Probing an electron spin ensemble with squeezed microwave signals

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 GHz signals. We generate continuous variable microwave states with a squeezing of up to 5dB 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. Analyzing this signal using Wigner tomography, we observe a transfer efficiency of around 61% between the squeezed microwaves and the spin excitation. We successfully model our experimental results with a dedicated steady-state model based on the quantum input-output formalism and provide guidance for design parameters required to enable spin-based quantum memories.

Figures (7)

• Figure 1: Experimental setup. (a) By sending a vacuum state to the phase-sensitively operated JPA, squeezer (SQZ), we generate a propagating squeezed vacuum signal, $\hat{b}_\mathrm{in}$ with a frequency $\omega_{\text{SQZ}}$, which is directed to the spin-resonator system via superconducting coaxial cables and a cryogenic circulator. The transfer of the squeezed signal to the spin excitation is mediated via a superconducting lumped-element microwave resonator. The output signal from the spin-cavity system, $\hat{b}_\mathrm{out}$, propagates further through a cascade of cryogenic and room temperature amplifiers, is then down-converted and digitized to perform the Wigner tomography of microwave signals. By tuning the static magnetic field $B_0$, we can distinguish three coupling cases: (i) the SQZ is off-resonant from the spin-resonator hybrid; (ii) the SQZ is in resonance with the resonator, but off-resonant with the spin ensemble; (iii) the SQZ, resonator and spin ensemble are tuned in resonance. (b) Photo of the spin-resonator system. (c) Photo of the JPA device.
• Figure 2: Characterization of the spin-resonator hybrid. (a) Measured (left) and modeled (right) microwave reflection amplitude $|S_{11}|$ as a function of the coherent probe-resonator detuning $\Delta_\text{r}$ and spin-resonator detuning $\Delta_\text{sr}$. The spectrum is modeled based on Eq. \ref{['eq: scattering parameter']}. (b) Comparison of the measured (dots) and modeled (lines) data for the resonant ($\Delta_{\text{sr}}/2\pi=0$) and off-resonant ($\Delta_{\text{sr}}/2\pi=9.2MHz$) conditions, presented in blue and red, respectively.
• Figure 3: Squeezing levels of propagating microwave signals after interaction with the spin-resonator hybrid.(a) The measured squeezing level $S$ as a function of the SQZ pump power in the off-resonant case (black circles), in resonance with the resonator but off-resonant with the spins (red circles), and in resonance with the spin-resonator hybrid (blue circles). The lines are guides to the eyes. The crosses represent our model predictions based on Eq. \ref{['eq: input output variance']}, using the off-resonant squeezing states as reference input signals combined with independently determined coupling parameters $g_\text{eff}$, $\kappa_\text{ext}$, $\kappa_\text{int}$, and $\gamma_\text{s}$. (b) The measured and modeled $S$ in resonance with the spins indicate a squeezing below the vacuum level ($S>0)$. (c) Spin saturation measurements. A strong resonant microwave pulse saturates the ESR transition before performing a continuous wave squeezing measurement. This results in an increase of the squeezing levels approaching the reference experiment.
• Figure 4: Numerical calculation of the quantum transfer efficiency $|t(0)|^2$. The transfer efficiency is computed according to Eq. \ref{['eq: input output variance']} as a function of different coupling strengths for the resonance case, i.e. $\omega_{\text{SQZ}} = \omega_{\text{r}} = \omega_{\text{s}}$. (a) Transfer efficiency as a function of the external coupling rate $\kappa_\text{ext}$ and effective spin-resonator coupling $g_\text{eff}$ for $\gamma_\text{s}/2\pi=382kHz$. (c) Transfer efficiency as a function of the external coupling rate $\kappa_\text{ext}$ and spin dephasing $\gamma_\text{s}$ for $g_\text{eff}/2\pi=460kHz$. The spin dephasing rate and the spin-resonator coupling are fixed to $\gamma_{\text{s}}=382kHz$ and $g_{\text{eff}}=460kHz$, respectively. (d) Transfer efficiency as a function of the external and internal coupling rates, $\kappa_\text{ext}$ and $\kappa_\text{int}$, respectively. Optimal state transfer and maximum transfer efficiency is achieved in the limit of unit cooperativity, $C = 1$. Panels (b), (d), and (f) illustrate the calculated cooperativity for the maximum coupling efficiency.
• Figure 5: Coherence times of the Si:P ensemble. Experimentally determined coherence times $T_2$ (a) and $T_1$ (b) based on conventional Hahn echo and inversion recovery pulse sequences, respectively.