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arXiv:2309.01580 · Advanced Quantum Technologies

Dissipative Landau‐Zener Transitions in a Three‐Level Bow‐Tie Model: Accurate Dynamics with the Davydov Multi‐D 2 Ansatz

Lixing Zhang, Maxim F. Gelin, Yang Zhao

Published Jan 12, 2024• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/qute.202300285

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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 consider an adiabatic Landau-Zener model of two-level system diagonally coupled to an Ohmic bosonic bath of large spectral width and derive through fermionization its exact solution at a special value of the coupling constant. From this solution we obtain the characteristic function of the distribution of energy transferred to the bath during the evolution of the system ground state as a functional determinant of a single particle operator. At zero temperature this distribution is further found to be exponential and at finite temperature the first three moments of the distribution are calculated.
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Abstract We investigate the quantum dynamics of a multilevel bistable system coupled to a bosonic heat bath beyond the perturbative regime. We consider different spectral densities of the bath, in the transition from sub-Ohmic to super-Ohmic dissipation, and different cutoff frequencies. The study is carried out by using the real-time path integral approach of the Feynman–Vernon influence functional. We find that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the short time behavior and the time scales of the relaxation starting from a nonequilibrium initial condition depend nontrivially on the spectral properties of the heat bath.