Detection of Weak Microwave Fields with an Underdamped Josephson Junction

We construct a microwave detector based on the voltage switching of an underdamped Josephson junction that is positioned at a current antinode of a $\lambda /4$ coplanar waveguide resonator. By measuring the switching current and the transmission through a waveguide capacitively coupled to the resonator at different drive frequencies and temperatures, we are able to fully characterize the system and assess its detection efficiency and sensitivity. Testing the detector by applying a classical microwave field with the strength of a single photon yields a sensitivity parameter of 0.5, in qualitative agreement with theoretical calculations.

Figure 1

(a) An ($8\times 6$)-cm sample is displayed as a colored design picture consisting of a central conduction line (blue), two coupled $\lambda /4$ resonators (yellow), dc connections to the Josephson junctions (green), and test junction circuits in the corners of the chip (red). (b) A LM micrograph of the coupling capacitance of the upper resonator. The central conductor and the resonators are formed by coplanar lines. (c) LM micrograph of the junction’s position in the resonator current antinode. From the top-central point, the dc-bias line is visible. Beyond the junction, it continues as a central resonator line with a ground plane on each side. (d) SEM image of the Josephson junction shunting the resonator in its current antinode. The barbell-like structure is a layer of Nb deposited on top of the structured trilayer that forms the rest of the circuit, and the Josephson junctions are found in the overlap.

Figure 2

(Upper panel) The normalized transmission amplitude as a function of the probing frequency. From dark to light curves, the dc-bias current at the junction is increased in steps of $1\mu \mathrm{A}$. The crosses in the lower panel show the center frequency (cf) shifts as a function of the bias current. They are found by fitting the transmission dips in the upper panel to Lorentzian line shapes. The measured frequency shifts are in excellent agreement with the analytical fit in Eq. (1) (the solid line).

Figure 3

Mean switching current (the black curve) and standard deviation (the gray curve) of the switching-current histograms at different temperatures. The dashed red curves correspond to theoretical curves calculated as in Ref. [30]. While the temperature dependence of the standard deviation is reproduced quite well, the mean switching currents are underestimated by theory. The large variation around 300–500 mK is most probably due to additional noise present during the measurement time. (Inset) Examples of the histograms [the switching probability (sw pr) over the bias current] at temperatures of 600, 300, and 14 mK, marked by points, crosses, and stars, respectively.

Figure 4

Influence of microwave signals on the switching-current histograms. The difference between the mean switching and critical currents $I_c-I_s$ in the upper as well as the standard deviation $\sigma$ of the switching current in the lower picture is measured for different driving frequencies. From light to dark, the driving amplitude is decreased according to the legend in megahertz.

Figure 5

(Upper plot) Maximal shift of the mean switching current at different driving amplitudes ${\mathrm{\Omega }}_d$. (Inset) Enlargement of the region close to zero driving. (Lower plot) Reconstructed sensitivity of our detector as the extracted maximal shift of the histograms divided by the shift plus the standard deviation of the switching current of the undisturbed junction. The mean photon number in the resonator $N$ on the $x$ axis follows from the driving amplitudes ${\mathrm{\Omega }}_d$.

Figure 6

(Upper panel) The measured undisturbed histogram (the gray crosses) compared to the maximally shifted histograms for the lowest applied driving power (the black dots). They have a Hellinger distance [31] of 0.51. For comparison, the theoretical predictions are shown in the lower panel for the same parameters. The histograms shifted by the microwave signal in both cases show a characteristic peak structure.