Nonadiabatic Dynamics of a Dissipative Two-level System

Abstract

We study the dynamics of a two-level system described by a slowly varying Hamiltonian and weakly coupled to the Ohmic environment. We follow the Bloch--Redfield perturbative approach to include the effect of the environment on qubit evolution and take into account modification of the spectrum and matrix elements of qubit transitions due to time-dependence of the Hamiltonian. This formalism is applied to two problems. (1) We consider a qubit, or a spin-1/2, in a rotating magnetic field. We show that once the rotation starts, the spin has a component perpendicular to the rotation plane of the field that initially wiggles and eventually settles to the value proportional to the product of angular rotation velocity of the field and the Berry curvature. (2) We re-examine the Landau--Zener transition for a system coupled to environment at arbitrary temperature. We show that as temperature increases, the thermal excitation and relaxation become leading processes responsible for transition between states of the system. We also apply the Lindblad master equations to these two problems and compare results with those obtained from the Bloch--Redfield equations.

18 pages, 15 figures submitted to PRA

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Cited by in corpus (27)

• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Geometry and non-adiabatic response in quantum and classical systems
• Observation of topological transitions in interacting quantum circuits
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Measuring a topological transition in an artificial spin 1/2 system
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Topological Andreev bands in three-terminal Josephson junctions
• Driven dissipative dynamics and topology of quantum impurity systems
• Landau-Zener transitions in a two-level system coupled to a finite-temperature harmonic oscillator
• Finite-time Landau-Zener processes and counter-diabatic driving in open systems: beyond Born, Markov and Rotating-wave approximations
• Landau-Zener transitions in an open multilevel quantum system
• Steering random spin systems to speed up the quantum adiabatic algorithm
• Landau-Zener transition in a two-level system coupled to a single highly-excited oscillator
• Topology of a dissipative spin: dynamical Chern number, bath induced non-adiabaticity and a quantum dynamo effect
• Suppression of the Landau-Zener transition probability by a weak classical noise
• Floquet topological phases coupled to environments and the induced photocurrent
• Effects of charge noise on a pulse-gated singlet-triplet $S-T_{-}$ qubit
• Assessment of weak-coupling approximations on a driven two-level system under dissipation
• Control of spectroscopic features of multiphoton transitions in two coupled qubits by driving fields
• Signal amplification in a qubit-resonator system
• Dissipative dynamics of a driven qubit: interplay between non-adiabatic dynamics and noise effects from weak to strong coupling regime
• Investigation of robust population transfer using quadratically chirped laser interacting with two-level system
• Phonon-induced decoherence of a charge quadrupole qubit
• On Landau-Zener transitions for dephasing Lindbladians
• Spin flip locking by the tunneling and relaxation in a driven double quantum dot with spin-orbit coupling
• Dynamical phase and quantum heat at fractional frequencies