Engineering near-unitary one-axis twisting evolution via a driven Tavis-Cummings model

Abstract

One-axis twisting (OAT) interaction is a pivotal resource for manipulating quantum states of atomic ensembles, enabling spin squeezing, atomic-cat-state generation, and weak-phase amplification. Current implementations of OAT dynamics predominantly rely on the Tavis-Cummings model of light-atoms coupling; however, this approach inevitably introduces an additional Stark term that entangles the light with the atoms, which compromises the unitarity of OAT evolution and thereby degrades the OAT-based control precision. Here we propose a scheme based on a driven Tavis-Cummings model to achieve near-unitary OAT evolution. We demonstrate that both constant and time-varying driving of an atoms-cavity hybrid system can realize near-unitary OAT evolution, albeit with distinct coupling strength. Furthermore, when atomic dissipation is taken into account, we find that the time-varying-driving scheme exhibits superior resistance to decoherence. Our approach is broadly applicable to a variety of atomic platforms, including cold atoms, trapped ions, and nitrogen-vacancy centers.

Figures (4)

• Figure 1: (a) Schematic of the setup for realizing unitary OAT interaction. Atoms are confined in a cavity with linewidth $\kappa$, and the cavity mode $\hat{a}$ couples off-resonantly to each atom (with detuning $\Delta$), driving transitions from the ground state $\ket{\uparrow}$ to the excited state $\ket{\downarrow}$. The cavity system is driven by a classical control field $\Omega$. (b) The unitary OAT evolution generates a pure SSS for $\chi t \ll 1$ and a GHZ state at $\chi t = \pi/2$ (left column), whereas the nonunitary evolution results in mixed entangled states (right column). The Stark term induces dephasing of the OAT state, which broadens the spin uncertainty along the squeezed direction and results in the admixture of the ideal GHZ state with another orthogonal GHZ state (see main text).
• Figure 2: (a) Time evolution of the spin-squeezing parameter $\xi^2$ induced by the ideal OAT Hamiltonian (purple dotdashed line), the Hamiltonian of Eq. (\ref{['eq2']}) (red dashed line), and the Hamiltonian of Eq. (\ref{['eq16']}) for constant driving amplitudes $\Omega_0=16$ (blue solid line), $\Omega_0=32$ (orange solid line), and $\Omega_0=160$ (cyan solid line). (b) Time evolution of the fidelity of GHZ-state preparation induced by the Hamiltonian of Eq. (\ref{['eq2']}) (red dashed line) and the Hamiltonian of Eq. (\ref{['eq16']}) for constant driving amplitudes $\Omega_0=32$ (orange solid line) and $\Omega_0=160$ (cyan solid line). Plot of the Winger functions for the peak states I (c) and II (d) in (b). (e) Schematic of unitary OAT evolution under a constant drive. The initial CSS has its MSD aligned along the $z$-axis. The drive induces rapid Larmor precession of the MSD about the $x$-axis. Dephasing of the OAT state occurs when the MSD points along $+y$, and rephasing occurs when it points along $-y$. The net effect cancels the Stark term, leaving the system in a pure OAT evolution. Here we take $N=10$, and the bosonic mode is in a coherent state with $\alpha=1$, and $t$ is the unit of $1/\chi$ while $\Omega_0$ is in unit of $\chi$.
• Figure 3: (a) Time evolution of the spin-squeezing parameter $\xi^2$ induced by the ideal OAT Hamiltonian (purple dotdashed line), the Hamiltonian of Eq. (\ref{['eq2']}) (red dashed line), and the Hamiltonian of Eq. (\ref{['eq16']}) for time-varying driving $d=0.3$ (orange solid line), $0.01$ (cyan solid line). (b) Time evolution of the fidelity of GHZ-state preparation induced by time-varying driving with $d=0.2$ (orange solid line), $0.04$ (cyan solid line), $0$ (red dashed line). (c) The amplitude distribution of the driving field in the time domain. (d) Schematic of unitary OAT evolution under a time-varing drive. The initial CSS has its MSD aligned along the $x$-axis. The time-varying drive induces Larmor precession of the MSD about the $x$-axis. In the absence of the driving field, the OAT state undergoes dephasing. The narrow rectangular pulses instantaneously rotate the collective spin by an angle $\pi$ around the $x$-axis, after which rephasing begins. The net effect cancels the Stark term, leaving the system in a purely OAT-evolved state. Here we take $N=10$, $T_d=0.1$, and $\Omega_0=0$. The bosonic mode is in a coherent state with $\alpha=1$ and $t$ is in unit of $1/\chi$.
• Figure 4: The spin squeezing (a) and the GHZ-state fidelity (c) versus time $t$ in the presence of dissipations calculated from the master equations (\ref{['eq26']}) (green dotdashed line) and (\ref{['eq27']}) (blue solid line). The orange dashed line is also calculated from Eq. (\ref{['eq26']}), but with the coupling strength increased by a factor of two. The maximal achievable squeezing (b) and the fidelities (d) as a function of dissipation $\Gamma$. Here we take $N=10$ and $t$ is in unit of $1/\chi$ while $\Gamma$ is in unit of $\chi$.