Rectified momentum transport for a kicked Bose-Einstein condensate

Floquet Second-Order Topological Phases in Momentum Space

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.

Directed transport of symmetrically periodic system induced by "color" breaking of noise

In general, no transport can emerge in a spatially symmetric periodic system subjected to an unbiased dichotomous periodic driving. Here, we used a noise, which switches synchronously with the driving in three cases [switch between Gaussian white noise and colored noise, two colored noises with different colors (e.g., autocorrelation rate), and Gaussian white noise and harmonic velocity noise], to drive such a symmetric system. Numerical results for the cases indicate that the directed transport of the symmetric system can be induced merely by the color breaking (the difference in two autocorrelation rates) of the switch noise. The amplitude of current depends on the difference, i.e., the greater the difference, the greater the current. Also, the greater autocorrelation rate between the two noises determines the direction of current. The current as a function of the noise intensity for all cases has in common that appropriate noise intensity induces optimal transport. Further investigations show that the color breaking comes from the difference of barrier heights between the left and right-tilted potentials induced by the different autocorrelation rates.

Resonant Quantum Kicked Rotor as A Continuous-Time Quantum Walk

We analytically investigate the analogy between a standard continuous-time quantum walk in one dimension and the evolution of the quantum kicked rotor at quantum resonance conditions. We verify that the obtained probability distributions are equal for a suitable choice of the kick strength of the rotor. We further discuss how to engineer the evolution of the walk for dynamically preparing experimentally relevant states. These states are important for future applications of the atom-optics kicked rotor for the realization of ratchets and quantum search.

Directed momentum current induced by the PT-symmetric driving

We investigate the directed momentum current in the quantum kicked rotor model with PT-symmetric deriving potential. For the quantum nonresonance case, the values of quasienergy become complex when the strength of the imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous PT symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasienergy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of "quantized" increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.

Impact of Lattice Vibrations on the Dynamics of a Spinor Atom-Optics Kicked Rotor

We investigate the effect of amplitude and phase noise on the dynamics of a discrete-time quantum walk and its related evolution. Our findings underline the robustness of the motion with respect to these noise sources, and can explain the stability of quantum walks that has recently been observed experimentally. This opens the road to measure topological properties of an atom-optics double kicked rotor with an additional internal spin degree of freedom.

Quantum coherent tractor beam effect for atoms trapped near a nanowaveguide

We propose several schemes to realize a tractor beam effect for ultracold atoms in the vicinity of a few-mode nanowaveguide. Atoms trapped near the waveguide are transported in a direction opposite to the guided mode propagation direction. We analyse three specific examples for ultracold (23)Na atoms trapped near a specific nanowaveguide (i.e. an optical nanofibre): (i) a conveyor belt-type tractor beam effect, (ii) an accelerator tractor beam effect, and (iii) a quantum coherent tractor beam effect, all of which can effectively pull atoms along the nanofibre toward the light source. This technique provides a new tool for controlling the motion of particles near nanowaveguides with potential applications in the study of particle transport and binding as well as atom interferometry.

Applications of fidelity measures to complex quantum systems

We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space.

Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏ_{eff} values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏ_{eff} and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.

Experimental control of transport resonances in a coherent quantum rocking ratchet

The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose–Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport.

The ratchet effect can be used as a tool to control coherent quantum transport of ultra-cold atoms. Here, the authors demonstrate a rocking quantum ratchet with a rubidium BEC, and reveal the existence of quantum transport resonances.

Classical to quantum correspondence in dissipative directed transport

We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏ(eff) values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results-obtained for the mean currents and asymptotic distributions only-and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.

