Dissipative dynamics of a driven qubit: Interplay between nonadiabatic dynamics and noise effects from the weak to strong coupling regime

Abstract

We study the exact solution of the Schrödinger equation for the dissipative dynamics of a qubit, achieved by means of Short Iterative Lanczos method (SIL), which allows us to describe the qubit and the bath dynamics from weak to strong coupling regimes. We focus on two different models of a qubit in contact with the external environment: the first is the Spin Boson Model (SBM), which gives a description of the qubit in terms of static tunnelling energy and a bias field. The second model describes an externally driven qubit, where both the bias field and the tunnelling rate are controlled by a time-dependent magnetic field obeying to a finite time protocol. We show that in the SBM case, our solution correctly describes the crossover from coherent to incoherent behavior of the magnetization, occurring at the Toulouse point. Furthermore, we show that the bath response dramatically changes during the system dynamics, going from non-resonant at small times to resonant behavior at long times. When the external driving field is present, for fixed values of the drive duration our results show that the bath can provide beneficial effects to the success of the protocol. We find evidence for a complex interplay between non-adiabaticity of the protocol due to the external drive and dissipation effects, which strongly depends on the detailed form of the qubit-bath interaction.

Variational approach to time-dependent fluorescence of a driven qubit

“…To quantify how faithfully the variational results follow the Schrödinger equation, we calculate the deviation defined in Eq. (32), which is fully determined by the inner product of the deviation vector and can be derived straightforwardly as follows:…”

“…Numerical simulation of fluorescence spectra based on a bosonic observable has been carried out by means of the time-dependent density matrix renormalization group, exploring the suppression of spectral diffusion with optical pulses [29]. More recently, the reservoir information in open quantum systems has been studied by the dynamical polaron ansatz [30], the stochastic c-number Langevin equation [31], and the short iterative Lanczos method [32]. However, so far there is no direct evaluation of fluorescence spectrum from the bosonic degrees of freedom in the strong coupling regime.…”

Exactly solvable model of calorimetric measurements

“…The average value of the energy of the resonant level E 0 (t ) is given by Eq. (9) in which ρ 00 (t ) has the form (29). Substituting expression (30) in Eq.…”

“…This method ensures quick convergence to the exact result if one increases the number of reaction coordinates [26,27]. The exact strongcoupling dynamics of the energy exchange between a driven two-level system and its environment has been studied within the spin-boson model [28,29]. It was found that the strong coupling manifests itself in the significant role of the interaction energy in the overall energy balance [28,30] and in the nonexponential time relaxation of the energies.…”

Nonadiabatic evolution and thermodynamics of a time-dependent open quantum system

“…Slowly driven and periodically driven systems are the two cases studied most, and formalisms based on the adiabatic master equation [15,16] and Floquet's theory [17][18][19][20] have been widely employed. Moreover, various numerical methods have been proposed for this issue, such as quasiadiabatic propagator path integral (QUAPI) [21], influence functional formalism [22], short-iterative Lanczos method [23], hierarchical equations of motion [24], quantum trajectories [25], and variational method [26,27].…”