Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

New Journal of Physics

Dynamics of dissipative coupled spins: decoherence, relaxation and effects of a spin-boson bath

Peter Nägele, Gabriele Campagnano, U Weiss

Published Nov 20, 2008• 16 citations
Publisher

Abstract

We study the reduced dynamics of interacting spins, each coupled to its own bath of bosons. We derive the solution in analytic form in the white-noise limit and analyze the rich behaviors in diverse limits ranging from weak coupling and/or low temperature to strong coupling and/or high temperature. We also view the single spin as being coupled to a spin-boson environment and consider the regimes in which it is effectively nonlinear and in which it can be regarded as a resonant bosonic environment.

DOI
10.1088/1367-2630/10/11/115010

Related papers

Dynamics of dissipative coupled spins: decoherence and relaxation

Peter Nägele, Gabriele Campagnano, Weiss, U.

We study the reduced dynamics of interacting spins, each coupled to its own bath of bosons. We derive the solution in analytic form in the white-noise limit and analyze the rich behaviors in diverse limits ranging from weak coupling and/or low temperature to strong coupling and/or high temperature. We also view the one spin as being coupled to a spin-boson environment and consider the regimes in which it is effectively nonlinear, and in which it can be regarded as a resonant bosonic environment.

arXiv:0807.2342•Jul 15, 2008•0 citations

Decoherence and relaxation of a pair of interacting spins coupled to independent environments

Peter Nägele

In this thesis, a scheme for calculating the dynamics of two coupled dissipative spins is developed, where each of the spins is coupled to its own boson bath. We derive analytic path sum results both in the Markov-regime and in the one-boson exchange regime. The analysis is also performed with the Bloch-Redfield method. It is shown that the two different approaches lead to identical results for the dynamics. This is not obvious a priori because both methods are based on different procedures. The path sum method gives detailed insight into the internal dynamics of two coupled spins because we consider every path sequence that contributes to the time evolution. While most studies of coupled spins are restricted to one type of coupling, e.g., Ising type, we will generalize here to linear combinations of possible couplings. Especially interesting is the occurrence of a frustration of decoherence, if the spins are interacting via a linear combination of longitudinal and transverse coupling and, when in addition, some of the eigenfrequencies become degenerate. Our analysis shows that degenerate but mutual exclusive ground states lead to increased coherence times. Maximization of coherence is one of the crucial goals of quantum state engineering. Another topic of interest is the impact of non-linear quantum environments, formed by surrounding dissipative spins. A distribution of bistable background charges is known to be responsible for $1/f$ noise in solid state devices, like the superconducting quantum interference devices. Since $1/f$ noise is seemingly the dominating source of decoherence at very low temperature, there is a profound theoretical interest in modeling it. Therefore, we analyze two interacting spins, where one of them is coupled to a boson bath and thereby represents a resonant non-linear quantum environment. We study the crossover from a non-linear to a linear bath and study the corresponding time scale for the relevant bath correlations. Interestingly, for large and increasing temperature we find a decreasing decoherence for the central spin.

•Jan 1, 2009•0 citations

Spin-boson model under dephasing: Markovian versus non-Markovian dynamics

Naushad Ahmad Kamar, Daniel A. Paz, Mohammad F. Maghrebi

The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.

arXiv:2305.00110•Physical review. B./Physical review. B•Aug 12, 2024•6 citations

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach

Marlon Brenes, Brett Min, Nicholas Anto-Sztrikacs +2 more

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

arXiv:2403.03386•The Journal of Chemical Physics•Jun 25, 2024•12 citations

Simple qubit systems in bosonic baths.

N. Pumulo

The study is focused on the thermal entanglement of spin chains. Chains consisting of two and three qubits are considered. These chains are considered open because they are coupled to bosonic baths at different temperatures. The baths represent the environment. The dynamics of these open systems are examined as are the effects of different parameters - such as bath temperature - on the entanglement of the spins. The measure of entanglement used in these cases is the concurrence. Comparisons are made between a model that assumes a strong spinspin interaction and one that assumes a weak one. In all these cases, analytical solutions for the system dynamics are presented. It is found that at large times, all systems converge to a state that depends only on bath temperature. It is also found that increases in bath temperatures diminish the entanglement between spins and that at high enough temperatures the entanglement vanishes altogether. The time and temperature dependence of the entanglement is different for the two models that are studied.

