Dynamics of the spin-boson model with a structured environment

TL;DR

This paper studies the dynamics of a spin-boson model with a structured environment featuring a resonance, revealing new properties and analytical dephasing rates, with applications to superconducting qubits.

Contribution

It introduces a detailed analysis of the spin-boson model with a resonant spectral density and provides analytical dephasing rates at resonance, extending understanding beyond the standard Ohmic case.

Findings

Identification of new dynamical properties compared to the Ohmic model

Analytical calculation of dephasing rates at resonance

Application to superconducting flux qubits with dc-SQUID detectors

Abstract

We investigate the dynamics of the spin-boson model when the spectral density of the boson bath shows a resonance at a characteristic frequency $\Omega$ but behaves Ohmically at small frequencies. The time evolution of an initial state is determined by making use of the mapping onto a system composed of a quantum mechanical two-state system (TSS) which is coupled to a harmonic oscillator (HO) with frequency $\Omega$. The HO itself is coupled to an Ohmic environment. The dynamics is calculated by employing the numerically exact quasiadiabatic path-integral propagator technique. We find significant new properties compared to the Ohmic spin-boson model. By reducing the TSS-HO system in the dressed states picture to a three-level system for the special case at resonance, we calculate the dephasing rates for the TSS analytically. Finally, we apply our model to experimentally realized superconducting flux qubits coupled to an underdamped dc-SQUID detector.