Squeezed superradiant lasing of a quantum many-body emitter

Abstract

In conventional lasers, the emitters are typically incoherent, radiating photons independently; in superradiant lasers, many coherent emitters radiate photons collectively, but they essentially do not interact with each other. Here, we present the concept of quantum many-body lasers, in which the emitters interact coherently and radiate collectively. In this proof-of-concept study, we consider a cavity coupled to many pumped spin-1/2 emitters with all-to-all interaction. We find that the squeezing induced by the coherent many-body interaction can be transferred from the spins to photons through superradiant lasing. This work illustrates the concept of using a pumped quantum many-body system to generate bright quantum light with quantum correlations beyond conventional optical coherence, which can facilitate quantum technologies and the study of nonlinear optics in the quantum realm.

Figures (6)

• Figure 1: Schematics of different types of lasers. (a) In a conventional laser, population-inverted emitters are independently injected into the cavity. (b) In a superradiant laser, many non-interacting emitters couple collectively to a cavity. (c) In a quantum many-body laser (proposed in this work), many spins interact coherently and couple collectively to a cavity and the photons are emitted by transitions between quantum many-body states (which can have non-trivial correlations).
• Figure 2: Superradiant lasing of a pumped cavity-spin system with varying pump rate and spin-spin interaction strength. (a) Phase diagram shown by the number of photons in the cavity $\left|{{}} a{{{}}}\right|^2$ normalized by the number of spins $N$, including: I. normal phase, where $\left|{{}} a{{{}}}\right|^2/N=0$ for $N\rightarrow\infty$, II. superradiant lasing phase, where $\left|{{}} a{{{}}}\right|^2/N\sim O\left(1\right)$, and III. bistable phase. Parameters are such that $\gamma=0.01$ and $\gamma_\phi=\kappa=g\sqrt{N}=\Delta=1$. (b) The stationary total spin $J_{\rm MF}$ (vertical) and its $z$-component ${{}} J^z{{{}}}$ with increasing/decreasing (red/blue arrows) for weak, strong, and moderate spin-spin interaction. The red/blue dotted line in the diagram for $\epsilon=3$ indicates the jump from the lasing/normal state to the normal/lasing state in the bistable phase. Inset shows the polarization-dependent blockade effect for moderate spin-spin interaction, that is, due to the mean-field energy, the spin transition is far off-resonant from the cavity mode when the polarization is large and become near resonant with reducing the polarization.
• Figure 3: Squeezing in superradiant lasing from spins with all-to-all interactions. (a) Evolution of Husimi Q-representation in the phase space from an initial coherent state for spin interaction strength $\chi=0$ (upper row) and $\chi=1$ (lower row). The lines are the principal axes of the quadrature fluctuations at zero frequency. (b) The angle of the axis along which the zero-frequency noise is mimimum [i.e., the axis for $S_-(0)$]. Here, we set $\kappa_a=1,D_a=0.1,D_\phi=0.01$, and $\vert {{}} a{{{}}}\vert^2=100$ to illustrate the twisting effect. (c) Principal noise spectra $S_{\pm}(\omega)$ of the laser for $\epsilon=0$ (blue dash-dotted line) and $\epsilon=3$ (red solid and magnet dashed lines). The pump rate is set as $w=0.2$. (d) Decibel squeeze parameter $\zeta(0)$ as a function of the pump rate and interaction strength. In the bistable phase, only the superradiant lasing state is considered. Parameters not otherwise specified are the same as in Fig. \ref{['fig:figure2']}.
• Figure 4: (a) Effective cooperativities ${C}^{(\pm)}$ versus pump rate $w$ for different interaction strengths: $\epsilon=1$ (red), $\epsilon=3$ (magenta), and $\epsilon=4.7$ (blue). Solid/dashed curves denote ${C}^{(+/-)}$. The black dashed line indicates the lasing threshold $C=1$. (b) Phase boundaries $\epsilon_{1/2/3/4}\left(w\right)$ as functions the pump rate $w$. The normal phase, the superradiant lasing phase, and the bistable phase occur correspondingly for $1>{C}^{(+)}>{C}^{(-)}$, ${C}^{(+)}>1>{C}^{(-)}$, and ${C}^{(+)}>{C}^{(-)}>1$.
• Figure 5: Photon Q-distribution. (a) Calculated by solving the effective Fokker–Planck equation Eq. (\ref{['eq:FPEff4']}). (b) Calculated by diagonalizing the Liouvilllian of the effective quantum model in Eq. (\ref{['eq:effMasterEq']}) of main text. Parameters are the same as in Fig. 3a,b of main text.