High-order quantum resonances observed in a periodically kicked Bose-Einstein condensate

We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.     

On periodically kicked quantum systems

The time evolution of a multi-dimensional system which is kicked periodically with a potential is obtained. The most interesting aspects of the investigation are (i) if the operator corresponding to the potential has invariant subspaces (a characteristic property of multi-dimensional systems), the states belonging to these subspace in its evolution are confined to these invariant subspaces respectively and there cannot be any mixing of states between these subspaces. Further, (ii) it leads to the existence of quasi-stationary states (determined again by the potential) which evolves independent of other similar quasi-stationary states. The method followed in the paper is the direct integration of the Schrödinger equation and then to construct the wave function from the initial wave function.     

The periodically kicked quantum spin

It is shown that the same kind of deterministic chaos that occurs in classical systems can occur in certain quantum mechanical, many-body systems. The example of the physical realization of the periodically kicked quantum spin (PKQS) is considered in detail. The quantum mechanical equations of motion for this system can be converted into the three-dimensional PKQS map, which exhibits deterministic chaos and Arnold diffusion. Although the case of quantum spin s= 1/2 is assumed, it is shown that the same map results for s=1 (but not for s>/=3/2), and for a suitably chosen classical particle with orbital angular momentum. A simple generalization of the PKQS model gives rise to stochastic webs on the surface of the unit sphere very similar to the Zaslavsky stochastic webs in a plane.     

Rectified momentum transport for a kicked Bose-Einstein condensate

We report the experimental observation of rectified momentum transport for a Bose-Einstein condensate kicked at the Talbot time (quantum resonance) by an optical standing wave. Atoms are initially prepared in a superposition of the 0 and -2hkl momentum states using an optical pi/2 pulse. By changing the relative phase of the superposed states, a momentum current in either direction along the standing wave may be produced. We offer an interpretation based on matter-wave interference, showing that the observed effect is uniquely quantum.     

Macroscopic quantum tunneling of a bose condensate

We study, by means of a variational method, the stability of a condensate in a magnetically trapped atomic Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the critical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropriate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly.     

Spectral properties of a periodically kicked quantum Hamiltonian

We study the spectral properties of the Floquet operator for the periodically kicked HamiltonianH(t) =H ₀+ ₊ ^– (t–nT),H ₀ being self-adjoint and pure point. We show that the Floquet operator is pure point for almost every , if is cyclic forH ₀ and has absolutely convergent expansion in the basis of eigenstates ofH ₀. When this last condition is not satisfied, the Floquet operator can have a continuous spectrum, as we show by an example.     

Floquet states of a periodically kicked particle

We present explicit expressions for the Floquet states of a periodically kicked particle in coordinate and momentum representations. These states have been used to evaluate the energy of the particle after an arbitrary number of kicks.     

周期驱动玻色-爱因斯坦凝聚系统的棘齿效应

研究了周期脉冲驱动下的玻色-爱因斯坦凝聚体系（BEC）的动力学演化.其中着重考虑了BEC原子间的非线性相互作用对量子棘齿效应的影响.数值计算结果表明,较弱的非线性相互作用可以减弱定向动量流的强度.而较强的非线性相互作用则会使量子棘齿效应消失甚至发生反转,即系统会出现反向的定向动量流,而且随着时间的演化,动量流会表现出微弱的饱和趋势.计算还发现,高阶量子共振下系统的棘齿效应变得很不明显,而且外部驱动势的周期噪声很容易破坏体系的棘齿效应. 关键词： 玻色-爱因斯坦凝聚 量子混沌 量子共振 棘齿效应     

Transition to instability in a kicked bose-einstein condensate

A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor. For weak interactions between atoms, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.     

Quantum instability for a wave packet kicked periodically by a quadratic potential

The quantal behaviour of wave packet periodically kicked by a quadratic potential has been investigated using Floquet theory. The wave function of the particle afterN kicks has been determined. This wave function has been utilized to obtain the packet width, energy and loss of memory as a function of the number of kicks. It has also been shown that the free particle wave packet quasienergy spectrum makes a transition from discrete to absolutely continuous atɛ T=2. The behaviour forɛT>2 is quantum mechanically irregular.     

Classical and quantum chaos for a kicked top

We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the quantum dynamics takes place in a finite dimensional Hilbert space. We find a distinction between regular and irregular behavior for times exceeding the quantum mechanical quasiperiod at which classical behavior, whether chaotic or regular, has died out in quantum means. The degree of level repulsion depends on whether or not the top is endowed with a generalized time reversal invariance.     

