Nonclassical phonon pair

Abstract

Quantum-correlated photon pairs are crucial resources for modern quantum information science. Similarly, the reliable generation of nonclassical phonon pairs is vital for advancing engineerable solid-state quantum devices and hybrid quantum networks based on phonons. Here, we present a novel approach to generate quantum-correlated phonon pairs in a suspended silicon microstructure initialized in its motional ground state. By simultaneously implementing red- and blue-detuned laser pulses, equivalent high-order optomechanical nonlinearity -- specifically, an effective optomechanical four-wave mixing process -- is achieved for generating a nonclassical phonon pair, which is then read out via a subsequent red-detuned pulse. We demonstrate the nonclassical nature of the generated phonon pair through the violation of the Cauchy-Schwarz inequality. Our experimentally observed phonon pair violates the classical bound by more than 5 standard deviations and maintains a decoherence time of 132 ns. This work reveals novel quantum manipulation of phonon states enabled by equivalent high-order optomechanical nonlinearity within a pulse scheme and provides a valuable quantum resource for mechanical quantum computing.

Figures (4)

• Figure 1: Schematic of the nonclassical phonon pair generation. (a) An OMC nanobeam cavity is simultaneously driven by optical pulses at laser frequencies of $\omega_{\mathrm{a}}\pm\omega_{\mathrm{m}}$ to generate a photon pair $\left|20\right\rangle _{\mathrm{a,m}}$ or a phonon pair $\left|02\right\rangle _{\mathrm{a,m}}$. The inset graphically illustrates the "weight engineering" of linear and quadratic terms in $U(t)$ with $a^{\dagger}$ (or $m^{\dagger}$) by adjusting the pulse duration $\tau$. (b) Energy level diagrams of optomechanical SFWM for optical (left) and mechanical (right) effective counterparts. The entire process corresponds to the equivalent high-order optomechanical nonlinearity interaction in Eq. \ref{['eq:1']}. (c) Optomechanical energy diagram describing a virtual process in which a photon– phonon pair $\left|11\right\rangle _{\mathrm{a,m}}$ is first generated by a blue-detuned pump and then transitions to $\left|20\right\rangle _{\mathrm{a,m}}$ or $\left|02\right\rangle _{\mathrm{a,m}}$ via an interaction with a red-detuned pump.
• Figure 2: (a) Experimental set-up. AOM, acousto-optic modulator; SNSPD, superconducting nanowire single-photon detector. (b) Schematic of the preparation-measurement protocol. The desired optomechanical quantum state $\left|\Phi\right\rangle _{\mathrm{a,m}}$ is prepared via the first pulses and measured by the second red-detuned pulse which coherently retrieves phonons into signal photons and directly checks the nonclassical correlation of the phonon pair. The red shadow region with duration $\tau_{f}$ in the measurement pulse indicates the duration used for the statistics of twofold coincidence events. (c) Normalized counts of signal photons ($\omega_{\mathrm{a}}$) launched into two SNSPDs in the HBT setup during pulse 1 and pulse 2 for various preparation-measurement time delays $\Delta T$. The purple and pink shadow areas represent the results for pulses 1 and 2, respectively .
• Figure 3: Experimental demonstration of a phonon pair. (a-b) Experimental $g_{\mathrm{pre}}^{\left(2\right)}\left(\Delta N\right)$ and $g_{\mathrm{meas}}^{\left(2\right)}\left(\Delta N\right)$ for the preparation and measurement pulses, respectively. (c) Exponential decay $g_{\mathrm{meas}}^{\left(2\right)}\left(0,\tau_{f}\right)$ as a function of $\tau_{f}$ with $\Delta T=30\,\mathrm{ns}$. The red fitting line shows an exponential decay constant of $t_{\mathrm{d1}}\thickapprox15\,\mathrm{ns}$. The shadow areas indicate the 99% confidence and prediction intervals. (d) shows almost identical $g_{\mathrm{pre}}^{\left(2\right)}\left(0\right)$ values while $g_{\mathrm{meas}}^{\left(2\right)}\left(0,48\,\mathrm{ns}\right)$ decays into the thermal state as the time interval $\Delta T$ increases. The dashed blue line shows the fitted decoherence lifetime $t_{\mathrm{d2}}$ of approximately $132\,\mathrm{ns}$. The shadow area indicates the 75% confidence interval. All error bars indicate +/ one standard deviation.
• Figure 4: (a) Coincidence counts of two-photon click events and zero-photon click events between pulses 1 and 2, obtained from $N\thickapprox1.4\times10^{8}$ independent equally distributed experiments with $\Delta T=150\,\mathrm{ns}$. (b) Pump-probe measurement in mechanical breathing mode. A short blue-detuned pulse (pump) is sent to excite phonon occupation, and then, the mechanical response is measured via a red-detuned optical probe pulse as a function of the pump-probe time delay $\Delta T$. (c) The red and blue lines are the exponential theoretical fits, corresponding to $t_{l}=1.46\,\mathrm{\mu s}$ and $t_{s}=0.22\,\mathrm{\mu s}$, respectively. All error bars indicate +/ one standard deviation.