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

arXiv:1608.04163 · Physical Review A

Deriving Lindblad master equations with Keldysh diagrams: Correlated gain and loss in higher order perturbation theory

Clemens Müller, Thomas M. Stace

Published Jan 27, 2017• 51 citations
arXivHTMLPDF

Abstract

Motivated by correlated decay processes producing gain, loss, and lasing in driven semiconductor quantum dots [Phys. Rev. Lett. 113, 036801 (2014); Science 347, 285 (2015); Phys. Rev. Lett. 114, 196802 (2015)], we develop a theoretical technique by using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second-order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behavior at the same order of perturbation theory. We then apply these results to analyze the phonon-assisted steady-state gain of a microwave field driving a double quantum dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing-assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.

DOI
10.1103/physreva.95.013847

Related papers

Synthesising Keldysh and Lindblad - Correlated decay processes in higher order perturbation theory

Clemens Müller, Thomas M. Stace

Motivated by correlated decay processes driving gain, loss and lasing in driven semiconductor quantum-dots, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms terms contribute to the system behaviour at the same order of perturbation theory, and make substantial contributions to the behaviour of the system.

•Aug 15, 2016•0 citations

Lindblad theory of dynamical decoherence of quantum-dot excitons

P. R. Eastham, A. O. Spracklen, Jonathan Keeling

We use the Bloch-Redfield-Wangsness theory to calculate the effects of acoustic phonons in coherent control experiments where quantum-dot excitons are driven by shaped laser pulses. This theory yields a generalized Lindblad equation for the density operator of the dot, with time-dependent damping and decoherence due to phonon transitions between the instantaneous dressed states. It captures similar physics to the form recently applied to Rabi oscillation experiments [Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)] but guarantees positivity of the density operator. At sufficiently low temperatures, it gives results equivalent to those of fully non-Markovian approaches [L\"uker et al., Phys. Rev. B 85, 121302 (2012)] but is significantly simpler to simulate. Several applications of this theory are discussed. We apply it to adiabatic rapid passage experiments and show how the pulses can be shaped to maximize the probability of creating a single exciton using a frequency-swept laser pulse. We also use this theory to propose and analyze methods to determine the phonon density of states experimentally, i.e., phonon spectroscopy, by exploring the dependence of the effective damping rates on the driving field.

arXiv:1208.5001•Physical Review B•May 15, 2013•41 citations

Kadanoff-Baym Equations for Interacting Systems with Dissipative Lindbladian Dynamics

Gianluca Stefanucci

The extraordinary quantum properties of nonequilibrium systems governed by dissipative dynamics have become a focal point in contemporary scientific inquiry. The nonequilibrium Green's functions (NEGF) theory provides a versatile method for addressing driven nondissipative systems, utilizing the powerful diagrammatic technique to incorporate correlation effects. We here present a second-quantization approach to the dissipative NEGF theory, reformulating Keldysh ideas to accommodate Lindbladian dynamics and extending the Kadanoff-Baym equations accordingly. Generalizing diagrammatic perturbation theory for many-body Lindblad operators, the formalism enables correlated and dissipative real-time simulations for the exploration of transient and steady-state changes in the electronic, transport, and optical properties of materials.

arXiv:2402.10824•Physical Review Letters•Aug 5, 2024•12 citations

Many-Body Perturbation Theory for Driven Dissipative Quasiparticle Flows and Fluctuations

Thomas Blommel, Enrico Perfetto, Gianluca Stefanucci +1 more

We present a unified many-body perturbation theory for open quantum systems that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh-Lindblad formalism, we introduce a diagrammatic treatment of dissipative interaction lines representing quasiparticle flows and fluctuations. Two new Feynman rules render the evaluation of dissipative diagrams compact and systematically improvable, while preserving the Keldysh and anti-Hermitian symmetries of the closed-system theory. Consequently, the structure of the Kadanoff-Baym equations remains unchanged, enabling existing numerical methods to be directly applied. To illustrate this, we derive dissipative versions of the second Born and GW approximations and identify the physical content of the self-energy components. Moreover, we demonstrate that time-linear approximations to the full Kadanoff-Baym equations retain their closed-form structure and can be efficiently used to simulate relaxation and decoherence dynamics. The impact of dissipation-induced correlations is illustrated in the driven Haldane model, where quasiparticles exhibit nontrivial stabilization and acquire lifetimes that far exceed those of the bare system. This framework establishes a general route toward first-principles modeling of correlated, driven, and dissipative quantum materials.

arXiv:2510.19124•Physical Review Letters•May 21, 2026•0 citations

A comparison of different master equations for driven-dissipative dynamics in composite quantum systems: Dispersive readout in structured electromagnetic environments

Prakritish Gogoi, Angela Riva, Émile Cochin +1 more

Driven-dissipative qubit-resonator dynamics, which are the basis of most dispersive superconducting qubit measurement schemes, are often modeled with Lindblad master equations built from subsystem local jump operators, even when the qubit and resonator are appreciably hybridized. In this work we revisit this setting using a microscopic Bloch-Redfield approach, where dissipation is constructed in the eigenbasis of the coupled qubit-resonator Hamiltonian with a complete, frequency dependent, open system description of the transmission line environment. Here, we show that the Lindblad and Bloch-Redfield decay rates can be quantitatively different in the absence of driving, while in the driven case we demonstrate that the time-independent Redfield dissipator and its time-dependent generalization can show qualitatively different behaviors as a function of driving strength. Finally, we investigate the effects of driving in structured spectral densities, recovering the suppression of measurement-induced relaxation in the presence of a so called Purcell filter.

