Low-noise Optomechanical Single Phonon-photon Conversion for Quantum Networks

Abstract

Nano-structured optomechanical crystals (OMC) form an interface between mechanical modes with long coherence times and telecom optical photons, ideal for long-distance distribution of quantum information. However, the implementation of scalable quantum networks based on OMCs has been inhibited by thermal mechanical noise. Here, we overcome this limitation using a quasi-two-dimensional OMC and generate single photons via single phonon-photon conversion. In this work, we verify the low thermal noise and high purity of the generated single photons through a Hanbury Brown-Twiss experiment with $g^{(2)}(0)=0.35^{+0.10}_{-0.08}$. We perform Hong-Ou-Mandel interference of the emitted photons showcasing the indistinguishability and coherence with visibility $V=0.52 \pm 0.15$ after 1.43 km fiber delay. Lastly, we use two-photon interference to measure the temporal wavepackets of optomechanically generated single photons demonstrating narrow bandwidths as low as 10 MHz. Our results pave the way for multinode quantum networks of mechanical oscillators and hybrid entanglement generation between mechanical oscillators and telecom quantum emitters.

Figures (14)

• Figure 1: Quantum network based on optomechanical crystals.a Schematic illustration of a quantum network consisting of cavity optomechanical systems as network nodes with optical cavity frequency $\omega_\mathrm{c}$, mechanical frequency $\omega_\mathrm{m}$, and single-photon optomechanical coupling strength $g_0$. b Scanning electron microscope image of a 2D OMC device, which can form one of the telecom-wavelength quantum network nodes. The principal axis of the OMC cavity is aligned to the [100] direction of the silicon crystal lattice. c FEM simulations of the electric field (left) of the optical mode $E_\mathrm{y}$ at design wavelength $\lambda = \qty{1537.24}{nm}$ and the displacement field (right) of the mechanical mode at design frequency $\omega_\mathrm{m}/2\pi = \qty{10.18}{GHz}$. d Schematic illustration of the optical measurement setup. Write (read) laser pulses detuned to the blue (red) optomechanical sideband are sent to the OMC device inside a dilution refrigerator at base temperature $T=\qty{20}{mK}$ via lensed fiber coupling. Single photons created through optomechanical interaction are filtered from the reflected light using optical filters locked to the optical cavity resonance of the OMC. e Illustration of the optomechanical Stokes- and anti-Stokes scattering processes used for single-phonon generation and phonon-photon conversion. Top: photons from the blue-detuned write pulse at frequency $\omega_\mathrm{b} = \omega_\mathrm{c} + \omega_\mathrm{m}$ undergo a Stokes scattering process resulting in the probabilistic creation of a single photon at the optical cavity frequency $\omega_\mathrm{c}$ and a single phonon at the mechanical frequency $\omega_\mathrm{m}$. Detection of a single photon heralds the preparation of the mechanical mode in the Fock state $\left|1\right\rangle_\mathrm{m}$. Bottom: the red-detuned readout pulse at frequency $\omega_\mathrm{r} = \omega_\mathrm{c} - \omega_\mathrm{m}$ induces an anti-Stokes scattering process converting the single phonon in the mechanical mode to a single photon in the telecom band.
• Figure 2: Thermal performance and quantum cross-correlations.a The blue dots show the thermal phonon occupancy $n_\mathrm{th}$ of the mechanical mode as a function of intracavity photon number (bottom) and anti-Stokes scattering probability (top). Error bars originate from errors in the calibration of the detection path efficiency (see Supplementary Information). The orange dots indicate the signal-to-noise (SNR) ratio in the conversion process. b Cross-correlation function $g^{(2)}_\mathrm{S, aS}$ between optomechanically scattered photons from the write and read pulse as a function of anti-Stokes scattering probability of the readout pulse. The insert shows the pulse sequence used for the cross-correlation measurement. A blue-detuned write pulse creates a single phonon, which is read out by a red-detuned read pulse after a delay time of $T_\mathrm{delay}=\qty{150}{ns}$. The pulse sequence is repeated with a repetition period of $T_\mathrm{rep}=\qty{10}{\micro s}$. The Stokes scattering probability of the write pulse is fixed at $p_\mathrm{S}=1.3\%$. The blue shaded area corresponds to the theoretically expected dependence $g^{(2)}_\mathrm{S,aS} = 1+e^{-T_\mathrm{delay}/\tau_\mathrm{m}}/(p_\mathrm{s} + n_\mathrm{th})$ (see Supplementary Information), where $n_\mathrm{th}$ is calibrated from the results in a and $\tau_\mathrm{m}=\qty{1.0}{\micro s}$ is the phonon lifetime of the mechanical mode (see Supplementary Information). The dashed horizontal line and shaded area underneath indicate the regime of classical correlations $g^{(2)}_\mathrm{S, aS} \leq 2$. The error bars are calculated from the photon counting statistics and correspond to the $68\%$ confidence interval of the binomial distribution.
