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arXiv:2406.14461 · Physical Review Research

Engineering interactions by collective coupling of atom pairs to cavity photons for entanglement generation

Sankalp Sharma, Jan Chwedeńczuk, Tomasz Wasak

Published Feb 20, 2025• 2 citations

Abstract

Engineering atom-atom interactions is essential both for controlling novel phases of matter and for efficient preparation of many-body entangled states, which are key resources in quantum communication, computation, and metrology. In this work, we propose a scheme to tailor these interactions by coupling driven atom pairs to optical cavity photons via a molecular state in the dispersive regime, resulting in an effective photon-field-dependent potential. As an illustrative example, by analyzing the quantum Fisher information, we show that such induced interactions can generate robust many-body entanglement in two-mode ultracold bosons in an optical cavity. By tuning the photon-induced interactions through the cavity drive, we identify conditions for preparing highly entangled states on timescales that mitigate decoherence due to photon loss. Our results show that entanglement formation rate scales strongly with both photon and atom number, dramatically reducing the timescale compared to bare atomic interactions. We also identify an optimal measurement for exploiting the metrological potential of the atomic state in an interferometric protocol with significant photon losses, saturating the quantum Cramer-Rao lower bound. Furthermore, we show that despite these losses the atomic state exhibits strong Bell correlations. Our results pave the way for engineering atom-atom interactions to study novel phases of light and matter in hybrid atom-photon systems, as well as for tailoring complex quantum states for new quantum technology protocols and fundamental tests of quantum mechanics.

DOI: 10.1103/physrevresearch.7.l012038

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We propose a simple and efficient method for generating metrologically useful quantum entanglement in an ensemble of spin-1 atoms that interacts with a high-finesse optical cavity mode. It requires straightforward preparation of N atoms in the m_{F}=0 sublevel, tailoring of the atom-field interaction to give an effective Tavis-Cummings model for the collective spin-1 ensemble, and a photon counting measurement on the cavity output field. The photon number provides a projective measurement of the collective spin length S, which, for the chosen initial state, is heavily weighted around values S≃sqrt[N], for which the corresponding spin states are strongly entangled and exhibit Heisenberg scaling of the metrological sensitivity with N, as quantified by the quantum Fisher information.

We propose a scheme to enhance the light-matter coupling in a cavity QED system where two $\mathrm{\ensuremath{\Lambda}}$ atoms are weakly coupled to a single-mode cavity via multiphoton interaction. By introducing a second-order nonlinear (parametric) driving of the cavity, the original

N

-photon exchanges between the atoms, and the cavity can be reduced to either an effective single- or two-photon transition depending on the odevity of

N

, with the effective atom-field interaction strength being significantly enhanced. This results in an

N

-dependent effective coupling strength on top of the exponential enhancement induced only by the parametric driving. As an example, we demonstrate that our proposal can be exploited for the preparation of high-fidelity steady-state entanglement. The proposed scheme could provide a feasible alternative for diverse applications in quantum technologies.

We propose a component-selective scheme for improving two-photon sources in a cavity-coupled two-atom system, where a single cavity mode interacts with two two-level atoms driven by phase-controlled classical fields of the same frequency. By controlling the atomic detunings and driving phase, the system can be tailored toward optimized cavity-field two-photon blockade or strongly correlated fluorescence photon-pair emission. When the two-cavity-photon component is enhanced, the cavity field exhibits optimized two-photon blockade with simultaneous suppression of unwanted one- and three-photon components at a comparable two-photon population. In another parameter regime, strongly correlated fluorescence photon pairs can also be generated from the two atoms by selecting the double-atomic-excitation component in the same two-excitation manifold. This approach provides a route toward high-quality and versatile two-photon sources, with potential applications in few-photon quantum optics and quantum information processing.

We show that collective three-body interactions (3BIs), implementable with

N

atoms loaded inside an optical cavity, offer a significant advantage for preparing complex multipartite entangled states. Firstly, they enable a speedup of order

\sim N

in preparing generalized Greenberger-Horne-Zeilinger (GHZ) states, outperforming conventional methods based on all-to-all two-body Ising interactions. Secondly, they saturate the Heisenberg bound in phase estimation tasks using a time-reversal protocol realized through simple rotations and followed by experimentally accessible collective spin measurements. Lastly, compared with two-body interactions (2BIs), in the presence of cavity losses and single particle decoherence, 3BIs feature a high gain in sensitivity for moderate atom numbers and in large ensembles a fast entanglement generation despite constraints in parameter regimes where they are implementable.

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.

In the context of quantum metrology, optical cavity-QED platforms have primarily been focused on the generation of entangled atomic spin states useful for next-generation frequency and time standards. Here, we report a complementary application: the use of optical cavities to generate nonclassical states of light for electric field sensing below the standard quantum limit. We show that cooperative atom-light interactions in the strong collective coupling regime can be used to engineer generalized atom-light cat states which enable quantum enhanced sensing of small displacements of the cavity field even in the presence of photon loss. We demonstrate that metrological gains of 10-20 dB below the standard quantum limit are within reach for current cavity-QED systems operating with long-lived alkaline-earth atoms.