Fermionized Photons in an Array of Driven Dissipative Nonlinear Cavities

We theoretically investigate the optical response of a one-dimensional array of strongly nonlinear optical microcavities. When the optical nonlinearity is much larger than both losses and intercavity tunnel coupling, the nonequilibrium steady state of the system is reminiscent of a strongly correlated Tonks-Girardeau gas of impenetrable bosons. Signatures of strong correlations are identified in the transmission spectrum of the system, as well as in the intensity correlations of the transmitted light. Possible experimental implementations in state-of-the-art solid-state devices are discussed.

Figure 1

Left panel: Sketch of the system under consideration. Right panel: Total transmission spectra as a function of the frequency $\Delta {\omega }_p={\omega }_p-{\omega }_0$ of the pump beam. System of $M=5$ cavities in the impenetrable boson limit $U/J=\infty$, with $J/\gamma =20$. Different curves correspond to increasing values of the pump amplitude $F_p/\gamma =0.1,0.3,1,2,3$. The vertical dotted lines indicate the spectral positions of the peaks predicted by the fermionization procedure.

Figure 2

(a),(b) Spectra of the population in the $k=0$ and $k=2\pi /3$ bosonic modes as a function of pump frequency for a fixed pump amplitude $F_p/\gamma =0.5$ and different values of the nonlinear coupling $U/J$. (c),(d): Position of the peak and relative occupation $n_{k=2\pi /3}/n_{k=0}$ at the peak position as a function of $U/J$. The background signal due to the one-particle peak has been subtracted out from $n(k=2\pi /3)$. Blue dashed lines: Asymptotic values in the weak $U/J\ll 1$ and strong $U/J\gg 1$ interaction limits. System of $M=3$ cavities with $J/\gamma =20$.

Figure 3

Plot of the auto- (black, solid line) and cross- (red, dashed line) intensity correlations as a function of the interaction strength $U/J$. Red, dotted line: Analytical prediction for the cross-intensity correlation in the impenetrable boson limit. The same system parameters as in Fig. 2.