Photon Emission from a Cavity-Coupled Double Quantum Dot

We study a voltage biased InAs double quantum dot (DQD) that is coupled to a superconducting transmission line resonator. Inelastic tunneling in the DQD is mediated by electron phonon coupling and coupling to the cavity mode. We show that electronic transport through the DQD leads to photon emission from the cavity at a rate of 10 MHz. With a small cavity drive field, we observe a gain of up to 15 in the cavity transmission. Our results are analyzed in the context of existing theoretical models and suggest that it may be necessary to account for inelastic tunneling processes that proceed via simultaneous emission of a phonon and a photon.

Figure 1

(a) Optical micrograph of the hybrid system. Inset: scanning electron micrograph of an InAs nanowire DQD. (b) The DQD is formed by biasing gates $B_L$, $B_R$, and $C$ at negative voltages to form left and right tunnel barriers with rates ${\mathrm{\Gamma }}_L$ and ${\mathrm{\Gamma }}_R$, and an interdot tunnel barrier with rate $t_c/\hslash$. Cavity photons are coupled to the input and output ports with rates ${\kappa }_{\text{in}}$ and ${\kappa }_{\text{out}}$. A source-drain bias $V_{\text{SD}}=({\mu }_D-{\mu }_S)/e$ is applied to the device. (c) Schematic of the charge stability diagram near the ($M$, $N$+1)$\leftrightarrow$($M$+1, $N$) interdot charge transition. Sequential tunneling is allowed within FBTs in the charge stability diagram (gray triangles). Inset: DQD energy level configuration in the lower FBT.

Figure 2

(a) DQD current $I$ plotted as a function of $V_L$ and $V_R$ with $V_{\text{SD}}$ = 2.5 mV. (b) The corresponding normalized transmission $|⟨A⟩{|}^2$. Gain is observed at positive detuning ($\epsilon >0$). (c) Energy level diagram at the ($M$, $N$+1)$\leftrightarrow$($M$+1, $N$) interdot charge transition, illustrating a possible gain mechanism. (d) $|⟨A⟩{|}^2$ as a function of $\epsilon$ with $V_{\text{SD}}$ = 0 (upper panel) and $V_{\text{SD}}$ = 2.5 mV (lower panel). Dashed lines are best fits to theory (see main text). At finite bias, the model underestimates the gain and range of detuning where gain occurs by a factor of $\sim$4.

Figure 3

(a) $|⟨A⟩{|}^2$ as a function of $V_L$ and $V_R$ with the device configured to have larger tunnel rates to the leads. Hot spots with a gain above 15 are observed. (b) $|⟨A⟩{|}^2$ measured as a function of $f_{\mathrm{in}}$ near a hot spot (squares) and deep in Coulomb blockade (circles). Solid lines are fits to a Lorentzian. Inset: the same data are plotted with normalized peak amplitudes. At the hot spot, the cavity linewidth is reduced by a factor of $\sim$3.

Figure 4

Photon emission from the voltage biased DQD in the absence of a cavity drive. (a) Simplified schematic of the experimental setup. Photons are emitted from the input and output ports of the cavity. Photons from the output port are amplified with gain $G$ (adding noise $h_{\text{amp}}$) and then detected by a spectrum analyzer. (b) Photon emission rate plotted as a function of $V_L$ and $V_R$ for the same device configuration as in Fig. 3. The photon emission rate exceeds the background noise floor of the HEMT amplifier by $\sim$10 MHz at the hot spots.