Non-Gaussian state generation with time-gated photon detection

Abstract

Non-Gaussian states of light, which are essential in fault-tolerant and universal optical quantum computation, are typically generated by a heralding scheme using photon detectors. Recently, it is theoretically shown that the large timing jitter of the photon detectors deteriorates the purity of the generated non-Gaussian states [T. Sonoyama, $\textit{et al}$., Phys. Rev. A $\textbf{105}$, 043714 (2022)]. In this study, we generate non-Gaussian states with Wigner negativity by time-gated photon detection. We use a fast optical switch for time gating to effectively improve the timing jitter of a photon-number-resolving detector based on transition edge sensor from 50 ns to 10 ns. As a result, we generate non-Gaussian states with Wigner negativity of $-0.011\pm 0.004$, which cannot be observed without the time-gated photon detection method. These results confirm the effect of the timing jitter on non-Gaussian state generation experimentally for the first time and provide the promising method of high-purity non-Gaussian state generation.

Figures (4)

• Figure 1: Schematic diagram of non-Gaussian-state preparation by a heralding scheme using a continuous-wave (CW) entangled light source. (a) Conventional photon detection method. The detector's output is used as a time reference for determining state preparation timing. Thus, the temporal resolution is determined by the original timing jitter of photon detector $\Delta T_p$. Here, we note that $\Delta T_{\rm w}$ is the temporal width of the each wave packet. (b) Time-gated photon detection method. An optical switch is put just before the photon detector and operated in a short time window. By using the driving signal as a time reference, the temporal resolution is determined by the time window $\Delta T_s$, which becomes the effective timing jitter.
• Figure 2: Simple schematic diagram of the experimental setup for Shrödinger-cat-state generation with time-gated photon detection. An optical switch consists of a Pockels cell and a Polarizing Beam Splitter (PBS). OPO: Optical Parametric Oscillator (HWHM = 58.4 MHz), FC: Filter Cavity (HWHM = 8 MHz), ppKTP: periodically poled ${\rm KTiOPO_{4}}$, LO: Local Oscillator.
• Figure 3: (a) Response of the optical switch to an input of classical light. To improve visibility, each signal has different offsets in the horizontal axis. (b) The estimated temporal mode functions $f_1(t)$ of the generated quantum states. Here, when the optical switch is not used, the timing jitter is TES's original jitter $\Delta T_{\rm p} = 58$ ns. As in (a), each signal has different offsets. (c) The plots of the time width (FWHM) of the estimated temporal mode functions and the time width (FWHM) of the theoretically calculated temporal mode functions. $\Delta T_{\rm w}$ corresponds to the time width when the timing jitter $\Delta T_{\rm p}$ or $\Delta T_{\rm s}$ is 0. In the numerical calculations, the bandwidth of the OPO (HWHM), the bandwidth of the Filter cavity (HWHM) are assumed to be 58.4 MHz, 8 MHz, respectively. In addition, the distribution function of the timing jitter $j(t)$ is assumed to be a rectangular function. Here, the bootstrap method is used to obtain the error of the temporal mode function estimation.
• Figure 4: (a)-(e) The reconstructed Wigner functions, their cross sections at $X=0$, and photon number distributions with the optical switch ($\Delta T_{\rm s} =$ 8.3, 29.7, 49.5 and 70.4 ns) and without the optical switch ($\Delta T_{\rm p}$ = 58 ns). The local minimums around the origin of the Wigner functions are $-0.011 \pm 0.004, 0.019 \pm 0.004, 0.059 \pm 0.004, 0.094 \pm 0.003$ ($\Delta T_{\rm s} =$ 8.3, 29.7, 49.5 and 70.4 ns), $0.063 \pm 0.003$ ($\Delta T_{\rm p}$ = 58 ns), respectively. The bootstrap method is also used to obtain the estimation error. We note that the minimum value near the origin and the value at the origin differ slightly in these reconstructed Wigner functions.