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

Quantum effects of dissipative couplings to conjugate variables

Dominik Maile

Published Jan 1, 2021• 0 citations
OpenAlex

Abstract

For the realistic theoretical descriptions of quantum devices, we have to take the unavoidable coupling to their surrounding environment into account. A lot of effort in theoretical physics has been made to describe decoherence effects and the corresponding quantum to classical transition in the past. In these studies, baths are coupled to certain observables making their behavior more classical. In the most general case, a quantum device is affected by environments coupled to different observables. In this thesis, we study the differences emerging from coupling the bath to different observables. In particular, we investigate the situation, where two baths are coupled simultaneously to two conjugate variables (e.g. xˆ and pˆ, denoted dissipative frustration). We study how the interplay of these two baths can lead to interesting effects. After an introduction of the topic, we discuss the results of this thesis in Part II and Part III. In Part II, we study the effect of quantum tunneling in presence of a dissipative interaction with two Ohmic environments to the position xˆ and/or to the momentum pˆ of a particle. In chapter 2, we consider a symmetric double well potential which is important in the context of coherent state preparation, as its ground state is a superposition of being in the left and in the right well. Using the semiclassical approximation to calculate instanton paths within the path integral method, we find that momentum dissipation enhances the coherent tunnel splitting. In presence of dissipative couplings to xˆ and pˆ, the momentum dissipation acts in favor of the delocalization of the particle shifting the critical coupling strength of the dissipative phase transition induced by the position dissipation. Chapter 3 contains a study of the escape rate out of a metastable well in presence of dissipation. Here we find that the incoherent tunneling rate is exponentially enhanced in presence of momentum dissipation. We further show that the influence of momentum dissipation depends on the slope of the part of barrier the particle escaping through. In presence of both dissipative couplings, we find a non-monotonic behavior of the escape rate as a function of the dissipative couplings strengths. In Part III, we show that it is possible to realize the situation of "dissipative frustration" in Josephson junction chains. In particular, we introduce charge dissipation as a physical realization of the afore introduced momentum coupling. After presenting the circuit elements needed for charge dissipation, we study a chain of Josephson junctions affected by Ohmic baths coupled to the charge and/or the phase. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a non-monotonic behavior as a function of the dissipative coupling strength. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that dissipative frustration increases the range in which the phase transition is second order. The non-monotonic behavior is also reflected in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.

Related papers

Exponential speedup of incoherent tunneling via dissipation

D. Maile, Sabine Andergassen, Wolfgang Belzig +1 more

We study the escape rate of a particle in a metastable potential in the presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In particular, the influence of momentum dissipation depends on the slope of the barrier that the particle is tunneling through. We investigate also the influence of dissipative baths coupled to the position, and to the momentum of the particle, respectively. In this case the rate exhibits a nonmonotonic behavior as a function of the dissipative coupling strengths. Remarkably, even in the presence of position dissipation, momentum dissipation can enhance exponentially the escape rate in a large range of the parameter space. The influence of the momentum dissipation is also witnessed by the substantial increase of the average energy loss during inelastic (environment-assisted) tunneling.

arXiv:2102.02660•Physical Review Research•Jul 6, 2021•4 citations

Quantum phase transition with dissipative frustration

Dominik Maile, Sabine Andergassen, Wolfgang Belzig +1 more

We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two noncommuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The nonmonotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.

arXiv:1711.11346•Physical review. B./Physical review. B•Apr 23, 2018•23 citations

Quantum dynamics of the dissipative two-state system coupled with a sub-Ohmic bath

