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arXiv:1712.06058 · Physical Review A

Dynamics of dissipative Landau-Zener transitions

Zhongkai Huang, Yang Zhao

Published Jan 3, 2018• 39 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.013803

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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 study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.
Developed originally for the Holstein polaron, the Davydov D1 ansatz is an efficient, yet extremely accurate trial state for time-dependent variation of the spin-boson model [N. Wu, L. Duan, X. Li, and Y. Zhao, J. Chem. Phys. 138, 084111 (2013)]. In this work, the Dirac-Frenkel time-dependent variational procedure utilizing the Davydov D1 ansatz is implemented to study entanglement dynamics of two qubits under the influence of two independent baths. The Ohmic spectral density is used without the Born-Markov approximation or the rotating-wave approximation. In the strong coupling regime finite-time disentanglement is always found to exist, while at the intermediate coupling regime, the entanglement dynamics calculated by Davydov D1 ansatz displays oscillatory behavior in addition to entanglement disappearance and revival.
We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
The quantum dynamics of the Landau-Zener transition in a dissipative environment is studied and analytical results for the transition probability are given in terms of temperature, coupling strength, and the Landau-Zener time. For short Landau-Zener time there is no effect of dissipation. In the oppotise limit we distinguish various temperature regimes: The adiabatic limit is shown to be restricted to low temperatures and no effect of dissipation is present at zero temperature. At intermediate temperatures thermal transitions dominate for weak coupling and high temperatures correspond to the strong-coupling limit.
We investigate the influence of temperature and dissipation on the Landau–Zener transition probability in circuit QED. Dissipation is modelled by coupling the transmission line to a bath of harmonic oscillators, and the reduced density operator is treated within Bloch–Redfield theory. A phase-space representation allows an efficient numerical implementation of the resulting master equation. It provides reliable results which are valid even for rather low temperatures. We find that the spin-flip probability as a function of temperature and dissipation strength exhibits a non-monotonic behaviour. Our numerical results are complemented by analytical solutions for zero temperature and for vanishing dissipation strength.
Ansatz, we investigate Landau-Zener (LZ) transitions in a qubit coupled to a photon mode with various initial photon states at zero temperature. Thanks to the multiple Davydov trial states, exact photonic dynamics taking place in the course of the LZ transition is also studied efficiently. With the qubit driven by a linear external field and the photon mode initialized with Schrödinger-cat states, asymptotic behavior of the transition probability beyond the rotating-wave approximation is uncovered for a variety of initial states. Using a sinusoidal external driving field, we also explore the photon-assisted dynamics of Landau-Zener-Stückelberg-Majorana interferometry. Transition pathways involving multiple energy levels are unveiled by analyzing the photon dynamics.