Self-Calibrating Superconducting Pair-Breaking Detector

We propose and experimentally demonstrate a self-calibrating detector of Cooper pair depairing in a superconductor based on a mesoscopic superconducting island coupled to normal metal leads. On average, exactly one electron passes through the device per broken Cooper pair, independent of the absorber volume, device, or material parameters. The device operation is explained by a simple analytical model and verified with numerical simulations in quantitative agreement with experiment. In a proof-of-concept experiment, we use such a detector to measure the high-frequency phonons generated by another, electrically decoupled superconducting island, with a measurable signal resulting from less than 10 fW of dissipated power.

Figure 1

(a) Sketch of device. Cooper pairs are broken when radiation is absorbed in a superconducting island, and the resulting quasiparticles decay by tunneling to the normal metal leads (black arrows) with a rate $N_{\mathrm{QP}}{\mathrm{\Gamma }}_{\mathrm{tunn}}$ for $N_{\mathrm{QP}}$ excitations on the island. (b) Energies of states with $N=-1$, 0, 1, 2 excess electrons compared to charge neutrality on the island, when the gate offset is close to $n_g=0.5$. Black arrows indicate transitions that remove a quasiparticle through the left (solid lines) or right (dashed lines) tunnel junction, while red arrows indicate transitions that add a quasiparticle into the island. The quasiparticle population is set by transitions between charge states $N=0$, 1, while net current flows via cycles involving the excited charge states $N=-1$, $+2$. (c) Numerical verification of operation. The ideal response $I=e{\mathrm{\Gamma }}_{\mathrm{pb}}$ (solid line) is reproduced by our simulations (dashed line) within 1% up to ${\mathrm{\Gamma }}_{\mathrm{pb}}=500\mathrm{kHz}$. Symbols show the experimental response, where ${\mathrm{\Gamma }}_{\mathrm{pb}}$ is linearly proportional to the measured $I_{\text{emitter}}$. (d) Proof-of-concept experiment and sketch of measurement setup, with pair-breaking detector (top), superconducting phonon emitter (bottom left), and normal-metallic reference source (bottom right).

Figure 2

Measured (left column and symbols in right column) and simulated (middle column and solid lines in right column) subgap current through our pair-breaking detector. On the first row, no current is applied to the emitter or reference source, while the current increases substantially when the current through the phonon emitter is increased to 30 pA (second row) or 120 pA (third row). This is reproduced quantitatively in the simulations by changing only the rate of pair-breaking radiation ${\mathrm{\Gamma }}_{\mathrm{pb}}$. In contrast, increasing the current through the reference emitter up to 7.5 nA (bottom row) creates nearly no change in the detector response, proving that the response is indeed due to pair-breaking phonons. White dashed lines in panels (d),(e),(g),(h) indicate the regions where the self-calibrating response is expected. The rightmost column shows cuts in the data at $V_b=-50\mu \mathrm{V}$, $-100\mu \mathrm{V}$, and $-150\mu \mathrm{V}$, also indicated by colored lines in the left and middle columns.

Figure 3

(a) Detector current vs gate offset $n_g$ at $V_b=110\mu \mathrm{V}$ with varying $I_{\text{emitter}}$ in the experiment (symbols) and different Cooper pair-breaking rates ${\mathrm{\Gamma }}_{\mathrm{pb}}=A{I}_{\text{emitter}}/e$ in the simulations (solid lines). $A=7.8\times {10}^{-5}$ is used for all simulated curves. (b) $I$ extracted at the self-calibrating operating point ($n_g=0.5$, circles) and for comparison at $n_g=1$ and $n_g=0$, where the current is due to Andreev reflection. Simulated curves (solid lines) for all three values of $n_g$ are calculated assuming ${\mathrm{\Gamma }}_{\mathrm{pb}}=A{I}_{\text{emitter}}/e$ with $A=7.8\times {10}^{-5}$. (c) Measured $I$ at $n_g=0.5$ and the corresponding pair-breaking rate in the detector, vs current through either the phonon emitter (black circles) or reference source (magenta triangles).