Triggered Superradiance and Spin Inversion Storage in a Hybrid Quantum System

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Triggered Superradiance and Spin Inversion Storage in a Hybrid Quantum System

Wenzel Kersten, Nikolaus de Zordo, Oliver Diekmann, Tobias Reiter, Matthias Zens, Andrew N. Kanagin, Stefan Rotter, Jörg Schmiedmayer, and Andreas Angerer

Phys. Rev. Lett. 131, 043601 – Published 25 July 2023

Abstract

We study the superradiant emission of an inverted spin ensemble strongly coupled to a superconducting cavity. After fast inversion, we detune the spins from the cavity and store the inversion for tens of milliseconds, during which the remaining transverse spin components disappear. Switching back on resonance enables us to study the onset of superradiance. A weak trigger pulse of a few hundred photons shifts the superradiant burst to earlier times and imprints its phase onto the emitted radiation. For long hold times, the inversion decreases below the threshold for spontaneous superradiance. There, the energy stored in the ensemble can be used to amplify microwave pulses passing through the cavity.

Received 18 January 2023
Revised 19 May 2023
Accepted 12 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.043601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics NV centers Optical & microwave phenomena Superradiance & subradiance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wenzel Kersten ^1,*, Nikolaus de Zordo ¹, Oliver Diekmann ², Tobias Reiter ², Matthias Zens ², Andrew N. Kanagin ¹, Stefan Rotter ², Jörg Schmiedmayer ^1,†, and Andreas Angerer¹

¹Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, A-1020 Vienna, Austria
²Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria

^*Corresponding author. wenzel.kersten@tuwien.ac.at
^†Corresponding author. hannes-joerg.schmiedmayer@tuwien.ac.at

Article Text

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Issue

Vol. 131, Iss. 4 — 28 July 2023

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Images

Figure 1
(a) Schematic of the MW cavity located in a dilution refrigerator at 25 mK and connected to a homodyne MW setup. Two sapphire chips with opposing split ring structures and the diamond sample are stacked inside a copper box. Between the center holes the oscillating magnetic field homogeneously penetrates the sample. A superconducting wire loop wrapped around the chips enables rapid spin detuning. Port 1 is connected to the pump line, which can be decoupled at the 1 K stage using a solenoid switch for noise suppression. Port 2 is connected to the out line for acquiring data, and the attenuated probe line for injecting weak trigger pulses. (b) Experiment sequence: we use a modified chirp pulse (red and blue) to invert the spin ensemble and subsequently modulate the spin detuning $δ$ to store the inversion. After a variable hold time we bring the spins back into resonance and measure the cavity amplitude $| a |$ of the SR decay, optionally triggered by a short probe pulse (orange). (c) SR decays for varying hold times, triggered by the pump-line amplifier noise. The inset shows the SR decay maxima with an exponential fit in a semilog plot. (d) Example data and simulation of an SR decay and its quadratures $I / Q$ , with simulated inversion $p$ . The vertical line indicates $t_{D}$ , the time of maximum cavity amplitude. The number of cavity photons $n = | a |^{2}$ (calibration in Supplemental Material [17]) agrees well with the estimated number of decaying spins $Δ S_{z}$ .
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Figure 2
Triggering the SR decay with 100 ns pulses containing different numbers of photons, color coded according to (e). (a) Maxima of the SR decay amplitudes plotted over delay times $t_{D}$ . (b) Corresponding SR decay phases $φ$ plotted over a rescaled $t_{D}$ axis. The rescaled $t_{D}$ values result from a transformation that aligns the dashed curve in (a) onto the vertical line. (c) Initial state of the collective spin vector with coordinates $(θ, ϕ)$ close to the north pole of the Bloch sphere: in-plane distribution before (blue) and after (red) the coherent displacement $η$ in units of the width $\bar{θ}$ induced by the trigger pulse. (d) Phase average over all runs $⟨ \cos (φ_{i} - φ_{j}) ⟩$ quantifying the phase randomness from the measured sets of $φ$ . (e) Swarm plots of the delay time $t_{D}$ data. The solid lines in (d) and (e) are obtained from our theoretical description, varying only the parameter $η$ .
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Figure 3
(a) Cavity amplitude $| a |$ for a series of 100 ns pulses, each injecting $n_{trig} \approx 1.5 \times 10^{9}$ photons, amplified by the partially inverted spin ensemble in the reduced effective cooperativity regime $p C < 1$ for different hold times (red). In comparison, we plot the signal obtained with an empty cavity where spins are far detuned (blue). For choosing the parameters in our semiclassical model (black), we ignore noise below a certain threshold (green line at the top). (b) Ensemble inversion as a function of hold time, extracted by simulations in the two regimes above and below $p C = 1$ . Above this threshold, the pulse maxima (right $y$ axis) follow the values of $p$ from simulations of the self-decays shown in Fig. 1. A stretched exponential with exponent $1 / 2$ (characteristic for spin diffusion in three dimensions [29]) is fitted to the inversion.
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