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arXiv:2411.01787 · Physica Scripta

Local boson-nonlocal boson coupling in a four-level system: adiabatic, non-adiabatic, and non-hermitian effects

Chen-Huan Wu

Published Nov 28, 2025• 1 citation
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Abstract

Abstract We investigate the dynamics of an open quantum system comprising a two-level electronic system coupled to local boson mode and a bosonic bath. The system is described by four distinct states, including the ground and excited electronic states, each with its corresponding zero- and one-boson vibrational levels. The dissipative dynamics arising from interactions with an external environment are modeled using two distinct theoretical frameworks: the standard Lindblad master equation and a non-Hermitian effective Hamiltonian approach. We derive the full Liouvillian superoperator for both formalisms, revealing a crucial distinction: while the Lindblad equation accounts for both state decay and repopulation via quantum jumps, the non-Hermitian formalism only captures the decay, leading to non-conservation of the total system probability.

DOI
10.1088/1402-4896/ae25a4

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Abstract We investigate the dynamics of an open quantum system comprising a two-level electronic system coupled to local boson mode and a bosonic bath. The system is described by four distinct states, including the ground and excited electronic states, each with its corresponding zero- and one-boson vibrational levels. The dissipative dynamics arising from interactions with an external environment are modeled using two distinct theoretical frameworks: the standard Lindblad master equation and a non-Hermitian effective Hamiltonian approach. We derive the full Liouvillian superoperator for both formalisms, revealing a crucial distinction: while the Lindblad equation accounts for both state decay and repopulation via quantum jumps, the non-Hermitian formalism only captures the decay, leading to non-conservation of the total system probability.
We theoretically investigate the state evolution and decoherence of Bell states in a two-qubit system coupled to local bosonic thermal baths. By employing a hybrid Liouvillian formalism with a tuning parameter , we systematically explore the transition from purely non-Hermitian coherent evolution ( ) to complete Lindblad master equation dynamics ( ) in a bosonic environment. Our results demonstrate that at , dynamically encircling a second-order exceptional point (EP) enables a near-perfect chiral transfer between the Bell states and . This phenomenon is shown to be globally robust against variations in the bosonic thermal occupation numbers of the environment. However, the introduction of quantum jump processes ( ) significantly suppresses the directional selectivity, and the chirality completely disappears in the full Liouvillian limit ( ). Furthermore, we find that the dissipative protocol is unable to generate entanglement starting from a maximally mixed state, highlighting the role of initial state purity. This work elucidates the interplay between non-Hermitian topology and bosonic decoherence, providing insights for state evolution in realistic open quantum systems.
We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on postselection, raising questions about their relevance for unconditional dynamics. Using a minimal two-qubit setup mediating a heat current, we compare local and global Markovian master equations with their non-Hermitian counterparts. We observe that exceptional points emerge only in the local master equation and in the corresponding non-Hermitian Hamiltonian at sufficiently strong nonequilibrium. We further consider hybrid configurations, where one bath is treated with a Lindblad description and the other with a non-Hermitian approach, interpolating between the two extremes. Our results contribute understanding the role of quantum jumps and exceptional points in nonequilibrium open quantum systems and identify a simple, experimentally accessible architecture, realizable, for instance, in circuit-QED platforms, for their exploration.
Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.
We develop the algebraic method based on the Lie algebra of quadratic combinations of left and right superoperators associated with matrices to study the Lindblad dynamics of multimode bosonic systems coupled a thermal bath and described by the Liouvillian superoperator that takes into account both dynamical (coherent) and environment mediated (incoherent) interactions between the modes. Our algebraic technique is applied to transform the Liouvillian into the diagonalized form by eliminating jump superoperators and solve the spectral problem. The temperature independent effective non-Hermitian Hamiltonian, H^eff\hat{H}_{eff}H^eff​, is found to govern both the diagonalized Liouvillian and the spectral properties. It is shown that the Liouvillian exceptional points are represented by the points in the parameter space where the matrix, HHH, associated with H^eff\hat{H}_{eff}H^eff​ is non-diagonalizable. We use our method to derive the low-temperature approximation for the superpropagator and to study the special case of a two mode system representing the photonic polarization modes. For this system, we describe the geometry of exceptional points in the space of frequency and relaxation vectors parameterizing the intermode couplings and, for a single-photon state, evaluate the time dependence of the speed of evolution as a function of the angles characterizing the couplings and the initial state.
We study the quantum dynamics of the opened three-level su(1, 1) bosonic model. The effective non-Hermitian Hamiltonians describing the system of the Lindblad equation in the short time limit are constructed. The obtained non-Hermitian Hamiltonians are exactly solvable by the Algebraic Bethe Ansatz. This approach allows representing biorthogonal and nonorthogonal bases of the system. We analyze the biorthogonal expectation values of a number of particles in the zero mode and represent it in the determinantal form. The time-dependent density matrix satisfying the Lindblad master equation is found in terms of the nonorthogonal basis.
One possible realization of non-Hermitian systems is based on open quantum systems by omitting quantum jumping terms in the master equation. This is a good approximation at short times where the effects of quantum jumps can be ignored. However, the jumps can affect the long-time dynamics of the system, motivating us to take the jumps into account in these studies. In this paper, by treating the quantum jumps as perturbations, we examine the effect of the quantum jumps on the non-Hermitian system. For this purpose, we first derive an effective Hamiltonian to describe the dynamics of the open quantum system based on the master equation, then expand the eigenstates and eigenenergies up to the first and second order in the quantum jumps. Finally, we apply our theory to a dissipative two-level system and dissipative fermionic superfluids. The effect of the quantum jump on the dynamics and the nonequilibrium phase transition is demonstrated and discussed.