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arXiv:2303.18159 · Journal of the Optical Society of America B

Self-consistent description of relaxation processes in systems with ultra- and deep-strong coupling

Timofey T. Sergeev, A. A. Zyablovsky, E. S. Andrianov, Yu. E. Lozovik

Published Sep 15, 2023• 0 citations
arXivHTMLPDF

Abstract

An ultra-strong coupling regime takes place in a compound system when a coupling strength between the subsystems exceeds one-tenth of the system eigenfrequency. It transforms into a deep-strong coupling regime when the coupling strength exceeds the system eigenfrequency. In these regimes, there are difficulties with the description of relaxation processes without explicit consideration of environmental degrees of freedom. To correctly evaluate the relaxation rates, it is necessary to consider the interaction of the system with its environment taking into account the counter-rotating wave and diamagnetic terms. We develop a self-consistent theory for the calculation of the relaxation rates in the systems, in which the coupling strength is of the order of the system eigenfrequency. We demonstrate that the increase in the coupling strength can lead to a significant decrease in the relaxation rates. In particular, we show that, for frequency-independent density of states of the environment, the relaxation rates decrease exponentially with the increase in the coupling strength. This fact can be used to suppress losses by tuning the strength coupling and the environment states.

DOI
10.1364/josab.501199

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An ultra-strong coupling regime takes place in a compound system when a coupling strength between the subsystems exceeds one-tenth of the system eigenfrequency. It transforms into a deep-strong coupling regime when the coupling strength exceeds the system eigenfrequency. In these regimes, there are difficulties with the description of relaxation processes without explicit consideration of environmental degrees of freedom. To correctly evaluate the relaxation rates, it is necessary to consider the interaction of the system with its environment taking into account the counter-rotating wave and diamagnetic terms. We develop a self-consistent theory for the calculation of the relaxation rates in the systems, in which the coupling strength is of the order of the system eigenfrequency. We demonstrate that the increase in the coupling strength can lead to a significant decrease in the relaxation rates. In particular, we show that, for frequency-independent density of states of the environment, the relaxation rates decrease exponentially with the increase in the coupling strength. This fact can be used to suppress losses by tuning the strength coupling and the environment states.
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.
Strong and ultra-strong coupling in "cavity - single atom" system are of great interest for both fundamental and applied physics. It is considered that the increase in the coupling strength between a cavity mode and an atom leads, first, to transition from weak to strong coupling and, second, to ultra-strong coupling regime. In this letter, we refute this common opinion and demonstrate that the transitions between the coupling regimes occur in different sequence for the correlations' functions of different orders. We show that for n-th order correlations' functions, the transition to the strong coupling regime requires the coupling strength approximately by n2/3n^{2/3}n2/3 times greater than the one for first order correlations' functions. In contrast, the transition to the ultra-strong coupling regime manifests in the dynamics of n-th order correlations' functions at the less coupling strength than in the dynamics of first order correlations' functions. As a result, there is the order of correlations' functions, above which the increase in the coupling strength leads, first, to the transition from the weak coupling first to the ultra-strong coupling regime, and second to the strong coupling regime. We argue that the measurement of high orders correlations' functions makes it possible to observe the ultra-strong coupling in "cavity mode - single atom" when the coupling strength is much less than one tenth of the oscillation frequency.
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.
The resonant response of a multilevel atomic system to strong coherent radiation is analyzed using an extension of the methods of time-independent scattering theory, adapted to the density-matrix formalism in order to include thermal bath effects. General steady-state expressions are derived for self-attenuation and resonance scattering rates in strong saturating fields, as functions of the coupling strengths, relaxation parameters, and frequency detunings. Formal expressions are given for radiative-damping and collision-broadening relaxation parameters, relating the latter to scattering amplitudes. Modifications of collision-broadening parameters by the presence of very strong fields are discussed. The Bloch equations are derived by transformation to the time domain, under specified conditions.
To date, studies of the quantum Zeno and anti-Zeno effects focus on quantum systems that are weakly interacting with their environment. In this paper, we investigate what happens to a quantum system under the action of repeated measurements if the quantum system is strongly interacting with its environment. We consider as the quantum system a single two-level system coupled strongly to a collection of harmonic oscillators. A so-called polaron transformation is then used to make the problem in the strong system-environment coupling regime tractable. We find that the strong coupling case exhibits quantitative and qualitative differences as compared with the weak coupling case. In particular, the effective decay rate does not depend linearly on the spectral density of the environment. This then means that, in the strong coupling regime that we investigate, increasing the system-environment coupling strength can actually decrease the effective decay rate. We also consider a collection of two-level atoms coupled strongly with a common environment. In this case, we find that there are further differences between the weak and strong coupling cases since the two-level atoms can now indirectly interact with one another due to the common environment.