Entanglement in a driven two-qubit system coupled to common cavity

Abstract

A system, comprised of a qubit pair coupled to a common cavity, is studied with the aim of establishing qubit entanglement. This study is the sequel of the paper Phys. Rev. A 111, 043705 (2025), where similar model was investigated for an initially vacuum cavity. In the present manuscript the cavity with finite initial occupancy is considered and the effect of asymmetric qubit cavity couplings is investigated. For a closed system scenario, the ratio of the qubit-cavity couplings shows a threshold beyond which no maximally-entangled qubit state is available. The threshold value is shown to depend on the excitation level of the cavity. For a driven-dissipative case steady state entanglement is shown to depend non-monotonically on the qubit drive. Intricate interplay of drive, dissipation, and coupling asymmetry is shown to be pivotal for steady-state entanglement generation.

Figures (5)

• Figure 1: Entanglement is plotted against coupling asymmetry for various $N_{ph}$, when closed system is considered. (a) Peak entanglement is plotted against $g_2/g_1$ when $N_{ph}=0$ (solid), $1$ (dashed), $2$ (dotted). The vertical dotted lines from left to right mark the $(g_2/g_1)_{th}$ for $N_{ph}=0, 1, 2$, respectively. (b) $(g_2/g_1)_{th}$ is plotted against $N_{ph}$. (c) Entanglement dynamics for $g_2/g_1=1.0$ (solid), $0.8$ (dashed), and $0.6$ (dotted), when $N_{ph}=1.0$. (d) Entanglement dynamics for $N_{ph}=0$ (solid), $1.0$ (dashed), and $2.0$ (dotted), when $g_2/g_1=0.6$.
• Figure 2: Qubit dynamics is plotted for $N_{\rm ph}=1.0$, $g_1=g_2$, and decay constants $\kappa=g_1$ and $\gamma=0.005g_1$ when (a) there is no qubit drive applied and (b) second qubit is driven with the drive strength $d=0.01g_1$. Average values of $s^1_z$ and $s^2_z$ are plotted by solid and dashed lines, respectively. The insets show entanglement dynamics attaining steady-state values. For case (a) $\omega=50g_1$ and $\epsilon=10g_1$ and for case (b) $\omega_d=9.99g_1$. $\omega$ and $\epsilon$ values are same as in (a).
• Figure 3: Steady-state entanglement is plotted for $N_{ph}=1.0$, when open system is considered with $\kappa=g_1$ and $\gamma=.005g_1$. (a) $E_{ss}$ is plotted against drive strength when $g_2/g_1=1.0$ (+), $0.7$ (dashed), $0.5$ (solid), $0.4$ (dotted), $0.3$ (filled square), and $0.2$ (*). (b) $E_{ss}$ is plotted against $g_2/g_1$ for $d/g_1=.016$ (solid), $0.012$ (dotted), $0.01012$ (dashed), and $.006$ (open square).
• Figure 4: (a) The range of $g_2$ resulting $E_{ss}=0$ valley (as discussed in Fig. \ref{['fig2']} (b)) is plotted against $d/g_1$. Here $g_{2r}$ is the difference between maximum and minimum $g_2/g_1$ values producing $E_{ss}=0$. (b) The $g_{2p}=g_{2}/d_1$ values corresponding to the peak $E_{ss}$ (as shown in Fig. \ref{['fig2']} (b)) is plotted against $d/g_1$. Here $N_{ph}=1.0$, $\kappa=g_1$ and $\gamma=.005g_1$. The solid straight lines in both the figures present straight-line fitting for the data obtained in the specific regions.
• Figure 5: Steady-state values of entanglement ('+' markers) and cross correlation $C_{ss}/10$ ('x' markers) are plotted against coupling asymmetry for $N_{ph}=1.0$, when open system is considered with $\kappa=g_1$ and $\gamma=.005g_1$. (a) $d=0.01g_1$. (b) $d=.012g_1$.