Superconducting Nanowire Photon-Number-Resolving Detectors Integrated with Current Reservoirs

Photon-number-resolving detectors (PNRDs) play pivotal roles in many quantum-photonic applications; and intrinsic and multiplexed PNRDs have been reported previously. However, for intrinsic PNRDs, the maximum resolvable photon number is limited to a few photons; for the multiplexed PNRDs, the fidelity generally decreases when the to-be-resolved photon number becomes large. Here, to resolve more photons with high fidelity, we report on combined PNRDs, based on a spatial multiplexing configuration of multiple elements, each capable of resolving a few photons. After setting up a model and calculating the fidelity, we propose a possible physical system to realize the combined PNRDs. The proposed detectors are based on the superconducting nanowire multiphoton detectors integrated with current reservoirs that we recently reported, but are designed and configured into PNRDs. Specifically, information about the detected photon numbers is stored in the format of the supercurrent in the current reservoir and then readout by an integrated yTron. We present in detail the operating principle and show a design that can resolve up to 11 photons with high fidelity.

Figure 1

Calculated fidelity of space-multiplexed, multielement, photon-number-resolving detectors. Each element is capable of resolving up to $r$ photons ($r=1$, 2, 3, and 4). The upper row shows three cases for the number of elements $M=20$: (a) $\eta =1$, (b) $\eta =0.95$, and (c) $\eta =0.8$. The lower row shows three cases for the number of elements $M=100$: (d) $\eta =1$, (e) $\eta =0.95$, and (f) $\eta =0.8$.

Figure 2

Comparison of the fidelity for resolving $n$ photons, using space-multiplexed, multielement, photon-number-resolving detectors with different configurations but the same maximum resolvable photon numbers ($n\le 40$). We compare the three cases $M=10,r=4$; $M=20,r=2$; and $M=40,r=1$. Here $\eta$ is assumed to be 1.

Figure 3

Device structure and operating principle of a superconducting nanowire photon-number-resolving detector (SNPNRD) integrated with the current reservoir ($M=2,r=2$). (a) Schematic of the device layout. The detector is composed of two photosensitive superconducting nanowires ($N_1$ and $N_2$) and a wider superconducting nanowire functioning as a current reservoir ($R$). All of them are electrically connected in parallel. (b) Circuit model for the SNPNRD integrated with the current reservoir. (c) Schematic of the temporal sequences of optical pulses, $I_{\mathrm{read}}$, $I_{\mathrm{bias}}$, and $I_R$. (d1) Simulated temporal sequences of $I_1$, $I_2$, and $I_R$. (d2) Details of the current dynamic in the stage of “preset”; (d3) details of the current dynamic in the stage of “photon trigger”; (d4) details of the current dynamic in the stage of “reset.” (e) The final states of $I_R$ for different photon numbers and multiplexing configurations.

Figure 4

Readout of the supercurrent in the current reservoir by the yTron. (a) Device structure of the yTron. The width of the read arm is 560 nm, the same as the width of the current reservoir. The angle between the two arms is ${10}^{\circ }$. The radius of the curvature of the junction is 15 nm. (b) Plot of $I_{\mathrm{read}}^{\mathrm{sw}}$ vs $I_R$, calculated using the vortex-crossing model. The red dashed line shows the critical current of a single straight nanowire with a width of 560 nm. The square shows the working point corresponding to the distribution of the current density shown in (a). (c) Dependence of $I_R^{\mathrm{sw}}$ when $I_{\mathrm{read}}=0$ and the slope of the $I_{\mathrm{read}}^{\mathrm{sw}}\text{−}{I}_R$ curve on the inner radius of the yTron.

Figure 5

Superconducting nanowire photon-number-resolving detector with $M=20$ and $r=2$. (a) Device structure. (b) Steady-state supercurrent in the current reservoir after the detector detects $n$ photons. From left to right, the black squares represent the cases in which each fired element of the SNPNRDs is triggered by a single photon, the red circles represent the cases in which one element of the PNRDs is triggered by two photons and the other fired elements are each triggered by a single photon, and the blue triangles represent the cases in which two elements of the SNPNRDs are each triggered by two photons and the other fired elements are each triggered by a single photon. Other symbols, coded in different colors and shapes, can be similarly understood. (c) The minimum gap of the supercurrent in the steady state for each $n$.

Figure 6

Simulated results of the yTron. (a) Simulated current density distribution in the yTron. (b) Simulated current density distribution along the $y$ axis. (c) Simulated self-energy, work and Gibbs free-energy distribution along $y$ axis for $I_R=60\mu \mathrm{A}$ and $I_{\mathrm{read}}=100\mu \mathrm{A}$.

Figure 7

Initial conditions in the preset stage. (a) Normalized switching current distribution along the $x$ direction of the current reservoir. (b) Normalized switching current of the current reservoir versus $I_{\mathrm{read}}$. The square shows the working point corresponding to the distribution of the current density shown in (a). (c) Normalized switching current distribution of the current reservoir along the length direction from the point of the intersection.