Tunneling of bosonic qubits under local dephasing through microscopic approach

TL;DR

This work derives a microscopic, time-local master equation for two bosonic qubits tunneling between spatial modes under local dephasing baths with Lorentzian spectral densities, by starting from the full system-environment Hamiltonian and applying second-order Born approximation. The Lorentzian spectrum is $|g_X(\omega)|^2 = \frac{g_0}{\pi} \frac{\lambda}{(\omega-\omega_0)^2+\lambda^2}$, and the resulting dynamics are intrinsically non-Markovian, with a Kossakowski matrix eigenvalue $\gamma_-(t)$ always negative and a resonance condition $\omega_0 \approx J$ enabling noise-assisted stabilization of coherence and entanglement. Off-resonance, dephasing suppresses coherence as in standard models, while on-resonance, the system exchanges information with a single pseudomode, driving the steady state toward a correlated entangled state with high fidelity to a Bell state $|\Psi_+\rangle = \frac{1}{\sqrt{2}}(|L\uparrow,R\downarrow\rangle+|L\downarrow,R\uparrow\rangle)$. The approach reproduces short-time phenomenology, agrees with exact pseudomode simulations beyond weak coupling, and provides a microscopic basis for dephasing models in bosonic tunneling, with practical routes for experimental realization in photonic and ultracold-atom systems; extensions to finite temperature and common baths are discussed.

Abstract

We present a microscopic derivation of a master equation for two-component bosons (bosonic qubits) which tunnel between spatially separated modes under local dephasing noise. Starting from the full system-bath Hamiltonian with Lorentzian coupling distributions, we analytically obtain a time-local master equation whose structure reveals intrinsic non-Markovian features and recovers the standard phenomenological dephasing model in the short-time limit. Comparison with exact pseudomode simulations confirms its validity beyond weak-coupling and Markovian regimes. We identify a resonance condition between tunneling and bath frequencies for which dephasing drives the system towards correlated steady states, stabilizing coherence and entanglement instead of suppressing them. These results establish a rigorous microscopic foundation for dephasing models in bosonic tunneling systems and reveal a noise-induced mechanism for steady-state entanglement.

Figures (11)

• Figure 1: Illustration of the system. Two spatial regions $L$ and $R$ can exchange bosons via tunneling of amplitude $J$. Each region hosts a bosonic qubit (gray circle) with a given pseudospin (double-headed arrow) and is subject to local dephasing from its own bosonic bath.
• Figure 2: Off-resonance dynamics of coincidence probability for equal-pseudospin bosons, as a function of the deformation angle $Jt$, from numerical simulations using the full master equation (solid blue line), the phenomenological master equation (dotted green line), and the unitary pseudomode evolution (dashed red line). The inset displays a zoom of the main plot around the first minimum of the coincidence probability, also showing the noiseless evolution (dash-dotted orange line). Parameters: $J = 2.5$, $g_0=0.5$, $\lambda=1.8$, $\omega_0=0$, $\omega_s=1$, $\hbar = 1$.
• Figure 3: On-resonance evolution of first-order correlation function (a) and of entanglement negativity (b) for equal-pseudospin bosons from numerical simulations using the full master equation (solid blue line) and the unitary pseudomode evolution (dashed red line). At the steady state, the trace distance is $\mathcal{T}= 0.010981$. Parameters: $J = 2.5$, $g_0=0.5$, $\lambda=1.8$, $\omega_0=0$, $\omega_s=1$, $\hbar = 1$
• Figure 4: Off-resonance dynamics of entanglement, quantified by concurrence, for opposite-pseudospin bosons from numerical simulations using the full master equation (solid blue line), the phenomenological master equation (dotted green line), and the unitary pseudomode evolution (dashed red line). The inset displays the evolution of the off-diagonal element $\bra{L\,\uparrow,R\,\downarrow}\hat{\varrho}_S(t)\ket{R\,\uparrow,L\,\downarrow}$, where the noiseless case is also shown (dashed orange line). Parameters: $g_0=0.1$, $\lambda=0.5$, $J = \omega_0=2.5$, $\omega_s=1$, $\hbar = 1$.
• Figure 5: On-resonance dynamics of entanglement, quantified by concurrence, of the distilled state (a) and of fidelity to the Bell state $\ket{\Psi_+}$ (b) for opposite-pseudospin bosons from numerical simulations using the full master equation (solid blue line) and the unitary pseudomode evolution (red dashed line). At the steady state, the trace distance is $\mathcal{T}=0.013790$. Parameters: $g_0 = 0.1, \lambda=0.5, J= \omega_0 = 2.5, \omega_s = 1, \hbar = 1$.