Quantum Ratchet Research Articles

QUANTUM-RESONANCE RATCHETS: THEORY AND EXPERIMENT

A theory of quantum ratchets for a particle periodically kicked by a general periodic potential under quantum-resonance conditions is developed for arbitrary values of the conserved quasimomentum β. A special case of this theory is experimentally realized using a Bose–Einstein condensate (BEC) exposed to a pulsed standing light wave. While this case corresponds to completely symmetric potential and initial wave-packet, a purely quantum ratchet effect still arises from the generic noncoincidence of the symmetry centers of these two entities. The experimental results agree well with the theory after taking properly into account the finite quasimomentum width of the BEC. This width causes a suppression of the ratchet acceleration occurring for "resonant" β, so that the mean momentum saturates to a finite ratchet velocity, strongly pronounced relative to that for nonresonant β.

Directed Transport of Atoms in a Hamiltonian Quantum Ratchet

Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.

Moving Cold Atoms with Quantum Ratchets

Moving Cold Atoms with Quantum Ratchets

Coherent Ratchets in Driven Bose-Einstein Condensates

We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior, and space and time symmetries must both be broken to produce a current. For strong driving, the behavior becomes chaotic and the resulting effective irreversibility means that it is unnecessary to explicitly break time symmetry. Spatial asymmetry alone is then sufficient to produce the ratchet effect, even in the absence of interactions, and although the system remains completely coherent.

Entropy in quantum ratchet for a delta-kicked model

We investigate the evolution of Shannon entropy in quantum ratchet effect for a delta-kicked model, where a particle with initial momentum zero is periodically kicked by an asymmetric potential. It is shown that the evolution of Shannon entropy of the particle can remarkably reflect whether quantum resonance emerges and gives rise to ratchet current or not. Furthermore, for different kinds of quantum resonances, low-order or high-order quantum resonances, the evolutions of the entropy are quite different.

Chaos and correspondence in classical and quantum Hamiltonian ratchets: A Heisenberg approach

Previous work [Gong and Brumer, Phys. Rev. Lett. 97, 240602 (2006)] motivates this study as to how asymmetry-driven quantum ratchet effects can persist despite a corresponding fully chaotic classical phase space. A simple perspective of ratchet dynamics, based on the Heisenberg picture, is introduced. We show that ratchet effects are in principle of common origin in classical and quantum mechanics, although full chaos suppresses these effects in the former but not necessarily the latter. The relationship between ratchet effects and coherent dynamical control is noted.

Quantum ratchet accelerator without a bichromatic lattice potential

In a quantum ratchet accelerator system, a linearly increasing directed current can be dynamically generated without using a biased field. Generic quantum ratchet acceleration with full classical chaos [J. B. Gong and P. Brumer, Phys. Rev. Lett. 97, 240602 (2006)] constitutes a new element of quantum chaos and an interesting violation of a sum rule of classical ratchet transport. Here we propose a simple quantum ratchet accelerator model that can also generate linearly increasing quantum current with full classical chaos. This model does not require a bichromatic lattice potential. It is based on a variant of an on-resonance kicked-rotor system, periodically kicked by two optical lattice potentials of the same lattice constant, but with unequal amplitudes and a fixed phase shift between them. The dependence of the ratchet current acceleration rate on the system parameters is studied in detail. The cold-atom version of our quantum ratchet accelerator model should be realizable by introducing slight modifications to current cold-atom experiments.

A one-way street for spin current

A way to generate and control spin currents without magnetic fields or magnetic materials may be possible using dissipative quantum ratchets in the presence of spin–orbit coupling.

Quantum ratchet effects induced by terahertz radiation in GaN-based two-dimensional structures

Photogalvanic effects are observed and investigated in wurtzite (0001)-oriented GaN/AlGaN low-dimensional structures excited by terahertz radiation. The structures are shown to represent linear quantum ratchets. Experimental and theoretical analysis exhibits that the observed photocurrents are related to the lack of an inversion center in the GaN-based heterojunctions.

Transport phenomena in the asymmetric quantum multibaker map

By studying a modified (unbiased) quantum multibaker map, we were able to obtain a finite asymptotic quantum current without a classical analog. This result suggests a general method for the design of purely quantum ratchets and sheds light on the investigation of the mechanisms leading to net transport generation by breaking symmetries of quantum systems. Moreover, we propose the multibaker map as a resource to study directed transport phenomena in chaotic systems without bias. In fact, this is a paradigmatic model in classical and quantum chaos, but also in statistical mechanics.

Publisher's Note: Quantum ratchets for quantum communication with optical superlattices [Phys. Rev. A76, 052304 (2007)

Received 12 November 2007DOI:https://doi.org/10.1103/PhysRevA.76.059904©2007 American Physical Society

Quantum ratchets for quantum communication with optical superlattices

We propose to use a quantum ratchet to transport quantum information in a chain of atoms trapped in an optical superlattice. The quantum ratchet is created by a continuous modulation of the optical superlattice which is periodic in time and in space. Though there is zero average force acting on the atoms, we show that indeed the ratchet effect permits atoms on even and odd sites to move along opposite directions. By loading the optical lattice with two-level bosonic atoms, this scheme permits us to perfectly transport a qubit or entangled state imprinted in one or more atoms to any desired position in the lattice. From the quantum computation point of view, the transport is achieved by a smooth concatenation of perfect swap gates. We analyze setups with noninteracting and interacting particles and in the latter case we use the tools of optimal control to design optimal modulations. We also discuss the feasibility of this method in current experiments.

