Magnon squeezing near a quantum critical point in a cavity-magnon-qubit system

Abstract

Preparing magnon nonclassical states is a central topic in the study of quantum magnonics. Here we propose to generate magnon squeezed states in a hybrid cavity-magnon-qubit system by engineering an effective Rabi-type magnon-qubit interaction. This is achieved by adiabatically eliminating the cavity mode and driving the qubit with two microwave fields, of which the driving frequencies and amplitudes are properly selected. By operating the system around the critical point associated with the ground-state superradiant phase transition in the normal phase, a magnon parametric amplification-like interaction is induced, leading to a dynamical magnon squeezing. We further analyze the effects of the dissipation, dephasing, and thermal noise on the magnon squeezing. Our results indicate that a moderate degree of squeezing can be produced using currently available parameters in the experiments.

Figures (6)

• Figure 1: (a) Schematic of the cavity-magnon-qubit system. A microwave cavity mode simultaneously couples to a magnon mode of a YIG sphere via the magnetic dipole interaction and to a superconducting qubit via the electric dipole interaction. The YIG sphere is placed inside a bias magnetic field $B_0$, and the qubit is further driven by two microwave fields. An effective magnon-qubit interaction is mediated by the off-resonant cavity mode. (b) Mode and drive frequencies of the system. The cavity mode with frequency $\omega_c$ is detuned from both the magnon mode with frequency $\omega_M$ and the qubit with frequency $\omega_Q$. The elimination of the cavity mode leads to the effective frequencies of the magnon mode and the qubit, denoted as $\omega_m$ and $\omega_q$, respectively. See text for the details of two drive fields (with frequencies $\omega_1$ and $\omega_2$) applied to the qubit.
• Figure 2: (a) The minimum variance of the quadrature $V_{\rm min}(X_{\theta})$ and (b) the degree of squeezing $S$ (dB) as a function of time, which are obtained at an optimal squeezing angle at each time point. In panels (a) and (b), the black curves are the results obtained from the full Hamiltonian in Eq. \ref{['eq1']} including the two-tone driving, the blue thinner curves are obtained from Eq. \ref{['eq:jcprime']} after adiabatic elimination of the cavity in the large-detuning regime, and the red thinnest curves correspond to the Hamiltonian in Eq. (\ref{['eq:rabi']}) after the RWA. (c) The optimal squeezing angle $\theta_{\rm opt}$ and (d) the mean magnon number $\braket{m^\dag m}$ during the evolution, which are obtained using the master equation in Eq. \ref{['eq:me2']}. The parameters adopted are provided in the main text.
• Figure 3: The degree of squeezing $S$ (dB) as a function of time for (a) different dissipation rates of the magnon mode; and (b) different bath temperatures. We take $T = 10~\text{mK}$ in (a), and $\kappa/2\pi = 0.5~\text{MHz}$ in (b). The other parameters are the same as those in Fig. \ref{['fig:fig2']}.
• Figure 4: (a) The maximum degree of squeezing $S$ versus the magnon and qubit dissipation rates $\kappa$ and $\gamma$. Here, the maximum degree of squeezing is achieved by optimizing the squeezing angle and evolution time at each value of $\kappa$ and $\gamma$. (b) The Wigner function of the magnon mode corresponding to the maximum squeezing at an optimal time. The other parameters are the same as those in Fig. \ref{['fig:fig2']}.
• Figure 5: The effect of the relative phase between the two driving fields on the dynamics of the magnon squeezing. The gray area denotes $S \le 0$. The other parameters are the same as those in Fig. \ref{['fig:fig2']}.