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Chinese Physics B

Dissipative phase transitions in multilevel cavity superradiance: phase space dynamics and continuous quantum sensing

Kang Shen, J. Xu, Xiangming Hu, F. S. Wang

Published Mar 10, 2026• 0 citations
Publisher

Abstract

Abstract We investigate the non-equilibrium dynamics and quantum metrological potential of an ensemble of four-level atoms interacting with a dissipative optical cavity. By deriving an effective master equation for the atomic degrees of freedom, we identify first-order dissipative phase transitions driven by the competition between coherent driving and collective decay. Focusing on a specific parametric trajectory, we employ Liouvillian spectral projections in the thermodynamic limit to rigorously delineate the basins of attraction corresponding to the multistable phases. Furthermore, the mean-field superradiance potential reveals that the dissipative phase transition manifests as a saddle-node bifurcation where a metastable trapping potential vanishes. In the vicinity of the critical point, the system exhibits critical slowing down, leading to a vanishing Liouvillian spectral gap. Utilizing the matrix product state formalism, we demonstrate that due to this dissipative phase transition, the system possesses the potential to achieve Heisenberg-limited precision in continuous sensing. Our results confirm that the driven four-level superradiant model serves as a robust platform for exploiting critical dynamics to enhance metrological performance.

DOI
10.1088/1674-1056/ae4f70

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Abstract We investigate the non-equilibrium dynamics and quantum metrological potential of an ensemble of four-level atoms interacting with a dissipative optical cavity. By deriving an effective master equation for the atomic degrees of freedom, we identify first-order dissipative phase transitions driven by the competition between coherent driving and collective decay. Focusing on a specific parametric trajectory, we employ Liouvillian spectral projections in the thermodynamic limit to rigorously delineate the basins of attraction corresponding to the multistable phases. Furthermore, the mean-field superradiance potential reveals that the dissipative phase transition manifests as a saddle-node bifurcation where a metastable trapping potential vanishes. In the vicinity of the critical point, the system exhibits critical slowing down, leading to a vanishing Liouvillian spectral gap. Utilizing the matrix product state formalism, we demonstrate that due to this dissipative phase transition, the system possesses the potential to achieve Heisenberg-limited precision in continuous sensing. Our results confirm that the driven four-level superradiant model serves as a robust platform for exploiting critical dynamics to enhance metrological performance.
Recently, there has been considerable interest in studying quantum sensing near the critical points of a system evolving unitarily and undergoing a phase transition. However, there are many quantum systems in which dissipation is very important. The quantum phase transition in such systems results as a result of competition between nonlinearity, drive, and dissipation. These quantum phase transitions belong to the class of nonequilibrium phase transitions. In this work, we present a detailed study of quantum sensing of the system parameters near the critical points of a dissipative phase transition. We illustrate the key results by considering a coherently driven nonlinear Kerr medium interacting with environment. The first-order quantum phase transition is characterized by the closing of the gap in eigenvalues of the underlying Liouvillian. The steady-state sensing away from the critical point has standard quantum limit scaling with respect to the effective system size, whereas Heisenberg scaling is found at the critical point. The latter is subject to a critical slowing down. We have also examined sensing of system parameters using the metastable states and find better sensing performance at intermediate timescales, i.e., when the system has not yet settled in steady state. Detailed results on the scaling behavior in different time domains are given.
Critical metrology relies on the high sensitivity of systems to parameter changes near a phase transition to extract information with high precision. Such methods usually require working under adiabatic conditions, which implies long preparation times due to critical slowing down. Here instead we demonstrate how favorable sensitivity can be maintained for preparation rates exceeding the adiabatic limit by exploiting knowledge of the nonequilibrium dynamics of the system. Our work focuses on a model of collective dissipation (superradiance) balanced by collective pumping, analyzing the sensitivity around a first order dissipative phase transition. We devise a sensing protocol based on characterizing the hysteresis formed beyond adiabatic conditions, finding the sensing uncertainty r^{α}/N, exhibiting a favorable Heisenberg-like scaling with the particle number N and only a weak power-law dependence α≈0.17 on the preparation rate r. We discuss the implementation of the model and potential applications to metrology within cavity QED setups.
In this work, we study the driven-dissipative dynamics of a coherently-driven spin ensemble with a squeezed, superradiant decay. This decay consists of a sum of both raising and lowering collective spin operators with a tunable weight. The model presents different critical non-equilibrium phases with a gapless Liouvillian that are associated to particular symmetries and that give rise to distinct kinds of non-ergodic dynamics. In Ref. [1] we focus on the case of a strong-symmetry and use this model to introduce and discuss the effect of dissipative freezing, where, regardless of the system size, stochastic quantum trajectories initialized in a superposition of different symmetry sectors always select a single one of them and remain there for the rest of the evolution. Here, we deepen this analysis and study in more detail the other type of non-ergodic physics present in the model, namely, the emergence of non-stationary dynamics in the thermodynamic limit. We complete our description of squeezed superradiance by analysing its metrological properties in terms of spin squeezing and by analysing the features that each of these critical phases imprint on the light emitted by the system.
The interplay between many-body interactions and controlled dissipation provides a rich setting for nonequilibrium quantum phases. We explore the superradiant phase transitions in a Rydberg-interacting open Dicke model with cavity loss and local dissipation. We find that the nonlinear feedback from atomic interactions stabilizes the atomic collective excited state and induces resonant collective motion, which can be further converted into robust superradiant oscillations with the inclusion of local dissipation. Beyond the mean-field approximation, we prove this system can support the finite-size local dissipative temporal order, i.e., continuous time crystal, from evidences of the decreasing damping of a finite-frequency Liouvillian mode and the linear-size scaling of quantum fluctuations. The correlation between the atomic colletive dynamics and the cavity photon number makes our findings easy to detect from output optical signal. By bridging interacting atomic matter and driven-dissipative cavity QED, our Rydberg-interacting Dicke model provides a unique spin-1/2 platform for exploring dynamical phase transitions and macroscopic temporal order in open quantum matter.
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.
Precise control of criticality in superradiant phase transitions is essential for quantum state engineering and the simulation of nonequilibrium phase transitions. Here, we investigate theoretically multicritical phenomena in a dissipative two-Rydberg-atom cavity--QED system. The intrinisic dipole--dipole interaction between the two Rydberg atoms restructures the energy-level landscape of the atomic subsystem, thereby significantly modifying the boundary of the continuous second-order superradiant phase transition, and shifting both the phase boundary and the multicritical point toward weaker atom--cavity strengths. For sufficiently strong dipole--dipole interactions, the continuous second-order phase transition and the multicritical point both disappear, leaving only a discontinuous first--order phase transition that enables the emergence of a superradiant phase even at arbitrarily weak atom--cavity coupling. This work is of fundamental interest for studying dissipative quantum phase transitions, with potential implications for quantum precision measurement and quantum sensing.