Stabilizing correlated pair tunneling of spin-orbit-coupled bosons in a non-Hermitian driven double well

Abstract

We present an analytical framework for stabilizing second-order correlated tunneling of two spin-orbit-coupled bosons in a periodically driven non-Hermitian double-well potential. By combining Floquet theory with multiple-scale asymptotic analysis, we derive effective second-order dynamics and exact quasienergy spectra in the strongly interacting regime. Our analysis reveals distinct stability mechanisms for three fundamental tunneling channels: interwell spin-conserving, interwell spin-flipping, and intrawell spin-flipping. For balanced gain and loss, we identify discrete, well-defined parameter regions where stable pair tunneling emerges, with the spin-flipping channel exhibiting a characteristic symmetry absent in its spin-conserving counterpart. Under unbalanced gain-loss conditions, stability is achieved only when the gain and loss coefficients satisfy specific parametric relations, enabling dissipation-controlled tunneling. Most notably, stable intrawell spin-flipping, while inherently unstable for an initial Fock state, becomes accessible when the system is prepared in a coherent superposition state, thereby revealing that initial-state coherence can serve as a control parameter for dynamical stability in non-Hermitian systems. These results expand the possibilities for controlling correlated tunneling in many-body systems with engineered dissipation.

Figures (5)

• Figure 1: (a) Im($\zeta$) as a function of $2U_{1}/\omega$ and $2f/\omega$. (b) The time-averaged probabilities of the unpaired state $\bar{P_7}$ as a function of $2U_{1}/\omega$ for $2f/\omega=1.6$ (dash-dotted line) and $2f/\omega=5.57$ (solid line), respectively. (c)-(d) The time evolutions of the probabilities for (c) $2U_{1}/\omega=1.4, 2f/\omega=1.6$, and (d) $2U_{1}/\omega=1.1, 2f/\omega=1.6$. The initial state of the system is state $|0020\rangle$, and the other parameters are chosen as $\nu=\alpha=1$, $\delta=0$, $\omega=40$, $\Omega=40$, and $\beta_{1}=\beta_{2}=0.01$. Hereafter, circle points label the analytical results and solid curves denote the numerical correspondences. All parameters adopted in these figures are dimensionless.
• Figure 2: The time evolutions of the probabilities $P_k$ ($k=2,5,7$) and the total probability $P$ for different gain and loss coefficients. (a) $\beta_{1}=0.01$, $\beta_{2}=0.02$, $f=90.491$; (b) $\beta_{1}=0.005$, $\beta_{2}=0.015$, $f=78.28$. The initial state of the system is state $|0020\rangle$, and the other parameters are chosen as $\nu=\alpha=1$, $\delta=0$, $\omega=\Omega=40$, and $U_{1}=70$.
• Figure 3: (a) Im($\xi$) as a function of $2U_{1}/\omega$ and $2f/\omega$. (b)The time-averaged probabilities of the unpaired state $\bar{P_{9}}$ as a function of $2U_{1}/\omega$ for $2f/\omega=11.83$ (dash-dotted line) and $2f/\omega=15.37$ (solid line), respectively. (c)-(d) The time evolutions of probabilities for (c) $2U_{1}/\omega=1.4, 2f/\omega=11.83$, and (d) $2U_{1}/\omega=1.1, 2f/\omega=11.83$. The initial state of the system is state $|0020\rangle$, and the other parameters are chosen as $\nu=1$, $\alpha=0.5$, $\delta=0$, $\omega=40$, $\Omega=200$, and $\beta_{1}=\beta_{2}=0.01$.
• Figure 4: The time evolutions of the probabilities $P_{k}$ ($k=3,5,9$) and the total probability $P$ for different gain and loss coefficients. (a) $\beta_{1}=0.01$, $\beta_{2}=0.02$, $f=143.3$; (b) $\beta_{1}=0.005$, $\beta_{2}=0.015$, $f=118.28$. The initial state of the system is state $|0020\rangle$, and the other parameters are chosen as $\nu=1$, $\alpha=0.5$, $\delta=0$, $\omega=\Omega=40$, and $U_{1}=70$.
• Figure 5: The time evolutions of the probabilities $P_{k}$ and the total probability $P=\sum_{k} P_{k}$ ($k=1,2,...,6$). The initial state of the system is state $|\psi(0)\rangle=\frac{1}{\sqrt{2}}|0020\rangle+\frac{1}{\sqrt{2}}|2000\rangle$. The parameters are chosen as $\nu=\alpha=\delta=1$, $\omega=40$, $U_{1}=51.4586$, $U_{2}=24$, $f=110$, $\Omega=40$, $\beta_{1}=0$, and $\beta_{2}=0.1$.