Exact open dynamics of a generalized class of dephasing-type spin-boson models

TL;DR

This paper presents an exact solution for a generalized dephasing spin-boson model involving multiple qubits and bosonic modes, revealing tunable interactions and dephasing effects based on the system's multipartite structure.

Contribution

It introduces an exactly solvable generalized model that captures multipartite effects, including tunable effective interactions and dephasing rates dependent on coherence order.

Findings

Bosons mediate effective, tunable interactions among spins.

Dephasing rate depends exponentially on the coherence order.

The relative strength of Lamb-shift and dephasing can be controlled.

Abstract

We discuss a generalization of the dephasing-type spin-boson model in which N qubits are connected to K bosonic modes in an arbitrary way. The model can be solved exactly for any initial state and coupling type. We found that this leads to two important effects, which are specific of the multipartite nature of the problem. First, the bosons can mediate an effective interaction among the spins, which corresponds to a type of time-dependent Lamb-shift. By tuning the types of couplings, this interaction can also be varied at will. Second, the dephasing rate of the qubits is found to depend on the order of the coherence, with superpositions that have drastically different magnetizations being exponentially more affected. The relative strength of the Lamb-shift and dephasing can also be tuned by changing the spin-boson couplings.