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arXiv:2401.06222 · Physical Review Letters

Engineering One Axis Twisting via a Dissipative Berry Phase Using Strong Symmetries

Jeremy T. Young, Edwin Chaparro, Asier Piñeiro Orioli, James K. Thompson, Ana María Rey

Published Jan 27, 2025• 5 citations
arXivHTMLPDF

Abstract

We show how a driven-dissipative cavity coupled to a collective ensemble of atoms can dynamically generate metrologically useful spin-squeezed states. In contrast to other dissipative approaches, we do not rely on complex engineered dissipation or input states, nor do we require tuning the system to a critical point. Instead, we utilize a strong symmetry, a special type of symmetry that can occur in open quantum systems and emerges naturally in systems with collective dissipation, such as superradiance. This symmetry preserves coherence and allows for the accumulation of an atom number-dependent Berry phase which in turn creates spin-squeezed states via emergent one axis twisting dynamics. This work shows that it is possible to generate entanglement in an atom-cavity resonant regime with macroscopic optical excitations of the system, going beyond the typical dispersive regime with negligible optical excitations often utilized in current cavity-QED experiments.

DOI
10.1103/physrevlett.134.040801

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We show how a driven-dissipative cavity coupled to a collective ensemble of atoms can dynamically generate metrologically useful spin-squeezed states. In contrast to other dissipative approaches, we do not rely on complex engineered dissipation or input states, nor do we require tuning the system to a critical point. Instead, we utilize a strong symmetry, a special type of symmetry that can occur in open quantum systems and emerges naturally in systems with collective dissipation, such as superradiance. This symmetry preserves coherence and allows for the accumulation of an atom number-dependent Berry phase which in turn creates spin-squeezed states via emergent one axis twisting dynamics. This work shows that it is possible to generate entanglement in an atom-cavity resonant regime with macroscopic optical excitations of the system, going beyond the typical dispersive regime with negligible optical excitations often utilized in current cavity-QED experiments.
Harnessing dissipation in the presence of strong symmetries has recently emerged as a promising route for generating entanglement in atomic clocks. However, previous proposals relied on regimes where cavity photons can be adiabatically eliminated, significantly limiting their applicability to experimentally relevant cavity-QED regimes that lie in or near the resolved vacuum Rabi splitting regime. Here we show that symmetry-protected dissipative spin squeezing can be realized even when cavity photons actively participate in the dynamics, extending the experimental relevance of the protocol. We study a three-level ensemble of 87Sr^{87}\mathrm{Sr}87Sr atoms coupled to an optical cavity in the resolved vacuum Rabi splitting regime and demonstrate that, with smooth ramps of the drive amplitude and detunings, the driven-dissipative dynamics enters a stable low-photon regime in which nonadiabatic cavity excitations and sector-resolving photon leakage can be controlled. Within this low-photon operating window, sector-resolving photon leakage is suppressed and the sector-dependent geometric phase realizes effective one-axis twisting. At the end of the protocol the entanglement can also be efficiently transferred directly onto the long-lived clock states by turning the drive off. For experimentally realistic parameters, we theoretically show that more than 25 dB25\,\mathrm{dB}25dB of squeezing can be generated for 10510^5105 atoms, closely saturating the ideal one-axis twisting scaling ξmin⁡2∝N−2/3ξ_{\min}^2 \propto N^{-2/3}ξmin2​∝N−2/3. At fixed cooperativity, the optimized squeezing remains broadly comparable to the unresolved-regime implementation, while the resolved-regime implementation reaches comparable squeezing on a substantially shorter physical timescale. These results establish symmetry-protected dissipative dynamics as a practical route to beyond the standard-quantum-limit performance in optical-clock platforms.
