Graphene-Based Josephson-Junction Single-Photon Detector

We propose to use graphene-based Josephson junctions (GJJs) to detect single photons in a wide electromagnetic spectrum from visible to radio frequencies. Our approach takes advantage of the exceptionally low electronic heat capacity of monolayer graphene and its constricted thermal conductance to its phonon degrees of freedom. Such a system could provide high-sensitivity photon detection required for research areas including quantum information processing and radio astronomy. As an example, we present our device concepts for GJJ single-photon detectors in both the microwave and infrared regimes. The dark count rate and intrinsic quantum efficiency are computed based on parameters from a measured GJJ, demonstrating feasibility within existing technologies.

Figure 1

Device concept to detect single photon using a graphene-based Josephson junction.

Figure 2

Device schematic for (a) microwave and (b) infrared single-photon detection. (a) The graphene flake is located at the current antinode of a half-wave microwave resonator for maximizing input efficiency. Two stages of inductors and capacitors form a high-impedance network at microwave frequency for the dc measurement of the GJJ. (b) A graphene sheet lies on top of a PC cavity to increase its absorption through critical coupling. Light is coupled into the cavity through an in-chip waveguide. (c) Simulation results for critical coupling. Top view of the PC structure overlaid with the mode profile $|\mathit{E}{|}^2$ using a decibel scale normalized to a maximum of 1. (d) Spectra showing the wavelength dependence of the reflection $R_r$, absorption $T_a$, and scattered power $T_s$. (e) Cross-sectional and (f) planar view of close-ups of the cavity mode $|\mathit{E}{|}^2$ using a linear scale. The parameters of the structure are as follows: membrane thickness, $h=250\mathrm{nm}$; lattice period, $a=0.27\lambda$; hole radius, $r=0.31a$; cavity slot width, $w_s=0.032\lambda$; cavity hole shifts, $d_1=0.365a$ and $d_2=0.153a$; waveguide width, $w_w=2(W\sqrt{3}a/2-r)$, where $W=1.04$. The holes at the termination of the PC waveguide are shifted along the $x$ axis by $s_1=0.44a$, $s_2=0.27a$, and $s_3=0.1a$.

Figure 3

(a) The specific heat of a $1\text{−}\mu {\mathrm{m}}^2$ graphene sheet as a function of base temperature. (b) The initial temperature rise vs frequency with electron density $n_0=1.7\times {10}^{12}{\mathrm{cm}}^{-2}$ (solid, used for modeling), ${10}^{11}{\mathrm{cm}}^{-2}$ (dashed), or ${10}^{10}{\mathrm{cm}}^{-2}$ (dotted) at a base temperature of 25 mK (blue) or 3 K (purple). For an infrared detector $T_0=3\mathrm{K}$ will suffice but for microwave detection a lower $T_0$ is required to acquire a noticeable temperature change. (c) Energy resolution and temperature fluctuation of a $1\text{−}\mu {\mathrm{m}}^2$ graphene sheet at $n_0$, representing the intrinsic noise of the calorimeter.

Figure 4

(a) Thermal diagram depicting three heat-transfer pathways from graphene electrons ($e$) to the thermal reservoir (base) via graphene EP coupling (ph), to the electrical contacts (elec) via diffusion, or to the electrical environment, such as an amplifier (amp), via photon emission (rad). The thermal conductances in the linear response regime are denoted as $G_{\mathrm{EP}}$, $G_{\mathrm{diff}}$, and $G_{\mathrm{rad}}$, correspondingly. (b) The thermal conductance vs base temperature for clean graphene with a $T^4$ EP coupling law (blue), for disordered graphene with a $T^3$ EP coupling law (red), and for the radiation channel (purple). (c) The thermal time constant ${\tau }_{\mathrm{th}}=C_e/G_{\mathrm{th}}$ in the linear response regime for clean [green (blue) including (excluding) radiation] and disordered [orange (red) including (excluding) radiation] graphene. (d) The transient thermal response of the graphene sheet upon absorbing a 26-GHz microwave photon for clean (green) and disordered (orange) graphene including radiation.

Figure 5

(a) Measured $R_n$ (blue) and $I_s$ (red) as a function of $V_G$; (b) $I_s{R}_n$ versus $V_G$. Inset: Optical micrograph of the measured GJJ whose device performance parameters are used in this report. The blue colored region is the graphene channel encapsulated by $h$-BN and the region emphasized by orange colored lines are the NbN electrodes. The scale bar (white) is $1.5\mu \mathrm{m}$.

Figure 6

(a) Measured GJJ $I\text{−}V$ characteristics for electron temperature at $T_0=25\mathrm{mK}$ (green) and $T_{\mathrm{peak}}=200\mathrm{mK}$ (orange) with a carrier density of $1.7\times {10}^{12}{\mathrm{cm}}^{-2}$. Inset: The measured average switching current vs temperature. (b) The JJ voltage and the expected voltage noise from an amplifier at 1-MHz bandwidth. The blue dotted line depicts, for a given bias current in a photon event, the order of magnitude of the JJ voltage $V=I_b{R}_n$. (c) The switching probability (left) and escape rate (right) of the phase particle as a function of the JJ current bias. The solid line in the left panel is the best-fit probability distribution to the data assuming the escape mechanism is MQT. Solid lines in the right panel are given by Eq. (9) with $I_c=3.565\mu \mathrm{A}$ (25 mK) and $I_c=3.425\mu \mathrm{A}$ (200 mK).

Figure 7

(a) Change of critical current and phase slipping probability due to a single microwave photon, impinging at $t=0\mathrm{s}$ and $T_0=0.025\mathrm{K}$, deduced from the graphene thermal properties and measured GJJ parameters. (b) Intrinsic efficiency $\eta$ and dark count probability at a 1-MHz count rate versus bias current. The vertical gray dashed line indicates the bias current for which $\eta >0.99$ for the measured $d{I}_c/dT$. (c) Trade-off between the intrinsic quantum efficiency and the dark count rate at various bias currents from (b). Gray circle corresponds to gray line from (b).