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. The momentum diffusion constant is thus modified by kick-to-kick correlations which show a momentum dependence. We exploit this, and a technique involving a moving optical potential, to create an asymmetry in the momentum diffusion that is due entirely to the chaotic dynamics.
We study the effect of different heating rates of a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms. The average energy of the atoms is localized after a large number of kicks and the system reaches a nonequilibrium steady state. A numerical simulation of the experimental data suggests that the localization is due to energetic atoms leaking over the barrier. Our data also indicates a correlation between collisions and the destruction of the Bose-Einstein con…
We experimentally investigate the sub-Fourier behavior of a $δ$-kicked rotor resonance by performing a measurement of the fidelity or overlap of a Bose-Einstein condensate (BEC) exposed to a periodically pulsed standing wave. The temporal width of the fidelity resonance peak centered at the Talbot time and zero initial momentum exhibits an inverse cube pulse number ($1/N^{3}$) dependent scaling compared to a $1/N^{2}$ dependence for the mean energy width at the same resonance. A theoretical analysis shows that for an accelerating potential the width of the resonance in acceleration space depen…
We demonstrate perfect coherence preservation in an atom interferometer perturbed by kicks from off-resonant standing wave pulses. Under most conditions, the decoherence induced by the pulses reduces the signal; however, the coherence is perfectly preserved when the kicking period is equal to the rational fraction of the inverse atomic recoil frequency, independent of the number or the randomness of the strength of the applied kicks. The width narrowing of coherence revival as a function of increasing kick number and strength provides a new accurate measurement of the recoil frequency.
We experimentally investigate the effect of atomic $δ$-kicked rotor potentials on the mutual coherence between wavepackets in an atom interferometer. The differential action of the kicked rotor degrades the mutual coherence, leading to a reduction of the interferometry fringe visibility; however, when the repetition rate of the kicked rotor is at or near the quantum resonance, we observe revival of matter-wave coherence as the number of kicks increases, resulting in non-vanishing coherence in the large kick number limit. This coherence saturation effect reflects a saturation of fidelity decay …
We present a concrete theoretical proposal for detecting topological phase transitions in double kicked atom-optics kicked rotors with internal spin-1/2 degree of freedom. The implementation utilizes a kicked Bose-Einstein condensate evolving in one-dimensional momentum space. To reduce influence of atom loss and phase decoherence we aim to keep experimental durations short while maintaining a resonant experimental protocol. Experimental limitations induced by phase noise, quasimomentum distributions, symmetries, and the AC-Stark shift are considered. Our results thus suggest a feasible and op…
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…
We study the mechanisms responsible for quantum diffusion in the quasiperiodic kicked rotor. We report experimental measurements of the diffusion constant on the atomic version of the system and develop a theoretical approach (based on the Floquet theorem) explaining the observations, especially the ``sub-Fourier'' character of the resonances observed in the vicinity of exact periodicity, i.e. the ability of the system to distinguish two neighboring driving frequencies in a time shorter than the inverse of the difference of the two frequencies.
We present an approach of the kicked rotor quantum resonances in position-space, based on its analogy with the optical Talbot effect. This approach leads to a very simple picture of the physical mechanism underlying the dynamics and to analytical expressions for relevant physical quantities, such as mean momentum or kinetic energy. The ballistic behavior, which is closely associated to quantum resonances, is analyzed and shown to emerge from a coherent adding of successive kicks applied to the rotor thanks to a periodic reconstruction of the spatial wavepacket.
We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, epsilon-classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamica…
In this work we apply the formalism developed in [M. Lepers \emph{et al}., Phys. Rev. A \textbf{77}, 043628 (2008)] to different initial conditions corresponding to systems usually met in real-life experiments, and calculate the observable quantities that can be used to characterize the dynamics of the system. The position space point of view allows highly intuitive pictures of the physics at play.
We report an experimental and theoretical study of the dynamics of cold atoms subjected to closely-spaced pairs of pulses in an optical lattice. The experiments show the interplay between fully coherent quantum dynamics and a novel momentum-diffusion regime: for all previously-studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2 or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged 'global' correlations, between all kick-pairs, which control transport through trapping regions in phase-space. Analytical formulae are presen…
We experimentally explore the underlying pseudo-classical phase space structure of the quantum delta kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.
