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In this chapter we investigate the dynamics of classical nonlinear Hamiltonian systems, which—a priori—are examples of continuous dynamical systems. As in the discrete case (see examples in Chap. 2), we are interested in the classification of their dynamics. After a short review of the basic concepts of Hamiltonian mechanics, we define integrability (and therewith regular motion) in Sect. 3.4. The non-integrability property is then discussed in Sect. 3.5. The addition of small non-integrable parts to the Hamiltonian function (Sects. 3.6.1 and 3.7) leads us to the formal theory of canonical perturbations, which turns out to be a highly valuable technique for the treatment of systems with one degree of freedom and shows profound difficulties when applied to realistic systems with more degrees of freedom. We will interpret these problems as the seeds of chaotic motion in general. A key result for the understanding of the transition from regular to chaotic motion is the KAM theorem (Sect. 3.7.4), which assures the stability in nonlinear systems that are not integrable but behave approximately like them. Within the framework of the surface of section technique, chaotic motion is discussed from a phenomenological point of view in Sect. 3.8. More quantitative measures of local and global chaos are finally presented in Sect. 3.9.

We present a classical approximation for the peaks of survival resonances occurring when diffracting matter waves from absorption potentials. Generally our simplified model describes the absorption-diffraction process around the Talbot time very well. Classical treatments of this process are presently lacking. For purely imaginary potentials, the classical model duplicates quantum mechanical calculations. The classical model allows for simple evolution of phase-space probability densities, which in the limit of the effective Planck's constant going to zero allows for a compact analytical expression of the survival probability as a function of remaining parameters. Our work extends the range of processes that can be described through classical analogues.

This paper investigates the feasibility of simulating Fuzzy Dark Matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in $(1+1)$-dimensional space time, that - under well controlled system conditions - is capable of realizing important aspects of the full-fledged $(3+1)$-FDM phenomenology by means of one-dimensional analogues. Based on the coupled, nonlinear and nonlocal $(3+1)$-Schr\"odinger-Poisson equation under periodic boundary conditions, we derive two distinct one-dimensional models that differ in their transversal matter distribution and consequently in their nonlocal interaction along the single dimension of interest. We show that these discrepancies change the relaxation process of initial states as well as the asymptotic, i.e., thermalized and virialized, equilibrium state. Our investigation includes the dynamical evolution of artificial initial conditions for non-expanding space, as well as cosmological initial conditions in expanding space. The findings of this work are relevant for the interpretation of numerical simulation data modelling nonrelativistic fuzzy cold dark matter in reduced dimensions, in the quest for testing such models and for possible laboratory implementations of them., Comment: 24 pages, 14 figures, accepted for publication in Physical Review D

We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, non-stationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time, and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the time scale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process., 15 pages, 12 figures

The difficulty in combining high fidelity with fast operation times and robustness against sources of noise is the central challenge of most quantum control problems, with immediate implications for the realization of quantum devices. We theoretically propose a protocol, based on the widespread stimulated Raman adiabatic passage technique, which achieves these objectives for quantum state transfers in generic three-level systems. Our protocol realizes accelerated adiabatic following through the application of additional control fields on the optical excitations. These act along frequency sidebands of the principal adiabatic pulses, dynamically counteracting undesired transitions. The scheme facilitates experimental control, not requiring new hardly-accessible resources. We show numerically that the method is efficient in a very wide set of control parameters, bringing the timescales closer to the quantum speed limit, also in the presence of environmental disturbance. These results hold for complete population transfers and for many applications, e.g., for realizing quantum gates, both for optical and microwave implementations. Furthermore, extensions to adiabatic passage problems in more-level systems are straightforward.

We show that molecular nanomagnets have a potential advantage in the crucialrush toward quantum computers. Indeed, the sizable number of accessible low-energy states ofthese systems can be exploited to define qubits with embedded quantum error correction. Wederive the scheme to achieve this crucial objective and the corresponding sequence ofmicrowave/radiofrequency pulses needed for the error correction procedure. The effectivenessof our approach is shown already with a minimal S = 3/2 unit corresponding to an existingmolecule, and the scaling to larger spin systems is quantitatively analyzed.

