Intra-atomic frequency-comb-based photonic quantum memory using single-atom-cavity setup

On-demand and efficient storage of photons is an essential element in quantum information processing and long-distance quantum communication. Most of the quantum memory protocols require bulk systems in order to store photons. However, with the advent of integrated photonic chip platforms for quantum information processing, on-chip quantum memories are highly sought after. In this paper, we propose a protocol for multimode photonic quantum memory using only a single-atom-cavity setup. We show that a single atom containing a frequency comb coupled to an optical cavity can store photons efficiently. Further, this scheme can also be used to store polarization states of light. As examples, we show that rubidium and cesium atoms coupled to nanophotonic waveguide cavities can serve as promising candidates to realize our scheme. This provides the possibility of a robust and efficient on-chip quantum memory to be used in integrated photonic chips.

Figure 1

(a) Schematic diagram of an IAFC inside a cavity. Here, the IAFC is interacting with a single cavity mode with decay rate $\kappa$. ${\widehat{a}}_{\mathrm{in}}$ and ${\widehat{a}}_{\mathrm{out}}$ represent the input and output field mode operators. $\gamma$ is the spontaneous decay rate of the atom into free space. (b) Photon echo after a delay of 3.5 ns for an ideal IAFC coupled to a cavity with uniform comb spacing of $\mathrm{\Delta }=2\pi \times 300$ MHz, tooth width $\gamma =7.5$ MHz, and cavity detuning ${\mathrm{\Delta }}_c=0$. The input field in Eq. (12) is a Gaussian pulse given by $e^{-{\omega }^2/\left(2b^2\right)}$, with $b=2\pi \times 270$ MHz. The two photon echoes shown by dashed purple and solid black curves correspond to cavity decay rates of 7 and 4 GHz, respectively, with corresponding efficiencies of $94.22\%$ and $72.02\%$, respectively. Here, $I_{\mathrm{out}}$ represents the rate of photons in the output field (${\mathrm{ns}}^{-1}$), which is related to the input field through Eq. (12). The blue dotted curve shows the corresponding input field intensity, $I_{\mathrm{in}}=\langle {\widehat{a}}_{\mathrm{in}}^{†}\left(t\right){\widehat{a}}_{\mathrm{in}}\left(t\right)\rangle$.

Figure 2

Effect of various parameters on the efficiency $\eta$ of quantum memory in the single-atom-cavity setup for an ideal comb. In (a) and (b), we plot the variation of $\eta$ as a function of the cavity detuning ${\mathrm{\Delta }}_c={\omega }_c-{\omega }_L$ and the comb finesse $\mathcal{F}$, respectively, for $(g^{\prime },\kappa )=(1.8,11)$ GHz with uniform comb spacing $\mathrm{\Delta }=2\pi \times 300$ MHz. (c) shows the plot of the variation of $\eta$ as a function of cooperativity, $C^{\prime }=g^{\prime 2}/\left(\kappa \gamma \right)$, for different values of $\kappa$. (d) shows the variation of $\eta$ as a function of $\kappa$ given in terms of the parameter $a$ such that $\kappa =a\times 5$ GHz for fixed values of cooperativities, as shown by the vertical lines in (c).

Figure 3

Plot for absorption of a joint atom-cavity system for an ideal frequency comb with uniform comb spacing $\mathrm{\Delta }=2\pi \times 300$ MHz, tooth width $\gamma =7.5$ MHz, and cavity detuning ${\mathrm{\Delta }}_c=0$.

Figure 4

(a) and (b) represent the frequency comb in Rb and Cs atoms for transitions between $5s_{1/2}\leftrightarrow 6p_{3/2}$ for Rb and $6s_{1/2}\leftrightarrow 7p_{3/2}$ for Cs. The applied magnetic field strengths for Rb and Cs are taken to be 0.15 and 0.1 T, respectively.

Figure 5

(a) Photon echo for the IAFC in Rb and Cs atoms. (b) Variation of efficiency as a function of $1/\kappa$ in Rb and Cs atoms.