Spectrotemporal processing in a dual gradient echo and electromagnetically-induced transparency memory

TL;DR

The paper addresses spectrotemporal processing of optical quantum information by implementing a fractional Fourier transform in a dual GEM–EIT memory, enabling rotations in the time–frequency phase-space. It demonstrates, via chirped GEM storage and chirped EIT recall, that a controllable FrFT can be realized without explicit dispersion management, effectively rotating the 2D time–frequency Wigner distribution by an angle $\theta$. The results show faithful eigenphase behavior for Hermite–Gauss test modes with $FrFT^{m}(\theta)$, while fidelity and efficiency depend on mode volume and the EIT window, highlighting tradeoffs between GEM and EIT performance. This approach offers a pathway to multi-stage spectrotemporal processing, including mode sorting and multiplexing, with potential applications in quantum sensing and communication where spectral-temporal control is essential.

Abstract

Spectrotemporal encoding of optical quantum information is emerging as a powerful tool in quantum information technology. Processing of spectrotemporal information has recently been demonstrated in multi-mode quantum memories, based on extensions to memory protocols. We simulate one such process, the fractional Fourier transform, in a system based on a dual quantum memory composed of successive gradient echo memory and electromagnetically-induced transparency operations. We demonstrate the potential of electromagnetically-induced transparency systems for spectrotemporal processing.

Figures (4)

• Figure 1: Conceptual implementation of the Fourier transform: (i) The GEM level scheme, where different frequencies of the input signal (shades of blue) are two-photon resonant with the control laser (pink) at different positions, producing a spinwave (dashed, green). (ii) Time and frequency components and WDF of the signal. WDF has positive (red) and negative (blue) regions. (iii) Partial storage; the first pulse is converted to spinwave (green). The gradient transports the spinwave in momentum ($k_z$). (iv) Complete storage; the second pulse is converted to spinwave, overlapping spatially and interfering with the first pulse to give a spatially modulated spinwave ($S(z,T)$). (v) EIT level scheme; the resonant control laser produces slow light and transports the spinwave in $z$. (vi) The spinwave WDF rotated by $-\pi/2$ to indicate the new transport dimension. (vii) Partial recall; spinwave reaches the end of the ensemble and is converted entirely to light (interface marked by pink line); the spatial envelope of the spinwave is converted to the temporal envelope of the output signal, the momentum distribution becomes the output spectrum. (viii) Complete recall; The output signal is the time-frequency Fourier transform of the input.
• Figure 2: Extension of the conceptual diagram to a fractional Fourier transform: (i) Increased gradient to accommodate frequency sweep, which follows the dotted pink arrow. (iii) The signal occupies a smaller part of the memory bandwidth, and the signal WDF is rescaled to $(t',\omega')$ to preserve the scale of $(k_z,z)$. Sweeping the control frequency changes the position of the interface in $z$ as a function of time, producing a sheared spinwave WDF. (v) The stored spinwave. The spatial envelope is smeared due to the shear, while the momentum distribution is only stretched (vii-viii) The EIT velocity, $z\rightarrow t$ is modified to reverse the distortion from 2-shear rotation. The rescaled $z'$ sets the spinwave WDF at the same width as the rotated output signal. (x) The output signal, rotated $-\pi/4$ in time-frequency.
• Figure 3: Simulation of a rotation of two Gaussian pulses by $-\pi/4$, as in the concept diagram. a) WDF of the input, stored spinwave, and outputs. The WDF amplitudes are not to scale. b) Intensity of the input and output signals.
• Figure 4: Simulation results. a) Eigenphase measurement of the Hermite-Gauss modes for $HG_n$ and $m=10$. Lines show the expected phase for each mode vs rotation. b) Conditional fidelity for selected HG modes and rotations at $m=10$. c) Efficiency of a $\pi/4$ rotation in GEM-EIT and GEM-GEM for $HG_m$ for $m<10$. d) Example of a $HG_2$ mode with $FrFT^{m=10}(-\pi/4)$ rotation.