Quantum Vacuum Radiation Spectra from a Semiconductor Microcavity with a Time-Modulated Vacuum Rabi Frequency

We develop a general theory of the quantum vacuum radiation generated by an arbitrary time modulation of the vacuum Rabi frequency of an intersubband transition in a doped quantum well system embedded in a planar microcavity. Both nonradiative and radiative losses are included within an input-output quantum Langevin framework. The intensity and the spectral signatures of the extra-cavity emission are characterized versus the modulation properties. For realistic parameters, the photon pair emission is predicted to largely exceed the blackbody radiation in the mid and far infrared. For strong and resonant modulation a parametric oscillation regime is achievable.

Figure 1

Top: a sketch of the considered semiconductor planar microcavity system. Bottom: a scheme of the quantum model.

Figure 2

Top panel: rate of emitted photons $d{N}_{\mathbf{k}}^{\mathrm{out}}/dt$ (in units of ${\omega }_{12}$) as a function of the normalized modulation frequency ${\omega }_{\mathrm{mod}}/{\omega }_{12}$. Parameters: $({\omega }_{c,\mathbf{k}}+2D_k)/{\omega }_{12}=1$, $\Gamma /{\omega }_{12}=0.025$, ${\overline{\Omega }}_{R,\mathbf{k}}/{\omega }_{12}=0.2$, $\Delta {\Omega }_{R,\mathbf{k}}/{\omega }_{12}=0.04$. Note that, due to the scaling properties of the present model, the results do not depend on the specific value of ${\omega }_{12}$. The letters $A$, $B$, $C$ indicate three different resonantly enhanced processes. Bottom panels: the spectral density (arb. units) for the processes $A$, $B$, $C$, respectively. The resonant peaks occur at the LP (lower polariton) and/or UP (upper polariton) frequency.

Figure 3

Top panel: rate $d{N}_{\mathbf{k}}^{\mathrm{out}}/dt$ (in units of ${\omega }_{12}$) vs ${\omega }_{\mathrm{mod}}/{\omega }_{12}$ for different values of $\Gamma /{\omega }_{12}=0.025$ (solid line), 0.05 (dashed line), 0.075 (dot-dashed line). Other parameters as in Fig. 2. Bottom panel: normalized rate of emitted photons from a blackbody emitter vs ${\omega }_{12}$ for different temperatures.

Figure 4

Top panel: $d{N}_{\mathbf{k}}^{\mathrm{out}}/dt$ (in units of ${\omega }_{12}$) vs ${\omega }_{\mathrm{mod}}/{\omega }_{12}$ for $\Gamma /{\omega }_{12}=0.025$ and for different values of the modulation amplitude $\Delta {\Omega }_{R,k}/{\omega }_{12}=0.01$, 0.04, 0.07, 0.1 (from bottom to top). Bottom panel: instability boundaries for $\Gamma /{\omega }_{12}=0.025$ (solid line) and 0.05 (dashed line). Above the lines, the system is parametrically unstable.