Hanbury Brown–Twiss Correlations to Probe the Population Statistics of GHz Photons Emitted by Conductors

We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury Brown and Twiss correlations. The super-Poissonian and Poissonian photon statistics of thermal and coherent sources, respectively, made of a resistor and a radio frequency generator, are measured down to the quantum regime at milli-Kelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductors.

Figure 1

Schematics of the HBT experiment (a), of the GHz beam splitter (b), of the amplification and detection chains (c). A detailed description is given in the text.

Figure 2

Experiment A: Thermal source at $\nu =1.7\mathrm{G}\mathrm{H}z$. Main frame: quantum crossover at $T_Q/2\approx 40\mathrm{m}\mathrm{K}$ in the mean photon power $\overline{P_1}$ as function of temperature $T$, or effective occupation number $k_{B}T/h\nu$ for a beam splitter temperature $T_0\approx 17\mathrm{m}\mathrm{K}$. The solid line is a Bose-Einstein fit with an amplifier noise temperature $T_N\approx 15\mathrm{K}$. Inset: positive HBT correlations show the bunching of thermal photons and the absence of residual correlations at $T=0\mathrm{K}$. Experimental scatter lies within the expected statistical uncertainty (error bar).

Figure 3

Experiment B: Super-Poissonian correlations of a thermal source in the classical regime: mean photon power $\overline{P_i}$ and noise $\sqrt{\langle \Delta P_i\Delta P_j\rangle }$ (bandwidth $B=160\mathrm{k}\mathrm{H}z$) as a function source temperature $T$ with a beam splitter at $T_0\approx 4\mathrm{K}$. The temperature scale of $\sqrt{\langle (\Delta P_i{)}^2\rangle }$ and $\overline{P_i}$ is used as a calibration of the measuring line. Cross correlations $\sqrt{\langle \Delta P_1\Delta P_2\rangle }$ are deduced without extra parameter and found to extrapolate to $0$ for $T=T_0$, in agreement with Eq. (4).

Figure 4

Experiment C: Poissonian correlations of a coherent monochromatic source. Autocorrelations are linear in the input RF power with a large Fano factor $F$ due to amplification and attenuation. Cross correlations vanish in accordance with theoretical predictions.