• Figure 3: Hanbury Brown-Twiss measurement.a Measured second-order autocorrelation function $g^{(2)}$ of detection events from the read pulse conditioned on the detection of a Stokes-scattered photon during the blue-detuned write pulse. Each pulse sequence is labeled by a number $n$. Pulse sequences used for the $g^{(2)}$ calculation are shifted by $\Delta n$. The Stokes-scattering (anti-Stokes-scattering) probability are $p_\mathrm{S}=1.3\%$ ($p_\mathrm{aS} = 7\%$) corresponding to pulse energies of $E_\mathrm{p,S}=\qty{0.1}{pJ}$ ($E_\mathrm{p,aS}=\qty{1.0}{pJ}$). b Second-order autocorrelation function $g^{(2)}(0)$ at fixed Stokes-scattering probability $p_\mathrm{S}=1.3\%$ as a function of anti-Stokes read out probability. Solid blue line shows the result of simulations of the quantum systems using the Python package QuTIP (see Supplementary Information) johansson_qutip_2012johansson_qutip_2013. A value below unity demonstrates sub-Poissonian photon statistics (grey dashed line in a and b) whereas a value below $0.5$ unambiguously demonstrates a single-photon state (red dashed line in a and b). The error bars are calculated from the photon counting statistics using the exact binomial confidence interval (see Supplementary information). For all measurements, the optical pulse sequence is repeated with a repetition period of $T_\mathrm{rep}=\qty{10}{\micro s}$.
• Figure 4: Hong-Ou-Mandel interference.a Unbalanced Mach-Zehnder interferometer used for Hong-Ou-Mandel (HOM) measurements. BS, beam splitter; PC, polarization controller; OA, optical attenuator; SNSPD, superconducting nanowire single-photon detector. b Pump pulse sequence used for HOM measurements. The delay between the blue and red pulses is $T_\mathrm{d,1}=\qty{105}{ns}$ and $T_\mathrm{d,2} =\qty{225}{ns}$. The delay between the two red pulses equals the time delay induced by the fiber delay line with $T_\mathrm{delayline}=\qty{7.146}{\micro s}$. c Schematic of the measured detection events on SNSPDs. Time bins are labeled according to when the photon was created (E, early; L, late) and which interferometer arm it passed through (S, short; L, long). Photons generated from the first (second) blue-detuned pump pulses are shown in dark (light) blue. Simultaneous clicks during either combination of two dark and light blue-shaded time bins herald the generation of two phonons. The phonons are read out by the red pulses leading to two-photon interference during the time bin associated with the second red pulse (red shaded). d Number of four-fold coincidences measured on the two SNSPDs with co-polarized (blue) or cross-polarized (orange) arms of the interferometer during the same ($\Delta n = 0$) or different ($\Delta n \neq 0$) repetitions of the experiment normalized to the average value measured on the satellite peaks ($\Delta n \neq 0$). The error bars are calculated from the photon counting statistics and correspond to the $68\%$ confidence interval of the binomial distribution. The dashed bar at $\Delta n=0$ shows the value predicted from QuTiP simulations (see Supplementary Information). e Normalized number of threefold coincidences in co-polarized interferometer configuration during the same repetition of the experiment ($\Delta n = 0$) as a function of timing offset $\Delta t$ between the two red pulses for two different bandwidths $\Gamma_\mathrm{ph}$ of generated photons. The solid lines are fits to a phenomenological model based on the photon pulse shape (see Supplementary Information).
• Figure S1: Finite element simulation of the unit cell.a Schematic of the quasi-2D optomechanical crystal mirror unit cell consisting of both snowflakes and C-shape holes, $w_\mathrm{cell} = \qty{502} {nm}$ is the unit cell width along $x$ direction. The parameters for mirror unit cells are: $\left(l_\mathrm{snow}, w_\mathrm{snow}\right) = \left(201, 80.4\right)$ nm, $\left(l_\mathrm{arm}, l_\mathrm{pad}, w_\mathrm{arm}, w_\mathrm{pad}\right) = \left(203, 112, 104, 188\right)$ nm. For the rows of snowflakes which are closest to C-shapes, the length of the second half of the snowflake holes along $y$ direction is scaled by $1.2$. b and d show the photonic and phononic band diagrams of the mirror unit cell, respectively. The shaded grey areas represent modes of continuum. In the photonic band diagram, only transverse-electric (TE) modes are shown since they are predominantly guided in the silicon slab with a thickness of $\qty{250}{nm}$. The dashed red line represents the light cone. The solid blue lines on the band gap edges are the C-shape modes of interest. The dashed blue lines show other guided modes in the structure. In the phononic band diagram, the dashed black lines are for modes with symmetry group $\sigma_z = -1$, the dashed green lines are for modes with symmetry group $\left(\sigma_z = +1, \sigma_y = -1\right)$. The pink shaded areas indicate the optical and phononic band gaps formed from such mirror cells. The black ticks indicate the optical and mechanical frequency of the whole device, which are inside the band gaps. c and e indicate how the band edge modes of interest shift in frequency when we change the parameters from mirror cell (index $ncell = 7$) to defect center cell (index $ncell = 1$).