We examine the quantum dynamics of cold atoms subjected to {\em pairs} of closely spaced $δ$-kicks from standing waves of light, and find behaviour quite unlike the well-studied quantum kicked rotor (QKR). Recent experiments [Jones et al, {\em Phys. Rev. Lett. {\bf 93}, 223002 (2004)}] identified a regime of chaotic, anomalous classical diffusion. We show that the corresponding quantum phase-space has a cellular structure, arising from a unitary matrix with oscillating band-width. The corresponding eigenstates are exponentially localized, but scale with a fractional power, $L \sim \hbar^{-0.75…
We present experimental measurements of the mean energy in the vicinity of the first and second quantum resonances of the atom optics kicked rotor for a number of different experimental parameters. Our data is rescaled and compared with the one parameter epsilon--classical scaling function developed to describe the quantum resonance peaks. Additionally, experimental data is presented for the ``classical'' resonance which occurs in the limit as the kicking period goes to zero. This resonance is found to be analogous to the quantum resonances, and a similar one-parameter classical scaling functi…
The quantum dynamics of atoms subjected to pairs of closely-spaced $δ$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$δ$-kicked system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase-space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances whi…
We review the theoretical model and experimental realization of the atom optics $δ-$kicked rotor (AOKR), a paradigm of classical and quantum chaos. We have performed a number of experiments with an all-optical Bose-Einstein condensate (BEC) in a periodic standing wave potential in an AOKR system. We discuss results of the investigation of the phenomena of quantum resonances in the AOKR. An interesting feature of the momentum distribution of the atoms obtained as a result of short pulses of light, is the variance of the momentum distribution or the kinetic energy $<p^{2}>/2m$ in units of the re…
We study the dynamics of cold atoms subjected to {\em pairs} of closely time-spaced $δ$-kicks from standing waves of light. The classical phase space of this system is partitioned into momentum cells separated by trapping regions. In a certain range of parameters it is shown that the classical motion is well described by a process of anomalous diffusion. We investigate in detail the impact of the underlying classical anomalous diffusion on the quantum dynamics with special emphasis on the phenomenon of dynamical localization. Based on the study of the quantum density of probability, its second…
We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular, we consider the dynamical evolution of the momentum moments and find that all even-ordered momentum moments exhibit a power law growth. In the ultracold (zero-temperature) limit the exponent is determined by the order of the moment, whereas for a broad, thermal initial momentum distribution the exponent is reduced by one. To demonstrate the power law behavior…
We consider resonant dynamics in a dilute atomic gas falling under gravity through a periodically pulsed standing-wave laser field. Our numerical calculations are based on a Monte Carlo method for an incoherent mixture of noninteracting plane waves, and show that quantum resonances are highly sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. For particular values of the atomic acceleration, we observe fractional resonances. We investigate the effect of the initial atomic momentum width on the fractional resonances, and quantify the sensitivity …
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 …
We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2δ$-KP). Recent experimental studies with cold atoms implied an underlying classical diffusion of type very different from the well-known paradigm of Hamiltonian chaos, the Standard Map. The kicks in each pair are separated by a small time interval $ε\ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2δ$-KP is partitioned into momentum `cells' partially separated by momentum-trapping regions where…
We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field expe…
We study nonlinear dynamics of the kicked particle whose motion is confined by square billiard. The kick source is considered as localized at the center of square with central symmetric spatial distribution. It is found that ensemble averaged energy of the particle diffusively grows as a function of time. This growth is much more extensive than that of kicked rotor energy. It is shown that momentum transfer distribution in kicked billiard is considerably different than that for kicked free particle. Time-dependence of the ensemble averaged energy for different localizations of the kick source …
The quantum resonances (QRs) of the kicked particle are studied in a most general framework by also considering {\em arbitrary} periodic kicking potentials. It is shown that QR can arise, in general, for {\em any rational} value of the Bloch quasimomentum. This is illustrated in the case of the main QRs for arbitrary potentials. In this case, which is shown to be precisely described by the linear kicked rotor, exact formulas are derived for the diffusion coefficients determining the asymptotic evolution of the average kinetic energy of either an incoherent mixture of plane waves or a general w…
