Demonstration of a photonic time-frequency Fourier transform and temporal double slit using atomic quantum memory

TL;DR

The paper addresses the need for quantum memories capable of spectro-temporal processing by realizing a photonic time-frequency Fourier transform (TFFT) inside a single memory. It achieves this by combining Gradient Echo Memory (GEM) and Electromagnetically Induced Transparency (EIT) in a cold $^{87}$Rb ensemble, storing with GEM and recalling with EIT to swap encoding domains. The experimental results reveal a temporal double-slit interference in the recalled output, with the fringe frequency scaling linearly with the input pulse separation and the phase following the input relative phase, consistent with simulations based on the optical Bloch equations. This work demonstrates a quantum-memory-compatible route to in-memory time-frequency manipulation with potential implications for quantum communication and sensing.

Abstract

A quantum memory for light is expected to play a crucial role in quantum communication protocols and distributed quantum computing. In addition to storage and buffering, a quantum memory can be used for manipulations of stored states to allow more complex quantum network operations. In this work, we demonstrate an in-memory Fourier transform using a combination of two well-established quantum memory protocols: Gradient Echo Memory and Electromagnetically Induced Transparency. Our experiment is realised using an ensemble of rubidium atoms that are laser cooled in an elongated magneto-optic trap to maximise optical depth. The results of our time-frequency Fourier transform can be understood as a temporal double slit. We show that the interference between time-separated pulses depends on the relative phase and time between the pulses of light. The use of a quantum memory enables us to illuminate exactly where and how interference occurs between time separated pulses. Time-frequency Fourier manipulation is a well established technique in classical optical systems. Our combination of Fourier manipulation and quantum-compatible memory could be used to bring similar capability to quantum optical systems.

Figures (5)

• Figure 1: a) Level scheme for GEM showing the spatial gradient in the two-photon absorption and a large detuning from the excited state. b) Level scheme for EIT with no spatial gradient and optical fields resonant with the excited state. Not shown in these diagrams is the two-photon detuning, $\delta$, see Methods for details. Simulation results for intra-memory TFFT are shown in (c-e). The left column shows results for a double pulse input, while the right column shows results for a modulated Gaussian input. c) Input (blue) and output (orange) envelopes. A scaled Fourier transform (dashed) of the input envelope is placed over the output for comparison. d) Momentum distribution of the spinwaves, showing that GEM writes the input pulse envelopes into the momentum space of the spinwave. The insets show cross sections in momentum space after GEM storage into the spinwave is complete. e) Spatial distribution of the spinwaves, with EIT reading the spatial component as the time envelope of the output signal. The insets show cross sections in position space after GEM storage into the spinwave is complete.
• Figure 2: Schematic of the complete experimental system. a) Setup of the laser table showing the production of the two control fields, the signal and the local oscillator. AOM: acousto-optic modulator, LO: Local Oscillator, EOM: Electro-Optic Modulator, APD: Avalanche Photo Diode, SAS: Saturated Absorption Setup, Rb. Cell: Rubidium Cell, $\lambda$/2 : half wave plate, $\lambda$/4: Quarter wave plate b) Configuration of the cold Rb ensemble and optical setup for the heterodyne detection of the transformed signal.
• Figure 3: Input and output signals for a double-Gaussian (a) and modulated Gaussian (b). The GEM storage occurs from $0$–$13~\mu$s, rephasing ($13$–$29~\mu$s), and output ($\geq 29~\mu$s) windows; simulations are overlaid. (b) Modulated Gaussian input and output, with simulations overlaid. (c) The linear relation between frequency and pulse separation. The stars indicate the range of the chirp in the fringes. (d) Outputs for double-Gaussian inputs with varying pulse separations. (e) Outputs for double-Gaussian inputs with varying relative phases (separation fixed at $4~\mu$s). The output modulation phase follows the relative phase of the input pulses (f) Outputs for modulated Gaussian inputs at different modulation frequencies. The time separation of the output pulses increases linearly with the input modulation frequency (dotted line).
• Figure 4: Level scheme for the modelling. The signal $\mathcal{E}$ and the control field $\Omega$ couple to the atomic levels shown, and the OBEs describe the evolution of $\mathcal{E}$ and the atomic coherences $\sigma_{gs}$, $\sigma_{ge}$.
• Figure 5: (i) Demodulation cycle for a double Gaussian input with a pulse separation of 2 $\mu$s. (a), (b) Single-shot traces of the unfiltered input and output signals, respectively, recorded by the oscilloscope. (c) Filtered and demodulated output corresponding to the same shot as in (b). (d), (e) In-phase (I) and quadrature (Q) components of the phase-corrected output signal, averaged over 30 shots. (ii) Processed in-phase (I) components of the outputs for the two individual references, together with their corresponding non-linear fits; the Gaussians are centred at zero to improve the accuracy and consistency of the fitting. (iii) Demodulation cycle for the modulated Gaussian input with a modulation frequency of 300 kHz, following the same structure as in (i).