Laser from a many-body correlated medium

We consider a nonequilibrium system of interacting emitters described by the XXZ model, whose excitonic transitions are spatially and spectrally coupled to a single mode cavity. We demonstrate that the output radiation field is sensitive to an interplay between the hopping ($J$) and the interactions ($U$) of the excitons. Moderate values of the short-ranged interaction are shown to induce laser with maximal output at the Heisenberg point ($U=J$). In the laser regime, charge-charge correlations emerge and they are shown to strongly depend on the interaction-hopping ratio. In particular, the system shows charge-density correlations below the Heisenberg point and ferromagnetic correlations beyond the Heisenberg point. This contrast to the equilibrium behavior of the XXZ chain occurs since the laser explores highly excited states of the emitters.

Figure 1

Pictorial representation of the laser with a strongly interacting many-body system of emitters as the active medium. The microscopic energetic contributions of each possible interacting process are explicitly indicated.

Figure 2

Cavity photon number (left panel), second order correlation at zero time delay of the emitted radiation (top right panel), and the $Z$ component of the total atomic spin ($Z_T$) divided by the number of atoms, for the case with $L=4$ emitters (bottom right panel), as a function of the external pump and for different values of the interaction energy. The model parameters assumed in the calculations are $g=0.1J$ and $\kappa =0.5g$, respectively.

Figure 3

Cavity photon number for $P=J$ as a function of the interaction strength (top left panel), and scaling of the cavity photon number at the Heisenberg point, $U=J$ (bottom left panel). Second-order correlation at zero time delay for the output cavity radiation (right top panel) and $Z$ component of the total atomic spin ($Z_T$) divided by the number of atoms (right bottom panel), as a function of the correlation strength and for different numbers of emitters, in both cases for $P=J$. The system parameters assumed in the calculations are $g=0.1J$ and $\kappa =0.5g$, as before.

Figure 4

Cooperativity of the many-body laser as compared to single emitter lasers (left panel), as defined in Eq. (6). Cooperativity of the many-body laser as compared to the corresponding standard laser (right panel), as defined in Eq. (7). The system parameters used in these simulations are $g=0.1J, \kappa =0.5g$, and $P=J$.

Figure 5

(Top) The probabilities of the $H_{XXZ}$ eigenstates, as computed from ${\rho }_{\mathrm{NESS}}$. (Middle) The corresponding eigenenergies. (Bottom) The corresponding magnetization as a function of $U/J$. Data in all three plots were obtained for $L=3$. Highlighted in each plot are the three most probable states. The system parameters are $g=0.1J, \kappa =0.5g$, and $P=J$.

Figure 6

(Top) The probabilities of all the $H_{\text{XXZ}}$ eigenstates, as computed from ${\rho }_{\mathrm{NESS}}$ for $L=6$ and $J=U$. (Bottom) The corresponding eigenenergies as a function of their magnetization. Highlighted are the $|S,Z_T\rangle$ states. The system parameters are $g=0.1J, \kappa =0.5g$, and $P=J$.

Figure 7

(Top) Correlations between nearest neighbors and next-nearest neighbors with respect to the site $m=\mathrm{floor}(L/2)$ for a system of five emitters as a function of the interactions. (Middle) The correlations obtained from the stochastic Schrödinger equation, for specific values of the ratio between interaction and hopping strength ($U=0.8J$ and $U=J$) as a function of the number of emitters $L$. (Bottom) Spatial correlations obtained from the solution of the stochastic Schrödinger equation for a chain of 11 sites as a function of the distance between emitters. The system parameters of these simulations are $g=0.1J, \kappa =0.5g$, and $P=J$.