Spontaneous symmetry breaking in nonlinear superradiance

Abstract

Creation and manipulation of non-classical states of light is rapidly becoming the focus of modern attosecond science. Here, we demonstrate numerically how such states can arise by considering a modification of the well-known problem of superradiance encountered already by Dicke. Similarly to him, we investigate photon emission by ensembles of indistinguishable atoms. In contrast to him, however, we leverage symmetry-based selection rules to suppress emission of single photons by single atoms. A steady state is therefore only reached following a spontaneous transition into a collective symmetry-broken state of atoms and photonic modes. The novel non-Markovian, non-perturbative method applied allows us to observe a large quantum state of light form and exhibit drastically non-classical statistics once the system undergoes a symmetry-breaking transition.

Figures (3)

• Figure 1: Basic design of our setup. The classical radiation, resonant in our case with the atomic transitions, (orange) drives ultrafast currents in atoms (grey). This causes them to emit photons (blue) entangled with the emitters. The electromagnetic radiation confinement exhibited by e.g. a cavity (black) causes these photons to linger, allowing them to either be absorbed by the same or another atom, or leave the confining medium. In the latter case (right section), they can be observed by a detector positioned outside. By detuning the cavity's resonant frequency far from the atomic resonance, we restrict the emission of observable light to groups of atoms.
• Figure 2: Collective emission by classically driven atoms into a cavity tuned to the second harmonic of the driver. (a) The waveform of the driving field $F(t)$, set in resonance with a single atomic transition. (b) Average fraction of excited atoms (c) The isotropic correlator $\mathcal{I}$ vs time. (d) Average photon emission rate summed across every photonic mode. The time units are laser cycles. Emission is virtually non-existent absent correlations, and is accelerated by the transiently increased correlations around $t=2$ cycles. (e) As the evolution progresses, the relative dispersion $\mathcal{N} \equiv \text{Var } n/\expval{\hat{n}} \equiv \left(\expval{\hat{n}^2}/\expval{\hat{n}}\right) - \expval{\hat{n}}$ reaches into the classically prohibited region, marked in red. The initial region of this plot is omitted due to the high stochastic uncertainty caused by the vanishingly small $\expval{n}$.
• Figure 3: (top) Development of the multimode Husimi function for the different frequency modes left to right over the simulation time (top to bottom, in units of 1 laser cycle $2\pi/\omega$). While some modes display a ring-like Husimi function even on their own, in isolation their photon number dispersion remains decidedly super-Poissonian. (bottom) Discretized modes whose Husimi functions are displayed on top, the modes shown by circles and the exact dispersion relation (\ref{['omega-k']}) by the solid black line.