Dynamics of the spin-boson model with a structured environment

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.Comment: 26 pages, 11 figures, Chemical Physics Special Issue on the Spin-Boson Problem, ed. by H. Grabert and A. Nitzan, in pres

Decoherence and relaxation of a qubit coupled to an Ohmic bath directly and via an intermediate harmonic oscillator

“…Recently, this model receives much interest in the context of quantum computing with condensed matter systems, especially with superconducting flux qubit devices, see Ref. [5] and within. It is also useful to investigate the measurement of the solid-state qubit [6] and magnetic resonance force microscopy [7,8].…”

Entanglement and disentanglement in circuit QED architectures

“…Simultaneously, the bath causes coherence decay and, for low temperature, a relaxation from the state |↑, 1 to |↑, 0 occurs. We emphasize here that there is no transition |↑, 0 → |↓, 0 since the qubit experiences an effective heat bath with a spectral density sharply peaked at the oscillator frequency Ω [26,27,28,29]. Thus, for large times t ≫ Ω/v, the spectral density at the qubit splitting vt vanishes and, consequently, the 3 qubit is effectively decoupled from the bath.…”

Finite-temperature decoherence of spin states in a {Cu3} single molecular magnet

“…According to the results of [35,36], the weak coupling approximation is applicable when the coupling strength g ≪ γ. The dynamics of the spin states can also be evaluated by the method introduced by [37].…”

“…For an example, a traditional Lorentzian spectral density function is used to describe the thermal bosonic environment such as the quantized electromagnetic field inside a cavity. The weak interactions between the system and thermal environment are given by the spectral density function which is J(ω ′ ) = To further elaborate the validity of the weak coupling approximation mentioned above, we can equivalently map the model into another one which is widely used in the solidstate systems [35][36][37]. This new dissipation model includes an effective two-level system like the single molecular magnet which is weakly coupled to the normal cavity mode with the frequency ω 0 and operator a.…”