Symmetry constraints provide a powerful means to control the dynamics of open quantum systems. However, the set of accessible control parameters is often limited. Here, we show that a tunable phase in the collective light-matter coupling of a cavity QED system induces a phase-dependent strong symmetry of the Liouvillian, enabling dynamical control of the open quantum system evolution. We demonstrate that tuning this phase substantially reduces the critical driving strength for dissipative phase transitions between stationary and non-stationary phases. We illustrate this mechanism in two experimentally relevant cavity QED settings: a two-species ensemble of two-level atoms and a single-species ensemble of three-level atoms. Our results establish phase control as a versatile tool for engineering dissipative phase transitions, with implications for quantum state preparation.
We describe a method to create and store scalable and long-lived entangled spin-squeezed states within a manifold of many-body cavity dark states using collective emission of light from multilevel atoms inside an optical cavity. We show that the system can be tuned to generate squeezing in a dark state where it will be immune to superradiance. We also show more generically that squeezing can be generated using a combination of superradiance and coherent driving in a bright state, and subsequently be transferred via single-particle rotations to a dark state where squeezing can be stored. Our findings, readily testable in current optical cavity experiments with alkaline-earth-like atoms, can open a path for dissipative generation and storage of metrologically useful states in optical transitions.
We utilize multilevel atoms trapped in a driven resonant optical cavity to produce scalable multimode squeezed states for quantum sensing and metrology. While superradiance or collective dissipative emission by itself has been typically a detrimental effect for entanglement generation in optical cavities, in the presence of additional drives it can also be used as an entanglement resource. In a recent work [B. Sundar, D. Barberena, A. M. Rey, and A. Pi\~neiro Orioli, companion paper, Phys. Rev. Lett. 132, 033601 (2024)], we described a protocol for the dissipative generation of two-mode squeezing in the dark state of a six-level system with only one relevant polarization. There we showed that up to two quadratures can be squeezed. Here, we develop a generalized analytic treatment to calculate the squeezing in any multilevel system where atoms can collectively decay by emitting light into two polarization modes in a cavity. We show that in this more general system up to four spin squeezed quadratures can be obtained. We study how finite-size effects constrain the reachable squeezing, and analytically compute the scaling with NNN. Our findings are readily testable in current optical cavity experiments with alkaline-earth-like atoms.
Long-range interactions between emitters give rise to collective phenomena, including superradiance, spin squeezing, and coherence protection, that are important to both fundamental physics and quantum technologies. Despite progress in cold atoms, coherent cavity-mediated all-to-all interactions have not yet been realized in a solid-state ensemble. Here we demonstrate such interactions in a 171^{171}171Yb3+^{3+}3+:CaWO4_44​ crystal coupled to a microwave resonator, observing superradiant emission on resonance and unitary one-axis twisting dynamics in the dispersive regime. The same interaction also opens a many-body energy gap that suppresses inhomogeneous dephasing, extending the ensemble Ramsey coherence time from tens of microseconds to milliseconds without decoupling pulses. These results establish a solid-state platform for collective many-body physics with direct implications for quantum technologies. Specifically, the observed one-axis twisting dynamics opens a path towards spin squeezing for entanglement-enhanced quantum metrology, and the extended coherence due to gap-protection is relevant for both microwave photon storage and precision measurement.
One-axis twisting (OAT) interaction is a pivotal resource for manipulating quantum states of atomic ensembles, enabling spin squeezing, atomic-cat-state generation, and weak-phase amplification. Current implementations of OAT dynamics predominantly rely on the Tavis-Cummings model of light-atoms coupling; however, this approach inevitably introduces an additional Stark term that entangles the light with the atoms, which compromises the unitarity of OAT evolution and thereby degrades the OAT-based control precision. Here we propose a scheme based on a driven Tavis-Cummings model to achieve near-unitary OAT evolution. We demonstrate that both constant and time-varying driving of an atoms-cavity hybrid system can realize near-unitary OAT evolution, albeit with distinct coupling strength. Furthermore, when atomic dissipation is taken into account, we find that the time-varying-driving scheme exhibits superior resistance to decoherence. Our approach is broadly applicable to a variety of atomic platforms, including cold atoms, trapped ions, and nitrogen-vacancy centers.