Modulation and protection of entanglement in a two-qubit system via two interacting oscillator control

Abstract

We investigate the control and protection of two-qubit entanglement through engineered interactions between two auxiliary harmonic oscillators. Each qubit is coupled to a local oscillator via a dephasing interaction, while the oscillators interact through independently tunable position-position and momentum-momentum couplings. Employing the characteristic-function representation, we obtain analytical solutions for the composite-system dynamics and examine how the stability properties of the coupled oscillators determine the evolution of two-qubit concurrence. Our analysis reveals distinct dynamical regimes exhibiting entanglement revivals, suppression, or decay, and identifies configurations in which oscillator interactions effectively reduce entanglement degradation. We further investigate the influence of thermal dissipation using local and global master-equation descriptions, demonstrating that suitable oscillator couplings can preserve substantial two-qubit entanglement under the dissipative conditions considered. These results establish a connection between the dynamical stability of auxiliary bosonic modes and the controllability of entanglement in discrete-variable quantum systems, providing a potential strategy for entanglement protection through engineered oscillator interactions.

The paper asks whether interactions between auxiliary bosonic modes can reduce dephasing-induced loss of two-qubit entanglement. It studies two qubits with local couplings $g_1\sigma_z^{(1)}x_a+g_2\sigma_z^{(2)}x_b$ to harmonic oscillators interacting through independently tunable terms $\alpha x_ax_b+\beta p_ap_b$. Characteristic-function methods give analytical dynamics, including local thermal Lindblad damping and damping in the oscillator normal-mode basis. For an initial $|\Psi^+\rangle$ Bell state, concurrence equals the magnitude of one coherence function. A stability-matrix analysis distinguishes oscillatory and unstable oscillator dynamics, associated with concurrence revivals or predominantly decaying coherence in the examples studied. The oscillator Hamiltonian is positive definite for $|\alpha|,|\beta|<\sqrt{\Omega}$, where $\Omega$ is the oscillator-frequency ratio; some oscillatory regimes outside this region have unbounded Hamiltonians. Concurrence revivals also witness trace-distance information backflow. Within the positive-energy region, resonant oscillators with $\alpha=\beta=\eta$ have frequencies $1\mp\eta$. For equal qubit couplings, the Bell coherence couples only to the antisymmetric mode. At $\eta=-0.99$, this mode has frequency $1.99$, reducing conditional displacements and preserving more concurrence than the uncoupled reference; $\eta=0.99$ instead softens it to $0.01$ and enhances dephasing. Dissipative examples use $g=0.1,0.5$, damping rates $0.1$, and temperature $5$. The global treatment neglects qubit-dependent dressing of dissipative operators and Lamb shifts. The paper cautions about weak-coupling and secular approximations near soft modes. Its uncoupled reference uses a different reservoir description, and robustness to coupling asymmetry and additional noise remains untested.