Cooperative Light Emission in the Presence of Strong Inhomogeneous Broadening

Abstract

We study photon emission by an ensemble of two-level systems, with strong inhomogeneous broadening and coupled to a cavity mode whose frequency has linear time-dependence. The analysis shows that, regardless the distribution of energy level splittings, a sharp phase transition occurs between the weak and strong cooperative emission phases near a critical photonic frequency sweeping rate. The associated scaling exponent is determined. We suggest that this phase transition can be observed in an ensemble of negatively charged NV − centers in diamond interacting with a microwave half-wavelength cavity mode even in the regime of weak coupling and at strong disorder of two-level splittings.

Thermodynamics from indistinguishability: Mitigating and amplifying the effects of the bath

“…In this section we analyse the impact of small defects like homogeneities rising for instance from unequal subsystems or local disorder and variation of the subsystems' surrounding [97,98]. We also consider small interactions between the subsystems.…”

Coherent reaction between molecular and atomic Bose-Einstein condensates: integrable model

“…The probability (6) to find n molecules after the forward sweep satisfies a 15) in the main text. The joint probabilities Pm1m2 were obtained by solving the nonstationary Schrödinger equation numerically (plot markers) for the Hamiltonian (16). Solid lines are the corresponding predictions of Eq.…”

“…Both figures describe the number of produced atoms from molecules: in our case as a function of 1/β but as a function of time of the resonant interaction in [1]. We attribute this to the fact that g/β in our model characterizes the effective time of the transition through the resonance, so both figures describe essentially the same physics: it takes initially certain critical time for the process to evolve without visible effects, after which a macroscopic number of molecules dissociates quickly due to superradiance [16], which can occur before entering stationary equilibrium phases [17][18][19][20][21].…”

“…This map is not intuitive in the sense that the number of molecules n in ( 6) is not the same as the number of bosons in the DTCM. Instead, n| ψ † ψ|n = N − n. Therefore, the dynamics that was called the forward process in DTCM [16] is mapped to the reverse process in (6), and vice versa. Thus, we predict strongly different efficiencies in purely bosonic versus fermion-bosonic reactions.…”

“…) is the q-Pochhammer symbol. According to [16], this distribution predicts a dynamic phase transition. Namely, if the number of molecules N is initially macroscopically large, then the fraction of molecules converted to atoms, m /N = 1 − n /N, behaves discontinuously as a function of, g 2 /β.…”