Coherent spin ratchets: A spin-orbit based quantum ratchet mechanism for spin-polarized currents in ballistic conductors

We demonstrate that the combined effect of a spatially periodic potential, lateral confinement, and spin-orbit interaction gives rise to a quantum ratchet mechanism for spin-polarized currents in two-dimensional coherent conductors. Upon adiabatic ac driving, in the absence of a net static bias, the system generates a directed spin current while the total charge current is zero. We analyze the underlying mechanism by employing symmetry properties of the scattering matrix and numerically verify the effect for different setups of ballistic conductors. The spin current direction can be changed upon tuning the Fermi energy or the strength of the Rashba spin-orbit coupling.

Interaction-induced quantum ratchet in a Bose-Einstein condensate

We study the dynamics of a dilute Bose-Einstein condensate confined in a toroidal trap and exposed to a pair of periodically flashed optical lattices. We first prove that in the noninteracting case this system can present a quantum symmetry which forbids the ratchet effect classically expected. We then show how many-body atom-atom interactions, treated within the mean-field approximation, can break this quantum symmetry, thus generating directed transport.

Quantum resonances and ratchets in free-falling frames

Quantum resonance (QR) is defined in the free-falling frame of the quantum kicked particle subjected to gravity. The general QR conditions are derived. They imply the rationality of the gravity parameter eta , the kicking-period parameter tau/(2pi) , and the quasimomentum beta . Exact results are obtained concerning wave-packet evolution for arbitrary periodic kicking potentials in the case of integer tau/(2pi) (the main QRs). It is shown that a quantum ratchet generally arises in this case for resonant beta . The noninertial nature of the free-falling frame affects the ratchet by effectively changing the kicking potential to one depending on (beta,eta) . For a simple class of initial wave packets, it is explicitly shown that the ratchet characteristics are determined to a large extent by symmetry properties and by number-theoretical features of eta .

Periodically driven quantum ratchets: Symmetries and resonances

We study the quantum version of a tilting and flashing Hamiltonian ratchet, consisting of a periodic potential and a time-periodic driving field. The system dynamics is governed by a Floquet evolution matrix bearing the symmetry of the corresponding Hamiltonian. The dc-current appears due to the desymmetrization of Floquet eigenstates, which become transporting when all the relevant symmetries are violated. Those eigenstates that mostly contribute to a directed transport reside in phase space regions corresponding to classical resonances. Quantum dynamics leads to the dependence of the average velocity on the initial phase of the ac-field. A resonant enhancement (or suppression) of the dc-current, due to avoided crossings between different Floquet states, takes place upon tuning some control parameters. Our studies are predominantly aimed at experimental realizations of ac-driven quantum ratchets with cold atoms.

Mesoscopic rectification in a quantum dot with spin–orbit interaction

We investigate the conductance of an open quantum dot in which uniform Rashbaspin–orbit interaction (SOI) is present in the cavity region. The dot has a centraltriangular stopper (CTS) whose rotation angle controls the symmetry of the wholesystem. For a Fermi wavelength comparable to the linear dimension of the CTS, theSOI-dependence of the conductance is sensitive to both the direction of bias and therotation angle of the CTS. We propose a quantum ratchet which generates thedirected current against AC bias with time-average zero by using spin-polarizedelectron injection. The relationship between the symmetry of the dot and therectification effect is revealed, and is used as a mechanism for charge rectification.

Quantum ratchets for periodically kicked cold atoms and Bose-Einstein condensates

We study cold atoms and Bose-Einstein condensates exposed to time-dependent standing waves of light. We first discuss a quantum chaotic dissipative ratchet using the method of quantum trajectories. This system is characterized by directed transport emerging from a quantum strange attractor. We then present a very simple model of directed transport with cold atoms in a pair of periodically flashed optical lattices.Finally we study the dynamics of a dilute Bose-Einstein condensate confined in a toroidal trap and exposed to a pair of periodically flashed optical lattices. We show that the many-body atom-atom interactions, treated within the mean-field approximation, can generate directed transport.

Directed Motion for Delta-Kicked Atoms with Broken Symmetries: Comparison between Theory and Experiment

We report an experimental investigation of momentum diffusion in the delta-function kicked rotor where time symmetry is broken by a two-period kicking cycle and spatial symmetry by an alternating linear potential. We exploit this, and a technique involving a moving optical potential, to create an asymmetry in the momentum diffusion that is due to the classical chaotic diffusion. This represents a realization of a type of Hamiltonian quantum ratchet.

Fourier synthesis of optical potentials for atomic quantum gases

We demonstrate a scheme for the Fourier synthesis of periodic optical potentials with asymmetric unit cells for atoms. In a proof of principle experiment, an atomic Bose-Einstein condensate is exposed to either symmetric or sawtooth-like asymmetric potentials by superimposing a conventional standing wave potential of $\lambda/2$ spatial periodicity with a fourth-order lattice potential of $\lambda/4$ periodicity. The high periodicity lattice is realized using dispersive properties of multiphoton Raman transitions. Future applications of the demonstrated scheme could range from the search for novel quantum phases in unconventionally shaped lattice potentials up to dissipationless atomic quantum ratchets.