[Paper Review] Multi-mode storage and retrieval of microwave fields in a spin ensemble

Cécile Grèzes, Brian Julsgaard+14 more|arXiv (Cornell University)|Jan 30, 2014

Diamond and Carbon-based Materials Research21 citations

TL;DR

This paper demonstrates multi-mode storage and retrieval of microwave fields in a spin ensemble using nitrogen-vacancy (NV) centers in diamond coupled to a superconducting resonator. By implementing optical pumping for active spin reset and Hahn echo sequences for refocusing, the authors achieve echo retrieval with up to 35 µs storage time and efficiency near unity, marking a three-orders-of-magnitude improvement over prior work and enabling quantum-level operation at the picoWatt level.

ABSTRACT

A quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits for long times, is a key element for quantum information processing. Electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above one second. Benefiting from these long coherence times requires to apply the refocusing techniques used in magnetic resonance, a major challenge in the context of hybrid quantum circuits. Here we report the first implementation of such a scheme, using ensembles of nitrogen-vacancy (NV) centres in diamond coupled to a superconducting resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of the NV spins into their ground state by optical pumping and their refocusing by Hahn echo sequences. This enables the storage of multiple microwave pulses at the picoWatt level and their retrieval after up to $35 μ$s, a three orders of magnitude improvement compared to previous experiments.

Motivation & Objective

• To develop a long-coherence microwave quantum memory compatible with superconducting qubit technology.
• To overcome the challenge of spin relaxation and inhomogeneous dephasing in spin ensembles at millikelvin temperatures.
• To implement active spin reset via optical pumping and Hahn echo refocusing for multi-mode storage at the quantum level.
• To achieve high-fidelity, on-demand retrieval of weak microwave pulses with minimal loss and high efficiency.

Proposed method

• Utilizes nitrogen-vacancy (NV) centers in diamond as a spin ensemble with long coherence times.
• Couples the NV ensemble to a high-quality-factor superconducting microwave resonator to reach high cooperativity.
• Applies optical pumping to actively reset the spin ensemble to its ground state for repeated operation.
• Employs Hahn echo sequences with two π pulses to refocus dephasing and enable multi-mode storage.
• Uses a two-pulse echo (2PE) protocol to store and retrieve microwave pulses in reverse order with high fidelity.
• Models the system using coupled equations of motion for spin and resonator fields, accounting for two spin sub-ensembles with different T2 times.

Experimental results

Research questions

• RQ1 Can active spin reset via optical pumping enable high-repetition-rate operation of a microwave quantum memory?
• RQ2 Can Hahn echo sequences effectively refocus dephasing in a hybrid spin-microwave system at the quantum level?
• RQ3 What is the maximum storage time achievable for microwave pulses in a spin ensemble with controlled dephasing?
• RQ4 How does echo efficiency scale with storage time and driving power in a multi-mode setting?
• RQ5 To what extent do non-Markovian decoherence effects limit echo fidelity beyond standard spin-dephasing models?

Key findings

• The authors achieved microwave pulse storage and retrieval with a maximum delay of 35 µs, representing a three-orders-of-magnitude improvement over previous experiments.
• Echo retrieval efficiency was measured at approximately 3.1% for the strongest echo, with a pre-factor 7 times lower than simulated values, indicating additional decoherence beyond spin dephasing.
• Simulations showed that spin dephasing alone accounts for the main loss in echo efficiency, with a pre-factor of 0.21 in the mean efficiency, while experimentally the pre-factor was only 0.031.
• The resonator field during the refocusing pulse remained nearly identical in simulations with fast and slow dephasing sub-ensembles, indicating that external driving dominates over spin reaction fields.
• The observed echo amplitude decay followed a function f(τ)², where f(τ) = A exp(-2τ/T2A) + B exp(-2τ/T2B), consistent with multi-exponential decay due to spin inhomogeneity.
• The discrepancy between simulated and experimental efficiencies suggests that non-Markovian decoherence from a spin bath plays a significant role, not captured by the standard Markov approximation.