Zhiguo Lü, Hang Zheng

The decoherence of a two-state system coupled with a sub-Ohmic bath is investigated theoretically by means of the perturbation approach based on a unitary transformation. It is shown that the decoherence depends strongly and sensitively on the structure of environment. Nonadiabatic effect is treated through the introduction of a function ${\ensuremath{\xi}}_{k}$ which depends on the boson frequency and renormalized tunneling. The results are as follows: (i) the nonequilibrium correlation function $P(t)$, the dynamical susceptibility ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$, and the equilibrium correlation function $C(t)$ are analytically obtained for $s\ensuremath{\leqslant}1$; (ii) the phase diagram of thermodynamic transition shows the delocalized-localized transition point ${\ensuremath{\alpha}}_{l}$ which agrees with exact results and numerical data from the numerical renormalization group; (iii) the dynamical transition point ${\ensuremath{\alpha}}_{c}$ between coherent and incoherent phase is explicitly given. A crossover from the coherent oscillation to incoherent relaxation appears with increasing coupling (for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$, the coherent dynamics disappear); (iv) the Shiba's relation and sum rule are exactly satisfied when $\ensuremath{\alpha}\ensuremath{\leqslant}{\ensuremath{\alpha}}_{c}$; (v) an underdamping-overdamping transition point ${\ensuremath{\alpha}}_{c}^{*}$ exists in the function $S(\ensuremath{\omega})$. Consequently, the dynamical phase diagrams in both ohmic and sub-Ohmic case are mapped out. For $\ensuremath{\Delta}⪡{\ensuremath{\omega}}_{c}$, the critical couplings (${\ensuremath{\alpha}}_{l},{\ensuremath{\alpha}}_{c}$, and ${\ensuremath{\alpha}}_{c}^{*}$) are proportional to ${\ensuremath{\Delta}}^{1\ensuremath{-}s}$.

arXiv:quant-ph/0612042•Physical Review B•Feb 2, 2007•77 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

Dissipative Frustration in a One Dimensional Josephson Junction Chain

Dominik Maile, Sabine Andergassen, Wolfgang Belzig +1 more

We study the influence of dissipative frustration on the one dimensional Josephson junction chain. In particular we analyze the dissipative quantum phase transition between the chain being superconducting or insulating, the purity as a measure of quantum—environment correlation and the logarithmic negativity as an entanglement measure. The dissipative frustration is provided by coupling two non-commuting operators to the environment. A possible realization of these environmental couplings are shunt resistances between the superconducting islands and resistances to the ground. Using a self-consistent harmonic approximation we determine the critical line separating superconducting and insulating phases and find a nonmonotonic behavior as a function of the dissipative strength. The interplay between both environmental couplings is also reflected in the purity and the logarithmic negativity. We find a change in their behavior depending whether a second bath is present or not.

Italian Quantum Information Science Conference (IQIS)•Nov 19, 2019•0 citations

Effects of a dissipative coupling to the momentum of a particle in a double well potential

D. Maile, Sabine Andergassen, Gianluca Rastelli

This work shows that a dissipative coupling to the momentum of a particle in a double well potential increases its tunneling probability and therefore, opposite to dissipative couplings to the position, enhances quantum effects. In presence of both types of dissipation, the momentum dissipation shifts the critical coupling strength of the dissipative phase transition induced by the position dissipation.

