Recently, strong coupling between non-Hermitian physical systems of different nature is widely investigated due to it endows them with new properties. In this work, we investigate the energy transport between strongly coupled systems. We use a partial-secular approach for the description of an open quantum system to investigate the system dynamics during the transition from a weak to a strong coupling regime with an increase of coupling between subsystems. On the example of strongly coupled two-level atoms, we show that near the transition point enhancement of energy transport between the system and reservoirs takes place. This manifests in the fact that energy flow normalized to the coupling constant reaches the maximum both in the cases of zero and non-zero frequency detuning. We show that maximization of normalized energy flow can be used for the determination of the transition to the strong coupling regime in the case of non-zero detuning when there is no clear transition point from the weak to strong coupling regime. The suppression of the energy flow at high relaxation is demonstrated.
Recently, strong coupling between non-Hermitian physical systems of different nature is widely investigated due to it endows them with new properties. In this work, we investigate the energy transport between strongly coupled systems. We use a partial-secular approach for the description of an open quantum system to investigate the system dynamics during the transition from a weak to a strong coupling regime with an increase of coupling between subsystems. On the example of strongly coupled two-level atoms, we show that near the transition point enhancement of energy transport between the system and reservoirs takes place. This manifests in the fact that energy flow normalized to the coupling constant reaches the maximum both in the cases of zero and non-zero frequency detuning. We show that maximization of normalized energy flow can be used for the determination of the transition to the strong coupling regime in the case of non-zero detuning when there is no clear transition point from the weak to strong coupling regime. The suppression of the energy flow at high relaxation is demonstrated.
In this letter, we demonstrate that in both classical and quantum open systems, the Hamiltonian interaction between subsystems, along with relaxations caused by the interaction with reservoirs, results in the appearance of effective non-Hermitian coupling. It is determined by a gradient of density of states of reservoirs. We show that for a power-law frequency dependence of the density of states, the non-Hermitian coupling is proportional to a product of the Hermitian coupling strength and the relaxation rates. As a result, this non-Hermitian coupling begins to play a crucial role with increasing Hermitian coupling strength between the subsystems and leads to a qualitative change in the behavior of non-Hermitian systems. Namely, when the Hermitian coupling strength exceeds a critical value, the non-Hermitian coupling becomes so large that it guarantees that the system is in the strong coupling regime at any relaxation rate. This critical coupling can be associated with the transition point to the ultra-strong coupling regime, which, until now, has not been defined exactly.
Strong coupling regime takes place in open hybrid systems consisting of two or more physical subsystems when the coupling strength between subsystems exceeds the relaxation rate. The relaxation arises due to the interaction of the system with environment. For this reason, it is usually believed that the enhancement of the interaction with environment inevitably leads to a transition of the system from the strong to weak coupling regime. In this paper, we refute this common opinion. We demonstrate the interaction of the coupled system with environment induces an additional coupling between the subsystems that contribute to retention the system in the strong coupling regime. We show that the environmental-induced coupling strength is proportional to the product of the Rabi coupling strength by the gradient of the density of states of the reservoir. There is a critical Rabi coupling strength above which the environmental-induced coupling ensures that the system remains in the strong coupling regime at any relaxation rate. In this case, the strong coupling regime takes place even when the relaxation rate is significantly above the Rabi coupling strength between the subsystems. The critical coupling depends on the gradient of the reservoir density of states. We demonstrate that managing this gradient can serve as an additional tool to control the properties of the coupled systems.
The rate of the trace distance is used to evaluate quantum speed-up for arbitrary mixed states. Compared with some present methods, the approach based on trace distance can provide an optimal bound to the speed of the evolution. The dynamical transition from no speed-up region to speed-up region takes on in the spontaneous decay of an two-level atom with detuning. The evolution is characteristic of the alternating behavior between quantum speed-up and speed-down in the strong system-reservoir coupling regime. Under the off-resonance condition, the dynamical evolution can be accelerated for short previous times and then decelerated to a normal process either in the weak or strong coupling regime. From the time-energy uncertainty relation, we demonstrate that the potential capacity for quantum speed-up evolution is closely related to the energy flow-back from the reservoir to the system. The negative decay rate for short time intervals leads to the speed-up process where the photons previously emitted by the atom are reabsorbed at a later time. The values of the spontaneous decay rate becomes positive after a long enough time, which results in the normal evolution with no speed-up potential.
