The spin-boson model with a structured environment: a comparison of approaches

Abstract

In the spin boson model, the properties of the oscillator bath are fully characterized by the spectral density of oscillators J(ω). We study the case when this function is of Breit-Wigner shape and has a sharp peak at a frequency Ω with width Γ ≪ Ω. We use a number of approaches such as the weak-coupling Bloch-Redfield equation, the non-interacting blip approximation (NIBA) and the flow-equation renormalization scheme. We show, that if Ω is much larger than the qubit energy scales, the dynamics corresponds to an Ohmic spin boson model with a strongly reduced tunnel splitting. We also show that the direction of the scaling of the tunnel splitting changes sign when the bare splitting crosses Ω. We find good agreement between our analytical approximations and numerical results. We illuminate how and why different approaches to the model account for these features and discuss the interpretation of this model in the context of an application to quantum computation and read-out.

Coherent exciton dynamics in a dissipative environment maintained by an off-resonant vibrational mode

“…The form in Eq. (7) is that of a modified spin-boson Hamiltonian; the spin-boson model is one of the most utilized and investigated descriptions of open quantum system behavior [43][44][45][46][47][48]. While not exactly solvable (except in special cases) it contains information about the interplay between a two-level "spin" system and a harmonic bath.…”

Entanglement Spectroscopy of a Driven Solid-State Qubit and Its Detector

“…Until now, the effects of such a structured spectral density on decoherence and in presence of a resonant control field have only been studied in [8,9] within a perturbative approach in J eff . It was shown in [10,11] for the static case that a perturbative approach breaks down for strong qubit-detector coupling, and when the qubit and detector frequencies are comparable.In the presence of microwaves, multi-photon resonances are expected to occur when the frequency of the ac-field, or integer multiples of it, match characteristic energy scales of the system [12]. Such multiphoton resonances can be experimentally detected in an ac-driven flux qubit by measuring the asymptotic occupation probabilities of the qubit, as the dc-field is varied [3,13].…”

“…Until now, the effects of such a structured spectral density on decoherence and in presence of a resonant control field have only been studied in [8,9] within a perturbative approach in J eff . It was shown in [10,11] for the static case that a perturbative approach breaks down for strong qubit-detector coupling, and when the qubit and detector frequencies are comparable.…”

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.…”