Terahertz laser based on dipolaritons

We develop the microscopic theory of a terahertz (THz) laser based on the effects of resonant tunneling in a double quantum well heterostructure embedded in both optical and THz cavities. In the strong-coupling regime the system hosts dipolaritons, hybrid quasiparticles formed by the direct exciton, indirect exciton, and optical photon, which possess large dipole moments in the growth direction. Their radiative coupling to the mode of a THz cavity combined with strong nonlinearities provided by exciton-exciton interactions allows for stable emission of THz radiation in the regime of the continuous optical excitation. The optimal parameters for maximizing the THz signal output power are analyzed.

Figure 1

(a) Band diagram of the double QW system. In the presence of the optical microcavity the QW${}_1$ is coupled to the cavity mode. The energy bands are tilted by the applied electric field, bringing the electron levels into resonance. Dimensions and materials of the QWs and the barrier are indicated. (b) Sketch of the dipolariton system in a THz cavity. The QW${}_1$ is where direct excitons (DX) are excited. The electron can tunnel with a rate $J$ to the QW${}_2$, forming indirect excitons (IX). The distributed Bragg reflectors (DBR) provide the confinement of the cavity photon (C), which is strongly coupled to the direct exciton transition with a Rabi frequency $\Omega$, and decoupled from the QW${}_2$. The supplemental cavity hosts a THz photonic mode, which interacts with the exciton dipole moment. The bare double QW system lacks the DBR optical confinement, and therefore the microcavity mode.

Figure 2

Energy diagram showing the level repulsion between the direct (DX) and indirect excitons (IX) at resonance. New modes, the symmetric (SX) and antisymmetric exciton (AX) arise, split by the tunneling rate $J$. The resonant processes in the interaction Hamiltonian (9) of THz absorption and emission are shown.

Figure 3

(a) Occupation number dynamics of the indirect excitons in the double QW system under CW pumping. The exciton detuning is $\hslash {\delta }_J=1$ meV, and the pump energy is $\hslash {\Delta }_p=1.5$ meV. Pump strength is linearly turned on to $|{\tilde{P}}_0{|}^2=1.1\times {10}^{29}$ s${}^{-2}$ with a short turning on time, driving the system into the parametrically instable regime. The IX occupation number oscillates periodically, but not harmonically. (b) Spectral characteristics of the time dependence shown in (a). The oscillations are distributed between many harmonics, which lowers dramatically the efficiency of THz excitation.

Figure 4

(a) Energy diagram of the dipolariton system, as a function of the applied field $F$ in units of the resonance field $F_0$. The dashed lines correspond to the bare modes, the photonic (green and flat), the DX (blue), and the IX (red and steep) modes. The diagonalized modes, being the upper (UP), middle (MP), and lower (LP) dipolaritons, are indicated with solid lines. The energy of the pump is identified with a short horizontal line. The vertical line shows the value of the applied field chosen for the calculations. (b) Stability curve under CW pumping for pumping energy $\hslash {\Delta }_p=4.5$ meV. The bistability arises here due to the blueshift of the MP mode. The blue curve indicates the DX numbers (left axis), and the red curve is the IX numbers (right axis). Thin segments indicate stability of the population numbers, while the thick lines indicate parametric instability.

Figure 5

Plot of the occupation number dynamics of a THz cavity with $Q=100$ coupled to the dipolariton system under CW pumping. The excitonic detuning is $\hslash {\delta }_J=1$ meV, the cavity mode detuning is $\hslash {\delta }_{\Omega }=-3$ meV, and the relative pump energy is $\hslash {\Delta }_p=4.5$ meV, corresponding to the energy-level configuration in Fig. 4. The CW pump is rapidly turned on to $|{\tilde{P}}_0{|}^2=1.1\times {10}^{29}{\text{s}}^{-2}$. As a result, the system is driven into the parametrically instable regime, provoking oscillations in exciton numbers shown in the inset. For the dipolariton system, these oscillations are harmonic, and result in a stable population of the THz mode $N_{THz}\simeq 200$ photons.

Figure 6

Plot of the time-averaged emission power of THz radiation as a function of the quality factor of the THz cavity. The two lines indicate different pumping strengths, $|{\tilde{P}}_0{|}^2=1.1\times {10}^{29}$ s${}^{-2}$ (pump A, blue line) and $|{\tilde{P}}_0{|}^2=0.9\times {10}^{29}$ s${}^{-2}$ (pump B, green dotted line). The dashed line shows the low $Q$ Purcell effect prediction in Eq. (21) with the IX oscillation amplitude taken as $N_1=1.1\times {10}^4$, corresponding to pump A [29]. A peak in emission power is found at $Q=17$ (A) or $Q=30$ (B), before dropping due to increased feedback of the THz mode on the indirect exciton. The inset shows the number of THz photons as a function of time for $Q=1200$ for pump A. For such a high quality factor the number of THz photons is considerably large. The resulting feedback on the excitonic modes is so strong it does not allow for a steady-state solution. Rather, the number of THz photons oscillates, with a period of $\approx$70 ps, mimicking the output of a $Q$-switched THz laser.

Figure 7

Density plot of the emission power as a function of the applied field and cavity eigenfrequency. The optical cavity detuning is $\hslash {\delta }_{\Omega }=-1$ meV, the pump energy is $\hslash {\Delta }_p=4.5$ meV, and the pumping strength is $|{\tilde{P}}_0{|}^2=1.1\times {10}^{29}$ s${}^{-2}$. The quality factor of the THz cavity is $Q=17$, corresponding to the optimal emission power in Fig. 6. Lighter colors signify higher output power, with the maximum output power following closely the indirect exciton oscillation frequency (red solid line).