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arXiv:2411.06817 · Quantum

Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics

Stefano Marcantoni, Marco Merkli

Published Mar 6, 2025• 3 citations
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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.

DOI
10.22331/q-2025-03-06-1656

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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.
We study the dynamics of a d-level quantum system coupled to a bosonic reservoir when the coupling constant is large. It is known that in the limit of infinite coupling strength, the system undergoes an instantaneous nonselective measurement, resulting in the immediate decoherence in the measurement basis, followed by a unitary Zeno dynamics. Here we resolve this dynamical process by introducing a fine grained scaling regime of short times proportional to the inverse coupling. We provide a rigorous derivation of the open system dynamics in this regime of ultrastrong coupling and demonstrate how decoherence unfolds continuously in the new time scale. We show that Markovian dynamics which are not given by semigroups arise naturally, in contrast to what happens in the weak coupling theory.
We consider a quantum system dynamics caused by successive selective and nonselective measurements of the probe coupled to the system. For the finite measurement rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$ and the system-probe interaction strength $\ensuremath{\gamma}$ we derive analytical evolution equations in the stroboscopic limit $\ensuremath{\tau}\ensuremath{\rightarrow}0$ and ${\ensuremath{\gamma}}^{2}\ensuremath{\tau}=\mathrm{const}$, which can be considered as a deviation from the Zeno subspace dynamics on a longer time scale $T\ensuremath{\sim}{({\ensuremath{\gamma}}^{2}\ensuremath{\tau})}^{\ensuremath{-}1}\ensuremath{\gg}{\ensuremath{\gamma}}^{\ensuremath{-}1}$. Nonlinear quantum dynamics is analyzed for selective stroboscopic projective measurements of an arbitrary rank. Nonselective measurements are shown to induce the semigroup dynamics of the system-probe aggregate. Both nonlinear and decoherent effects become significant at the time scale $T\ensuremath{\sim}{({\ensuremath{\gamma}}^{2}\ensuremath{\tau})}^{\ensuremath{-}1}$, which is illustrated by a number of examples.
We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system-environment coupling strength and, thus, the strength of the dissipation.
We examine the appearance of Zeno and anti-Zeno effects (Misra and Sudarshan 1977 J. Math. Phys. 18 756; Kofman and Kurizki 2000 Nature 405 546; Kofman and Kurizki 1996 Phys. Rev. A 54 3750; Facchi et al 2001 Phys. Rev. Lett. 86 2699) in the entanglement dynamics of two qubits off-resonantly coupled to the same lossy cavity when the unitary evolution of the system is interrupted by repeated projective measurements. We describe in detail these quantum effects by comparing the measurement-induced coarse-grained dynamics to the entanglement evolution in the absence of measurements in several scenarios (Francica et al 2009 Phys. Rev. A 79 032310). In particular, we examine the strong and weak coupling regimes, the role of the relative coupling strengths between the two qubits and the reservoir and the effect of the detuning from the main cavity frequency. We show that the anti-Zeno effect can occur in the entanglement dynamics when the qubit frequencies are detuned from the main reservoir frequency. Furthermore, we find that Zeno and anti-Zeno effects can even appear sequentially many times as a function of the interval between the measurements. Finally, we show that, in the off-resonant regime, we can preserve the entanglement using the quantum Zeno effect more efficiently than in the resonant limit (Maniscalco et al 2008 Phys. Rev. Lett. 100 090503), even if, in this case, no sub-radiant state exists.
We examine the critical system parameters which affect the quantum Zeno–anti-Zeno transition in a spin–boson system by applying the notion of correlated Zeno subspaces beyond the qubit system to its decayed part represented by a collective reservoir of oscillators. We also examine the effect of coherent control via a periodic sequence of dynamical decoupling pulses prior to projective measurement. Our results show that depending on the system bias and measurement time interval of the spin–boson model, coherent control via periodic dynamical decoupling pulses eliminates the Zeno–anti-Zeno transition behavior. We extend the calculations to examine the entanglement dynamics of two initially entangled qubits coupled to independent reservoirs with varying configuration and subjected to frequent measurements. In a multipartite system, in which one or more qubit–reservoir system can undergo the Zeno–anti-Zeno transition, we show that the effects of measurements made in a one qubit–reservoir subsystem can reverberate noticeably throughout a whole array of N pairs of qubit–reservoir subsystems.