Probing an electron-spin ensemble with squeezed microwave signals

Phys. Rev. A 114, 022603 (2026) · DOI: 10.1103/f81b-px1l · arXiv: 2512.17490

License: CC BY 4.0.

Abstract

The efficient transfer of quantum states into a long-lived storage unit such as solid-state spin ensembles is widely recognized as a critical challenge with significant implications for quantum communication, sensing, and computing applications. Here, we experimentally investigate the interaction of propagating squeezed microwaves with an electron-spin-resonance transition in order to evaluate the use of spin ensembles as quantum memories for gigahertz signals. We generate continuous-variable microwave states with squeezing levels up to 5 dB below the vacuum level and let this signal interrogate a spin ensemble, which is inductively coupled to a lumped-element superconducting microwave resonator with a cooperativity of C = 0.3. By analyzing this signal using Wigner tomography and modeling our experimental results with a dedicated steady-state model based on the quantum input-output formalism, we extract a transfer efficiency of around 61 % between the squeezed microwaves and the spin excitations, resulting in squeezing levels of the spin mode up to 0.5 dB below the vacuum level.

Figures

18 panels with data across 5 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF. Page 2 of the PDF.

Fig. 2

• panel (a-1): Measured microwave reflection amplitude $|S_{11}|$ (norm.) as a function of the spin-resonator detuning $\Delta_{\mathrm{sr}}/2\pi$ and the probe-resonator detuning $\Delta_{\mathrm{r}}/2\pi$. Left map of the printed panel (a). data.csv
• panel (a-2): Modeled microwave reflection amplitude $|S_{11}|$ (norm.) from Eq. (7) as a function of the spin-resonator detuning $\Delta_{\mathrm{sr}}/2\pi$ and the probe-resonator detuning $\Delta_{\mathrm{r}}/2\pi$. Right map of the printed panel (a), shown on every third grid point. data.csv
• panel (b): Measured (dots) and modeled (lines) reflection amplitude $|S_{11}|$ (norm.), on the horizontal axis, against the probe-resonator detuning $\Delta_{\mathrm{r}}/2\pi$, for the resonant ($\Delta_{\mathrm{sr}}/2\pi = 0$, blue) and off-resonant ($\Delta_{\mathrm{sr}}/2\pi = 9.2$ MHz, red) conditions. data.csv

Fig. 3

• panel (a): Measured squeezing level $S$ (dB) against SQZ pump power (dBm) for $\omega \neq \omega_{\mathrm{r}}, \omega_{\mathrm{s}}$ (black), $\omega = \omega_{\mathrm{r}} \neq \omega_{\mathrm{s}}$ (red) and $\omega = \omega_{\mathrm{r}} = \omega_{\mathrm{s}}$ (blue), with error bars and connecting lines. Crosses are the model predictions from Eq. (4); dashed line at $S = 0$. data.csv
• panel (b): Squeezing level $S$ (dB) against SQZ pump power (dBm) for $\omega = \omega_{\mathrm{r}} = \omega_{\mathrm{s}}$: the measured output microwave signal $\sigma^2_{\hat{b}_{\mathrm{out}}}$ (circles, with error bars) and the spin mode $\sigma^2_{\hat{s}}$ calculated from the effective rate model (triangles); lines connect the points. The printed broken $S$ axis is shown continuous. data.csv
• panel (c): Measured squeezing level $S$ (dB) against SQZ pump power (dBm) for $\omega = \omega_{\mathrm{r}} \neq \omega_{\mathrm{s}}$ (red), $\omega = \omega_{\mathrm{r}} = \omega_{\mathrm{s}}$ (blue) and $\omega = \omega_{\mathrm{r}} = \omega_{\mathrm{s}}$ with spin saturation (green), with error bars and connecting lines; dashed line at $S = 0$. The printed broken $S$ axis is shown continuous. data.csv