Quantum properties of double kicked systems with classical translational invariance in momentum

Double kicked rotors (DKRs) appear to be the simplest nonintegrable Hamiltonian systems featuring classical translational symmetry in phase space (i.e., in angular momentum) for an infinite set of values (the rational ones) of a parameter η. The experimental realization of quantum DKRs by atom-optics methods motivates the study of the double kicked particle (DKP). The latter reduces, at any fixed value of the conserved quasimomentum βℏ, to a generalized DKR, the "β-DKR." We determine general quantum properties of β-DKRs and DKPs for arbitrary rational η. The quasienergy problem of β-DKRs is shown to be equivalent to the energy eigenvalue problem of a finite strip of coupled lattice chains. Exact connections are then obtained between quasienergy spectra of β-DKRs for all β in a generically infinite set. The general conditions of quantum resonance for β-DKRs are shown to be the simultaneous rationality of η,β, and a scaled Planck constant ℏ(S). For rational ℏ(S) and generic values of β, the quasienergy spectrum is found to have a staggered-ladder structure. Other spectral structures, resembling Hofstadter butterflies, are also found. Finally, we show the existence of particular DKP wave-packets whose quantum dynamics is free, i.e., the evolution frequencies of expectation values in these wave-packets are independent of the nonintegrability. All the results for rational ℏ(S) exhibit unique number-theoretical features involving η,ℏ(S), and β.

Quantum parameter space of dissipative directed transport

Quantum manifestations of isoperiodic stable structures (QISSs) have a crucial role in the current behavior of quantum dissipative ratchets. In this context, the simple shape of the ISSs has been conjectured to be an almost exclusive feature of the classical system. This has drastic consequences for many properties of the directed currents, the most important one being that it imposes a significant reduction in their maximum values, thus affecting the attainable efficiency at the quantum level. In this work we prove this conjecture by means of comprehensive numerical explorations and statistical analysis of the quantum states. We are able to describe the quantum parameter space of a paradigmatic system for different values of ℏ(eff) in great detail. Moreover, thanks to this we provide evidence on a mechanism that we call parametric tunneling by which the sharp classical borders of the regions in parameter space become blurred in the quantum counterpart. We expect this to be a common property of generic dissipative quantum systems.

Nonlinearity effects on the directed momentum current

We investigate the quantum transport dynamics governed by the nonlinear Schrödinger equation with a periodically-δ-kicking potential and discover the emergence of a directed current in momentum space. With the increase of nonlinearity, we find strikingly that the momentum current decreases, reverses, and finally vanishes, indicating that the quantum transport can be effectively manipulated through adjusting the nonlinearity. The underlying dynamic mechanism is uncovered and some important implications are addressed.

Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops

The correspondence between exotic quantum holonomy, which occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expression of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, is obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher-order EP, which is broken into lower-order EPs with the application of small perturbations. The stability of exotic holonomy against such bifurcation is demonstrated.

Fidelity of the quantum δ-kicked accelerator

The sensitivity of the fidelity in the kicked rotor to an acceleration is experimentally and theoretically investigated. We used a Bose-Einstein condensate exposed to a sequence of pulses from a standing light wave followed by a single reversal pulse in which the standing wave was shifted by half a wavelength. The features of the fidelity "spectrum" as a function of acceleration are presented. This work may find applications in the measurement of temperature of an ultracold atomic sample.

Quantized adiabatic transport in momentum space

Though topological aspects of energy bands are known to play a key role in quantum transport in solid-state systems, the implications of Floquet band topology for transport in momentum space (i.e., acceleration) have not been explored so far. Using a ratchet accelerator model inspired by existing cold-atom experiments, here we characterize a class of extended Floquet bands of one-dimensional driven quantum systems by Chern numbers, reveal topological phase transitions therein, and theoretically predict the quantization of adiabatic transport in momentum space. Numerical results confirm our theory and indicate the feasibility of experimental studies.

