Motivated by recent experimental progress achieved with ultracold atoms in kilohertz-driven optical lattices, we provide a theoretical discussion of mechanisms governing the response of a particle in a cosine lattice potential to strong forcing pulses with smooth envelope. Such pulses effectuate adiabatic motion of a wave packet's momentum distribution on quasienergy surfaces created by spatiotemporal Bloch waves. Deviations from adiabaticity can then be deliberately exploited for exerting coherent control and for reaching target states which may not be accessible by other means. As one particular example, we consider an analog of the $\ensuremath{\pi}$ pulses known from optical resonance. We also suggest adapting further techniques previously developed for controlling atomic and molecular dynamics by laser pulses to the coherent control of matter waves in shaken optical lattices.
Motivated by recent experimental progress achieved with ultracold atoms in kilohertz-driven optical lattices, we provide a theoretical discussion of mechanisms governing the response of a particle in a cosine lattice potential to strong forcing pulses with smooth envelope. Such pulses effectuate adiabatic motion of a wave packet's momentum distribution on quasienergy surfaces created by spatiotemporal Bloch waves. Deviations from adiabaticity can then be deliberately exploited for exerting coherent control and for reaching target states which may not be accessible by other means. As one particular example, we consider an analog of the \ensuremathπ pulses known from optical resonance. We also suggest adapting further techniques previously developed for controlling atomic and molecular dynamics by laser pulses to the coherent control of matter waves in shaken optical lattices.
The scope of the present publication-based thesis on periodically forced optical lattices is twofold: In the first part, the reader is introduced to the main concepts required to formulate the central results of this thesis, and a review is given of landmark papers on coherently controlling ultracold atoms by subjecting them to periodic forces. The second part provides the author's own results of original research on the subject and consists of four publications and a preprint. It is shown how ultracold atoms in optical lattices can be used as strong-field simulators, dynamic localization in optical lattices are described in detail, and multiphoton-like processes are studied. A generalized acceleration theorem for spatiotemporal Bloch waves is developed and used to enable a controlled wave-packet manipulation in optical lattices.
Within the combined potential of an optical lattice and a harmonic magnetic trap, it is possible to form matter wave packets by intensity modulation of the lattice. An analysis of the production and motion of these wave packets provides a detailed understanding of the dynamical evolution of the system. The modulation technique also allows for a controllable transfer (deexcitation) of atoms from such wave packets to a state bound by the lattice. Thus, it acts as a beam splitter for matter waves that can selectively address different bands, enabling the preparation of atoms in localized states. The combination of wave packet creation and deexcitation closely resembles the well-known method of pump-probe spectroscopy. Here, we use the deexcitation for spectroscopy of the anharmonicity of the combined potential. Finally, we demonstrate that lattice modulation can be used to excite matter wave packets to even higher momenta, producing fast wave packets with potential applications in precision measurements.
The coherent manipulation of wave packets is an important tool in many areas of physics. We demonstrate the experimental realization of quasi-free wave packets of ultra-cold atoms bound by an external harmonic trap. The wave packets are produced by modulating the intensity of an optical lattice containing a Bose-Einstein condensate. The evolution of these wave packets is monitored in-situ and their reflection on a band gap is observed. In direct analogy with pump-probe spectroscopy, a probe pulse allows for the resonant de-excitation of the wave packet into localized lattice states at a long, controllable distance of more than 100 lattice sites from the main component. This coherent control mechanism for ultra-cold atoms thus enables controlled quantum state preparation, opening exciting perspectives for quantum metrology and simulation.
