Toward Highly Efficient Multimode Superconducting Quantum Memory

We experimentally demonstrate a microwave quantum storage for two spectral modes of microwave radiation in an on-chip system of eight coplanar superconducting resonators. Single-mode storage shows a power efficiency of up to $60\pm 3\mathrm{\%}$ at single photon energy and more than $73\pm 3\mathrm{\%}$ at higher intensity. The noiseless character of the storage is confirmed by coherent-state quantum process tomography. The demonstrated efficiency is an order of magnitude higher than the previously reported data for multimode microwave quantum memory. The proposed on-chip quantum memory architecture can be easily integrated into the state-of-the-art superconducting quantum circuit technology without any coherence compromises. The obtained results are in good agreement with the proposed theory, which pave the way for building a practical multimode microwave memory for superconducting quantum circuits.

Figure 1

(a) Image of the fabricated quantum memory device. The color area around the internal $\lambda /4$ resonators is a vortex-pinning hole array that helps achieve high internal $Q$ factor by magnetic vortices trapping [34]. Inset: optical micrograph of the quantum memory chip. “IN” indicates the input port that is connected to the common resonator with a voltage tap. (b) Principal scheme of the quantum memory device with the relative positions of the common resonator (\textcolor{green1}{green} line), first group internal resonators (\textcolor{blue1}{blue} line), second group of internal resonators (\textcolor{red1}{red} line), and input port (\textcolor{brown1}{brown} line). (c) Simplified scheme of the experimental setup: arbitrary waveform generator (AWG), analog-to-digital converter (ADC), continuous-wave local oscillator (LO), chain of attenuators (ATN), quantum-limited Josephson parametric amplifier (JPA), two low-noise amplifiers based on high-electron-mobility transistor (HEMT), phase shifter (PS). The colors indicate the different temperature stages for the components. (d) Simulated stationary reflection spectrum $S_{11}$ for the first (\textcolor{blue1}{blue} solid line) and the second (\textcolor{red1}{red} solid line) quantum memories and the frequency-shifted single common resonator (\textcolor{green1}{green} solid line). The carrier frequencies for first and second memory cells are indicated as dashed \textcolor{blue1}{blue} and \textcolor{red1}{red} vertical lines, respectively.

Figure 2

(a) The signals from the first (\textcolor{red1}{red} solid line) and second (\textcolor{green1}{green} solid line) memory cells at high power with large average photon number. (b) The signals from the first memory cell (\textcolor{red1}{red} solid line) at single-photon level input pulse intensities. The signals are normalized to the maximum intensity of the input Gaussian-shaped coherent pulse (\textcolor{blue1}{blue} solid line). The black dashed and dotted lines are theoretical simulations with parameters discussed in the text. Inset: efficiency dependence for average photon number. \textcolor{blue1}{Blue} dashed line corresponds to data in Fig. 2 and \textcolor{red1}{red} dashed line corresponds to data in Fig. 2. (c) Four pairs of experimentally acquired phase-space distribution for input pulses (“IN”) and the corresponding memory’s response (“OUT”). Single color and arrow indicate a single pair of phase-space distributions of conjugate position $X$ and momentum $P$ for the state of the mode being sent into the memory and recalled state. (d) Diagonal elements of the reconstructed quantum process tensor.

Figure 3

Filtering factor $M$($\omega$) (dashed lines) and transfer functions $|S(\omega ){|}^2$ (solid lines). \textcolor{green1}{Green} curves correspond to ${\gamma }_n={\gamma }_0=6\mathrm{kHz}$ and ${\mathrm{\Delta }}_0=145\mathrm{MHz}$. \textcolor{blue1}{Blue} lines are simulations for $n_{\mathrm{in}}<1$ where ${\gamma }_n={\gamma }_0$ increases to 165 kHz. The case of ${\mathrm{\Delta }}_0=0\mathrm{MHz}$ and $\kappa =217\mathrm{MHz}$ is shown as \textcolor{red1}{red} curves that correspond to the fulfillment of the impedance-matching condition.

Figure 4

(a) Theoretical efficiency dependencies of the quantum memory on decay rates of common (${\gamma }_0$, \textcolor{blue1}{blue} curve with circles) and internal (${\gamma }_n$, \textcolor{red1}{red} curve with squares) resonators, respectively. Storage time is of approximately $300\mathrm{ns}$. (b) Demonstration of the storage of two spectral modes and the time independence of the echo signals of these modes. Theoretical simulation of the echo signals of the first group of resonators with $\mathrm{\Delta }=3\mathrm{MHz}$ (\textcolor{red1}{red} curves) and the second group of resonators with $\mathrm{\Delta }=6\mathrm{MHz}$ (\textcolor{blue1}{blue} curves). The optimized parameters to meet the impedance-matching condition are $\kappa =280\mathrm{MHz}$, ${\gamma }_n={\gamma }_0=6\mathrm{kHz}$, $g_{\mathrm{\Delta }=3}=11.57\mathrm{MHz}$, $g_{\mathrm{\Delta }=6}=16.36\mathrm{MHz}$.

Figure 5

(a) Dependence of the efficiency on the common resonator frequency shift. The \textcolor{blue1}{blue} and \textcolor{red1}{red} solid lines correspond to the first and second groups of resonators, respectively, in the case of bright pulses. The \textcolor{blue1}{blue} dashed line is the dependence for the first group of resonators, the case of single-photon pulses. The black dashed vertical line shows the parameters corresponding to the experiment. The dependence maxima correspond to the case of complete impedance matching. (b) Dependence of the efficiency on relative statistical uncertainty of the coupling constant between the internal and the common resonators.

Figure 6

The concept of the iteratively reduction method.

Figure 7

(a) The input part of the common $8\times \lambda /4$ resonator for clarification of the $l_{\mathrm{short}}$ parameter and $t$ junction (b) The dependence of the coupling constant $\kappa$ on the length $l_{\mathrm{short}}$. \textcolor{red1}{Red} dot is the desired point with $\kappa =281\mathrm{MHz}$ and length $l_{\mathrm{short}}=1800\text{μ}\mathrm{m}$. (c) The dependence of resonant frequency of the common resonator $f_0$ on its additional length $l_{\mathrm{add}}$. \textcolor{red1}{Red} dot is the desired point with $f_0=6\mathrm{GHz}$ at $l_{\mathrm{add}}=465\text{μ}\mathrm{m}$. (d) The dependence of the coupling strength $g_n$ on the coupling capacitance $C_c$ between the common and the internal resonators. \textcolor{red1}{Red} dot is the desired point with $g_n=12\mathrm{MHz}$ at coupling capacitance of $C_c=4.65\mathrm{fF}$.

Figure 8

Description of the electrical and cryogenic setup of the experiment. The colors indicate the different temperature stages for the components.