Detection of Zeptojoule Microwave Pulses Using Electrothermal Feedback in Proximity-Induced Josephson Junctions

We experimentally investigate and utilize electrothermal feedback in a microwave nanobolometer based on a normal-metal (${\mathrm{Au}}_x{\mathrm{Pd}}_{1-x}$) nanowire with proximity-induced superconductivity. The feedback couples the temperature and the electrical degrees of freedom in the nanowire, which both absorbs the incoming microwave radiation, and transduces the temperature change into a radio-frequency electrical signal. We tune the feedback in situ and access both positive and negative feedback regimes with rich nonlinear dynamics. In particular, strong positive feedback leads to the emergence of two metastable electron temperature states in the millikelvin range. We use these states for efficient threshold detection of coherent 8.4 GHz microwave pulses containing approximately 200 photons on average, corresponding to $1.1\times {10}^{-21}\mathrm{J}\approx 7.0\mathrm{meV}$ of energy.

Figure 1

(a) Simplified diagram of the detector, including (b) a micrograph of the $S\text{−}N\text{−}S$ junctions formed by a ${\mathrm{Au}}_x{\mathrm{Pd}}_{1-x}$ nanowire contacted by Al islands and leads ($H$, $P$, and $G$). Here, $Z^{-1}$ is an admittance, $T_e$ is the temperature of the electrons in the nanowire, and $\mathrm{\Gamma }$ is the probe signal reflection coefficient. The micrograph is from a device nominally identical to the measured one. (c) Reflected fraction of probe power versus probe frequency $f_p$ for steady-state heating power $P_h$ of 1.9, 66, and 290 aW. They are measured at low probe power $P_p\ll P_h$. The solid curves are fits to the circuit model with a small phenomenological correction term [50]. The heater input is bandpass filtered ($8.41\pm 0.02\mathrm{GHz}$).

Figure 2

Linear ($P_p\ll P_h$) response. (a) The effective inductance (circles) and resistance (squares) of the short $S\text{−}N\text{−}S$ junctions as functions of external steady-state heating power $P_h$. The bath temperature $T_b$ is 12 mK. The curves are phenomenological fits that allow mapping a measured reflection coefficient into an equivalent $P_h$. (b) The effective inductance (circles) and thermal relaxation time after a short (filled squares) or long (open squares) heating pulse. (c) Measured differential thermal conductance $\tilde{G}$, the expected electron-phonon contribution ${\tilde{G}}_{e\text{−}p}$ (dashed line), and the quantum of thermal conductance $G_Q$ (solid line).

Figure 3

(a) Bistable parameter regime, as indicated by a nonzero difference ${\mathrm{\Delta }}_h-{\mathrm{\Delta }}_l$ in the power absorbed from the probe signal in high and low-temperature stationary states. (b) Numerically simulated values of the dimensionless susceptibility to external heating $\chi$ in the single-valued regime. The bistable regime is indicated in white.

Figure 4

(a) Amplitude modulation (AM) of the probe pulse used for detecting weak $1\mu \mathrm{s}$ heating pulses (also shown). The carrier frequencies are 757 MHz and 8.4 GHz for the probe and heating pulses, respectively. (b) Normalized histograms of the single-shot measurement outcome $s$ with a heating pulse energy of zero or $200\times h\times 8.4\mathrm{GHz}\approx 1.1\mathrm{zJ}$. The pulses for the two histograms were interleaved in time. (c) Same as (b) but for 3.0 zJ and $t_s=2.5\mu \mathrm{s}$.