Abstract Coupled systems subject to dissipation exhibit two different regimes known as weak coupling and strong coupling. Two damped coupled harmonic oscillators (CHOs) constitute a model system where the key features of weak and strong coupling can be identified. Several of these features are common to classical and quantum systems, as a number of quantum-classical correspondences have shown. However, the condition defining the boundary between weak and strong coupling is distinct in classical and quantum formalisms. Here we describe the origin of two widely used definitions of strong coupling. Using a classical CHO model, we show that energy exchange cycles and avoided resonance crossings signal the onset of strong coupling according to one criterion. From the classical CHO model we derive a non-Hermitian Hamiltonian describing open quantum systems. Based on the analytic properties of the Hamiltonian, we identify the boundary between weak and strong coupling with a different feature: a non-Hermitian degeneracy known as the exceptional point. For certain parameter ranges the classical and quantum criterion for strong coupling coincide; for other ranges they do not. Examples of systems in strong coupling according to one or another criterion, but not both, are illustrated. The framework here presented is suitable for introducing graduate or advanced undegraduate students to the basic properties of strongly coupled systems, as well as to the similarities and subtle differences between classical and quantum descriptions of coupled dissipative systems.
Almost all quantum systems are open; interactions with the surrounding \nenvironment generally lead to complex dissipative behaviour with a sensitive \ndependence on the details of the system-environment coupling. This \nthesis presents results from theoretical investigations into such behaviour \nin single and two-site quantum systems with a particular emphasis on \nstrong system-environment coupling regimes, and also the effects of spatial \ncorrelations in the environment fluctuations. \nWithin a weak system-environment coupling framework, it is found \nthat an increased level of correlation is able to protect coherence shared \nbetween two spatially separated two-level quantum systems. Moreover, \nit is found that these correlations are in fact able to generate coherence \nbetween the two systems, and in certain regimes, cause the systems to \nbecome entangled. \nUsing a polaron transform strong coupling master equation technique, \nthe discussion is extended to the strong system-environment coupling or \nhigh temperature regime. To assess the validity of this approach in an experimentally \nrelevant system, it is applied to the description of excitonic \nRabi oscillations in a resonantly driven quantum dot. For most of the \nparameters of interest, the strong coupling theory is found to be valid over \na far greater range of temperatures and coupling strengths than the standard \nweak-coupling theory. The coherent or incoherent nature of energy \ntransfer dynamics is then studied by applying the strong coupling theory \nto a donor-acceptor pair model. Increased spatial correlations are found \nto extend the range of temperatures which allow coherent energy transfer \nto take place. \nFinally, a variational theory is introduced which allows for exploration \nof certain parameter regimes where both the weak-coupling and strong coupling \ntheories become invalid. The variational theory is then used \nto investigate the ground state properties of a double two-level impurity \nmodel. High levels of spatial correlation are found to suppress the tunnelling \namplitude within each impurity.
The conventional time-dependent perturbation theory in quantum mechanics is established within the framework of Hermitian Hamiltonians, applicable for describing quantum transitions and associated energy level responses in such systems. However, this theory has fundamental limitations when applied to non-Hermitian systems. Consequently, researchers have systematically extended time-dependent perturbation theory to non-Hermitian systems, establishing a corresponding mature framework. Building on this foundation, this study extends the theory to investigate the transition dynamics induced by non-Hermitian interactions in non-Hermitian Hamiltonian systems. We employ a biorthogonal basis representation for a three-level non-Hermitian system. This work investigates a system comprising an unperturbed static non-Hermitian Hamiltonian and a periodically driven time-dependent perturbation Hamiltonian. Taking the three-level system as a concrete example, we combine analytical methods with numerical simulations to solve and analyze its dynamical evolution equations. These complementary approaches reveal that when system parameters complete a full cycle around an exceptional point, the transitional behavior exhibits specific evolutionary patterns. In this system, quantum transition probabilities exhibit significant asymmetry and non-conservation that depend on the initial and final states, revealing inherent directional characteristics in the dynamical process. Furthermore, for a three-level, periodically driven non-Hermitian system with time-dependent perturbations, this asymmetry is even more pronounced, manifesting as a distinct disparity between forward and reverse transition probabilities. The periodic driving actively amplifies the asymmetry in the transition process. By designing the perturbation spectrum, selective manipulation of specific quantum states can be achieved. Moreover, transition probabilities can be significantly enhanced under resonance conditions, while non-Hermiticity further breaks the system's inherent symmetry, leading to substantial amplification of transitions in a single direction. By precisely tuning the drive frequency, interactions between specific coupling channels can be selectively enhanced or suppressed. The amplification of channel asymmetry by non-Hermitian properties provides a novel mechanism for directional control of quantum states and opens new pathways for realizing related quantum technologies.