Quantum properties of the radiation emitted by a conductor in the Coulomb blockade regime

We present an input-output formalism describing a tunnel junction strongly coupled to its electromagnetic environment. We exploit it in order to investigate the dynamics of the radiation being emitted and scattered by the junction. We find that the nonlinearity imprinted in the electronic transport by a properly designed environment generates strongly squeezed radiation. Our results show that the interaction between a quantum conductor and electromagnetic fields can be exploited as a resource to design simple sources of nonclassical radiation.

Figure 1

Schematics of the considered circuits: (a) A tunnel junction with quasiparticle current ${\widehat{I}}_{\text{qp}}$ is embedded in an $LC$ circuit described by conjugated fields at the depicted node: the inductive magnetic flux $\mathrm{\Phi }$, and the capacitive influence charge $Q$. (b) A transmission line in series with the inductor damps the circuit by radiating outgoing modes $a_{\text{out}}$, which can be detected with a matched detection chain (not shown). (c) A high resistance $\left(R>R_{\mathrm{K}}\right)$ $RC$ circuit is connected to the junction. The resulting quantum flux fluctuations ${\mathrm{\Phi }}_B\left(t\right)$ are responsible for strong dynamical Coulomb blockade modifying the quasiparticle current ${\widehat{I}}_{\text{qp}}$, which can be efficiently collected in a matched detection band of the transmission line.

Figure 2

Lower panel: From Eq. (32), squeezing of the output quadrature $X_{\theta ,\omega }=e^{-i\theta }{a}_{\mathrm{out},\omega +{\omega }_0}+e^{i\theta }{a}_{\mathrm{out},{\omega }_0-\omega }^{†}$, at the resonant frequency ${\omega }_0$, as a function of the impedance-matching parameter $\mathcal{Q}{Z}_{LC}/R_T$ for very strong resistive DCB. The continuous line corresponds to the zero temperature limit, whereas the dashed and dotted curves correspond to temperatures of 7 and 14 mK, respectively, for a resonance at ${\omega }_0/2\pi =6$ GHz. The charging energy $E_c$, the quadrature angle $\theta$, and the bias voltage at the junction are chosen to optimize (minimize) $S_{X_1}$ for each $\mathcal{Q}{Z}_{LC}/R_T$. The middle and upper panels give the associated variations of $E_C,\theta$, and of $V_{\text{dc}}$ and $V_{\text{ac}}$ at 7 mK.