Fig. 4

• panel (a): Computed transfer efficiency $|t(0)|^2$ as a function of the effective spin-resonator coupling $g_{\mathrm{eff}}/2\pi$ and the external coupling rate $\kappa_{\mathrm{ext}}/2\pi$, for $\gamma_{\mathrm{s}}/2\pi = 382$ kHz. Shown on every third grid point. data.csv
• panel (b): Cooperativity C at maximum transfer efficiency, drawn as closely spaced dots against the effective spin-resonator coupling $g_{\mathrm{eff}}/2\pi$ and the external coupling rate $\kappa_{\mathrm{ext}}/2\pi$, on the printed 0.1 to 1.0 scale. The $g_{\mathrm{eff}}$ values are as deposited, a factor of about $\sqrt{2}$ (1.41) below the printed curve. data.csv
• panel (c): Computed transfer efficiency $|t(0)|^2$ as a function of the spin dephasing rate $\gamma_{\mathrm{s}}/2\pi$ and the external coupling rate $\kappa_{\mathrm{ext}}/2\pi$, for $g_{\mathrm{eff}}/2\pi = 460$ kHz. Shown on every third grid point. The $\gamma_{\mathrm{s}}$ values are as deposited, about twice those of the printed map. data.csv
• panel (d): Cooperativity C at maximum transfer efficiency, drawn as closely spaced dots against the spin dephasing rate $\gamma_{\mathrm{s}}/2\pi$ and the external coupling rate $\kappa_{\mathrm{ext}}/2\pi$, on the printed 0.2 to 1.0 scale. The $\gamma_{\mathrm{s}}$ values are as deposited, about twice those of the printed curve. data.csv
• panel (e): Computed transfer efficiency $|t(0)|^2$ as a function of the internal coupling rate $\kappa_{\mathrm{int}}/2\pi$ and the external coupling rate $\kappa_{\mathrm{ext}}/2\pi$, for $\gamma_{\mathrm{s}}/2\pi = 382$ kHz and $g_{\mathrm{eff}}/2\pi = 460$ kHz. Shown on every third grid point. data.csv
• panel (f): External coupling rate $\kappa_{\mathrm{ext}}/2\pi$ at maximum transfer efficiency against the internal coupling rate $\kappa_{\mathrm{int}}/2\pi$, coloured by the cooperativity C on the printed 0.5 to 1.0 scale. The printed line is drawn as closely spaced dots. data.csv

Fig. 5

• panel (a): Normalized spin-echo area $A_{\mathrm{echo}}$ against the Hahn-echo delay $2\tau$ (ms). The exponential fit curve of the print is not hosted. data.csv
• panel (b): Normalized spin-echo area $A_{\mathrm{echo}}$ against the inversion-recovery delay $T$ (s), on a logarithmic $T$ axis. The exponential fit curve of the print is not hosted. data.csv

Fig. 6

Illustrative figure, no extractable data. Shown in the paper PDF. Page 7 of the PDF.

Fig. 7

• panel (a): Microwave reflection amplitude $|S_{11}|$ (norm.) of the JPA as a function of the dc coil current (mA) and the probe frequency (GHz). Shown on every second frequency point. data.csv
• panel (b): Nondegenerate gain $G_{\mathrm{nd}}$ (dB) of the JPA as a function of pump power (dBm) and frequency (GHz), for a pump at $\omega_{\mathrm{pump}}/2\pi = 11.1$ GHz. data.csv
• panel (c): Measured squeezing level (dB) against pump power (dBm) for $\omega_{\mathrm{SQZ}}/2\pi = 5.645$ GHz, open circles joined by lines; the dotted line marks the vacuum limit at 0 dB. data.csv
• panel (d): Reconstructed purity against pump power (dBm), open circles joined by lines; the dotted line marks purity 1. data.csv

Cite

P. Oehrl, F. Fesquet, K. E. Honasoge, M. Handschuh, A. Marx, R. Gross, K. G. Fedorov, H. Huebl. Probing an electron-spin ensemble with squeezed microwave signals. Phys. Rev. A 114, 022603 (2026). https://doi.org/10.1103/f81b-px1l

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