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

Abstract

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...

Lyapunov equation in open quantum systems and non-Hermitian physics

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Full counting statistics for electron transport in periodically driven quantum dots

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Spectral properties of correlated quantum wires and carbon nanotubes within the Generalized Kadanoff-Baym Ansatz

“…In recent years there has been a growing interest into the properties of correlated systems under external perturbations; the latter being continuous drivings [1][2][3][4][5], coupling with macroscopic reservoirs with whom they can exchange energy and particles [6][7][8][9][10][11][12][13], or strong external pulses with a finite duration in time [14][15][16][17][18][19]. The field of application of these studies is broad, encompassing out-of-equilibrium phases [20][21][22][23][24], pump-probe experiments and time-resolved dynamical properties [25][26][27][28], band-gap and Floquet engineering [29][30][31][32][33][34], transport in correlated systems [35][36][37][38], equilibration and thermalization in strongly correlated materials [39][40][41] and quantum gases [42,43], and relaxation in nano-structures [44,45].…”