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)).

Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. II. Semiclassical-to-quantum boundary

“…Being based on neglecting the correlations between spins and the electromagnetic field they successfully describe many effects of lasers [16], superradiance [17][18][19], critical slowing down [20][21][22], and amplitude bistability [21][22][23][24][25][26][27]. In a separate companion paper we use the Maxwell-Bloch equations to study the dynamics of macroscopic spin ensembles near the critical point of amplitude bistability and analyze the effect of critical slowing down in the presence of inhomogeneous broadening [22]. Here, we will investigate to what extent the Maxwell-Bloch equations themselves are well-justified to describe the actual quantum dynamics of such systems on experimentally relevant time scales.…”

Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

“…with width γ s and mean frequency ω s , characterizing the frequency distribution of the spin ensemble [23,25,70]. For simplicity, we assume for the calculations presented in Fig.…”

Comparison of the semiclassical and quantum optical field dynamics in a pulse-excited optical cavity with a finite number of quantum emitters

“…( 1). This is different from studies investigating the case of a constant driving [32,33]. The influence of initial Fock-and coherent states are discussed in Ref.…”

“…x , coupled with strengths g (k) to a single light field mode with energy ω 0 and annihilation (creation) operator â (â † ). This leads to the Cavity Pulse ... Hamiltonian of the TC model [30,32,33]…”

“…3 ) and to the polarization (σ (k) ± ) of the QEs. In general, the transition frequencies and coupling strengths may be different for each QE [31][32][33][34]. Note that the Hamiltonian in Eq.…”