The effects of reversing the sinusoidal potential every q kick periods with q = 0, l, 2,3 are examined numerically with the q = 0, 1, 2 cases being verified experimentally. I have found that when considering the energy absorption of the system the q = 1 case is qualitatively and quantitatively the same as the standard kicked rotor, while the q = 2 case is qualitatively the same as the standard kicked rotor with an effective increase in the scaled dimensionless kick strength parameter, k, of k rarr; k+ p2 .In this thesis I detail the background, implementation and results of two experiments from relatively different fields of study, both of which involve ultra-cold Rubidium atoms trapped in an optical lattice. The first is an analysis of the superpositions of vibrational states of the lattice. This includes a characterization and modelling of the dephasing of the states, an effect inherent to the lattice. It is found that the lattice geometry is a primary factor in the observed dephasing. This geometry results in position-dependent energy eigenstates in the lattice. Modelling this distribution of energies allows the accurate prediction of several experimental observables and provides useful information for future experiments. Several methods of applying pulse echoes to recover the state in the face of this dephasing are demonstrated, characterized and successfully modelled. The second set of experiments centre around using the optical lattice and Rubidium atoms as a delta-kicked rotor system. First I examine quantum resonances in the delta-kicked rotor. These are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances exist when the effective Planck's constant, a parameter that determines how quantum-mechanically the system behaves, has a value of plank; d5;=rs dot;4p, for integers r and s. However only for plank; d5;=r dot;2p are resonances easily observable. Here I report on the first observation of high-order quantum resonances in a non-condensed atomic sample at values of plank; d5;=r16 dot;4p for integers r = 2--6. Quantum numerical simulations suggest that this observation of high-order resonances indicates a much longer spatial coherence than expected from an initially thermal atomic sample.
The effects of reversing the sinusoidal potential every q kick periods with q = 0, l, 2,3 are examined numerically with the q = 0, 1, 2 cases being verified experimentally. I have found that when considering the energy absorption of the system the q = 1 case is qualitatively and quantitatively the same as the standard kicked rotor, while the q = 2 case is qualitatively the same as the standard kicked rotor with an effective increase in the scaled dimensionless kick strength parameter, k, of k rarr; k+ p2 .In this thesis I detail the background, implementation and results of two experiments from relatively different fields of study, both of which involve ultra-cold Rubidium atoms trapped in an optical lattice. The first is an analysis of the superpositions of vibrational states of the lattice. This includes a characterization and modelling of the dephasing of the states, an effect inherent to the lattice. It is found that the lattice geometry is a primary factor in the observed dephasing. This geometry results in position-dependent energy eigenstates in the lattice. Modelling this distribution of energies allows the accurate prediction of several experimental observables and provides useful information for future experiments. Several methods of applying pulse echoes to recover the state in the face of this dephasing are demonstrated, characterized and successfully modelled. The second set of experiments centre around using the optical lattice and Rubidium atoms as a delta-kicked rotor system. First I examine quantum resonances in the delta-kicked rotor. These are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances exist when the effective Planck's constant, a parameter that determines how quantum-mechanically the system behaves, has a value of plank; d5;=rs dot;4p, for integers r and s. However only for plank; d5;=r dot;2p are resonances easily observable. Here I report on the first observation of high-order quantum resonances in a non-condensed atomic sample at values of plank; d5;=r16 dot;4p for integers r = 2--6. Quantum numerical simulations suggest that this observation of high-order resonances indicates a much longer spatial coherence than expected from an initially thermal atomic sample.
In this thesis we investigate quantum resonant effects in the atom-optical ὁ-kicked accelerator. Using Floquet analysis, we theoretically study the time evolution of quantum systems which have a classical counterpart that exhibits chaotic dynamics. We introduce quantum resonance and quantum antiresonance features of the quantum ὁ -kicked rotor by setting the pulse period to an integer multiple of the half-Talbot time. The model is generalised to the atom-optical ὁ -kicked accelerator by considering thermal alkali atoms subject to a periodically pulsed standing wave potential formed from counter-propagating laser beams. The dynamics of the momentum distribution is analysed by evaluating the momentum moments and momentum cumulants. We derive analytic solutions for these observables for the ultracold and thermal limiting cases, and observe fractional quantum resonant phenomena. Simulations have been developed to examine the time evolution for individual momentum eigenstates, which we use to construct a non-interacting finite temperature gas, based upon a Monte Carlo method. We investigate the temperature dependence of the ὁ-kicked rotor, neglecting gravitational effects, and show that the atomic dynamics is highly sensitive to the initial momentum width of the gas. A generalisation of the model to quantify the transition between the ultracold and thermal temperature regimes of the atom-optical ὁ -kicked accelerator is examined using linear regression analysis. High order quantum resonance features are found to be sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. We assess the dependence of the ὁ -kicked accelerator upon gravitational acceleration, quantifying the width of the high order quantum resonance features, which we use to assess the prospect for precision measurement using a finite temperature gas.
