Microwave Photon Counter Based on Josephson Junctions

We describe a microwave photon counter based on the current-biased Josephson junction. The junction is tuned to absorb single microwave photons from the incident field, after which it tunnels into a classically observable voltage state. Using two such detectors, we have performed a microwave version of the Hanbury Brown–Twiss experiment at 4 GHz and demonstrated a clear signature of photon bunching for a thermal source. The design is readily scalable to tens of parallelized junctions, a configuration that would allow number-resolved counting of microwave photons.

Figure 1

Microwave photon detector based on a Josephson junction. (a) Schematic diagram of the circuit. The junction is biased with a dc current, and microwaves are coupled to the junction via an on-chip capacitor. The voltage across the junction is read out by a room temperature preamplifier and comparator. (b) Junction potential energy landscape. The junction is initialized in the $|0⟩$ state. An incident photon induces a transition to the $|1⟩$ state, which rapidly tunnels to the continuum. (c) Calculated detection efficiency $\eta$ as a function of applied microwave frequency and current bias. The simulation parameters are $I_0=210\mu \mathrm{A}$, $C=45\mathrm{pF}$, $T_1=3\mathrm{ns}$, ${\omega }_R/2\pi =200\mathrm{MHz}$, and $t_{\det }=5\mathrm{ns}$, chosen to match the parameters of our measured device. (d) Experimentally measured detection efficiency. The efficiency shows a maximum of 0.7. The detection bandwidth is of order the Rabi frequency associated with the microwave drive.

Figure 2

(a) Experimental setup of microwave-frequency version of the Hanbury Brown–Twiss experiment. Coherent microwaves (upper left panel) are derived from a microwave generator whose output is coupled to the detector via a transmission line, with suitable attenuation. The thermal source (lower left panel) is realized by amplifying, filtering, and up-converting the Johnson noise of a room temperature resistor. A two-junction circuit (right panel) is used to probe the statistical nature of the microwave photon source; each junction has its own bias and readout. (b) Conditional switching probabilities $P_{00}$, $P_{10}$, $P_{01}$, and $P_{11}$ versus relative measurement delay $\tau$ for coherent microwaves (upper panel) and thermal microwaves (lower panel). Inset shows the timing diagram of the measurement pulses applied to the two junctions.

Figure 3

Temporal scale of photon bunching. (a) Noise power spectra of thermal sources with bandwidth 2 MHz (cross symbol), 4 MHz (dashed line), and 11 MHz (solid line). (b) The corresponding joint probabilities $P_{11}$ as a function of relative delay $\tau$. The $P_{11}$ enhancement decays on a time scale set by the coherence time of the source, which scales inversely with source bandwidth.

Figure 4

$P_{11}$ enhancement $R_{11}\equiv P_{11}/P_1^A{P}_1^B$ versus $(P_1^A{P}_1^B{)}^{1/2}$ for different bias points of the detector; the direction of the arrow indicates shallower bias points, corresponding to increased dark count rates. For each bias point, the probabilities $P_1^{A,B}$ are tuned by adjusting the input microwave noise power. The dashed line corresponds to $R_{11}=1/\sqrt{P_1^A{P}_1^B}$. At low power, $R_{11}$ exceeds 2. At lowest input powers, switching is dominated by uncorrelated dark counts and $R_{11}(\tau =0)$ drops to unity. See text for a detailed discussion.