Ultralong relaxation times in bistable hybrid quantum systems

Abstract

Amplitude bistability in a solid-state hybrid quantum system shows critical slowing down with ultralong relaxation times.

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

“…Moreover, we also assume that the cavity decay rate κ is orders of magnitude larger than the longitudinal relaxation rate, so that the following inequality holds in addition: γ κ. These two inequalities are very well fulfilled as, e.g., in the recent experiments mentioned in the introduction [31,32].…”

“…In a recent paper [32] involving also the present au-arXiv:1903.06892v2 [quant-ph] 3 Aug 2019 thors among others, it was shown how a hybrid system composed of a superconducting resonator coupled to an inhomogeneously broadened spin ensemble in diamond can be used to explore amplitude bistability in new regimes of cavity QED. In accordance with first theoretical findings based on a semiclassical approach, the experiment demonstrated a critical slowing down of the cavity population on the order of eleven hours -a timescale much longer than observed anywhere else for this phenomenon.…”

“…Neither will it be possible to solve the problem in the continuous limit. Instead, similar to previous work [32], we discretize the spectral density by performing the inverse transformation,…”

“…If not specified otherwise, our numerical calculations are performed with a set of parameters typical for the experiments with a λ/2 superconducting microwave coplanar waveguide resonator magnetically coupled to a spin ensemble of negatively charged NV centers in diamond [31][32][33]: the cavity decay rate κ/2π = 0.8 MHz, the coupling strength Ω/2π = 12 MHz, the transverse spin relaxation rate γ ⊥ /2π = 250 kHz, the dimensionless q-Gaussian parameter q = 1.39, and the FWHM of the q-Gaussian γ q /2π = 9.4 MHz. The mean frequency of the spectral density, the cavity frequency and the probe frequency of the driving signal are all taken to be in resonance, ω s = ω c = ω p = 2π × 2.6915 GHz.…”

“…We consider the thermodynamic limit justified for a very large number of spins where the problem can be treated in the framework of the Maxwell-Bloch equations. In accordance with the recent experimental realization [32], the cavity decay rate and the non-radiative dephasing of individual spins are chosen to be much larger than their radiative dephasing. Among other phenomena mentioned above, we find an interesting separation of time scales in the temporal dynamics.…”