•Oct 3, 2013•1 citation

Dynamics, synchronization, and quantum phase transitions of two dissipative spins

Peter P. Orth, David Roosen, Walter Hofstetter +1 more

We analyze the static and dynamic properties of two Ising-coupled quantum spins embedded in a common bosonic bath as an archetype of dissipative quantum mechanics. First, we elucidate the ground-state phase diagram for an Ohmic and a sub-Ohmic bath using a combination of bosonic numerical renormalization group (NRG), analytical techniques, and intuitive arguments. Second, by employing the time-dependent NRG we investigate the system's rich dynamical behavior arising from the complex interplay between spin-spin and spin-bath interactions. Interestingly, spin oscillations can synchronize due to the proximity of the common non-Markovian bath and the system displays highly entangled steady states for certain nonequilibrium initial preparations. We complement our nonperturbative numerical results by exact analytical solutions when available and provide quantitative limits on the applicability of the perturbative Bloch-Redfield approach at weak coupling.

arXiv:1007.2857•Physical Review B•Oct 14, 2010•117 citations
We study the reduced dynamics of interacting spins, each coupled to its own bath of bosons. We derive the solution in analytic form in the white-noise limit and analyze the rich behaviors in diverse limits ranging from weak coupling and/or low temperature to strong coupling and/or high temperature. We also view the single spin as being coupled to a spin-boson environment and consider the regimes in which it is effectively nonlinear and in which it can be regarded as a resonant bosonic environment.
In this thesis, a scheme for calculating the dynamics of two coupled dissipative spins is developed, where each of the spins is coupled to its own boson bath. We derive analytic path sum results both in the Markov-regime and in the one-boson exchange regime. The analysis is also performed with the Bloch-Redfield method. It is shown that the two different approaches lead to identical results for the dynamics. This is not obvious a priori because both methods are based on different procedures. The path sum method gives detailed insight into the internal dynamics of two coupled spins because we consider every path sequence that contributes to the time evolution. While most studies of coupled spins are restricted to one type of coupling, e.g., Ising type, we will generalize here to linear combinations of possible couplings. Especially interesting is the occurrence of a frustration of decoherence, if the spins are interacting via a linear combination of longitudinal and transverse coupling and, when in addition, some of the eigenfrequencies become degenerate. Our analysis shows that degenerate but mutual exclusive ground states lead to increased coherence times. Maximization of coherence is one of the crucial goals of quantum state engineering. Another topic of interest is the impact of non-linear quantum environments, formed by surrounding dissipative spins. A distribution of bistable background charges is known to be responsible for 1/f1/f1/f noise in solid state devices, like the superconducting quantum interference devices. Since 1/f1/f1/f noise is seemingly the dominating source of decoherence at very low temperature, there is a profound theoretical interest in modeling it. Therefore, we analyze two interacting spins, where one of them is coupled to a boson bath and thereby represents a resonant non-linear quantum environment. We study the crossover from a non-linear to a linear bath and study the corresponding time scale for the relevant bath correlations. Interestingly, for large and increasing temperature we find a decreasing decoherence for the central spin.
The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.
Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.
The study is focused on the thermal entanglement of spin chains. Chains consisting of two and three qubits are considered. These chains are considered open because they are coupled to bosonic baths at different temperatures. The baths represent the environment. The dynamics of these open systems are examined as are the effects of different parameters - such as bath temperature - on the entanglement of the spins. The measure of entanglement used in these cases is the concurrence. Comparisons are made between a model that assumes a strong spinspin interaction and one that assumes a weak one. In all these cases, analytical solutions for the system dynamics are presented. It is found that at large times, all systems converge to a state that depends only on bath temperature. It is also found that increases in bath temperatures diminish the entanglement between spins and that at high enough temperatures the entanglement vanishes altogether. The time and temperature dependence of the entanglement is different for the two models that are studied.
We analyze the static and dynamic properties of two Ising-coupled quantum spins embedded in a common bosonic bath as an archetype of dissipative quantum mechanics. First, we elucidate the ground-state phase diagram for an Ohmic and a sub-Ohmic bath using a combination of bosonic numerical renormalization group (NRG), analytical techniques, and intuitive arguments. Second, by employing the time-dependent NRG we investigate the system's rich dynamical behavior arising from the complex interplay between spin-spin and spin-bath interactions. Interestingly, spin oscillations can synchronize due to the proximity of the common non-Markovian bath and the system displays highly entangled steady states for certain nonequilibrium initial preparations. We complement our nonperturbative numerical results by exact analytical solutions when available and provide quantitative limits on the applicability of the perturbative Bloch-Redfield approach at weak coupling.