Statistics of an adiabatic charge pump

Abstract

We investigate the effect of time-dependent cyclic-adiabatic driving on the charge transport in quantum junction. We propose a nonequilibrium Greens function formalism to study statistics of the charge pumped (at zero bias) through the junction. The formulation is used to demonstrate charge pumping in a single electronic level coupled to two (electronic) reservoirs with time dependent couplings. Analytical expression for the average pumped current for a general cyclic driving is derived. It is found that for zero bias, for a certain class of driving, the Berry phase contributes only to the odd cumulants. To contrast, a quantum master equation formulation does not show Berry-phase effect at all.It is well known that the effect of adiabatically varying few parameters in the Hamiltonian in a cyclic manner enters in the wavefunction in the form of a phase factor. This phase factor consists of two parts, one is called dynamical part (which, in general, depends on how fast the parameters are varied) and the second one, generally known as Berry phase (also called geometric phase) that depends only on the path (area) traced in the parameter space and independent of how fast it is traced provided adiabatic condition is satisfied [1][2][3]. Somewhat counterintuitive, this phase factor may lead to changes in macroscopic observables, like finite spin or charge currents in one dimensional phase coherent rings at equilibrium [4][5][6]. Originally developed in the context of closed quantum systems, recent works have extended the geometric phase concept to the case of open quantum systems out of equilibrium [7,8]. This is usually treated within the quantum master equation (QME) approach [9]. Stochastic variation of system parameters is known to induce net flux in open systems like quantum heat pumps [10,11], quantum electron pumps [12] and also classical stochastic systems like enzyme kinetics, molecular motors and living cell locomotion [13]. On a similar footing, adiabatic cyclic variation of parameters in the Hamiltonian may also lead to finite flux [14]. Switkes et.al.,[15] have experimentally demonstrated an adiabatic quantum pump by modulating confining potential of an open quantum dot in a cyclic manner, leading to a finite voltage drop across the quantum dot. Modifying the potential at two ends of the dot changes the character of the wavefunction and therefore modifies the couplings to the electron reservoirs. In this work we explore this aspect within the most general framework based on non-equilibrium Greens function [16]. The adiabatic driving may also effect the statistics of charge transfer and the steadystate fluctuation relation due to Gallavoti Cohen (GC) type symmetry [17] may also get modified. Ren et.al.[10] have recently used QME to study heat pumping and fluctuations of heat transfer in a two-level system sandwiched between two thermal reservoirs. It was shown that in the case of time-dependent temperature modulations of the two heat reservoirs, heat transfer statistics does not admit GC type symmetry. It w...

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