Hybrid quantum memory leveraging slow-light and gradient-echo duality (2509.02810v1)

Abstract: We demonstrate a hybrid quantum memory that combines Gradient Echo Memory (GEM) and Electromagnetically Induced Transparency (EIT) protocols for reversible mapping between light and atomic coherence. By leveraging GEM and EIT complementarity, we realize time-to-frequency and frequency-to-time conversion mechanisms for spectro-temporal modes. This capability provides a versatile tool for quantum communication, where coherent frequency-time conversion enhances network interoperability. In addition, the protocol may enable fundamental studies of atomic coherence, including investigations of Rydberg polaritons and mapping of single Rydberg excitations and ionic impurities.

• The paper presents a hybrid quantum memory protocol integrating GEM and EIT to achieve reversible mapping of photonic and atomic coherence.
• It employs cold 87Rb atoms in a MOT and heterodyne detection to validate dual mapping of narrow and broad spectral/temporal pulses.
• Numerical simulations and experiments confirm that reversible time-frequency conversion enhances quantum communication and metrology.

Hybrid Quantum Memory Leveraging Slow-Light and Gradient-Echo Duality

Introduction

This work presents a hybrid quantum memory protocol that integrates Gradient Echo Memory (GEM) and Electromagnetically Induced Transparency (EIT) for reversible mapping between photonic and atomic coherence. The protocol exploits the complementary nature of GEM and EIT to enable time-to-frequency and frequency-to-time conversion of spectro-temporal modes, providing a versatile tool for quantum communication and coherent information processing. The experimental realization utilizes cold $^{87}$Rb atoms in a magneto-optical trap, with heterodyne detection for simultaneous time and frequency domain analysis.

Figure 1: Schematic of the hybrid protocol, including relevant $^{87}$Rb energy levels, experimental setup, and protocol sequences for GEM/EIT write-in and readout.

Theoretical Framework

The hybrid protocol is based on a $\Lambda$-type photon-atom interface, where both GEM and EIT can be implemented. In GEM, a magnetic field gradient induces inhomogeneous broadening, mapping the frequency components of the input optical field to spatial positions in the atomic ensemble. The mapping is described by:

$\delta(z) = \beta z + \omega_0$

where $\beta$ is the magnetic gradient, $z$ is the position, and $\omega_0$ is the resonance frequency. The atomic coherence after GEM storage is:

$$\varrho_{gh}(T,z) \propto e^{i\beta z T} \tilde{A}(\beta z)$$

with $\tilde{A}(\omega)$ the Fourier transform of the input pulse.

EIT, in contrast, relies on strong dispersion to slow and halt the optical pulse, mapping its temporal profile to spatial position. The group velocity is given by:

$$v_g = \frac{c}{1 + \frac{c g OD \Gamma}{L \hbar \Omega_C^2}}$$

where $g$ is the atom-field coupling, $OD$ is optical depth, $\Gamma$ is the excited state decay rate, $L$ is ensemble length, and $\Omega_C$ is the coupling beam Rabi frequency. The atomic coherence for EIT storage is:

$$\varrho_{gh}(T,z) \propto A\left(\frac{v_g T - z}{v_g}\right)$$

By combining GEM and EIT in complementary configurations, the protocol enables reversible time-frequency conversion. Storage in GEM followed by EIT readout yields frequency-to-time mapping, while EIT storage followed by GEM readout yields time-to-frequency mapping.

Numerical Simulations

Simulations were performed using the XMDS2 package, solving the optical Bloch equations for both GEM and EIT regimes. The GEM protocol was modeled with spatially dependent detuning, while EIT propagation was modeled via coupled equations for the electric field and atomic coherences.

Figure 2: Simulated time traces and coherence profiles for GEM storage/EIT readout and EIT storage/GEM readout, demonstrating the dual mapping capability.

Simulations confirm that spectrally narrow pulses stored in GEM and read out in EIT are delayed according to their mapped position, while spectrally broad pulses experience minimal delay due to full cloud coverage. The reverse mapping is also validated, with temporal separation in EIT storage resulting in frequency separation upon GEM readout.

Experimental Implementation

The experimental setup utilizes cold $^{87}$Rb atoms in a MOT, with optical depth up to 80 and ensemble temperature of $80~\mu$K. The $\Lambda$ system is realized with $\sigma^{-}$-polarized signal and $\sigma^{+}$-polarized coupling beams, with the coupling beam Rabi frequency up to $2\pi \times 6.9$ MHz. Heterodyne detection enables simultaneous measurement of time and frequency domain properties of the retrieved light.

Results

GEM Write-In, EIT Readout

Pulses stored in GEM map frequency components to spatial positions. Upon EIT readout, different frequencies are delayed according to their propagation distance in the atomic medium. For pulses with bandwidth much smaller than the memory bandwidth, frequency-dependent delays are observed.

Figure 3: Experimental and simulated delays for narrow and broad spectral pulses stored in GEM and read out in EIT, showing strong frequency-dependent delay for narrowband pulses.

For pulses with bandwidth comparable to the memory bandwidth, the delay is nearly independent of frequency, as the entire cloud is utilized for storage.

EIT Write-In, GEM Readout

Reversing the protocol, pulses are stopped in EIT and read out via GEM. Temporal separation during EIT storage is mapped to frequency separation in the GEM readout.

Figure 4: Fourier transform of readout signals for narrow and broad time-domain pulses stored in EIT and read out in GEM, demonstrating time-to-frequency mapping.

Heterodyne detection confirms the mapping, with two temporally separated pulses yielding two distinct frequency peaks upon GEM readout.

Dual-Pulse Mapping

Experiments with dual-frequency and dual-time pulses further validate the protocol's reversibility and mapping fidelity.

Figure 5: Dual-frequency and dual-time pulse mapping, showing frequency-dependent delays and time-dependent frequency shifts in the readout signals.

Implications and Future Directions

The demonstrated hybrid protocol enables reversible conversion between spectral and temporal modes, with direct applications in quantum communication, time-frequency multiplexing, and quantum-enhanced metrology. The ability to coherently map and retrieve spectro-temporal information enhances network interoperability and supports advanced quantum repeater architectures.

The protocol is compatible with further extensions, such as tomography of Rydberg polaritons and mapping of single Rydberg excitations or ionic impurities. Increasing atomic density and memory bandwidth will improve efficiency and support shorter pulse durations. The approach provides a pathway for non-destructive, camera-free tomography of propagating polaritons, leveraging coherence mapping for spatially resolved quantum state diagnostics.

Conclusion

This work establishes a hybrid quantum memory protocol integrating GEM and EIT, enabling reversible time-frequency conversion and coherent mapping of photonic states. The experimental and simulation results confirm the protocol's versatility and fidelity, with strong agreement between theory and measurement. The approach offers significant potential for quantum communication, metrology, and fundamental studies of atomic coherence, with future developments likely to focus on enhanced efficiency, bandwidth, and integration with Rydberg-based quantum systems.