ac field-induced quantum rectification effect in tunnel junctions

Abstract

We study the appearance of directed current in tunnel junctions (quantum ratchet effect), in the presence of an external ac field f (t). The current is established in a one-dimensional discrete inhomogeneous "tight-binding model". By making use of a symmetry analysis we predict the right choice of f (t) and obtain the directed current as a difference between electron transmission coefficients in opposite directions, ∆T = T LR − T RL . Numerical simulations confirm the predictions of the symmetry analysis and moreover, show that the directed current can be drastically increased by a proper choice of frequency and amplitudes of the ac field f (t).PACS numbers: 05.60. Gg, 73.23.Ad, 73.40.Gk A great attention has been devoted to theoretical and experimental studies of a transport rectification in various physical, chemical and biological systems [1,2]. In particular this peculiar effect appears in the form of a directed current as a system is exposed to a time-dependent ac force with zero mean. Such a directed motion (current) has been observed in molecular motors [1,3], in Josephson junction coupled systems [4,5], and in systems of cold Rb atoms in laser fields [6], just to name a few.In most studies the appearance of directed current has been analyzed by making use of the model of a particle moving in the presence of both space and time periodic potentials [2,7,8,9]. The effects of dissipation and interaction with a heat bath have been taken into account, and in many cases the decrease of dissipation as a system approaches the Hamiltonian limit, leads to a substantial increase of the directed current [9]. By making use of a symmetry analysis of the dynamic equations of motion it has been shown that the directed current occurs as a space-periodic potential is asymmetric (ratchet potential) and/or all important symmetries of an ac force, i.e. time-reversal and shift symmetry, are broken [2,9]. Notice here, that the latter case can be easier realized in experiments. It has been established that more complex systems described by generic Bolzman transport equation [10], Fokker-Planck equation [7,8,11], etc. also display a directed current. Moreover, the directed energy transport has been obtained in the case of interacting many particle systems described by nonlinear partial differential equations [12,13].Most previous studies analyzing both the dissipative and Hamiltonian limits, were heavily based on a classical nonlinear regime of particle motion. A next step is to obtain the directed transport in systems displaying quantum-mechanical behavior. The quantum regime of directed transport for a few particular systems has been studied in Refs. [5,14,15,16]. It was shown that a dissipationless quantum system in a single energy band tight-binding approximation does not support directed current [14], and although a quantum Brownian particle can display a directed motion and even numerous current reversal in the presence of an asymmetric ratchet potential, one still needs to take into account the dissipative effects [15]....

Optimal control of ratchets without spatial asymmetry

“…Also, that the harmonic functions appearing in the scaling laws are independent of har 1 is a consequence of the invariance of V under time translation. As expected, one finds that such scaling laws are quite general, i.e., they confirm and explain previous results for a great diversity of systems [7,14,15,22,25] subjected to a biharmonic force f h1,h2 (t). I now discuss how the aforementioned scaling laws change when the violation of the time-reversal symmetry of the system's dynamic equations cannot be absorbed in the temporal force.…”

“…of the biharmonic force f h1,h2 (t) in leading order for the usual case [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]24,25] of small amplitudes (1/ǫ 1,2 → ∞). For the sake of clarity, consider first the case where the violation of the time-reversal symmetry of the system's dynamic equations can be absorbed in the temporal force because dissipation is negligible and the Lagrangian (Hamiltonian) of the system does not contain any additional term explicitly breaking the time-reversal symmetry.…”

Tunable transport with broken space–time symmetries

“…Other wave equations can be considered as well, and the ratchet concept can be adapted likewise to any other sort of physical current. For instance, the symmetry analysis was applied to the energy current generated by a nonlinear field equation which describes a long Josephson junction [160,161,162]. The predicted symmetry breaking was linked to the presence of solitons, and the corresponding soliton ratchet was subsequently successfully realized experimentally with a fluxon trapped in an annular Josephson junction which was driven by a microwave field [163].…”

Dynamical control in a quasi-periodically modulated optical lattice

“…It was shown that not only the strength of the ac force but also its phase is of experimental relevance [20,21]. The generalization of the monochromatic ac force to a multi-frequency ac force leads to nontrivial results in ultra cold atom dynamics [22][23][24][25][26][27][28][29][30][31][32][33]. The relationship between symmetries and transport was explored for a cold atom ratchet with multifrequency driving [25].…”