Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results

Purkayastha, Archak; Dhar, Abhishek; Kulkarni, Manas

doi:10.1103/physreva.93.062114

Cited by 113 publications

(146 citation statements)

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“…Therefore, such exact methods are difficult to use in our ac drive set-up. However, as has been recently established, RQME gives the correct time dynamics of approach to steady state under dc bias of two-point correlation functions for our set-up as long as Born-Markov approximation is satisfied [63]. This fact has allowed us to use RQME for ac drive case to go beyond the adiabatic approximation easily.…”

Section: Resonances and Currentsmentioning

confidence: 96%

“…This, however, is not a completely rigorous statement, and requires further investigation. In Ref [63], the long time behaviour of the correlation functions for the dc bias case of our set-up have been shown to be given correctly by the Redfield equation. Since our protocol breaks down the ac drive process into a series of such dc drive steps, this gives further support regarding validity of our results.…”

Section: Resonances and Currentsmentioning

confidence: 99%

“…It has been recently shown that microscopically derived Redfield Quantum Master Equation (RQME) under Born-Markov approximation can be used to overcome the drawbacks of phenomenological Lindblad equations and to obtain correct results up-to leading order in system-bath coupling [63]. To our knowledge, there has been no work in extending the RQME to the case when thermodynamic parameters of the baths are periodically modulated.…”

Section: A Introductionmentioning

confidence: 98%

“…4) on time scales, breaks down the ac drive process into steps of time independent processes where Born-Markov approximation can be applied. For such time independent processes, the Born-Makov approximated Redfield Qunatum Master Equation (RQME), as well as the evolution equation for two point correlation functions from the RQME have been derived for Hamiltonian (1) recently [63] (see Appendix A). Going through the above protocol with the RQME only has the effect of making the fermi (bose) distribution functions time-dependent with the instantaneous temperatures and chemical potentials (see Appendix C).…”

Section: B Set-up and Protocolmentioning

confidence: 99%

“…However, Floquet theory has the drawback of converting a finitedimensional problem to an infinite dimensional one. Consequently, most interesting results from Floquet theory are often obtained as a perturbation expansion in terms of inverse drive frequency, giving results primarily for high frequency driving.Moreover, from calculations in the absence of timeperiodic modulations, the commonly used phenomenological Lindblad Quantum Master Equations are known to have several drawbacks, especially in an out-ofequilibrium situation [63][64][65][66]. It has been recently shown that microscopically derived Redfield Quantum Master Equation (RQME) under Born-Markov approximation can be used to overcome the drawbacks of phenomenological Lindblad equations and to obtain correct results up-to leading order in system-bath coupling [63].…”

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confidence: 99%

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Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

Purkayastha

2017

Phys. Rev. B

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Evaluating the time-dependent dynamics of driven open quantum systems is relevant for a theoretical description of many systems, including molecular junctions, quantum dots, cavity-QED experiments, cold atoms experiments and more. Here, we formulate a rigorous microscopic theory of an out-of-equilibrium open quantum system of non-interacting particles on a lattice weakly coupled bilinearly to multiple baths and driven by periodically varying thermodynamic parameters like temperature and chemical potential of the bath. The particles can be either bosonic or fermionic and the lattice can be of any dimension and geometry. Based on Redfield quantum master equation under Born-Markov approximation, we derive a linear differential equation for equal time two-point correlation matrix, sometimes also called single-particle density matrix, from which various physical observables, for example, current, can be calculated. Various interesting physical effects, such as resonance, can be directly read-off from the equations. Thus, our theory is quite general gives quite transparent and easy-to-calculate results. We validate our theory by comparing with exact numerical simulations. We apply our method to a generic open quantum system, namely a double-quantum dot coupled to leads with modulating chemical potentials. Two most important experimentally relevant insights from this are : (i) time-dependent measurements of current for symmetric oscillating voltages (with zero instantaneous voltage bias) can point to the degree of asymmetry in the system-bath coupling, and (ii) under certain conditions, time-dependent currents can exceed time-averaged currents by several orders of magnitude, and can therefore be detected even when the average current is below the measurement threshold. A. IntroductionThe dynamics of a quantum system coupled to an external environment (so-called "open" quantum system) are a result of the intricate interplay between the coherent evolution of the quantum degrees of freedom, the structure of the environment and the form and strength of the system-environment coupling. From quantum cavities [1-3] and superconducting qubits [4][5][6][7][8][9] , through quantum dots [10][11][12][13][14][15], molecular junctions [16][17][18][19][20][21][22][23][24][25][26][27] and cold atoms [28][29][30][31] , to excitons traveling in photosynthetic complexes [32][33][34][35], open quantum systems show dynamics which can be far richer and more surprising than their coherent (environment-free) counterparts.Recent ideas of designing a quantum state by engineering a specific environment [36][37][38][39][40][41][42] or by a periodic modulation of the open system's Hamiltonian [16,43,44] open a path to new forms of control over quantum systems. Combining these two concepts of time-periodic modulations and environment (bath) engineering, here we study the dynamics of open quantum systems where the environment thermodynamic parameters are periodically modulated. Even though there exists formally exact methods of treating such set-ups...

