Persistent spin squeezing of a dissipative one-axis twisting model embedded in a general thermal environment

We investigate spin squeezing for a one-axis twisting (OAT) model coupled to a general non-Markovian environment in a finite-temperature regime. Using the non-Markovian quantum state diffusion and master equation approach, we numerically study non-Markovian spin-squeezing generation in the OAT model. Our results show that the total spin number $N$, energy $k_{B}T$, and certain coefficients in the OAT model can play a crucial role in generating spin squeezing. In particular, it shows that the maximum spin squeezing can be significantly enhanced when the participating environment has a relatively long memory time.

Figure 1

Time evolution of the coefficients $F_{ij}$ in the $O$ operator. The parameters are $a=1,b=-1,\mathrm{\Gamma }=0.01,\gamma =5,kT=10$, and $N=10$.

Figure 2

The time evolution of the spin-squeezing parameter ${\xi }^2$ with (a) different memory parameter $\gamma$ and (b) different spin number $N$. The parameters are (a) $\mathrm{\Gamma }=0.005,kT=100,N=10,a=1$, and $b=-1$ with different memory parameter $\gamma$ and (b) $\mathrm{\Gamma }=0.01,\gamma =0.1,kT=10,a=1$, and $b=-1$ with different spin number $N$. Solid blue line, $N=10$; dash-dotted orange line, $N=20$; dotted green line, $N=50$; and dashed purple line, $N=100$.

Figure 3

The time evolution of spin-squeezing parameter ${\xi }^2$ with the different damping rate $\mathrm{\Gamma }$ and with the different temperature $kT$. The parameters are $\gamma =0.01,a=1,b=-1$, and $N=20$.

Figure 4

The time evolution of spin-squeezing parameter ${\xi }^2$ with different ratio $a/b$ and different ratio $b/a$. The parameters are $\mathrm{\Gamma }=0.01,\gamma =2,kT=10$, and $N=20$.