Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. I. Semiclassical approach

Abstract

We present a theoretical study on the nonlinear dynamics and stationary states of an inhomogeneously broadened spin ensemble coupled to a single-mode cavity driven by an external drive with constant amplitude. Assuming a sizeable number of constituents within the ensemble allows us to use a semiclassical approach and to formally reduce the theoretical description to the Maxwell-Bloch equations for the cavity and spin amplitudes. We explore the critical slowing-down effect, quench dynamics, and asymptotic behavior of the system near a steady-state dissipative phase transition accompanied by a bistability effect. Some of our theoretical findings have recently been successfully verified in a specific experimental realization based on a spin ensemble of negatively charged nitrogen-vacancy centers in diamond strongly coupled to a single-mode microwave cavity (see Science Adv. 3, e1701626 (2017)).

arXiv comment11 pages, 6 figures

References in corpus (25)

• Cavity Optomechanics
• Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
• Quantum technologies with hybrid systems
• Quantum phase transitions
• Spectral theory of Liouvillians for dissipative phase transitions
• Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble
• Dissipative Phase Transition in Central Spin Systems
• Cavity QED with magnetically coupled collective spin states
• Probing a dissipative phase transition via dynamical optical hysteresis
• Towards a theory of metastability in open quantum dynamics
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Observation of the photon-blockade breakdown phase transition
• Protecting a Spin Ensemble against Decoherence in the Strong-Coupling Regime of Cavity QED
• Power-laws in the dynamic hysteresis of quantum nonlinear photonic resonators
• Strong magnetic coupling of an inhomogeneous NV ensemble to a cavity
• Dynamical Exploration of Amplitude Bistability in Engineered Quantum Systems
• Non-Markovian dynamics of a single-mode cavity strongly coupled to an inhomogeneously broadened spin ensemble
• Extreme non-linear response of ultra-narrow optical transitions in cavity QED for laser stabilization
• Optical bistability in strong-coupling cavity QED with a few atoms
• Metastability in the driven-dissipative Rabi model
• Few-mode geometric description of a driven-dissipative phase transition in an open quantum system
• Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. II. Semiclassical-to-quantum boundary
• Scaling of Saddle-Node Bifurcations: Degeneracies and Rapid Quantitative Changes
• Non-adiabatic effects in periodically driven-dissipative open quantum systems
• Bistability effect in the extreme strong coupling regime of the Jaynes-Cummings model

Cited by in corpus (9)

• Echo trains in pulsed electron spin resonance of a strongly coupled spin ensemble
• Few-mode geometric description of a driven-dissipative phase transition in an open quantum system
• Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. II. Semiclassical-to-quantum boundary
• Collective dynamics of inhomogeneously broadened emitters coupled to an optical cavity with narrow linewidth
• A trapped ion in an optical cavity: numerical study of an optomechanical transition in the few-photon regime
• Exploring the limits of the generation of non-classical states of spins coupled to a cavity by optimal control
• Protecting information in a parametrically driven hybrid quantum system
• Comparison of the semiclassical and quantum optical field dynamics in a pulse-excited optical cavity with a finite number of quantum emitters
• pyBoLaNO: A Python symbolic package for normal ordering involving bosonic ladder operators