Emission of Nonclassical Radiation by Inelastic Cooper Pair Tunneling

We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and intercorrelations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This nonclassical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.

Figure 1

Principle and setup of the experiment. (a) A Josephson junction in series with two resonators with frequencies ${\nu }_{a,b}$ emits a photon pair in the resonators each time a Cooper pair tunnels through it at a dc bias voltage $V$ such that $2eV=h{\nu }_a+h{\nu }_b$. Microwave radiations leaking out of the resonators at rates ${\kappa }_{a,b}$ should present strong quantum correlations. (b) Setup: The sample consists of a SQUID [SEM micrograph shown in (d)] working as a magnetically tunable Josephson junction in series with two three-quarter-wave transformer resonators whose optical micrograph is shown in (c). Two bias tees make it possible to dc voltage bias the SQUID while collecting radiation from the resonators. A HBT setup with a hybrid coupler, isolators, amplifiers, filters, and power detectors is used to measure all powers and power-power correlations (see the text).

Figure 2

Detected power spectral density $S$ as a function of frequency $\nu$ and dc bias voltage $V$, reexpressed in terms of photon rate per unit bandwidth at the output of the resonators. Emission occurs at one photon per Cooper pair along the line $2eV=h\nu$ (see left two-dimensional map), and at two identical photons per Cooper pair along the $2eV=2h\nu$ line and one pair of photons in modes $a$, $b$ along the vertical line $2eV=h{\nu }_a+h{\nu }_b$ (see right two-dimensional map). The leftmost panel is a cut along the $2eV=h\nu$ line showing the emitted power (blue bold line). The rightmost panel is a cut at $V=24.1\mu V=h({\nu }_a+{\nu }_b)/(2e)$. Spectral density for the two-photon processes has been multiplied by 100 for clarity. The red curves show the predictions of the $P(E)$ theory with $E_J=1.42\mu \mathrm{eV}\pm 0.07\mu \mathrm{eV}$ being the only adjustable parameter.

Figure 3

Non classicality of the emitted radiation at bias $V=24.1\mu \mathrm{V}$, as a function of the photon pair emission rate. Left scale: Zero delay power-power correlation functions $g_{aa}^{(2)}(0)$ (red open squares), $g_{ab}^{(2)}(0)$ (magenta open squares) and $g_{bb}^{(2)}(0)$ (blue open squares). Right scale: the corresponding NRF (green open squares) extracted from Eq. (1) does not reach the ideal value of 0.5 (horizontal dashed line), but remains well below 1, which demonstrates two-mode amplitude squeezing. Inset: Time dependence of $g_{ab}^{(2)}(\tau )$. The solid lines are theoretical predictions without adjustable parameters. In the inset, the magenta curve includes the effect of the detector finite response time, while the dark blue dashed corresponds to the prediction for infinitely fast detectors.