Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a ${\ensuremath{\chi}}_{K}^{2}$ distribution where $K$ is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.
Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a \ensuremathχK2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.
The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular, and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. In this Letter, the first direct experimental verification of this effect, known as resonance trapping, is presented. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.
We investigate the decay dynamics of a three-level artificial atom, a superconducting transmon qubit, weakly coupled to a continuum of modes in a broadband, one-dimensional cavity. Using the resolvent formalism, we derive analytical expressions for the resonance frequency shifts and widths, which are then evaluated numerically for a Gaussian density of states. We identify two distinct dynamical regimes, differentiated by the ratio of the qubit's coupling strength to the continuum bandwidth. When this ratio is much less than one, the system exhibits a Markovian regime in which the resonance width is practically independent of energy within the continuum band. As the ratio increases, the system transitions to a non-Markovian regime where the resonance width becomes strongly energy-dependent. In this regime, the qubit interacts with the continuum faster than the continuum can erase the information from the qubit's past. Furthermore, we demonstrate that the coupling between the transmon's second level and its ground state significantly influences the decay dynamics of the third level. The interaction between these two levels opens a fast two-photon decay channel, which broadens the transmon's second level.
This is the second in a series of three papers on nonlinear resonance effects in multilevel quantum systems in which quantum-mechanical systems are considered that are under the influence of any number of classically described driving fields (well defined in amplitude and phase) and are in weak contact with a thermal reservoir, such that relaxation may be described by means of phenomenological decay constants. In the first paper, referred to as I, a projection-operator formalism was developed for separating the equation of motion for the density operator into a part which may be treated by conventional time-dependent perturbation techniques and another part which, because it would give rise to secular terms using a time-dependent perturbation theory, must be treated by more exact means. In this paper three applications of the formalism developed in I are considered. The first application is to a system in which a multiple-quantum transition is taking place between two levels of the system which contains many levels between the two levels under consideration. In particular, the transition probability is calculated for these two levels, which are not directly connected by matrix elements of the interaction but are connected indirectly through intermediate states. The next application considered is the Raman effect in a four-level system. As a final application of the formalism developed in I an expression is derived for the magnetization M+(t)=Mx(t)+iMy(t) of a system of N noninteracting spins under the influence of a static field in the z direction and an arbitrary number of rf fields in the x direction. As in I, a phenomenological form is assumed for the relaxation in all of these applications. It is shown in this problem that fields which are not involved in directly causing transitions in this system give rise to frequency shifts in the resonance conditions, which are accounted for in this treatment in a very natural and straightforward manner. For these fields, the rotating as well as the counter-rotating fields give shifts in the resonance condition.
The emission spectrum is found for transitions between a pair of atomic levels which are coupled by a coherent applied field, in the case in which decay to other levels of lower energy takes place during the emission process. The problem is solved by first finding the spectral distribution of radiation emitted by an atom which is initially prepared in some combination of the two coupled states, and which then decays to states of lower energy. (The solution found to this initial-value problem is valid even when many photons are emitted before the decay takes place.) It is then shown how the solution so obtained may be used to describe the case in which the atom is continually excited to the pair of levels in question by a weak, incoherent pumping mechanism. Limiting cases are discussed and compared with those which apply when no decay out of the two-dimensional subspace of coupled states takes place. The method of solution, which is based on an evaluation of the appropriate atomic correlation function by means of the quantum fluctuation-regression theorem, is compared to the method of simply adding imaginary terms, proportional to the decay constants, to the state energies. The latter method is of far more restricted validity, in that it depends on a particular strong inequality which must be assumed to hold between the decay constants.
In this thesis, we study the dynamics of open quantum systems in the overlapping resonances regime. An open quantum system consists of a small, finite-dimensional system S and a reservoir R, which interacts with the system S via some operator. The reservoir is, for example, modeled by a spatially infinitely extended free Bose gas in thermal equilibrium at positive temperature. One of the main tasks in the theory of open quantum system is to examine quantum phenomena observed in the small system, such as return to equilibrium and decoherence, brought about by the interaction with the environment. To deal with such a problem, one tries to study the dynamics of the total system S + R, which is generated by the total Hamiltonian. By tracing out the degrees of freedom of the reservoir, we obtain the dynamics of the small system. Over the last decade and a half, a perturbation theory based on quantum resonance methods has been developed in the isolated resonances regime. The perturbation theory developed so far permits a mathematically rigorous treatment of the dynamics for fixed, small system-reservoir coupling parameter λ. However, in complex quantum systems, e.g. when the dimension of small system is large, the problem belongs to the overlapping resonances regime. The theory mentioned above is not applicable in this regime. In this thesis, we adapt the perturbation theory for the treatment of such a regime. We first obtain a representation formula of the reduced dynamics involving resonances of an associated operator. By analyzing the behaviour of resonances, we derive the reduced density matrix of the small system. Furthermore, we consider the spin-boson model and analyze the transition from the isolated resonances regime to the overlapping one by using the Feshbach map. We also find a critical value, related to the parameters, which separates the two regimes, marking a sharp transition in the behaviour of the resonance energies.
We connect quantum compact graphs with infinite leads, and turn them into scattering systems.We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph.The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads.Finally, we analyze the statistical properties of the resonance widths and compare our results with the predictions of Random Matrix Theory.Deviations appearing due to the dynamical nature of the system are pointed out and explained.