Quantum isoperiodic stable structures and directed transport

It has been recently found that the so-called isoperiodic stable structures (ISSs) have a fundamental role in the classical current behavior of dissipative ratchets [Phys. Rev. Lett. 106, 234101 (2011).]. Here I analyze their quantum counterparts, the quantum ISSs (QISSs), which have a fundamental role in the quantum current behavior. QISSs have the simple attractor shape of those ISSs which settle down in short times. However, in the majority of the cases they are strongly different from the ISSs, looking approximately the same as the quantum chaotic attractors that are at their vicinity in parameter space. By adding thermal fluctuations of the size of ħ(eff) to the ISSs I am able to obtain very good approximations to the QISSs. I conjecture that in general, quantum chaotic attractors could be well approximated by means of just the classical information of a neighboring ISS plus thermal fluctuations. I expect to find this behavior in quantum dissipative systems in general.

Fidelity for kicked atoms with gravity near a quantum resonance

Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultracold atoms. The parametric stability of the quantum dynamics is studied using the fidelity. In the case of a quantum resonance, it is shown that the behavior of the fidelity depends on arithmetic properties of the gravity parameter. Close to a quantum resonance, the long-time asymptotics of the fidelity is studied by means of a pseudoclassical approximation introduced by Fishman et al. [J. Stat. Phys. 110, 911 (2003)]. The long-time decay of fidelity arises from the tunneling out of pseudoclassical stable islands, and a simple ansatz is proposed which satisfactorily reproduces the main features observed in numerical simulations.

Long-lasting exponential spreading in periodically driven quantum systems

Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudoclassical map, both qualitatively and quantitatively. Possible applications of our findings are also briefly discussed.

Weak-chaos ratchet accelerator

Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. The system is a realistic, generalized kicked rotor and is exactly solvable to some extent, leading to analytical expressions for the momentum current. While this current arises also for relatively strong chaos, the maximal current is shown to occur, at least in one case, precisely in a limit of arbitrarily weak chaos.

Environmental stability of quantum chaotic ratchets

The transitory and stationary behavior of a quantum chaotic ratchet consisting of a biharmonic potential under the effect of different drivings in contact with a thermal environment is studied. For weak forcing and finite ℏ, we identify a strong dependence of the current on the structure of the chaotic region. Moreover, we have determined the robustness of the current against thermal fluctuations in the very weak coupling regime. In the case of strong forcing, the current is determined by the shape of a chaotic attractor. In both cases the temperature quickly stabilizes the ratchet, but in the latter it also destroys the asymmetry responsible for the current generation. Finally, applications to isomerization reactions are discussed.

Doubly excited ferromagnetic spin chain as a pair of coupled kicked rotors

We show that the dynamics of a doubly excited Heisenberg spin chain, subject to short pulses from a parabolic magnetic field may be analyzed as a pair of quantum kicked rotors. By focusing on the two-magnon dynamics in the kicked XXZ model we investigate how the anisotropy parameter--which controls the strength of the magnon-magnon interaction--changes the nature of the coupling between the two "image" coupled kicked rotors. We investigate quantum state transfer possibilities and show that one may control whether the spin excitations are transmitted together, or separate from each other.

Relatively robust classical structures in dissipative quantum chaotic systems

We study the stability of classical structures in chaotic systems when a dissipative quantum evolution takes place. We consider a paradigmatic model, the quantum baker map in contact with a heat bath at finite temperature. We analyze the behavior of the purity, fidelity and Husimi distributions corresponding to initial states localized on short periodic orbits (scar functions) and map eigenstates. Scar functions, that have a fundamental role in the semiclassical description of chaotic systems, emerge as robust relative to other states (which are localized on classical structures) against environmental perturbations. Also, purity and fidelity show a complementary behavior as decoherence measures.

Statistical approach to quantum chaotic ratchets

The quantum ratchet effect in fully chaotic systems is approached by studying statistical properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical regime are those that are phase-space uniform with the maximal possible resolution of one Planck cell. General arguments in this regime, for quantum-resonance values of a scaled Planck constant variant Planck's over 2pi , predict that the distribution of the current over all such states is a zero-mean Gaussian with variance approximately Dvariant Planck's over 2pi2/(2pi2) , where D is the chaotic-diffusion coefficient. This prediction is well supported by extensive numerical evidence. The average strength of the effect, measured by the variance above, is significantly larger than that for the usual momentum states and other states. Such strong effects should be experimentally observable.

