Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics

TL;DR

The paper analyzes open quantum systems in the ultrastrong coupling regime where a finite-dimensional system $\mathcal{H}_{\rm S}$ interacts with a bosonic reservoir via $H = H_{\rm S} + H_{\rm R} + \lambda G\otimes\varphi(g)$. It proves that as $|\lambda|\to\infty$, the reduced system dynamics collapses to a nonselective measurement of the coupling operator $G$ followed by Zeno evolution under $H_{\rm Z}=\sum_l P_l H_{\rm S} P_l$, independently of reservoir details and for a broad class of Gaussian states. The results extend to multiple reservoirs, revealing a rich, generally non-Markovian dynamics and an entanglement-breaking effect when $G$ acts nontrivially on subsystems. The proofs combine a Dyson-series expansion with a careful resummation, leveraging Gaussian reservoir properties to show the off-diagonal terms vanish in the ultrastrong limit, and they handle unbounded cases via regularity assumptions. Overall, the work exposes a fundamental link between ultrastrong system–reservoir coupling, nonselective measurements, and quantum Zeno dynamics with broad implications for decoherence, control, and thermodynamics in open quantum systems.

Abstract

We study the dynamics of an open quantum system linearly coupled to a bosonic reservoir. We show that, in the ultrastrong coupling limit, the system undergoes a nonselective measurement and then evolves unitarily according to an effective Zeno Hamiltonian. This dynamical process is largely independent of the reservoir state. We examine the entanglement breaking effect of the ultrastrong coupling on the system. We also derive the evolution equation for systems in contact with several reservoirs when one coupling is ultrastrong. The effective system dynamics displays a rich structure and, contrarily to the single reservoir case, it is generally non-Markovian. Our approach is based on a Dyson series expansion, in which we can take the ultrastrong limit termwise, and a subsequent resummation of the series. Our derivation is mathematically rigorous and uncomplicated.

Figures (1)

• Figure 1: Different coupling regimes: From noninteracting to ultrastrong. Here, $\Delta$ represents a typical system Bohr frequency. Energy shifts in ${\rm S}$ due to the interaction with ${\rm R}$ are typically $\propto \lambda^2$. In all regimes one can consider static and dynamical properties of the system, except for the ultraweak coupling regime. That one is a purely dynamical regime in which time is coarse grained to the value $\tau=\lambda^2t$. In the current paper we focus on the ultrastrong coupling regime $\lambda\rightarrow\infty$. We show that it gives rise to a nonselective measurement of the system followed by a quantum Zeno dynamics.

Theorems & Definitions (5)

• Theorem 1
• Theorem 2
• Theorem 3
• Lemma 1
• Lemma 2