Magnon squeezing in the quantum regime

Abstract

Squeezed states, crucial for quantum metrology and emerging quantum technologies, have been demonstrated in various platforms, but quantum squeezing of magnons in macroscopic spin systems remains elusive. Here we report the experimental observation of quantum-level magnon squeezing in a millimeter-scale yttrium iron garnet (YIG) sphere. By engineering a strong dispersive magnon-superconducting qubit coupling via a microwave cavity, we implement a significant self-Kerr nonlinearity to generate squeezed magnon states with their mean magnon number less than one. Harnessing a magnon-assisted Raman process, we perform Wigner tomography, revealing quadrature variances of $\sim\!0.8$ ($\sim\!1.0$~dB squeezing) relative to the vacuum. These results lay the groundwork for quantum nonlinear magnonics and promise potential applications in quantum metrology.

Figures (4)

• Figure 1: Experimental platform and qubit-magnon control scheme.a, Schematic of the hybrid quantum system, where a 1-mm-diameter YIG sphere and a transmon qubit are placed at the magnetic and electric field antinodes of the $\rm{TE}_{102}$ mode of a 3D rectangular microwave cavity, respectively. The system is operated in a dilution refrigerator at $\sim$10 mK. An external magnetic field $\mathbf{B}$ magnetizes the sphere, biasing the Kittel mode to $\omega_{\rm m}/2\pi = 6.231$ GHz. b, Autler-Townes (AT) splitting of the qubit. The measured qubit spectrum is plotted as a function of the AT drive amplitude $\Omega_{\rm AT}$. The splitting forms two dressed states, $\vert + \rangle$ and $\vert - \rangle$, with the transitions from $\vert g \rangle$ to them shown as the upper and lower branches. Dashed lines are numerical fits. c, Energy level diagram of the hybrid quantum system. The cavity mode is far-detuned from both the qubit and the magnon, mediating an effective qubit-magnon coupling $g_{\rm qm}$. A large detuning, $\Delta_{\rm qm} \approx 3.8 g_{\rm qm}$, ensures that the qubit-magnon system is in the dispersive regime and induces a strong self-Kerr nonlinearity on the magnons. d, Pulse sequence for squeezing and tomography. The sequence is divided into three parts: (i) preparation of the squeezed state via Kerr nonlinearity, (ii) Wigner tomography of the magnon state, and (iii) final measurement of the qubit. Frequencies of the qubit (purple) and magnon (green) are indicated, along with the required microwave control pulses (wavy lines). e, Tunable magnon-qubit state swapping. Top: A magnon-assisted Raman drive induces coherent Rabi oscillations between $\vert f,0 \rangle$ and $\vert g,1 \rangle$. The population in $\vert f,0 \rangle$ is plotted versus the interaction time. Bottom: The effective swap coupling strength $g_0$, extracted by FFT, is shown to be linearly tunable with the Raman drive amplitude $\Omega$. The solid line is a linear fit.
• Figure 2: Wigner tomography and density matrices of the vacuum and squeezed states of magnons.a, Top row: experimentally measured Wigner function for the vacuum state ($\tau=0$) and for five squeezed states at $\tau=50$, 100, 150, 200, and 250 ns. Bottom row: the corresponding Wigner functions derived from the numerically simulated density matrices. Both experimental and numerical data clearly illustrate the transition from a vacuum state (circular distribution) to nonclassical squeezed states (quasi-elliptical distributions), with the strongest squeezing emerging at around $\tau=150$ ns, where the minimum variance $V_{\mathrm{min}}(\tilde{X})\approx0.799 \pm 0.068$ ($\sim\!1.0$ dB). b, Density matrices (blue bars) for the vacuum state at $\tau=0$ and two squeezed states at $\tau=100$ and 200 ns. The red bars represent the corresponding numerical simulations (see supplemental for details). Each density matrix is truncated at the magnon Fock state $|n\rangle$ with $n=6$ for clarity.
• Figure 3: Quadrature variance and mean magnon number of the magnon state.a, Quadrature variances $\tilde{X}(\theta)$ versus rotation angle $\theta$ for the evolution times $\tau=$ 150 and 250 ns. The light and dark blue circles (with 1 s.d. error bars) represent the variances that are extracted from the density matrices obtained from measured Wigner functions for $\tau=$ 150 and 250 ns, respectively. The corresponding light and dark blue solid curves show the numerical simulations. Dashed line is the ground state variance and the shaded region highlights quantum squeezing. b, Minimum and maximum quadrature variances versus evolution time $\tau$. Red circles (with 1 s.d. error bars) denote the measured minimum variance of the quadrature $\tilde{X}(\theta)$, and orange squares (with 1 s.d. error bars) represent the variance of its conjugate counterpart (the maximum quadrature variance). Solid curves show numerical simulations. Dashed line is the ground state variance and the shaded region highlights quantum squeezing. The largest squeezing of $\sim\!1.0$ dB appears at around 150 ns. Notably, the upper bounds of the error bars for the minimum variance (red circles) remain below 1.0. c, Mean magnon number $\langle n\rangle$ as a function of $\tau$. Filled circles (with 1 s.d. error bars) are experimental data, and the solid curve is the numerical simulation. The mean magnon number remains below one, a hallmark of extremely low excitations that is characteristic of magnon squeezing in the quantum regime.
• Figure 4: Decay and preservation of the squeezed magnon state.a, Experimentally measured Wigner functions of the squeezed state evolving at selected waiting times $\tau_{\rm w}$. Top row: In the absence of nonlinearity ($\delta=0$), the initial squeezed state (elliptical distribution) gradually decays to the vacuum state $\vert 0 \rangle$ (circular distribution). Bottom row: With a persistent nonlinearity ($\delta/2\pi=0.25$ MHz), the phase-space distribution remains distinctly non-circular for a much longer duration, visually confirming the prolonged squeezing quantified below. b, Squeezed state evolution. The left column shows the intrinsic decay when the Kerr nonlinearity is turned off ($\delta=0$), while the right column shows the evolution with a persistent nonlinearity ($\delta/2\pi=0.25$ MHz). Top row: Time evolution of the minimum ($V_{\rm min}$, red circles) and maximum ($V_{\rm max}$, orange squares) quadrature variances. Bottom row: Corresponding decay of the mean magnon number $\langle n\rangle$. Experimental data (points) are shown with 1 s.d. error bars. Dashed lines in the top panels indicate the ground state variance and the shaded regions highlight quantum squeezing. Solid curves in the top panels are numerical simulations, while those in the bottom panels are exponential fits, which consistently give rise to a magnon lifetime of $T_{1,m}\approx~$145 ns.