This thesis deals with an investigation of the chaotic dynamics of an atom optics δ-kicked rotor (AOKR) system, a paradigm of classical and quantum chaos. The AOKR rotor is realized by subjecting a Bose-Einstein condensate (BEC) of ⁸⁷Rb atoms to a periodic potential. The potential in the form of a standing wave, obtained from a far detuned laser beam is turned on and off periodically in time, producing short pulses (kicks) of laser light. For certain values of the period between the kicks, resonant effects known as quantum resonances are observed that are purely quantum effects. Quantum resonances have been examined in the AOKR for a series of kicks. For large number of kicks, the width of these resonances have been shown to become narrow. Higher order resonances corresponding to fractional Talbot times have been observed in the system. These quantum resonant effects have been found to depend sensitively on the initial velocity of the atoms. The first three primary resonances have been studied in detail, by measuring the momentum distribution and the kinetic energy of the atoms, for two and four kicks. A sinusoidal dependence of the energy on the initial momentum has been observed for two kicks. By increasing the number of kicks, the system becomes extremely sensitive to the initial momentum of the atoms. For four kicks, a more complex behavior is observed in the system energy. A scheme for investigating Loschmidt time reversal of chaotic dynamics of the atomic deBroglie waves have been described in the AOKR system. It has been demonstrated that the initial wave function of an ensemble of ultracold atoms is restored, after a series of delta-kicks in what is essentially a multiple beam interferometry experiment. During the process, the evolution of the system for a fraction of the atoms with a very small initial momentum is reversed, which results in a narrowing of the momentum distribution. It is hoped that the research presented in this thesis will significantly contribute to the understanding of the connection between the classical and quantum worlds.
Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.
This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the delta-kicked rotor, a paradigm in classical chaos theory, and the novel delta-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate delta-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity’s effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential’s effect. Each system’s dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms’ mean kinetic energy on the number and time period of the delta-kicks. The phenomena of dynamical localisation and quantum resonances in the delta-kicked rotor, which have no counterparts in the system’s classical analogue, are observed and investigated. Similar experiments on the delta-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system’s classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a technique for measuring gravity, and a method of preparing atoms in a particular region of phase space. This may allow measurement of quantum phase space stability, and hence investigation of quantum chaos and quantum-classical correspondence.
The study of quantum resonances in the chaotic atom-optics kicked rotor system is of interest from two different perspectives. In quantum chaos, it marks out the regime of resonant quantum dynamics in which the atomic cloud displays ballistic mean energy growth due to coherent momentum transfer. Secondly, the sharp quantum resonance peaks are useful in the context of measurement of Talbot time, one of the parameter that helps in precise measurement of fine structure constant. Most of the earlier works rely on fidelity based approach and have proposed Talbot time measurement through experimental determination of the momentum space probability density of the periodically kicked atomic cloud. Fidelity approach has the disadvantage that phase reversed kicks need to be imparted as well which potentially leads to dephasing. In contrast to this, in this work, it is theoretically shown that, without manipulating the kick sequences, the quantum resonances through position space density can be measured more accurately and is experimentally feasible as well.
The central theme of this thesis is the directed transport of cold atoms in optical lattices. Several methods for producing such an outcome are proposed, experimentally realised and characterised, in both dissipative and non-dissipative regimes. Accordingly, this thesis may be thought to be composed of two parts. The first section reports results of directed transport in non-dissipative optical lattices, where we used the atom optics realisation of the delta-kicked rotor (DKR) as a model system. Initial experiments performed on this system showed evidence of dynamical localisation, the signature of quantum chaos, and we exploited the presence of the momentum boundary (a barrier to diffusion arising from the approximation of delta-kicks with finite width impulses) to produce asymmetric momentum diffusion. Breaking the DKR system symmetries produced directed diffusion due to chaotic dynamics alone. We observed directed transport in a spatially symmetric system whenever temporal symmetry was broken, and also when the spatial and temporal symmetry of the DKR were simultaneously broken. We also report the first experimental evidence for a 'double-DKR', where experiments performed using a kick sequence composed of closely spaced pairs of kicks instead of single kicks caused significant alterations in the observed behaviour of the kicked rotor system. The origin of this new behaviour was explained in the framework of kick-to-kick correlations and our results were found to be in excellent agreement with numerical simulations. The second part of this thesis describes the realisation of a Brownian ratchet in a 3D dissipative lattice, where fluctuations between different potential surfaces acted as the source of noise. These fluctuations were rectified by the application of a periodic, bi-harmonic driving force, which broke the temporal symmetry of the system. Both current reversal and stochastic resonance behaviour characteristic of a Brownian ratchet were observed.