The realization of effective Hamiltonians featuring many-body interactions beyond pairwise coupling would enable the quantum simulation of central models underpinning topological physics and quantum computation. We overcome crucial limitations of perturbative Floquet engineering and discuss the highly accurate realization of a purely three-body Hamiltonian in superconducting circuits and molecular nanomagnets., Comment: 6+8 pages, 3+4 figures

We introduce a method to speed up adiabatic protocols for creating entanglement between two qubits dispersively coupled to a transmission line, while keeping fidelities high and maintaining robustness to control errors. The method takes genuinely adiabatic sweeps, ranging from a simple Landau-Zener drive to boundary cancellation methods and local adiabatic drivings, and adds fast oscillations to speed up the protocol while canceling unwanted transitions. We compare our protocol with existing adiabatic methods in a state-of-the-art parameter range and show substantial gains. Numerical simulations emphasize that this strategy is efficient also beyond the rotating-wave approximation and that the method is robust against random static biases in the control parameters and with respect to damping and decoherence effects., Comment: 15 pages, 9 figures

We study the quantum tunneling of two one-dimensional quasi-condensates made of alkali-metal atoms, considering two different tunneling configurations: side-by-side and head-to-tail. After deriving the quasiparticle excitation spectrum, we discuss the dynamics of the relative phase following a sudden coupling of the independent subsystems. In particular, we calculate the coherence factor of the system, which, due to the nonzero tunneling amplitude, it exhibits dephasing-rephasing oscillations instead of pure dephasing. These oscillations are enhanced by a higher tunneling energy, and by higher system densities. Our predictions provide a benchmark for future experiments at temperatures below $T \lesssim 5 \, \mbox{nK}$., 15 pages, 4 figures

This editorial remembers Shmuel Fishman, one of the founding fathers of the research field “quantum chaos”, and puts into context his contributions to the scientific community with respect to the twelve papers that form the special issue.

The atom-optics kicked rotor can be used to prepare specific momentum distributions on a discrete basis set. We implement a continuous-time quantum walk and a quantum search protocol in this momentum basis. In particular we propose ways to identify a specific marked state from the final momentum distribution after the walker's evolution. Our protocol is guided by current experimental possibilities making it accessible to experimentally implemented quantum walks with Bose-Einstein condensates.

We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at all times. The strategy is based on the introduction of an effective counterdiabatic scheme: a correcting Hamiltonian is constructed which approximatively cancels nonadiabatic effects, inducing an evolution tracking the adiabatic states closely. This can be absorbed into the initial Hamiltonian by adding a fast oscillation in the control parameters. We show that a consistent speedup can be achieved without requiring strong control Hamiltonians, using it both as a stand-alone shortcut-to-adiabaticity and as a weak correcting field. A number of examples are treated, dealing with quantum state transfer in avoided-crossing problems and entanglement creation., 15 pages, 9 figures

We study the current of Bose particles between two reservoirs connected by a one-dimensional channel. We analyze the problem from first principles by considering a microscopic model of conductivity in the noninteracting limit. Equations for the transient and the stationary current are derived analytically. The asymptotic current has a form similar to the Landauer-B\"uttiker equation for electronic current in mesoscopic devices.

We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly flexible and can provide a platform for a wide range of applications such as quantum search algorithms, the observation of topological phases, and the realization of walks with higher dimensionality. Along with the investigation of the quantum-to-classical transition, we demonstrate the distinctive features of a quantum walk and contrast them to those of its classical counterpart. Also, by manipulating either the walk or coin operator, we show how the walk dynamics can be steered or even reversed., 5 pages, 3 figures

A Bose gas in a double well is investigated in the presence of single-particle, two-body and three-body asymmetric loss. The loss induces an interesting decay behavior of the total population as well as a possibility to control the dynamics of the system. In the noninteracting limit with asymmetric single-body dissipation, the dynamics of the populations can be obtained analytically. The general many-body problem requires, however, an adequate approximation. We use a mean-field approximation and the Bogoliubov back-reaction beyond mean-field truncation, which we extend up to three-body loss. Both methods are compared with exact many-body Monte-Carlo simulations., to appear in PRA

We analytically investigate the recently proposed and implemented discrete-time quantum walk based on a kicked Bose-Einstein condensate. We extend previous work on the effective dynamics by taking into account spontaneous emission due to the kicking light. Spontaneous emission affects both the internal and external degrees of freedom, arising from the entanglement between them during the walk dynamics. The result is a measurable degrading of the experimental walk signal that we characterise., Comment: comments and suggestions welcome

Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counter-intuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.