Coherent control of ballistic energy growth for a kicked Bose-Einstein condensate

We consider a Bose-Einstein condensate which is split into two momentum components and then “kicked" at the Talbot time by an optical standing wave. The mean energy growth is shown to be suppressed or enhanced depending on the quantum phase between the two momentum components. Experimental verification is provided and we discuss possible implications of our results for recently suggested applications of kicked atoms.     

Dyson-Wick expansions for nonlinear bose systems

We give the general relation between different values of the equal-time contractions in the Dyson-Wick expansion of the S-matrix and different factor orderings of the noncommuting operators in the interaction hamiltonian. Different orderings lead to different expansions with different Feynman rules.     

Recurrent versus diffusive dynamics for a kicked quantum system

We study the dynamics of a two-level quantum system subject to a time-dependent kicking perturbation modulated along the Thue-Morse sequence. For a nontrivial set of the parameters, the quantum autocorrelation function is explicitly calculated, and splits into a purely recurrent and a purely diffusive part. Furthermore, the diffusive part is directly related to the (singular continuous) correlation measure of the Thue-Morse sequence.     

Production of a bose einstein condensate of metastable helium atoms

We recently observed a Bose-Einstein condensate in a dilute gas of ⁴He in the 2³S₁ metastable state. In this article, we describe the successive experimental steps which led to the Bose-Einstein transition at 4.7 μK: loading of a large number of atoms in a MOT, efficient transfer into a magnetic Ioffé-Pritchard trap, and optimization of the evaporative cooling ramp. Quantitative measurements are also given for the rates of elastic and inelastic collisions, both above and below the transition. Received 15 October 2001     

Leggett-Garg inequality with a kicked quantum pump

A kicked quantum nondemolition measurement is introduced, where a qubit is weakly measured by pumping current. Measurement statistics are derived for weak measurements combined with single-qubit unitary operations. These results are applied to violate a generalization of the Leggett-Garg inequality. The violation is related to the failure of the noninvasive detector assumption, and may be interpreted as either intrinsic detector backaction, or the qubit entangling the microscopic detector excitations. The results are discussed in terms of a quantum point contact kicked by a pulse generator, measuring a double quantum dot.     

Localization in frequency for periodically kicked light propagation in a dispersive single-mode fiber

We show a special effect of localization in the temporal frequency domain of light pulses that propagate in a dispersive single-mode fiber in the presence of a time-periodic phase modulation that is repeatedly applied at equally spaced locations along the fiber. The effect is analogous to the dynamical localization that occurs for the quantum kicked rotor, which is similar to Anderson localization in disordered solids. The wave behavior eliminates the diffusive spread of sidebands (harmonics). The light propagation, which is described by a Schr?dinger-like propagation equation, can provide a new testing ground for the investigation of localization besides shedding light on technologically important pulse propagation in fibers and mode-locked lasers.     

Classical quantum crossover for a bose system in the largen-limit

Summary On the basis of the Hartree approximation, the lowtemperature properties of ad-dimensionaln-vector Bose model are discussed in detail, for both normal and ordered phase. The change of critical behaviour which occurs for 2<d<4 when the temperature goest to zero is described in terms of the usual crossover theory. In particular, several crossover scaling functions and the corresponding effective critical exponents are calculated. The results constitute a useful guide for future renormalization group investigations of the classical quantum crossover in a Bose system.

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Riassunto Le proprietà a bassa temperatura di un gas di Bosen-vettore ind dimensioni sono discusse in dettaglio nell'approssimazione di Hartree, sia per la fase normale che per quella ordinata. Il cambiamento del comportamento critico che interviene per 2<d<4 quando la temperatura va a zero è descritto in termini dell'usuale teoria del crossover. In particolare, si effettua un calcolo di alcune funzioni di scaling di crossover e dei corrispondenti esponenti critici effettivi. I risultati costituiscono un'utile guida per futuri studi del crossover classico quantistico in un sistema di Bose sulla base del gruppo di rinormalizzazione.

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Резюме На основе приближения Хартри подробно обсуждаутся свйстваn-векторной модели Ъозе в случаеd-измерений для нормальной и упорядоченной Фаз. Используя теорию обычного кроссовера, описывается изменение критического поведения, которое имеет место для 2<d<4, когда температура стремится к нулю. В частности, вычисляются некотоые функции подобия кроссовера и соответствующие эффективные критические экспоненты. Полученные результаты представляют полезное руководство для дальнеИших исследований классичесииквантового кроссовера в Бозе-системе на основе группы перенормировки.