Entanglement generation of arbitrary squeezed Fock states

Abstract

We propose an efficient and robust protocol for the generation of entanglement between a superconducting qubit and a squeezed cavity. By applying a parametric drive to the cavity coupled to the qubit, the dynamical evolution of the system is precisely described by an anisotropic Rabi model within a squeezed reference frame. Utilizing high-order time-averaging methods, we analytically derive the resonance conditions and the effective Rabi frequency for the high-order three-photon process. By implementing an adiabatic passage, slowly tuning the cavity frequency across the resonance, the system is steered into a maximally entangled state, e.g., between the three-photon state $\ket{g,3}$ and the qubit excited state $\ket{e,0}$ in the squeezed picture. Numerical simulation results confirm the high fidelity and robustness of the proposed protocol. Our method provides a practical pathway for generating complex non-Gaussian entangled states, which are of significant value for fault-tolerant quantum computation and quantum metrology beyond the standard quantum limit.

Figures (8)

• Figure 1: Comparison of the energy level splitting $\Delta E$ as a function of the interaction strength $g$ obtained from the analytical result (blue solid curve) and the numerical calculation (red dashed curve). The relevant parameters are $r = 0.9$, $\omega_c=\omega_c'$, and $\omega_q = 1$.
• Figure 2: Schematic diagram illustrating the transition processes between the bare states $|e,0\rangle$ and $|g,3\rangle$ in squeezed picture. The excitation-number non-conserving processes are represented by blue dashed arrows, with $\lambda_2$, $\sqrt{2}\lambda_1$, and $\sqrt{3}\lambda_2$ denoting the corresponding transition matrix elements.
• Figure 3: Time evolution of the probabilities $|\langle e,0 | \hat{S}^{\dagger}(r)\varphi(t) \rangle|^2$ (blue line) and $|\langle g,3 |\hat{S}^{\dagger}(r) \varphi(t) \rangle|^2$ (red line), obtained from the numerical simulation of the dynamics governed by the Hamiltonian $H_{Ra}$ in Eq. $(\ref{['eq5']})$. The highest probability of $\hat{S}(r)|g,3\rangle$ is $99.63\%$. The parameters are $r = 0.9$, $g = 0.01$, $\omega_c=\omega_c'$, and $\omega_q = 1$.
• Figure 4: Oscillation period $t_f$ of the isotropic Rabi model (red line) and the anisotropic Rabi model (blue line) as a function of the squeezing parameter $r$. The fundamental coupling parameter is $g = 0.01\omega_q$, $\omega_c=\omega_c'$, and $\omega_q = 1$. For ease of observation, the range of $r$ is set to $[0.4, 2]$.
• Figure 5: Fidelity of the three-photon state $|g,3\rangle$ as a function of parameter $r$, with $g = 0.01\omega_q$, $\omega_c=\omega_c'$, and $\omega_q = 1$.