Antibunched Photons Emitted by a dc-Biased Josephson Junction

We show experimentally that a dc biased Josephson junction in series with a high-enough-impedance microwave resonator emits antibunched photons. Our resonator is made of a simple microfabricated spiral coil that resonates at 4.4 GHz and reaches a $1.97\mathrm{k}\mathrm{\Omega }$ characteristic impedance. The second order correlation function of the power leaking out of the resonator drops down to 0.3 at zero delay, which demonstrates the antibunching of the photons emitted by the circuit at a rate of $6\times {10}^7$ photons per second. Results are found in quantitative agreement with our theoretical predictions. This simple scheme could offer an efficient and bright single-photon source in the microwave domain.

Figure 1

Principle of the experiment: (a) A Josephson junction in series with a resonator of frequency ${\nu }_R$ and characteristic impedance $Z_c$ of the order of $R_Q=h/(2e{)}^2$ is voltage biased so that each Cooper pair that tunnels produces a photon in the resonator (1). (b) Photon creation and relaxation: A tunneling Cooper pair shifts the charge on the resonator capacitance by $2e$. The tunneling rate ${\mathrm{\Gamma }}_{n\to n+1}$ starting with the resonator in Fock state $|n⟩$ is proportional to the overlap between the wave function ${\mathrm{\Psi }}_n(q)$ shifted by $2e$ and ${\mathrm{\Psi }}_{n+1}(q)$. This overlap depends itself on $Z_C$ via the curvature of the resonator energy. At a critical $Z_c$, ${\mathrm{\Gamma }}_{1\to 2}=0$ and no additional photons can be created (2) until the photon already present has leaked out (3). The photons produced are thus antibunched, which is revealed by measuring the $g^{(2)}$ function of the leaked radiation.

Figure 2

Experimental setup. (a) Optical micrography of the sample showing the $\mathrm{Al}/\mathrm{AlOx}/\mathrm{Al}$ SQUID (inset) implementing the Josephson junction and the resonator made of a Nb spiral inductor with stray capacitance to ground. (b) Schematic of the circuit showing the sample (green), the coil circuit for tuning the Josephson energy (brown), the dc bias line (red), and the bias tee connected to the microwave line (blue) with bandpass filters, isolators (not shown here), and a symmetric splitter connected to two measurement lines with amplifiers at 4.2 K and demodulators at room temperature [32].

Figure 3

Emitted microwave power and impedance seen by the junction. (a) 2D map of the emitted power spectral density (PSD) as a function of the frequency $\nu$ and bias voltage $V$, expressed in photon occupation number (logarithmic color scale). (b) Spectral line at $V=9.11\mu V$ (blue points) obtained from a cut in the 2D map along the horizontal white arrows and real part of the impedance $\mathrm{Re}[Z(\nu )]$ seen by the SQUID (red points). The solid blue (black) line is a Gaussian (Lorentzian) fit.

Figure 4

Antibunching of the emitted radiation at bias $V=h{\nu }_R/2e=9.11\mu \mathrm{V}$. (a) Experimental (dots) and theoretical (dashed line) second order correlation function $g^{(2)}$ as a function of delay $\tau$ for $n=0.08$ photons in the resonator. Error bars indicate $\pm$ the statistical standard deviation. (b) Experimental (dots) and theoretical (dashed line) $g^{(2)}(0)$ as a function of $n$. The solid line is the theoretical prediction not taking into account the finite detection bandwidth.