Critical steady states of all-to-all squeezed and driven superradiance: An analytic approach

Abstract

We analyse the properties across steady state phase transitions of two all-to-all driven-dissipative spin models that describe possible dynamics of N two-level systems inside an optical cavity. We show that the finite size behaviour around the critical points can be captured correctly by carefully identifying the relevant non-linearities in the Holstein-Primakoff representation of spin operators in terms of bosonic variables. With these tools, we calculate analytically various observables across the phase transitions and obtain their finite size scalings, including numerical prefactors. In particular, we look at the amount of spin squeezing carried by the steady states, of relevance for quantum metrology applications, and describe in analytical detail the mechanism by which the optimal spin squeezing acquires logarithmic corrections that depend on the system size. We also demonstrate that the logarithmic nature of these corrections is difficult to characterize through numerical procedures for any experimentally realistic and/or simulable values of particle number. We complement all of our analytical arguments with numerical benchmarks.

10+5 pages, 4+3 figures

References in corpus (23)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Quantum Simulators: Architectures and Opportunities
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Dissipative Phase Transition in Central Spin Systems
• Entanglement-Enhanced Optical Atomic Clock
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Dissipative Preparation of Spin Squeezed Atomic Ensembles in a Steady State
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• Symmetry breaking and error correction in open quantum systems
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• Prospects and challenges for squeezing-enhanced optical atomic clocks
• Dissipative phase transitions: Independent versus collective decay and spin squeezing
• Scaling behavior in the adiabatic Dicke Model
• Reservoir-engineered spin squeezing: macroscopic even-odd effects and hybrid-systems implementations
• Dynamical phase transitions in dissipative quantum dynamics with quantum optical realization
• Mathematical Methods in Quantum Optics: the Dicke Model
• Non-equilibrium criticality in quench dynamics of infinite-range spin models
• Quantum metrology with critical driven-dissipative collective spin system
• Dissipative stabilization of dark quantum dimers via squeezed vacuum
• Squeezed superradiance enables robust entanglement-enhanced metrology even with highly imperfect readout

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