Optics and interferometry with matter waves is the art of coherently manipulating the translational motion of particles like neutrons, atoms and molecules. Coherent atom optics is an extension of techniques that were developed for manipulating \emph{internal} quantum states. Applying these ideas to translational motion required the development of techniques to localize atoms and transfer population coherently between distant localities. In this view position and momentum are (continuouse) quantum mechanical degree of freedom analogous to discrete internal quantum states. In our contribution we start with an introduction into matter-wave optics in section 1, discuss coherent atom optics and atom interferometry techniques for molecular beams in section 2 and for trapped atoms in section 3. In section 4 we then describe tools and experiments that allow us to probe the evolution of quantum states of many-body systems by atom interference.
The long range goal of this project was the creation of nanostructures using light fields to manipulate atoms. By passing an atomic beam through one or more standing wave light fields, it is possible to create modulations in the atomic density having periods which are a fraction of the period of the standing wave light fields. Patterns having periods as small as lambda/10 were observed using optical masks and clear evidence for matter-wave effects were established. Several theoretical methods for achieving sub-lambda matter wave patterns were developed, Moreover it was shown that it is possible to create optical lattices having reduced periodicity using Raman transitions in a novel atom-field geometry Experiments were carried out in both magneto-optical traps and atomic beams. In both experimental set-ups, pulsed standing wave optical fields were used to excite the atoms. At some later time the atoms were probed by a traveling wave field, revealing the spatial patterns that had evolved as a result of the atom-field interaction.
The discovery and development of methods to cool, trap and manipulate atomic ensembles have generated a revolution in atomic physics, culminating in the ever expanding research field of ultra-cold matter through the realization of Bose-Einstein condensates (BECs). Since the first realization of BEC more than two decades ago, the majority of studies were concerned with systems displaying short-range contact interaction. Following pioneering experiments in ultra-cold KRb, systems involving ultra-cold mixtures have rose to considerable interest through their capability to form diatomic polar molecules. The long-range character of dipolar particle interactions enables the study of a whole new spectrum of quantum many-body phenomena by giving access to the strongly correlated regime. In this context, NaK is a splendid candidate to investigate dipolar effects due to its large electric dipole moment of $2.72 \, $Debye, its chemical stability and the large history of spectroscopic studies devoted to its ground and excited state manifolds. This thesis reports on the first ever realization of a dual-species degenerate mixture of
23Na and
39K. The experimental apparatus combines two pre-cooled atomic sources into a UHV collection region, where a two-color magneto-optical trap is operated. After transferring both species into an optically plugged quadrupole trap, the
23Na ensemble is cooled by selectively removing the hottest atoms from the trap through microwave transitions, while
39K is sympathetically cooled through its thermal contact to
23Na. Following the transfer into an optical dipole trap, the mixture operation suffers from strong losses as the atomic clouds approach the high-density regime. Interspecies interactions are identified as the system parameter that drives the loss mechanism. In order to realize a quantum degenerate mixture, the dual-species collisional properties are investigated both theoretically and experimentally. By preparing both optically trapped ensembles in the spin state
∣f=1,mf=−1⟩, atom loss spectroscopy is performed in a magnetic field range from
0 to
1000G. The observed features include several s-wave poles and a zero crossing of the interspecies scattering length as well as inelastic two-body contributions in the
M=mNa+mK=−2 submanifold. Different magnetic field regions are identified for the purposes of sympathetic cooling of
39K and achieving a quantum degenerate mixture. Forced evaporation creates two Bose-Einstein condensates simultaneously at a magnetic field that provides sizable intra- and interspecies scattering rates needed for fast thermalization. The impact of the differential gravitational sag on the miscibility criterion for the mixture is discussed. The experimental setup and measurements are complemented by theoretical calculations that form a feasibility study of molecular NaK. Starting from ultra-cold Feshbach molecules, the study demonstrates possible pathways for the creation of ultra-cold polar NaK molecules in their absolute electronic and rovibrational ground state. In particular, a multi-channel analysis of the electronic ground and K(4p)+Na(3s) excited state manifold of NaK is presented. It analyzes the spin character of both the Feshbach molecular state and the electronically excited intermediate states and discusses possible coherent two-photon transfer paths from Feshbach molecules to rovibronic ground state molecules. %The theoretical study is complemented by the demonstration of STIRAP transfer from the X1Σ+(v=0) state to the a3Σ+ manifold on a molecular beam experiment. The experimental results serve as a promising starting point for the magnetoassociation into quantum degenerate
23Na39K Feshbach molecules. The theoretical analysis assures qualitative understanding as well as quantitative statements for the feasibility of the subsequent ground state conversion. In combination, they fill a critical gap towards the creation of chemically stable ultra-cold molecular Bose-Einstein condensates of NaK.
This research program investigated the dynamics of open quantum systems in manifestly quantum or nonclassical domains. The research program exploited recently discovered possibilities in the microscopic realm of quantum mechanics to accomplish tasks that would otherwise be impossible by traditional classical means, including new capabilities for precision measurement and for the processing and distribution of information. Within this setting, the particular investigations related to strong coupling in optical physics whereby nonlinear interactions require only single atoms and photons. The research achieved capabilities beyond traditional nonlinear optics and laser physics and moved into a new regime with dynamical processes involving atoms and photons taken one by one. The research program addressed fundamental issues related to quantum metrology, to quantum communications, and to the general development of quantum information sciences. The most important accomplishments of this work have been the following: (1) The first demonstration of a laser that operates with a single atom; (2) The first realization of a deterministic source for single photons that generates single photons "on demand" from one atom trapped in a cavity; (3) The development of a protocol for the real-time determination of the number of trapped atoms inside an optical cavity in a regime of strong coupling, with N = 0,1,2,3...atoms; and (4) The first experiment to achieve manifestly quantum or nonclassical photon correlations suitable for the implementation of scalable quantum communications networks.
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.