Nonclassical Many-Body Superradiant States with Interparticle and Spin-Momentum Entanglement

Abstract

We present a cross-cavity system in which steady-state superradiance is achieved using solely collective dissipative dynamics. Two cavities symmetrically couple an ensemble of four-level atoms by driving transitions between two electronic states and two motional states along perpendicular cavity axes. Both cavities operate in the bad-cavity regime: one cavity mediates collective atomic decay, while the other cavity, together with a coherent drive, mediates collective pumping via an off-resonant Raman transition. With this, we find steady-state superradiant states that possess nonclassical properties, such as super-Poissonian photon statistics. The system thus requires a beyond mean-field description, and so we develop an exact master equation simulation technique utilizing strong symmetries of the system's jump operators. Because superradiant decay is accompanied by a momentum impulse along the corresponding cavity axis, the system exhibits substantial hybrid entanglement between the atoms' spin and motional degrees of freedom at steady state. We also demonstrate that heralded measurements of the two cavity outputs prepare a state with significant particle-particle entanglement with prospects for quantum-enhanced acceleration sensing.

Figures (6)

• Figure 1: (a) Schematic of the cross-cavity system, also pumped from the side by a coherent field. Both cavity fields can decay into free-space modes, while spontaneous emission from the atoms is neglected. (b) Level diagram of atom $j$ with three internal states, $\lvert g\rangle_j$, $\lvert e\rangle_j$, and $\lvert a\rangle_j$. (c) Effective $\mathrm{SU}(4)$ system for atom $j$ constructed from the spin-$x$-momentum states of Eq. \ref{['SU4_States']}. Green arrows indicate $\hat{J}_{\pm}$, orange arrows indicate $\hat{E}_{\pm}$, and pink arrows indicate $\hat{K}_{\pm}$.
• Figure 2: Intensity of the (a) $x$-cavity and (b) $z$-cavity, signifying superradiance when $\mathcal{O}(N^2)$. The inset in (b) displays the spin inversion around the transition. Expectation values of the quadratic Casimir operator for the (c) $E$ and (d) $J$ subgroups. The $N \rightarrow \infty$ curves (dotted black lines) are from the fit in Eq. \ref{['fN_fit']}, suggesting a potential phase transition at $W = \Gamma_c$.
• Figure 3: Second-order coherence at zero time delay for the (a) $x$-cavity and (b) $z$-cavity. The $N \rightarrow \infty$ curves (dotted black lines) are from the fit in Eq. \ref{['fN_fit']}.
• Figure 4: Steady-state coherent information $I(X \rangle Y)[\hat{\rho}_{\mathrm{ss}}]$ from Eq. \ref{['CoherentInformation']} for the subspaces $X \neq Y \in \{ J, K \}$. We use the algorithm from Ref. ActuallyJarrodsPaper3 with $N = 10$. The dotted black line marks $I(X \rangle Y)[\hat{\rho}_{\mathrm{ss}}] = 0$; any point above it indicates quantum correlations (hybrid entanglement) between the spin and $x$-momentum degrees of freedom.
• Figure 5: The maximum quantum Fisher information $\lambda_{\mathrm{max}}$ for $N_{\mathrm{traj}} = 50$ different Monte-Carlo wave function trajectories. The different trajectories are signified by different colors, while the dotted gray line indicates the standard quantum limit $\lambda_{\mathrm{max}} = N$. Each figure has $N = 50$, and the pump values are given by (a) $W = 0.1 \Gamma_c$, (b) $W = \Gamma_c$, and (c) $W = 10 \Gamma_c$.