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arXiv:2303.08234 · The Journal of Chemical Physics

Dynamics of dissipative Landau–Zener transitions in an anisotropic three-level system

Lixing Zhang, Lu Wang, Maxim F. Gelin, Yang Zhao

Published May 25, 2023• 6 citations
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Abstract

We investigate the dynamics of Landau-Zener (LZ) transitions in an anisotropic, dissipative three-level LZ model (3-LZM) using the numerically accurate multiple Davydov D2Ansatz in the framework of the time-dependent variational principle. It is demonstrated that a non-monotonic relationship exists between the Landau-Zener transition probability and the phonon coupling strength when the 3-LZM is driven by a linear external field. Under the influence of a periodic driving field, phonon coupling may induce peaks in contour plots of the transition probability when the magnitude of the system anisotropy matches the phonon frequency. The 3-LZM coupled to a super-Ohmic phonon bath and driven by a periodic external field exhibits periodic population dynamics in which the period and amplitude of the oscillations decrease with the bath coupling strength.

DOI
10.1063/5.0150284

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We investigate the dynamics of Landau-Zener (LZ) transitions in an anisotropic, dissipative three-level LZ model (3-LZM) using the numerically accurate multiple Davydov D2Ansatz in the framework of the time-dependent variational principle. It is demonstrated that a non-monotonic relationship exists between the Landau-Zener transition probability and the phonon coupling strength when the 3-LZM is driven by a linear external field. Under the influence of a periodic driving field, phonon coupling may induce peaks in contour plots of the transition probability when the magnitude of the system anisotropy matches the phonon frequency. The 3-LZM coupled to a super-Ohmic phonon bath and driven by a periodic external field exhibits periodic population dynamics in which the period and amplitude of the oscillations decrease with the bath coupling strength.
Abstract Landau‐Zener (LZ) transitions in the three‐level bow‐tie model (3L‐BTM) in a dissipative environment are investigated by using the numerically accurate method of multiple Davydov Ansätze. The 3L‐BTM coupled to a single harmonic mode is first considered, and evolutions of transition probabilities for selected values of model parameters are studied and interpreted with the aid of the energy diagram method. Then the 3L‐BTM coupled to a boson bath of a continuum spectral density is explored. The simulations demonstrate that sub‐Ohmic, Ohmic and super‐Ohmic boson baths have substantially different influences on the 3L‐BTM dynamics, which cannot be grasped by the standard phenomenological Markovian single‐rate descriptions. Novel bath‐induced phenomena are also described, which are absent in two‐level LZ systems.
Effects of a periodic driving field on Landau–Zener (LZ) processes are studied using a nonlinear two-mode model that describes the mean-field dynamics of a many-body system. A variety of different dynamical phenomena in different parameter regimes of the driving field are discussed and analyzed. These include shifted, weakened, or enhanced phase dependence of nonlinear LZ (NLZ) processes, nonlinearity-enhanced population transfer in the adiabatic limit and Hamiltonian chaos on the mean-field level. The emphasis of this work is based on how the impact of a periodic driving field on LZ processes with self-interaction differs from those without self-interaction. Apart from gaining knowledge of driven NLZ processes, our findings can be used to gauge the strength of nonlinearity and for efficient manipulation of the mean-field dynamics of many-body systems.
A nonperturbative treatment, the Dirac-Frenkel time-dependent variation is employed to examine dynamics of the Landau-Zener model with both diagonal and off-diagonal qubit-bath coupling using the multiple Davydov trial states. It is shown that steady-state transition probabilities agree with analytical predictions at long times. Landau-Zener dynamics at intermediate times is little affected by diagonal coupling, and is found to be determined by off-diagonal coupling and tunneling between two diabatic states. We investigate effects of bath spectral densities, coupling strengths, and interaction angles on Laudau-Zener dynamics. Thanks to the multiple Davydov trial states, detailed boson dynamics can also be analyzed in Landau-Zener transitions. The results presented here may help provide guiding principles to manipulate the Laudau-Zener transitions in circuit QED architectures by tuning off-diagonal coupling and tunneling strength.
We study Landau-Zener-St\"uckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from an LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to ten energy levels.
We study Landau-Zener transitions in a fermionic dissipative environment where a two-level (up and down states) system is coupled to two metallic leads kept with different chemical potentials at zero temperature. The dynamics of the system is simulated by an iterative numerically exact influence functional path integral method. In the pure Landau-Zener problem, two kinds of transition (from up to down state and from down to up state) probability are symmetric. However, this symmetry is destroyed by coupling the system to the bath. In addition, in both kinds of transitions, there exists a nonmonotonic dependence of the transition probability on the sweep velocity; meanwhile nonmonotonic dependence of the transition probability on the system-bath coupling strength is only shown in one of them. As in the spin-boson model, these phenomena can be explained by a simple phenomenological model.
We consider the Landau-Zener problem for a multilevel quantum system that is coupled to an external environment. In particular, we consider a number of cases of three-level systems coupled to a harmonic oscillator that represents the external environment. We find that, similar to the case of the Landau-Zener problem with a two-level system, when the quantum system and the environment are both initially in their ground states the probability that the system remains in the same quantum state is not affected by the coupling to the environment. The final occupation probabilities of the other states are well described by a common general principle: the coupling to the environment turns each Landau-Zener transition process in the closed system into a sequence of smaller transitions in the combined Hilbert space of the system and environment, and this sequence of transitions lasts a total duration that increases with increasing system-environment coupling strength. These results provide an intuitive understanding of Landau-Zener transitions in open multilevel quantum systems.