Quantum Metamaterial for Broadband Detection of Single Microwave Photons

Detecting traveling photons is an essential primitive for many quantum-information processing tasks. We introduce a single-photon detector design operating in the microwave domain, based on a weakly nonlinear metamaterial where the nonlinearity is provided by a large number of Josephson junctions. The combination of weak nonlinearity and large spatial extent circumvents well-known obstacles limiting approaches based on a localized Kerr medium. Using numerical many-body simulations we show that the single-photon detection fidelity increases with the length of the metamaterial to approach one at experimentally realistic lengths. A remarkable feature of the detector is that the metamaterial approach allows for a large detection bandwidth. The detector is nondestructive and the photon population wavepacket is minimally disturbed by the detection. This detector design offers promising possibilities for quantum information processing, quantum optics and metrology in the microwave frequency domain.

Figure 1

(a) Sketch of the JTWPD. Standard transmission lines (black) are coupled to both ends of a one-dimensional metamaterial (orange) of length $z$ and linear dispersion relation, $\omega =vk$. A cross-Kerr interaction $\chi$ between the metamaterial and the giant probe mode (blue) leads to a phase shift in the strong measurement tone (yellow) while the signal photon (red) travels through the metamaterial. (b) Phase-space picture of the probe mode. With respect to the idle coherent state $|\alpha ⟩$, the presence of a signal photon displaces the states by $gz/v$, with $g=\chi \alpha$.

Figure 2

Schematic representation of the JTWPD. The probe resonator with ground plane on top and the center conductor below (blue), as well as a readout port on the right, acts as a giant probe. The light blue arrows illustrate the fundamental mode function of a $\lambda /2$ resonator. The probe resonator is coupled via a position-dependent cross-Kerr interaction $\chi (x)$, mediated by an array nonlinear quarton couplers (inset), to a metamaterial waveguide (orange). The metamaterial is coupled to impedance matched input and output transmission lines at $x=-z/2$ and $x=z/2$ (gray). An incoming photon of Gaussian shape $\xi (x,t)$ is illustrated (red).

Figure 3

The top panel shows snapshots of the photon-number population along the matrix-product-state (MPS) sites at three different times $t_1$ (red) $<t_2$ (green) $<t_3$ (blue). The white region corresponds to the linear waveguide and the orange region to the metamaterial with its coupling to the probe resonator. The bottom three panels show the Wigner function $W(x,y)$ of the intracavity probe field at the three respective times. When the photon is only partially inside the metamaterial, the probe is in a superposition of displaced states (middle panel). Parameters are ${\kappa }_a=\chi (x)=K=0$, $g\tau =2$, and $\gamma \tau =2$.

Figure 4

Time evolution of the intracavity probe displacement $⟨\hat{y}⟩$ [(a),(c),(e)] and fluctuations $⟨\mathrm{\Delta }{\hat{y}}^2⟩$ [(b),(d),(f)], in the idealized case $\chi (x)=K=0$. Top row: ${\kappa }_a=0$ and $g\tau =2$. Middle row: ${\kappa }_a=0$ and spatially varying $g(x)$ with average value $\overline{g}\tau =2$. Bottom row: ${\kappa }_a\tau =1.0$ and $g\tau =2$. The solid lines correspond to MPS simulations with different photon widths $\gamma \tau =2$ (blue), 4 (orange), 6 (green), and 10 (bright purple), while the dotted lines are from integrating Eq. (6).

Figure 5

(a) 75 filtered homodyne currents (arbitrary units) for $g\tau =3$, ${\kappa }_a\tau =1.0$, $|K|/{\kappa }_a={10}^{-2}$, and $g/\chi =5$. Red traces are obtained with an incoming Gaussian photon of unitless width $\gamma \tau =6$, and blue traces for vacuum. The horizontal gray line is the threshold chosen to maximize the assignment fidelity. (b) Infidelity versus $g\tau$ for $\gamma \tau =2$ (blue), 4 (orange), and 6 (green), found by averaging over $N_{\mathrm{traj}}=2000$ trajectories. Other parameters as in (a). The shaded regions indicate the standard error defined as $\pm \sqrt{\mathcal{F}(1-\mathcal{F})/N_{\mathrm{traj}}}$.

Figure 6

Number of unit cells needed to reach $g\tau$ in the range 1–3 as a function of self-Kerr nonlinearity $K_Q$, for $\alpha =5$, $\overline{\omega }/(2\pi )=5$ GHz, $I_s=E_Q/{\phi }_0=1.1\mu \mathrm{A}$, and $Z_0=50\mathrm{\Omega }$. The total Kerr nonlinearity of the resonator $K=K_Q+K_J$ can be tuned close to zero by introducing another nonlinearity with $K_J<0$.