Emission of Microwave Photon Pairs by a Tunnel Junction

We report the observation of photon pairs in the photoassisted shot noise of a tunnel junction in the quantum regime at very high frequency and very low temperature. We have measured the fluctuations of the noise power generated by the junction at two different frequencies, $f_1=4.4$ and $f_2=7.2\mathrm{GHz}$, while driving the junction with a microwave excitation of frequency $f_0=f_1+f_2$. We observe clear correlations between the fluctuations of the two noise powers even when the mean photon number per measurement is much smaller than one. This is strong evidence for photons being emitted in pairs. We also demonstrate that the electromagnetic field generated by the junction exhibits two-mode amplitude squeezing, a proof of its nonclassicality. The data agree very well with predictions based on the fourth cumulant of the current fluctuations generated by the junction.

Figure 1

Experimental setup.

Figure 2

Reduced power-power correlator $G_2$ vs dc bias voltage for various ac excitation amplitudes at frequency $f_0=f_1+f_2=11.6\mathrm{GHz}$. Symbols are experimental data and solid lines theoretical expectations of Eqs. (1) and (2). Symbol sizes represent experimental uncertainty and each point was averaged over 773 s ($3.1\times 10^{11}$ samples) for curves $V_{\text{ac}}=15\mu {\mathrm{V}}_{\text{ac}}$ and above, 1546 s ($6.2\times 10^{11}$ samples) at $V_{\text{ac}}=11\mu {\mathrm{V}}_{\text{ac}}$ and $1.5\times 10^4\mathrm{s}$ ($6.3\times 10^{12}$ samples) at $V_{\text{ac}}=0\mu {\mathrm{V}}_{\text{ac}}$.

Figure 3

Left scale: Normalized photon-photon correlator $g_2$ vs dc bias voltage for a fixed ac bias $V_{\text{ac}}=22\mu \mathrm{V}$. Red circles are experimental data, where each point was averaged over 773 s ($3.1\times 10^{11}$ samples), and the full line represents theoretical expectations from Eq. (3). Right scale (dashed lines): Number of emitted photons per unit bandwidth per unit time $⟨n_{1,2}⟩$ in branches 1 and 2.

Figure 4

Noise reduction factor vs dc bias voltage for a fixed ac bias $V_{\text{ac}}=22\mu \mathrm{V}$. Red circles are experimental data, where each point was averaged over 773 s ($3.1\times 10^{11}$ samples), and the full line represents theoretical expectations. The shaded region NRF$<1$ corresponds to nonclassical electromagnetic field.