseudo-spin 1/2 encoded by two atomic momentum states. To realize this interaction, we apply two dressing tones that coax the atoms to exchange photons via the cavity to realize a virtual 6-photon process, while the lower-order interactions destructively interfere. The resulting photon mediated interactions are not only $n>2$-body but also all-to-all(-to-all) and therefore of great interest for fast entanglement generation and quantum simulation of exotic phases such as the long sought but not yet observed charge-Qe superconductors, with $Q=2n$ . The versatility of our experimental system can also allow for extending to 3-body interactions in multi-level systems or to higher-order interactions, such as the signature of a $n=4$-body interaction mediated by a virtual eight photon process that we also observe.

DOI
10.48550/arxiv.2410.12132

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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.
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.
The generation of high-performance nonclassical light remains a cornerstone of quantum technologies, yet faces a fundamental trade-off between emission purity and brightness. Here, we demonstrate that cavity-mediated many-body spin-exchange interactions provide a route to overcome this constraint by collectively amplifying spectral anharmonicity. In a cavity-coupled atomic array with a programmable relative phase φφφ, the resulting interference-interaction mechanism reshapes the dressed-state manifold and enables deterministic switching between distinct quantum emission regimes. For φ=0φ=0φ=0, constructive interference yields high-purity single-photon emission with antibunching improved by four orders of magnitude while preserving strong photon flux. Conversely, for φ=πφ=πφ=π, destructive interference creates a dark single-photon manifold, resonantly activating two-photon processes to produce bright and pure photon-pair bundles. Our work establishes interference-engineered many-body interactions as a scalable mechanism for on-demand quantum light generation and open a new avenue for harnessing collective many-body physics in quantum photonics.
Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction-enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields.
The controlled generation of nonclassical light beyond single photons remains a central challenge in quantum optics, due to the difficulty of enhancing multiphoton processes while suppressing lower-order excitations. Here we propose an interference-interaction-engineered scheme for programmable few-photon emission in a cavity-QED system of three atoms coupled to orthogonal cavity modes. By adiabatically eliminating an auxiliary Fabry-Pérot cavity, we generate a tunable cavity-mediated spin-exchange interaction χχχ, which, combined with a controllable geometric phase φφφ, reshapes the many-body dressed-state spectrum. This interplay enables selective addressing of excitation manifolds (N=1,2,3N=1,2,3N=1,2,3), establishing a direct mapping between excitation structure and photon-emission channels. For φ=0φ=0φ=0, constructive interference enhances the spectral anharmonicity of low-excitation manifolds, yielding tunable single- and two-photon emission associated with the N=1N=1N=1 and N=2N=2N=2 manifolds. In contrast, for φ=2π/3φ=2π/3φ=2π/3, destructive interference suppresses lower-order excitation pathways and activates a resonant three-photon channel originating from the N=3N=3N=3 manifold. Importantly, the cavity-mediated interaction χχχ further enhances spectral separation between manifolds, enabling a substantial improvement in multiphoton purity while maintaining a sizable photon population. We demonstrate a three-order-of-magnitude enhancement in two-photon purity and more than two orders of magnitude improvement in three-photon emission. Our results establish a unified interference-interaction framework in which effective optical nonlinearities can be programmably engineered through phase and interaction, providing a scalable route toward high-purity multiphoton sources and programmable quantum photonic devices.