We present a two-band Bose-Hubbard model which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many-body problem is studied by sweeping the system across an avoided level crossing. The linear sweep generalizes Landau-Zener transitions from single-particle to many-body realizations. The temporal evolution of single- and two-body observables along the sweeps is investigated in order to characterize the non-equilibrium dynamics in our complex quantum system.

Open many-body quantum systems have recently gained renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. A series of results in diverse setups is presented, based on a Master equation approach to describe the dissipative dynamics of ultracold bosons in a one-dimensional lattice. The creation of mesoscopic stable many-body structures in the lattice is predicted and the non-equilibrium transport of neutral atoms in the regime of strong and weak interactions is studied.

We propose a realistic scheme to implement discrete-time quantum walks in the Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein condensate. Relying on a static optical lattice to suppress tunneling in real space, the condensate is displaced in quasimomentum space in discrete steps conditioned upon the internal state of the atoms, while short pulses periodically couple the internal states. We show that tunable twisted boundary conditions can be implemented in a fully natural way by exploiting the periodicity of the Brillouin zone. The proposed setup does not suffer from off-resonant scattering of photons and could allow a robust implementation of quantum walks with several tens of steps at least. In addition, onsite atom-atom interactions can be used to simulate interactions with infinitely long range in the Brillouin zone., 9 pages, 4 figures; in the new version, added a discussion about decoherence in the appendix

We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.

The expansion of an initially confined Bose-Einstein condensate into either free space or a tilted optical lattice is investigated in a mean-field approach. The effect of the interactions is to enhance or suppress the transport depending on the sign and strength of the interactions. These effects are discusses in detail in view of recent experiments probing non-equilibrium transport of ultracold quantum gases.

It has been recently shown that fast oscillating control fields can be used to speed up an otherwise slow adiabatic process, making the system always follow an instantaneous eigenvector closely. In applying this method though, one typically assumes perfect phase relations among the control fields. In this work, we discuss the effect of potential static phase errors. We show that the latter can in some cases produce higher fidelities, leading to an unexpected improvement of the method. This is shown numerically and explained via a perturbative expansion of the error produced by the control strategy. When high-precision phase control is accessible, the results suggest that the phases of the control field can be used as free parameters whose optimization can be beneficial for the control protocol.

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.

One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site., 6 pages, 6 figures

A many-body Wannier-Stark system coupled to an effective reservoir is studied within a non-Hermitian approach in the presence of a periodic driving. We show how the interplay of dissipation and driving dynamically induces a subspace of states which are very robust against dissipation. We numerically probe the structure of these asymptotic states and their robustness to imperfections in the initial-state preparation and to the size of the system. Moreover, the asymptotic states are found to be strongly entangled making them interesting for further applications., Comment: 8 pages, 5 figures! Comments are welcome!

We demonstrate quantum resonance ratchets created with Bose-Einstein condensates exposed to pulses of an off-resonant standing light wave. We show how some of the basic properties of the ratchets are controllable through the creation of different initial states of the system. In particular, our results prove that through an appropriate choice of initial state it is possible to reduce the extent to which the ratchet state changes with respect to time. We develop a simple theory to explain our results and indicate how ratchets might be used as part of a matter wave interferometer or quantum-random walk experiment., Comment: 6 pages, 8 figures

Each step in a quantum random walk is typically understood to have two basic components: a ``coin toss'' which produces a random superposition of two states, and a displacement which moves each component of the superposition by different amounts. Here we suggest the realization of a walk in momentum space with a spinor Bose-Einstein condensate subject to a quantum ratchet realized with a pulsed, off-resonant optical lattice. By an appropriate choice of the lattice detuning, we show how the atomic momentum can be entangled with the internal spin states of the atoms. For the coin toss, we propose to use a microwave pulse to mix these internal states. We present experimental results showing an optimized quantum ratchet, and through a series of simulations, demonstrate how our proposal gives extraordinary control of the quantum walk. This should allow for the investigation of possible biases, and classical-to-quantum dynamics in the presence of natural and engineered noise.

The dynamical evolution of a Bose-Einstein condensate in an open optical lattice is studied. Based on the Bose-Hubbard model we rederive the mean-field limit for the case of an environmental coupling including dissipation and phase-noise. Moreover, we include the next order correlation functions to investigate the dynamical behavior beyond mean field. We observe that particle loss can lead to surprising dynamics, as it can suppress decay and at the same time restore the coherence of the condensate. These behavior can be used to engineer the evolution, e.g. in the form of a stochastic resonance-like response, to inhibit tunneling or to create stable nonlinear structures of the condensate.

Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.

A kicking sequence of the atom optics kicked rotor at quantum resonance can be interpreted as a quantum random walk in momentum space. We show how to steer such a random walk by applying a random sequence of intensities and phases of the kicking lattice chosen according to a probability distribution. This distribution converts on average into the final momentum distribution of the kicked atoms. In particular, it is shown that a power-law distribution for the kicking strengths results in a L\'evy walk in momentum space and in a power-law with the same exponent in the averaged momentum distribution. Furthermore, we investigate the stability of our predictions in the context of a realistic experiment with Bose-Einstein condensates., Comment: detailed study of random walks and their implementation with a Bose condensate, 12 pages, 7 figures

We investigate the parametric fluctuations in the quantum survival probability of an open version of the delta-kicked rotor model in the deep quantum regime. Spectral arguments [Guarneri I and Terraneo M 2001 Phys. Rev. E vol. 65 015203(R)] predict the existence of parametric fractal fluctuations owing to the strong dynamical localisation of the eigenstates of the kicked rotor. We discuss the possibility of observing such dynamically-induced fractality in the quantum survival probability as a function of the kicking period for the atom-optics realisation of the kicked rotor. The influence of the atoms' initial momentum distribution is studied as well as the dependence of the expected fractal dimension on finite-size effects of the experiment, such as finite detection windows and short measurement times. Our results show that clear signatures of fractality could be observed in experiments with cold atoms subjected to periodically flashed optical lattices, which offer an excellent control on interaction times and the initial atomic ensemble., Comment: 18 pp, 7 figs., 1 table

We examine the effect of the initial atomic momentum distribution on the dynamics of the atom-optical realisation of the quantum kicked rotor. The atoms are kicked by a pulsed optical lattice, the periodicity of which implies that quasi-momentum is conserved in the transport problem. We study and compare experimentally and theoretically two resonant limits of the kicked rotor: in the vicinity of the quantum resonances and in the semiclassical limit of vanishing kicking period. It is found that for the same experimental distribution of quasi-momenta, significant deviations from the kicked rotor model are induced close to quantum resonance, while close to the classical resonance (i.e. for small kicking period) the effect of the quasi-momentum vanishes., Comment: 10 pages, 4 figures, to be published in J. Phys. A, Special Issue on 'Trends in Quantum Chaotic Scattering'

We establish a close quantitative analogy between the excitation and ionization process of highly excited one electron Rydberg states under microwave driving and charge transport across disordered 1D lattices. Our results open a new arena for Anderson localization - a disorder induced effect - in a large class of perfectly deterministic, decaying atomic systems.

The quantum resonances occurring with delta-kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analyzed in detail. Exact results about the momentum distribution at exact resonance are established, both in the case of totally coherent dynamics and in the case when decoherence is induced by Spontaneous Emission. A description of the dynamics when the kicking period is close to, but not exactly at resonance, is derived by means of a quasi-classical approximation where the detuning from exact resonance plays the role of the Planck constant. In this way scaling laws describing the shape of the resonant peaks are obtained. Such analytical results are supported by extensive numerical simulations, and explain some recent surprising experimental observations.

The interband dynamics of a two-band Bose–Hubbard (BH) model is studied with strongly correlated bosons forming single-site double occupancies referred to as doublons. Our model for resonant doublon interband coupling exhibits interesting dynamical features such as quantum Zeno effect, the generation of states such as a two-band Bell-like state and an upper-band Mott-like state. The evolution of the asymptotic state is controlled here by the effective opening of one or both of the two bands, which models decay channels.

Quantum-resonance ratchets have been realized over the last ten years for the production of directed currents of atoms. These non-dissipative systems are based on the interaction of a Bose-Einstein condensate with an optical standing wave potential to produce a current of atoms in momentum space. In this paper we provide a review of the important features of these ratchets with a particular emphasis on their optimization using more complex initial states. We also examine their stability close to resonance conditions of the kicking. Finally we discuss the way in which these ratchets may pave the way for applications in quantum (random) walks and matter-wave interferometry.

