We demonstrate theoretically the use of genetic-learning algorithms to coherently control the dynamics of a Bose-Einstein condensate. We consider specifically the situation of a condensate in an optical lattice formed by two counterpropagating laser beams. The frequency detuning between the lasers acts as a control parameter that can be used to precisely manipulate the condensate even in the presence of a significant mean-field energy. We illustrate this procedure in the coherent acceleration of a condensate and in the preparation of a superposition of prescribed relative phase.
We demonstrate theoretically the use of genetic-learning algorithms to coherently control the dynamics of a Bose-Einstein condensate. We consider specifically the situation of a condensate in an optical lattice formed by two counterpropagating laser beams. The frequency detuning between the lasers acts as a control parameter that can be used to precisely manipulate the condensate even in the presence of a significant mean-field energy. We illustrate this procedure in the coherent acceleration of a condensate and in the preparation of a superposition of prescribed relative phase.
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.
We report on the efficient design of quantum optimal-control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice.Our protocols operate on the momentum comb associated with the lattice.In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position.With this technique, we experimentally demonstrate a precise, robust, and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components.This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.
In 1924/25, Satyendranath Bose and Albert Einstein predicted that particles of integer spin (today called bosons) should undergo a statistical phase transition when cooled to temperatures very close to absolute zero (Bose, 1924; Einstein, 1925). This phenomenon, nowadays called Bose-Einstein condensation, has been experimentally observed seventy years later using (nanokelvin temperatures) of bosonic neutral atoms (Anderson et al., 1995; Bradley et al., 1995; Davis et al., 1995c). This spectacular experimental achievement was awarded the Nobel price in 1995 and has triggered a new research direction ultracold gases with more than 200 groups worldwide today. 1 Bose-Einstein condensates (BEC) of atomic represent a fascinating exotic state of matter with properties entirely determined by the laws of mechanics. Although they consisting of several thousands up to millions of atoms, the state can in most cases be described by a single collective wave function with a common phase. This wave function usually has a spatial extent ranging between 1-100 microns, allowing us to observe mechanics essentially by eye using basic magnification optics. The Bose-Einstein condensate can be described as a coherent matter wave in close analogy to the optical field emitted by (or inside) a laser. This analogy has brought about the field of quantum-atom-optics which aims to implement standard elements and experiments known from laser optics using matter waves. As heavy rest mass particles, such as atoms, are very sensitive to gravity or acceleration/rotations, matter-wave interferometers promise orders of magnitude in sensitivity gain compared to their photonic counterparts (Berman, 1996). Over the last decade, experimental tools for the creation and manipulation of matter have reached an impressive degree of sophistication. This allows the construction of tailored Hamiltonians for the system and the quantum simulation of more general physical situations, not connected to atomic physics alone. Optical lattice potentials allow to mimic solid state physics with a high degree of control over essentially all experimental parameters. Particle interactions can be tuned via Feshbach resonances, allowing the study of superconductivity, superfluidity and the formation of
We have performed a number of experiments with a Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Making use of the small momentum spread of a BEC and standard atom optics techniques, a high level of coherent control over an artificial solid-state system is demonstrated. We are able to load the BEC into the lattice ground state with a very high efficiency by adiabatically turning on the optical lattice. We coherently transfer population between lattice states and observe their evolution. Methods are developed and used to perform band spectroscopy. We use these techniques to build a BEC accelerator and a novel, coherent, large-momentum-transfer beam-splitter.
We study the dynamics of Bose–Einstein condensates in accelerated two-dimensional (2D) optical square lattices by numerically solving the Gross–Pitaevskii equation. We consider the regime with negligible mean-field interactions and examine in detail the pulses of atom clouds ejected from the condensate due to Landau–Zener tunnelling. The pulses exhibit patterned structures that can be understood from the momentum–space dynamics of the condensate. Apart from conceiving the realization of a pulsed 2D atom laser, we demonstrate that, by exploring the band structure of the lattice, the Landau–Zener tunnelling and Bragg reflection of the condensate inside the optical lattice can provide a means of manipulation of coherent atom waves.
We present experiments investigating different aspects concerning the coherent manipulation of a Bose-Einstein condensate wavefunction with far blue detuned dipole potentials. In a first set of experiments we study a waveguide for matter waves as an important atom optical element allowing to hold and guide the atoms for long observation times. We present a flexible realization of this waveguide based on a tube shaped Laguerre Gaussian laser beam and investigate the dynamics of a Bose condensed ensemble transferred into this guide. In a second set of experiments we study the dynamics of dark solitons created by the manipulation of the phase of the condensate wave function by temporally applied dipole potentials. This method of phase imprinting represents a powerful tool for the design of matter waves and the controlled creation of various excitations. The dynamics of dark solitons in matter waves is investigated in detail by experimentally and numerically studying the temporal evolution of the condensate density as well as by mapping the velocity field of the excited condensate wavefunction. In these measurements we directly detect the flux of the wave function associated with the dark soliton using spatially resolved Bragg scattering. Experiments investigating the creation and interaction of several dark solitons conclude this chapter.