Efficient and controlled symmetric and asymmetric Bell-state transfers in a dissipative Jaynes-Cummings model

TL;DR

This work addresses the problem of robust Bell-state transfer in dissipative non-Hermitian quantum systems. It employs a dissipative Jaynes-Cummings model and designs parameter loops that encircle an exceptional point (EP) to realize symmetric Bell-state exchange, and shows that asymmetric transfers can occur without a true EP by orbiting around an approximate EP (AEP) in both time-modulated and time-independent dissipation regimes. The approach suppresses nonadiabatic transitions to enable adiabatic, direction-independent symmetric transfer, while direction-controlled chiral transfers are achieved via topological features of the NH spectrum. The results offer a dissipation-engineering route to reliable entangled-state manipulation with potential extensions to GHZ and other multi-mode states.

Abstract

Realizing efficient and controlled state transfer is necessary for implementing a wide range of classical and quantum information protocols. Recent studies have demonstrated that both asymmetric and symmetric state transfer can be achieved by encircling an exceptional point (EP) in non-Hermitian (NH) systems. However, the application of this phenomenon has been restricted to scenarios where an EP exists in single-qubit systems and is associated with a specific type of dissipation. In this work, we demonstrate efficient and controlled symmetric and asymmetric Bell-state transfers by modulating system parameters within a Jaynes-Cummings model while accounting for atomic spontaneous emission and cavity decay. The effective suppression of nonadiabatic transitions enables a symmetric exchange of Bell states irrespective of the encircling direction. Furthermore, we report a counterintuitive finding: the presence of an EP is not indispensable for implementing asymmetric state transfers in NH systems. We achieve perfect asymmetric Bell-state transfers even in the absence of an EP, by dynamically orbiting around an approximate EP. Our work presents an approach to effectively and reliably manipulate entangled states with both symmetric and asymmetric characteristics, through the dissipation engineering in NH systems.

Figures (6)

• Figure 1: The eigenenergy spectrum $E_{\pm}(g,\gamma)$ and the system's time-evolution trajectory $E_{\pm}[g(t),\gamma(t)]$ for symmetric Bell-state transfer. (a) the imaginary part and (b) the real part of $E_{\pm}(g,\gamma)$ and $E_{\pm}[g(t),\gamma(t)]$. The blue (red) Riemann surface corresponds to $E_{+}(g,\gamma)$ [$E_{-}(g,\gamma)$], and the solid blue (dashed red) line represents $E_{+}[g(t),\gamma(t)]$ ($E_{-}[g(t),\gamma(t)])$, respectively. The pink point is an EP. The other parameters are chosen as $g_{0}=0.01,$$G_{0}=\Gamma_{0}=0.2,$$\alpha=-1$, and $\omega=\pi$.
• Figure 2: The time evolution of the fidelity $F_{m}=|\langle\widehat{{\phi_{m}}}(t)|\Psi(t)\rangle|^2$ for the time-depend right eigenstate $|\phi_{n}(t)\rangle$$(m=+,-)$. The initialized state in (a) and (c) [(b) and (d)] is chosen as $|\Psi(0)\rangle$=$|\phi_{+}(0)\rangle$ ($|\phi_{-}(0)\rangle$). The direction of trajectory in (a)-(b) is clockwise (CW) and in (c)-(d) is counterclockwise (CCW). The other parameters are chosen as $g_{0}$=0.01, $G_{0}$=$\Gamma_{0}$=0.2, and $\alpha$=-1. The state dynamics exhibits a purely adiabatic character, enabling one to implement a symmetric Bell-state switch.
• Figure 3: The eigenenergy spectrum $E_{\pm}(\gamma,\delta)$ and the system's time-evolution trajectory $E_{\pm}[\gamma(t),\delta(t)]$ for a asymmetric Bell-state transfer. The imaginary and real parts of the eigenenergy spectrum are depicted in panels (a) and (b) as three-dimensional surfaces, while in panels (c) and (d), they are presented as two-dimensional plots by fixing $\gamma \in (0, 0.001)$. The D line and L line represent the intersection lines of the surfaces corresponding to the imaginary and real parts of the eigenenergy spectrum $E_{\pm}(\gamma,\delta)$, respectively. The system's time-evolution trajectory is dynamically orbiting around an AEP, the black point $(0, 1 \times 10^{-4})$, in the parameter space $(\gamma,\delta)$. The other parameters are chosen as $g_{0}=0.1$, $\Delta_{0}=0.04$, $\Gamma_{0}=0.1$, and $\alpha=-1$, and $\omega=\pi$.
• Figure 4: The time evolution of the fidelity $F_{m}=|\langle\widehat{{\phi_{m}}}(t)|\Psi(t)\rangle|^2$ for the time-depend right eigenstate $|\phi_{m}(t)\rangle$$(m=+,-)$. The initialized state in (a) and (c) [(b) and (d)] is chosen as $|\Psi(0)\rangle$=$|\phi_{+}(0)\rangle$ ($|\phi_{-}(0)\rangle$). The selected trajectories in (a)-(b) exhibit a clockwise (CW) encircling, while those in (c)-(d) demonstrate a counterclockwise (CCW) encircling. Other parameters are set as follows: $g_{0}=0.1$, $\Delta_{0}=0.04$, $\Gamma_{0}=0.1$, and $\alpha=-1$. The state dynamics exhibits a chiral in nature, thus, enabling one to implement an asymmetric Bell-state switch.
• Figure 5: The eigenenergy spectrum $E_{\pm}(g,\delta)$ and the system's time-evolution trajectory $E_{\pm}[g(t),\delta(t)]$ for a dissipative system with time-independent dissipation. (a) the real part and (b) the imaginary part of $E_{\pm}(g,\gamma)$ and $E_{\pm}[g(t),\gamma(t)]$. The red (blue) Riemann surface corresponds to $E_{+}(g,\gamma)$ [$E_{-}(g,\gamma)$], and the solid red (dashed blue) line represents $E_{+}(g,\gamma)$ ($E_{-}(g,\gamma))$, respectively. The pink point is an AEP. Other parameters are set as follows: $g_{0}=G_{0}=\Delta_{0}=0.2$, $\gamma_{0}=0.1$, $\alpha=-1$, and $\omega=\pi$.