Multiresonator quantum memory with atomic ensembles

TL;DR

This work develops a comprehensive analytical theory for multiresonator quantum memory using atomic ensembles in a cascade of mini-resonators coupled to a common resonator. By deriving the Hamiltonian, input-output relations, and Fourier-domain solutions, it establishes impedance and spectral matching conditions that broaden the memory’s working bandwidth and reduce required coupling, enabling high-efficiency broadband storage with fewer atoms. The study details retrieval schemes, notably Dual CRIB and ROSE (with NLPE variants), and demonstrates how dispersion and noise can be controlled through phase engineering across many mini-resonators. It also discusses practical implementation paths in integrated optics platforms, including planar ring resonators and rare-earth ensembles, and outlines key parameters and decoherence considerations essential for experimental realization.

Abstract

The theory of multiresonator quantum memory with atomic ensembles has been developed. Using the obtained analytical solutions, the basic physical properties of such memory are analyzed and optimal conditions for its implementation are determined. Advantages of this quantum memory and its experimental implementation in integrated optical schemes are discussed.

Figures (7)

• Figure 1: Spatial scheme of multiresonator quantum memory with atomic ensembles: $\kappa$ and $g$ are the coupling constants of a common resonator with a waveguide and with mini-resonators; $A_{in}$ and $A_{out}$ are the input and output fields; 8 rings with smaller dark rings containing white dots represent mini-resonators with atomic ensembles located in them; $j$-th atom interacts with the mode of $m$-th mini-resonator with a coupling constant $f_{j,m}$.
• Figure 2: Spectrum of inhomogeneously broadened atomic ensemble (line shape $G(\Delta/\Delta_{in})$), mini-resonators and signal pulse; $\Delta$ is spectral distance between nearest frequencies of mini-resonators, $\Delta_{in}$, $\delta_{in}$ and $\delta\omega_s$ are the spectral widths of atomic ensembles, mini-resonators and signal pulse.
• Figure 3: Behavior of the spectral reflection function $|U(\omega)|^2$ depending on $\omega=2\pi\nu$ ($-1\leq \omega \leq 1$): the red dashed-dotted line corresponds to the reflection under the impedance matching condition \ref{['impedance_match']}, neglecting in this condition the interaction of mini-resonators with atoms; black solid line - taking into account in the condition \ref{['impedance_match']} the interaction of mini-resonators with atomic ensembles. where $\kappa=1$, $\delta_{in}=10$, $\Gamma_{\Sigma}=2$. For the convenience of demonstrating the spectral behavior of all the graphs, the same frequency unit in all figures, which is taken for calculating the graph with red dashed-dotted (and black solid) line All the graph are presented in the same units, but for different parameters of the system under study (the same relation are used in other figures); blue dashed line - taking into account two impedance matching conditions \ref{['impedance_match']} and \ref{['broaderning_condition']} where $\Gamma_{\Sigma}=2$, $\delta_{in}=10$, $\kappa=15.51$.
• Figure 4: Spectral reflection function $|U(\omega)|^2$ with two impedance matching conditions \ref{['impedance_match']} and \ref{['broaderning_condition']}: (a) linewidth $\delta_{in}=10$, $\Gamma_{\Sigma}=2,4,6,8,10$ ($\kappa=23.17$). (b)$\Gamma_{\Sigma}=0.1\delta_{in}$, linewidth $\delta_{in}=0.1,0.2,0.5$ ( $\kappa=0.766$).
• Figure 5: Spectral reflection function $|U(\omega)|^2$ with two impedance matching conditions \ref{['impedance_match']} and \ref{['broaderning_condition']}: (a)$\Gamma_{\Sigma}=0.5\delta_{in}$, linewidth $\delta_{in}=0.1,0.2,0.5$ ($\kappa=0.785$), (b)$\Gamma_{\Sigma}=\delta_{in}$, linewidth $\delta_{in}=0.1,0.2,0.5$ ($\kappa=1.159$).