This dissertation presents a theoretical analysis of methods to manipulate and control the momentum state of coherent matter waves. Of particular interest is the coherent acceleration of a quantum-degenerate atomic system, which, as a direct consequence of the form of the de Broglie wavelength, results in tunable source of matter waves. Such sources are of considerable importance for a number of potential applications in the field of atom optics, including the development of highly sensitive gyroscopes, accelerometers, gravity gradiometers or atom lithography and holography, as well as for potential uses in integrated atom optics. Our basic setup consists of a Bose-Einstein condensate in a moving optical lattice created by a pair of frequency-chirped counterpropagating laser beams acting as a "conveyor belt'' for ultracold atoms. Whereas the acceleration of ultracold but non-condensed atoms in such a lattice was demonstrated earlier, we extend this scheme to the case of Bose-Einstein condensates. As a first step, we investigate the acceleration efficiency for various acceleration rates and nonlinear interaction strengths. We find parameter regimes where efficient acceleration is possible, i.e. all atoms are accelerated to the same velocity and the initially sharp momentum distribution and thus its monochromaticity is preserved. However, in general we identify switch-on effects of the lattice, dynamical loss and nonlinear effects to be responsible for deterioration of the monochromaticity of the condensate: On the one hand, switch-on effects and dynamical loss induce a coupling of the initially populated momentum mode to other modes, thereby distributing the momentum over several modes. On the other hand, the nonlinear release of mean field energy during the acceleration process causes the mode profile itself to broaden, also leading to a contamination of the initial monochromaticity. As a second step, we discuss ways to improve this scheme by removing the restriction of constant accelerations. We employ genetic algorithms to optimize the time-dependent motion of the lattice. We show that with such flexibility, it is possible to achieve a fast and highly efficient coherent acceleration of condensates, even when mean-field effects cannot be neglected. The same scheme also enables the creation of arbitrary coherent superposition states in momentum space. The technique is thus suitable for building highly efficient momentum state beam splitters. In addition to simply accelerating condensates, it is desirable for many potential applications to transport atomic wave packets without dispersion over large distances. This can be achieved by launching bright atomic solitons, where the effects of the nonlinearity counterbalance the dispersion. Placing a Bose-Einstein condensate with repulsive interactions in a lattice, one can create a negative effective mass. Under these circumstances bright and stable soliton solutions exist, so-called gap solitons. After a careful analysis of the soliton properties, we use the tools we developed for condensate acceleration and demonstrate two feasible schemes to excite the solitons. Experimental data released after publication of our results demonstrating the acceleration of Bose-Einstein condensates in moving lattices and the very recent observation of atomic gap solitons indicates that our theoretical analysis was timely and indeed experimentally feasible. As an outlook, we briefly comment on a new direction in the field of atom optics that holds promise for future applications: the use of quantum degenerate Fermi gases. In atomic as well as in optical physics one often encounters situations where there exists a coupling between several modes of a system. Here, we illustrate the "toy model'' of a fermionic coupler where transitions between two internal states are induced by Raman coupling. Due to Fermi statistics and interatomic interactions, this is a simple example of a nonlinear multimode coupler. Investigation of this system consisting of only a few fermions already clearly illustrates the basic differences between bosonic and fermionic dynamics and sheds light on the role of two-body collisions. Understanding the basic mechanisms of this system is a first step towards more sophisticated coherent control of fermionic systems.
Experimental and theoretical work is presented on the control of wave packet dynamics in atomic and molecular systems. Using sequences of phase-locked optical pulses, the link between optical phase and quantum mechanical phase is explored in the Na atom and Naj dimer, representing a step towards the logical engineering of quantum states in more complicated systems. A novel apparatus, constructed to study and control the vibrational dynamics of vibrational wave packets on the Na ionic potential surface, is described in chapter 3. Theoretical simulations for proposed experiment are presented in chapter 4. Control is achieved by exploiting the phase-evolution of the constituent vibrational quantum states within the wave packet superposition. The phase relationship and the accumulated phase difference between the various components of the wave packet is determined, and a sequence of phase-locked optical pulses is employed to selectively enhance or depopulate specific vibrational states, or sets of vibrational states. The quantum state composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multi-pulse response of the time-dependent vibrational state populations. In chapter 5, the quantum interference between Rydberg electron wave packets in the Na atom is investigated using pairs of phase-locked wave packets, allowing manipulation of the total orbital angular momentum of Na Rydberg atoms. Initially the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows specific angular momentum compositions within the resultant wave packet to be engineered. Experimentally, this final quantum state distribution is analysed in the frequency domain using state selective field ionisation, and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets.
Optical lattices are periodic light shift potentials that are created by the interference of several laser beams. In this dissertation I investigate the motion of atoms in such potentials. The center-of-mass wave-packet motion is initiated by an application of a sudden shift to the lattice potentials. The resulting oscillations are observed using a photon redistribution technique. We first show that by utilizing a real-time feedback loop and shifting the lattice continuously in response to the wave-packet motion, we can increase, alter or damp this motion using different gains of the feedback loop. We further show that by splitting the wave-packet between two adiabatic potentials of the lattice via quantum projection, we can construct an atom interferometer. We observe interference signal when the two components of the original wave-packet overlap. The behavior of the interference is studied as a function of lattice parameters and a consistent theoretical picture is developed. Further, we study how well-to-well tunneling of atoms and sloshing-type wave-pocket dynamics affect each other. We find that in the regions where the well-to-well tunneling is significant, the sloshing type wave-packet oscillations are suppressed. Sloshing-type motion only occurs if the tunneling is sufficiently suppressed with an applied magnetic field. Finally we describe a new type of optical lattice that is based on two-photon Raman transitions. The basic period of this lattice is reduced by a factor of two, compared with traditional lattices. We also show that Sub-Doppler cooling mechanism is present in this lattice. The dissertation is concluded with the presentation of a new experimental set-up for Bose-Einstein Condensate production, which may in the future be used for the study of BEC dynamics in optical lattices.