quant-pharXiv:2605.30032•May 29, 2026•0 citations

Dissipative dynamics of quantum correlations in the strong-coupling regime

Ferdi Altintas, Resul Eryiğit

The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using a recently derived Lindblad type quantum optical master equation [F. Beaudoin, J. M. Gambetta, and A. Blais, Phys. Rev. A 84, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.

arXiv:1212.4071•Physical Review A•Feb 27, 2013•32 citations
Motivated by correlated decay processes producing gain, loss, and lasing in driven semiconductor quantum dots [Phys. Rev. Lett. 113, 036801 (2014); Science 347, 285 (2015); Phys. Rev. Lett. 114, 196802 (2015)], we develop a theoretical technique by using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second-order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behavior at the same order of perturbation theory. We then apply these results to analyze the phonon-assisted steady-state gain of a microwave field driving a double quantum dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing-assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.
Motivated by correlated decay processes driving gain, loss and lasing in driven semiconductor quantum-dots, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms terms contribute to the system behaviour at the same order of perturbation theory, and make substantial contributions to the behaviour of the system.
We use the Bloch-Redfield-Wangsness theory to calculate the effects of acoustic phonons in coherent control experiments where quantum-dot excitons are driven by shaped laser pulses. This theory yields a generalized Lindblad equation for the density operator of the dot, with time-dependent damping and decoherence due to phonon transitions between the instantaneous dressed states. It captures similar physics to the form recently applied to Rabi oscillation experiments [Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)] but guarantees positivity of the density operator. At sufficiently low temperatures, it gives results equivalent to those of fully non-Markovian approaches [L\"uker et al., Phys. Rev. B 85, 121302 (2012)] but is significantly simpler to simulate. Several applications of this theory are discussed. We apply it to adiabatic rapid passage experiments and show how the pulses can be shaped to maximize the probability of creating a single exciton using a frequency-swept laser pulse. We also use this theory to propose and analyze methods to determine the phonon density of states experimentally, i.e., phonon spectroscopy, by exploring the dependence of the effective damping rates on the driving field.
The extraordinary quantum properties of nonequilibrium systems governed by dissipative dynamics have become a focal point in contemporary scientific inquiry. The nonequilibrium Green's functions (NEGF) theory provides a versatile method for addressing driven nondissipative systems, utilizing the powerful diagrammatic technique to incorporate correlation effects. We here present a second-quantization approach to the dissipative NEGF theory, reformulating Keldysh ideas to accommodate Lindbladian dynamics and extending the Kadanoff-Baym equations accordingly. Generalizing diagrammatic perturbation theory for many-body Lindblad operators, the formalism enables correlated and dissipative real-time simulations for the exploration of transient and steady-state changes in the electronic, transport, and optical properties of materials.
We present a unified many-body perturbation theory for open quantum systems that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh-Lindblad formalism, we introduce a diagrammatic treatment of dissipative interaction lines representing quasiparticle flows and fluctuations. Two new Feynman rules render the evaluation of dissipative diagrams compact and systematically improvable, while preserving the Keldysh and anti-Hermitian symmetries of the closed-system theory. Consequently, the structure of the Kadanoff-Baym equations remains unchanged, enabling existing numerical methods to be directly applied. To illustrate this, we derive dissipative versions of the second Born and GW approximations and identify the physical content of the self-energy components. Moreover, we demonstrate that time-linear approximations to the full Kadanoff-Baym equations retain their closed-form structure and can be efficiently used to simulate relaxation and decoherence dynamics. The impact of dissipation-induced correlations is illustrated in the driven Haldane model, where quasiparticles exhibit nontrivial stabilization and acquire lifetimes that far exceed those of the bare system. This framework establishes a general route toward first-principles modeling of correlated, driven, and dissipative quantum materials.
Driven-dissipative qubit-resonator dynamics, which are the basis of most dispersive superconducting qubit measurement schemes, are often modeled with Lindblad master equations built from subsystem local jump operators, even when the qubit and resonator are appreciably hybridized. In this work we revisit this setting using a microscopic Bloch-Redfield approach, where dissipation is constructed in the eigenbasis of the coupled qubit-resonator Hamiltonian with a complete, frequency dependent, open system description of the transmission line environment. Here, we show that the Lindblad and Bloch-Redfield decay rates can be quantitatively different in the absence of driving, while in the driven case we demonstrate that the time-independent Redfield dissipator and its time-dependent generalization can show qualitatively different behaviors as a function of driving strength. Finally, we investigate the effects of driving in structured spectral densities, recovering the suppression of measurement-induced relaxation in the presence of a so called Purcell filter.
The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using a recently derived Lindblad type quantum optical master equation [F. Beaudoin, J. M. Gambetta, and A. Blais, Phys. Rev. A 84, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.