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Section: Resonances and Currentsmentioning

confidence: 96%

Section: Resonances and Currentsmentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 98%

Section: B Set-up and Protocolmentioning

confidence: 99%

mentioning

confidence: 99%

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Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

Purkayastha

2017

Phys. Rev. B

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Non-Markovian Dynamics of Macroscopic Quantum Systems in Interaction with Non-equilibrium Environments

2019

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We study the dynamics of a macroscopic superconducting qubit coupled to two independent nonstationary reservoirs by using time-dependent perturbation theory. We show that an equilibrium environment surpasses the coherent evolution of the macroscopic qubit completely. When the qubit couples to two different reservoirs, exemplifying a non-equilibrium environment, the short-time dynamics is affected by the interference between two reservoirs, implying the non-additivity of effects of two reservoirs. The non-additivity can be traced back to a non-Markovian effect, even though two reservoirs are independently assumed to be Markovian. Explicitly, the non-equilibrium environment intensifies both coherent and incoherent parts of the evolution. Therefore, the macroscopic qubit would evolve more coherently but at the price of a shorter decoherence time. INTRODUCTIONAn environment in thermal equilibrium destroys the coherence of a quantum system interacting with it [1][2][3][4]. Such decoherence process is one of the main obstacles in realizing quantum computers [5][6][7][8]. One approach to implement a quantum computer is based on superconductors, where the quantum effects become macroscopic, though at a price of extremely low temperatures [9][10][11][12]. Apart from this straightforward strategy, a number of schemes have been proposed to control the decoherence process by engineering the system-environment interaction (for a rather complete review, see [13]). One of the effective strategies, observed naturally in biological systems [14,15], is engineering non-equilibrium environments. Such an environment has the opportunity to influence the quantum evolution in a manner that is more rich and complex than simply acting to randomize relative phases and dissipate energy.The open quantum systems are mostly examined by Lindblad master equations [3,16,17], which are based on Born and Markov approximations, and depending on the context, an additional uncontrolled approximation [3, 18-20] on the environment. However, in non-equilibrium systems, such approximations may lead to incorrect predictions [21][22][23][26][27][28][29]. One of such predictions is that the effect of two initially uncorrelated environments on the system's dynamics is independent and additive in the weak-coupling limit [30]. The validity of this prediction has been examined in a number of contexts in the literature [22,26,28,[31][32][33][34][35][36][37][38]. In fact, the non-additive effect is not unfolded by Markovian approach, implying the non-Markovian property of the dynamics [39][40][41][42].Apart from the approach employed, among all the works mentioned, the lack of a macroscopic quantum system as the case study is deeply felt. Here, we examine the effective dynamics of a macroscopic superconducting qubit, in interaction with a non-equilibrium environment. To be macroscopic, conceptually, the dynamics should involve macroscopically distinguishable, entangled states [43]. The effective dynamics of the macroscopic superconducting qubit, particularly the p...

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Particle and thermal transport through one dimensional topological systems via Lindblad formalism

Chien

2023

Physics Letters A

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Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results

Cited by 113 publications

References 63 publications

Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

Non-Markovian Dynamics of Macroscopic Quantum Systems in Interaction with Non-equilibrium Environments

Particle and thermal transport through one dimensional topological systems via Lindblad formalism

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