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.

Noise-induced energy resonance for atoms in a periodic potential

We show that phase noise can induce nontrivial dynamics in atoms prepared in a superposition of momentum eigenstates of a periodic potential. Experimental measurements demonstrate a resonance in mean energy as a function of the size of applied random phase jumps. We discuss the mechanism for the observed behavior and show that it could also lead to noise-induced divergence between quantum and classical dynamics.

Behavior of the current in the asymmetric quantum multibaker map

Recently, a new mechanism leading to purely quantum directed transport in the asymmetric multibaker map has been presented. Here, we show a comprehensive characterization of the finite asymptotic current behavior with respect to the h value, the shape of the initial conditions, and the features of the spectrum. We have considered different degrees of asymmetry in these studies and we have also analyzed the classical and quantum phase-space distributions for short times in order to understand the mechanisms behind the generation of the directed current.

Chaotic dynamics of a Bose-Einstein condensate coupled to a qubit

We study numerically the coupling between a qubit and a Bose-Einstein condensate (BEC) moving in a kicked optical lattice using Gross-Pitaevskii equation. In the regime where the BEC size is smaller than the lattice period, the chaotic dynamics of the BEC is effectively controlled by the qubit state. The feedback effects of the nonlinear chaotic BEC dynamics preserve the coherence and purity of the qubit in the regime of strong BEC nonlinearity. This gives an example of an exponentially sensitive control over a macroscopic state by internal qubit states. At weak nonlinearity quantum chaos leads to rapid dynamical decoherence of the qubit. The realization of such coupled systems is within reach of current experimental techniques.

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.

Nonlinear resonances in delta-kicked Bose-Einstein condensates

We investigate the effect of atomic interactions on delta-kicked cold atoms. We show that the clearest signature of the nonlinear dynamics is a surprisingly abrupt cutoff that appears on the leading resonances. We show that this is due to an excitation path combining both Beliaev and Landau processes, with some analogies to nonlinear self-trapping. Investigation of dynamical instability reveals further symptoms of nonlinearity such as a regime of exponential oscillations.

Enhanced factoring with a bose-einstein condensate

We present a novel method to realize analog sum computation with a Bose-Einstein condensate in an optical lattice potential subject to controlled phase jumps. We use the method to implement the Gauss sum algorithm for factoring numbers. By exploiting higher order quantum momentum states, we are able to improve the algorithm's accuracy beyond the limits of the usual classical implementation.

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.

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.

Destruction of Anderson localization by a weak nonlinearity

We study numerically the spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schrödinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time proportional, variant t alpha, with the exponent alpha being in the range 0.3-0.4. For small nonlinearities the distribution remains localized in a way similar to the linear case.

Controlling the ratchet effect for cold atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.

Cooling by time reversal of atomic matter waves

We propose an experimental scheme which allows us to realized approximate time reversal of matter waves for ultracold atoms in the regime of quantum chaos. We show that a significant fraction of the atoms return back to their original state, being at the same time cooled down by several orders of magnitude. We give a theoretical description of this effect supported by extensive numerical simulations. The proposed scheme can be implemented with existing experimental setups.

Experimental realization of quantum-resonance ratchets at arbitrary quasimomenta

Quantum-resonance ratchets associated with the kicked particle are experimentally realized for arbitrary quasimomentum using a Bose-Einstein condensate (BEC) exposed to a pulsed standing light wave. The ratchet effect for general quasimomentum arises even though both the standing-wave potential and the initial state of the BEC have a point symmetry. The experimental results agree well with theoretical ones which take into account the finite quasimomentum width of the BEC. In particular, this width is shown to cause a suppression of the ratchet acceleration for exactly resonant quasimomentum, leading to a saturation of the directed current.