We discuss the relaxation dynamics for a bosonic tunneling junction with two modes in the central potential well. We use a master equation description for ultracold bosons tunneling in the presence of noise and incoherent coupling processes into the two central modes. Whilst we cannot quantitatively reproduce the experimental data of the setup reported in [Phys. Rev. Lett. 115, 050601 (2015)], we find a reasonable qualitative agreement of the refilling process of the initially depleted central site. Our results may pave the way for the control of bosonic tunneling junctions by the simultaneous presence of decoherence processes and atom-atom interaction.

Nonequilibrium dynamics and effective thermalization are studied in a resonant tunneling scenario via multilevel Landau-Zener crossings. Our realistic many-body system, composed of two energy bands, naturally allows a separation of degrees of freedom. This gives access to an effective temperature and single- and two-body observables to characterize the delocalization of eigenstates and the nonequilibrium dynamics of our paradigmatic complex quantum system.

This chapter discusses two important ways of defining quantum chaoticity. One access to characterize dynamical quantum systems is offered by the powerful approach of semiclassics. Here we compare the properties of the quantum system with its classical analogue, and we combine classical intuition with quantum evolution. The second approach starts from the very heart of quantum mechanics, from the quantum spectrum and its properties. Classical and quantum localization mechanisms are presented, again originating either from the classical dynamics of the corresponding problem and semiclassical explanations, or from the quantum spectra and the superposition principle. The essential ideas of the theory of random matrices are introduced. This second way of characterizing a quantum system by its spectrum is reconciled with the first approach by the conjectures of Berry and Tabor and Bohigas, Giannoni, and Schmit, respectively.

We provide a statistical characterization of the ionization yield of one-dimensional, periodically driven Rydberg states of atomic hydrogen, in the spirit of Anderson localization theory. We find excellent agreement with predictions for the conductance across an Anderson localized, quasi one-dimensional, disordered wire, in the semiclassical limit of highly excited atomic initial states. For the moderate atomic excitations typically encountered in state of the art laboratory experiments, finite-size effects induce significant deviations from the solid-state picture. However, large scale fluctuations of the atomic conductance prevail and are robust when averaged over a finite interval of driving field amplitudes, as inevitably done in the experiment., Comment: 13 pages, 9 figures

We report measurements of dynamical tunneling rates of a Bose-Einstein condensate across a barrier in classical phase space. The atoms are initially prepared in quantum states that extend over a classically regular island region. We focus on the specific system of quantum accelerator modes of the kicked rotor in the presence of gravity. Our experimental data is supported by numerical simulations taking into account imperfections mainly from spontaneous emission. Furthermore, we predict experimentally accessible parameter ranges over which direct tunneling could be readily observed if spontaneous emission was further suppressed. Altogether, we provide a proof-of-principle for the experimental accessibility of dynamical tunneling rates in periodically driven systems., Improved version

The particle transport through a chain of quantum dots coupled to two bosonic reservoirs is studied. For the case of reservoirs of non-interacting bosonic particles, we derive an exact set of stochastic differential equations, whose memory kernels and driving noise are characterised entirely by the properties of the reservoirs. Going to the Markovian limit an analytically solvable case is presented. The effect of interparticle interactions on the transient behaviour of the system, when both reservoirs are instantaneously coupled to an empty chain of quantum dots, is approximated by a semiclassical method, known as the Truncated Wigner approximation. The steady-state particle flow through the chain and the mean particle occupations are explained via the spectral properties of the interacting system., Comment: 7 pages, 4 figures

We analyze the decay of ultracold atoms from an optical lattice with loss form a single lattice site. If the initial state is dynamically stable a suitable amount of dissipation can stabilize a Bose-Einstein condensate, such that it remains coherent even in the presence of strong interactions. A transition between two different dynamical phases is observed if the initial state is dynamically unstable. This transition is analyzed here in detail. For strong interactions, the system relaxes to an entangled quantum state with remarkable statistical properties: The atoms bunch in a few "breathers" forming at random positions. Breathers at different positions are coherent, such that they can be used in precision quantum interferometry and other applications., Comment: 15 pages, 14 figures

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.

We show experimentally that precise phase modulation of an optical potential allows us to control quantum correlations for atomic wave packets in a way that greatly enhances momentum transport. Experimentally, this means that for the same laser power and pulse frequency, atoms are accelerated to much higher energies. We explain our results with a pseudoclassical analysis along with numerical simulations, highlighting the existence of transporting islands in phase space.