Capacity-time Trade-off in Highly Reliable Quantum Memory

Abstract

Reliable optical quantum memory is limited by real-world imperfections such as disordered coupling and detuning. Existing studies mostly address these factors separately, while in practice their correlated effects set a fundamental limit on storage performance. We develop a comprehensive model that simultaneously incorporates disordered coupling and detuning. It is shown that these disorders induce a random Berry's phase in the stored states, while decoherence from disordered coupling stems from correlations with detuning rather than individual imperfections. This mechanism imposes a fundamental trade-off among storage capacity, storage time, and driving time, setting a universal limit for reliable storage. Extending the analysis to memory based devices operating with multiple storage processes shows that enhancing parameter independence improves their reliability. We further provide a more precise relation for measuring and correcting global detuning, which is directly relevant to current experimental protocols.

Figures (4)

• Figure 1: Schematic of a quantum memory system composed of $N$ three-level atoms, where atoms are coupled to a classical control field (blue) and a quantum mode (red). The upper-right panel illustrates the classical driving pulse $\Omega(t)$ (black solid line) and the corresponding angle $\theta_{\bm g}(t)$ (purple dashed line) over three time intervals to realize a SIRO process. Here, a Gaussian pulse is taken as an example, $\Omega/\sum_jg_j^2=\xi\exp(-2\ln(\xi)(t/\tau_{\mathrm{d},1})^2)$ for store-in, with the inverse procedure used for retrieval, here we set $\xi=1000$.
• Figure 2: fidelity $\mathcal{F}$ versus $|\alpha|$ and storage time $\tau_{\mathrm{s}}$ with $\tau_{\mathrm{s}}^{(\mathrm{de})}/\tau_{\mathrm{d}}^{(\mathrm{de})}=1000$ and $\alpha_\theta=2.7$. Inset represents the fidelity $\mathcal{F}$ versus $\tau_{\mathrm{s}}$ for $|\alpha|=3$ (orange) and $|\alpha|=6$ (blue), which corresponds to the vertical dashed line.
• Figure 3: (a) fidelity $\mathcal{F}$ versus $\Gamma_{\bm{\xi}_0}(\tau)/N$ and $|\alpha|$, when storing cat state $\mathcal{N}_0(|\alpha\rangle+\exp(\eta+\mathrm{i}\theta)|-\alpha\rangle)$, $\eta,\ \theta\in\mathbb{R}$, here we set $\eta=1,\ \theta=\pi$. The curves represent contours of $\mathcal{F}=0.9,\ 0.8,\ 0.6,\ 0.4$ from left to right, with solid lines for the exact form, and dashed lines for the approximate form when $\langle\Delta n^2\rangle\gg1$ (here $\langle\Delta n^2\rangle\simeq|\alpha|^2$), following a relation $\Gamma_{\bm{\xi_0}}(\tau)/N\propto1/|\alpha|^2$. (b) $\mathcal{F}$ versus $\Gamma_{\bm{\xi}_0}\langle\Delta n^2\rangle/N$. The blue and orange solid lines represent storing the cat state ($\eta=0,\ \theta=0$) and the uniform superposition state, respectively, with $\langle\Delta n^2\rangle=10$. Squares and circles represent the approximate form. The dashed line is lower bound for arbitrary state fidelity, and the inset shows scaling as $(\Gamma_{\bm{\xi}_0}(\tau)\langle\Delta n^2\rangle/N)^{-1/2}$. Please see Sec... in SM for detailed derivation of such forms for these states.
• Figure A1: The key procedure of typical memory-based devices, i.e., the synchronizer and repeater chains: (a) the memory performs SIRO on a sequence of $k$ states, (b) a state undergoes $k$ memory-based repeaters.