Generation of squeezed states in coupled cavity chains via dissipation of gap-tunable qubits

A dissipative scheme is proposed to generate single- or two-mode squeezed states in a hybrid quantum system consisting of superconducting resonators and nitrogen-vacancy-center ensembles (NVEs). For the single-mode squeezing generation, we consider an array of linearly coupled superconducting resonators, each of which is magnetically coupled to a NVE. In addition, one of the resonators is coupled to a gap-tunable qubit. It is shown that at steady state all the resonators and NVEs in the array can enter into single-mode squeezed states via dissipation of the qubit. For the two-mode squeezing realization, we consider a pair of superconducting resonator chains, which are coupled to two gap-tunable qubits. We find that at steady state all the resonator pairs in the up and down chains will be steered into two-mode squeezed states via dissipation of the qubits. The present scheme has a remarkable feature: only one or two gap-tunable dissipative qubits are locally involved, and no squeezing resource is required.

Figure 1

(a) Schematic of the hybrid quantum circuit. Each resonator is magnetically coupled to a NVE. The resonators are capacitively coupled to each other, with the $j_0\text{th}$ one interacting with a driven superconducting qubit. (b) The energy-level configuration of a single NV center, where $|0\rangle =|m_s=0\rangle$ and $|1\rangle =|m_s=\pm 1\rangle$ is taken to be a two-level system. (c) The sideband transitions for the superconducting qubit.

Figure 2

(a) Squeezing $S_{a1}$ and $S_{a2}$ vs dimensionless time $\Gamma t$, with the parameters $\delta /2\pi =10$, $\omega /2\pi =3$, $g/2\pi =0.1$, $\Gamma /2\pi =0.02$, $J=0.01$ GHz, and ${\xi }_1=0.2$, ${\xi }_2=0.14$.

Figure 3

Squeezing $S_{b1}$ and $S_{b2}$ vs dimensionless time $\Gamma t$. In the present calculation, the following parameters are chosen: $\delta /2\pi =10$, $\omega /2\pi =3$, $g/2\pi =0.1$, $\Gamma /2\pi =0.02$, $J/2\pi =0.01$, $G/2\pi =0.01$ GHz, and ${\xi }_1=0.2$, ${\xi }_2=0.14$.

Figure 4

(a) Two arrays of capacitively coupled resonators in which the $j_0\text{th}$ and $N+j_0\text{th}$ resonators are interconnected by two superconducting qubits subject to two-color driving. (b) The engineering sideband couplings for the two superconducting qubits.

Figure 5

Variance $V_{13}$ and $V_{24}$ vs dimensionless time $\Gamma t$. The parameters in the present calculation are chosen to be $\delta /2\pi =10$, ${\omega }_1/2\pi =3$, ${\omega }_2/2\pi =6$, $g/2\pi =0.1$, $\Gamma /2\pi =0.02$, $J=0.01$ GHz, and ${\xi }_1^1={\xi }_2^2=0.2$, ${\xi }_2^1={\xi }_1^2=0.14$.