Creating a tunable spin squeezing via a time-dependent collective atom-photon coupling

We present an experimentally feasible method to produce a large and tunable spin squeezing when an ensemble of many four-level atoms interacts simultaneously with a single-mode photon and classical driving lasers. Our approach is to simply introduce a time-dependent collective atom-photon coupling. We show that the maximal squeezing factor measured experimentally can be well controlled by both its driving magnitude and driving frequency. In particular, when increasing the driving magnitude, the maximal squeezing factor increases and thus can be rapidly enhanced. We also demonstrate explicitly in the high-frequency approximation that this spin squeezing arises from a strong repulsive spin-spin interaction induced by the time-dependent collective atom-photon coupling. Finally, we evaluate analytically, by using current experimental parameters, the maximal squeezing factor, which can reach 40 dB. This squeezing factor is far larger than previous ones.

Figure 1

(a) Proposed experimental setup. (b) The atom energy levels are driven simultaneously by a single-mode photon of the optical cavity and a pair of classical driving lasers.

Figure 2

Numerical plot of MSF ${\xi }_{\text{M}}^2$ of the undriven Dicke model (2) (black solid curve) and the time-dependent Hamiltonian (5) (red dashed curve) when $N=10$. Inset shows the MSF ${\xi }_{\text{M}}^2$ for $N=20$. In these figures, the other parameters are chosen as ${\Delta }_p={\omega }_0$ and $\omega =10{\omega }_0$.

Figure 3

Numerical plot of MSF ${\xi }_{\text{M}}^2$ of the time-dependent Hamiltonian (5) when $g_d=20{\omega }_0$ and $N=10$.

Figure 4

Numerical plot of MSF ${\xi }_{\text{M}}^2$ as a function of the driving magnitude $g_d$, when $\omega =20{\omega }_0$ and $N=10$. Inset shows MSF ${\xi }_{\text{M}}^2$ versus driving frequency $\omega$, when $g_d=20{\omega }_0$ and $N=10$. In these figures, the black solid curves denote the results of the time-dependent Hamiltonian (5) and the red open symbols correspond to the results of the effective time-independent Hamiltonian (22).

Figure 5

Quantum dynamics of $2\langle S_z\left(t\right)\rangle /N$ for the different spin-spin interaction strengths: $q/N=0.01{\omega }_0,q/N=0.1{\omega }_0$, and $q/N={\omega }_0$, when $N=100$.

Figure 6

The MSF ${\xi }_{\text{M}}^2$ as a function of the driving magnitude $g_d$, when $\omega =20{\omega }_0$ and $N=100$. Inset shows MSF ${\xi }_{\text{M}}^2$ versus the driving frequency $\omega$, when $g_d=20{\omega }_0$ and $N=10$. In these figures, the black solid curves denote the direct numerical calculation of the effective time-independent Hamiltonian (24), and the red open symbols correspond to the analytical results in Eq. (31).