arXiv:1911.13134•Physical Review Research•Feb 28, 2020•7 citations
For the realistic theoretical descriptions of quantum devices, we have to take the unavoidable coupling to their surrounding environment into account. A lot of effort in theoretical physics has been made to describe decoherence effects and the corresponding quantum to classical transition in the past. In these studies, baths are coupled to certain observables making their behavior more classical. In the most general case, a quantum device is affected by environments coupled to different observables. In this thesis, we study the differences emerging from coupling the bath to different observables. In particular, we investigate the situation, where two baths are coupled simultaneously to two conjugate variables (e.g. xˆ and pˆ, denoted dissipative frustration). We study how the interplay of these two baths can lead to interesting effects. After an introduction of the topic, we discuss the results of this thesis in Part II and Part III. In Part II, we study the effect of quantum tunneling in presence of a dissipative interaction with two Ohmic environments to the position xˆ and/or to the momentum pˆ of a particle. In chapter 2, we consider a symmetric double well potential which is important in the context of coherent state preparation, as its ground state is a superposition of being in the left and in the right well. Using the semiclassical approximation to calculate instanton paths within the path integral method, we find that momentum dissipation enhances the coherent tunnel splitting. In presence of dissipative couplings to xˆ and pˆ, the momentum dissipation acts in favor of the delocalization of the particle shifting the critical coupling strength of the dissipative phase transition induced by the position dissipation. Chapter 3 contains a study of the escape rate out of a metastable well in presence of dissipation. Here we find that the incoherent tunneling rate is exponentially enhanced in presence of momentum dissipation. We further show that the influence of momentum dissipation depends on the slope of the part of barrier the particle escaping through. In presence of both dissipative couplings, we find a non-monotonic behavior of the escape rate as a function of the dissipative couplings strengths. In Part III, we show that it is possible to realize the situation of "dissipative frustration" in Josephson junction chains. In particular, we introduce charge dissipation as a physical realization of the afore introduced momentum coupling. After presenting the circuit elements needed for charge dissipation, we study a chain of Josephson junctions affected by Ohmic baths coupled to the charge and/or the phase. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a non-monotonic behavior as a function of the dissipative coupling strength. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that dissipative frustration increases the range in which the phase transition is second order. The non-monotonic behavior is also reflected in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.
We study the escape rate of a particle in a metastable potential in the presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In particular, the influence of momentum dissipation depends on the slope of the barrier that the particle is tunneling through. We investigate also the influence of dissipative baths coupled to the position, and to the momentum of the particle, respectively. In this case the rate exhibits a nonmonotonic behavior as a function of the dissipative coupling strengths. Remarkably, even in the presence of position dissipation, momentum dissipation can enhance exponentially the escape rate in a large range of the parameter space. The influence of the momentum dissipation is also witnessed by the substantial increase of the average energy loss during inelastic (environment-assisted) tunneling.
We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two noncommuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The nonmonotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.
The decoherence of a two-state system coupled with a sub-Ohmic bath is investigated theoretically by means of the perturbation approach based on a unitary transformation. It is shown that the decoherence depends strongly and sensitively on the structure of environment. Nonadiabatic effect is treated through the introduction of a function ${\ensuremath{\xi}}_{k}$ which depends on the boson frequency and renormalized tunneling. The results are as follows: (i) the nonequilibrium correlation function P(t)P(t)P(t), the dynamical susceptibility ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$, and the equilibrium correlation function C(t)C(t)C(t) are analytically obtained for $s\ensuremath{\leqslant}1$; (ii) the phase diagram of thermodynamic transition shows the delocalized-localized transition point ${\ensuremath{\alpha}}_{l}$ which agrees with exact results and numerical data from the numerical renormalization group; (iii) the dynamical transition point ${\ensuremath{\alpha}}_{c}$ between coherent and incoherent phase is explicitly given. A crossover from the coherent oscillation to incoherent relaxation appears with increasing coupling (for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$, the coherent dynamics disappear); (iv) the Shiba's relation and sum rule are exactly satisfied when $\ensuremath{\alpha}\ensuremath{\leqslant}{\ensuremath{\alpha}}_{c}$; (v) an underdamping-overdamping transition point ${\ensuremath{\alpha}}_{c}^{*}$ exists in the function $S(\ensuremath{\omega})$. Consequently, the dynamical phase diagrams in both ohmic and sub-Ohmic case are mapped out. For $\ensuremath{\Delta}⪡{\ensuremath{\omega}}_{c}$, the critical couplings (${\ensuremath{\alpha}}_{l},{\ensuremath{\alpha}}_{c}$, and ${\ensuremath{\alpha}}_{c}^{*}$) are proportional to ${\ensuremath{\Delta}}^{1\ensuremath{-}s}$.
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.
We study the influence of dissipative frustration on the one dimensional Josephson junction chain. In particular we analyze the dissipative quantum phase transition between the chain being superconducting or insulating, the purity as a measure of quantum—environment correlation and the logarithmic negativity as an entanglement measure. The dissipative frustration is provided by coupling two non-commuting operators to the environment. A possible realization of these environmental couplings are shunt resistances between the superconducting islands and resistances to the ground. Using a self-consistent harmonic approximation we determine the critical line separating superconducting and insulating phases and find a nonmonotonic behavior as a function of the dissipative strength. The interplay between both environmental couplings is also reflected in the purity and the logarithmic negativity. We find a change in their behavior depending whether a second bath is present or not.