Single-photon transfer using levitated cavityless optomechanics

We theoretically explore a quantum memory using a single nanoparticle levitated in an optical dipole trap and subjected to feedback cooling. This protocol is realized by storing and retrieving a single-photon quantum state from a mechanical mode in levitated cavityless optomechanics. We describe the effectiveness of the photon-phonon-photon transfer in terms of the fidelity, the Wigner function, and the zero-delay second-order autocorrelation function. For experimentally accessible parameters, our numerical results indicate robust conversion of the quantum states of the input signal photon to those of the retrieved photon. We also show that high fidelity single-photon wavelength conversion is possible in the system as long as intense control pulses shorter than the mechanical damping time are used. Our work opens up the possibility of using levitated optomechanical systems for applications of quantum information processing.

Figure 1

Schematic of photon-phonon-photon transfer with an optically levitated nanoparticle of mass $m$ in a dipole trap and subjected to nonlinear feedback cooling [40]. The particle oscillates in the optical dipole trap with frequency ${\omega }_x$ along the $x$ axis. A writing pulse along with the signal interact with the nanoparticle and causes the storage of the quantum states of the signal. The stored quantum state is retrieved at a later time by using a readout pulse.

Figure 2

Gaussian writing and readout pulses (top panel) and the calculated optical power of the storage and retrieval of the signal photon (solid line), along with the power of the stored mechanical oscillation (dotted line) as a function of time (bottom panel). The parameters used are ${\omega }_x=124\mathrm{kHz}, R=50\mathrm{nm}, m=1.2\times {10}^{-18}\mathrm{kg}, {\epsilon }_c=1.133$, signal wavelength $\left({\lambda }_s\right)=780\mathrm{nm}$, write wavelength $\left({\lambda }_w\right)=1064\mathrm{nm}$, readout wavelength $\left({\lambda }_r\right)=1064\mathrm{nm}$, central time of writing and signal pulse $(t_w,t_s)=0.09\mathrm{ms}$, central time of readout pulse $\left(t_r\right)=0.9\mathrm{ms}$, writing and readout pulse widths $(t_{1s},t_{2s})=7\mu \mathrm{s}$, single-photon signal optomechanical coupling $\left(g\right)=0.2\mathrm{mHz}$, effective writing (readout) optomechanical coupling $\left[G_{w0}\left(G_{r0}\right)\right]=79$ kHz (86 kHz), $\mathrm{\Delta }=0, \mathrm{\Delta }x=10\mathrm{nm}, {\ell }_x=19\mathrm{pm}, {\gamma }_g=0.0289\mathrm{Hz}, \delta \mathrm{\Gamma }=0.66\mathrm{kHz}$, pressure $\left(P\right)=7\times {10}^{-6}$ mbar, $T=4$ K, ${\mathcal{B}}_s=0.3\mathrm{Hz}, {\mathcal{B}}_w=0.04\mathrm{Hz}, {\mathcal{B}}_r=0.04\mathrm{Hz}, {\mathcal{A}}_t=27\mathrm{kHz}, {\mathcal{A}}_w=10\mathrm{kHz}, {\mathcal{A}}_r=10\mathrm{kHz}$, scaled optomechanical coupling $\left(\chi \right)=1.5\times {10}^{-9}$, numerical aperture $\left(\text{NA}\right)=0.9$, and nonlinear feedback gain $\left(\mathcal{G}\right)=20$.

Figure 3

Fidelity vs (a) $r$ and ${\left|\alpha \right|}^2$, (b) $G/{\omega }_x$ and ${\left|\alpha \right|}^2$, and (c) power of writing $\left[P_w\left(\text{mW}\right)\right]$ and readout pulses $\left[P_r\left(\text{mW}\right)\right]$. In plot (a) $t_{1s}=19\mu \mathrm{s}, t_{2s}=18\mu \mathrm{s}$, in plot (b) $G_{w0}=G_{r0}=G, r=0.05$, and in plot (c) $\alpha =\sqrt{0.3}$. Here, $t_f=0.5\mathrm{ms}$ and other parameters are the same as in Fig. 2.

Figure 4

(a) Fidelity vs $t_{1s}\left(\mu \text{s}\right)$ and ${\left|\alpha \right|}^2$. (b) Fidelity vs $t_{2s}\left(\mu \text{s}\right)$ and ${\left|\alpha \right|}^2$. In plot (a) $t_{2s}=7\mu \mathrm{s}$ and in plot (b) $t_{1s}=7\mu \mathrm{s}$ and other parameters are the same as in Fig. 3.

Figure 5

Fidelity versus (a) temperature (K) and (b) pressure (mbar). Here, $t_{1s}=t_{2s}=7\mu \mathrm{s}$ and the rest of the parameters are the same as in Fig. 3.

Figure 6

(a) Wigner function of the input Gaussian state of the signal. The Wigner function of the retrieved photon state for (b) $t_{1s}=t_{2s}=1\mu \text{s}$, (c) $t_{1s}=t_{2s}=50\mu \text{s}$, and (d) $t_{1s}=t_{2s}=100\mu \text{s}$. Other parameters are the same as in Fig. 3.

Figure 7

$g^2\left(0\right)$ function vs (a) ${\left|\alpha \right|}^2$ and $t_f$ and (b) $r$ and $t_f$. In plot (a) $r=0$, while in plot (b) $\alpha =\sqrt{0.3}$ and the rest of the parameters are the same as in Fig. 3.

Figure 8

(a) Transmission matrix coefficients vs frequency under impedance matching. (b) Pulse fidelity vs spectral width. All other parameters are the same as in Fig. 2.