We realize textbook experiments on Bose-Einstein condensate tunneling through thin repulsive potential barriers. In particular, we demonstrate atom tunneling though a single optical barrier in the quantum scattering regime where the de Broglie wavelength of the atoms is larger than the barrier width. Such a beam splitter can be used for atom interferometry and we study the case of two barriers creating an atomic Fabry-P\'erot cavity. Technically, the velocity spread of the atoms is reduced due to the use of a $^{39}\mathrm{K}$ Bose-Einstein condensate with no interactions. The potential barriers are created optically and their width is tunable due to the use of a digital micromirror device. In addition, our scattering experiments enable in situ characterization of the optical aberrations of the barrier optical system.
We realize textbook experiments on Bose-Einstein condensate tunneling through thin repulsive potential barriers. In particular, we demonstrate atom tunneling though a single optical barrier in the quantum scattering regime where the de Broglie wavelength of the atoms is larger than the barrier width. Such a beam splitter can be used for atom interferometry and we study the case of two barriers creating an atomic Fabry-P'erot cavity. Technically, the velocity spread of the atoms is reduced due to the use of a 39K Bose-Einstein condensate with no interactions. The potential barriers are created optically and their width is tunable due to the use of a digital micromirror device. In addition, our scattering experiments enable in situ characterization of the optical aberrations of the barrier optical system.
We realize textbook experiments on Bose-Einstein condensate tunnelling through thin repulsive potential barriers. In particular, we demonstrate atom tunnelling though a single optical barrier in the quantum scattering regime where the De Broglie wavelength of the atoms is larger than the barrier width. Such a beam splitter can be used for atom interferometry and we study the case of two barriers creating an atomic Fabry-P{é}rot cavity. Technically, the velocity of the atoms is reduced thanks to the use of a 39K Bose-Einstein condensate with no interactions. The potential barriers are created optically and their width is tunable thanks to the use of a digital micro-mirror device. In addition, our scattering experiments enable in-situ characterization of the optical aberrations of the barrier optical system.
This thesis presents a theoretical investigation into the transmission and tunneling dynamics of a Bose-Einstein condensate (BEC) through single and double barriers. We show how quantum tunneling differs from transmission and provide a method for separating them out. We then focus on finding an experimentally-realisable parameter regime for making an atomic Fabry-Perot interferometer (FPI) using two repulsive barriers and study how interatomic interactions affect the dynamics of resonant transmission. Finally, we show that an atomic FPI can be used as an acceleration sensor and we compare its sensitivity to that of a Mach-Zehnder atom interferometer. We first investigate the transmission of an interacting BEC incident on a repulsive Gaussian barrier through numerical simulation. We study the dynamics associated with interatomic interactions across a broad parameter range not previously explored. Comparing effective one-dimensional Gross-Pitaevskii equation (GPE) simulations to classical Boltzmann-Vlasov equation (BVE) simulations, we isolate purely coherent matterwave effects. We then define quantum tunneling as the portion of the GPE transmission not described by the classical BVE. Transmission shows an exponential dependence on barrier height in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, we find that the transmission is predominately described by classical effects, although interatomic interactions modify the magnitude of the quantum tunneling. We show that the interactions also affect the amount of classical transmission, producing transmission in regions where the non-interacting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms. In the second part, we numerically demonstrate atomic Fabry-Perot resonances for a pulsed interacting BEC source transmitting through double Gaussian barriers. These resonances are observable for an experimentally-feasible parameter choice. By simulating an effective one-dimensional GPE, we investigate the effect of atom number, scattering length, and BEC momentum width on the resonant transmission peaks. For Rb-85 atomic sources with the current experimentally-achievable momentum width, we show that reasonably high contrast Fabry-Perot resonant transmission peaks can be observed using a) non-interacting BECs of 100000 atoms, b) interacting BECs of 100000 atoms with s-wave scattering lengths a_s= +-0.1a_0, and c) interacting BECs of 1000 atoms with a_s=+-1.0a_0. Our theoretical investigation impacts any future experimental realisation of an atomic Fabry-Perot interferometer with an ultracold atomic source. Finally, we explore the possibility of using an atomic FPI as an acceleration sensor. Using Fisher information, we quantify the acceleration sensitivity of the system. We study the dependence of sensitivity on various parameters of the system and determine the optimum parameter regime that gives the best sensitivity. For a BEC with infinitely narrow momentum width, the sensitivity can be improved without limit by increasing cavity length. However, when the atomic cloud has a finite momentum width, there exists an optimum cavity length corresponding to each momentum width. By comparing the sensitivity of the atomic FPI to that of a Mach-Zender interferometer with similar parameters, we show that the sensitivity of the atomic FPI overcomes that of the Mach-Zehnder interferometer in low device length and low momentum width regimes. In short, we demonstrate that an atomic FPI can be successfully used for sensing acceleration and the sensitivity of the device can be increased by reducing its length and by using a BEC with lower momentum width compared to the cavity linewidth.
Collective quantum tunneling of a Bose-Einstein condensate between two parts of an optical lattice separated by an energy barrier is theoretically investigated. We show that by a pulsewise change of the barrier height, it is possible to switch between a tunneling regime and a self-trapped one. This property of the system is explained by effectively reducing the nonlinear dynamics of the system to that of a particle moving in a double square well potential. The analysis is performed for both attractive and repulsive interatomic forces, and emphasizes the experimental relevance of our findings.
This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.
The simplicity and versatility of ultra-cold atoms make it an ideal system for studying Quantum Mechanical phenomenon like tunneling. This thesis describes progress towards experimentally measuring the time spent by a tunneling particle in the classically forbidden region. A detailed analysis of the experimental requirements to measure the tunneling time is presented along with the experimental tools developed to meet these requirements. These include a thin \SI{1.3}{\micro m} optical tunnel barrier, a smooth atomic waveguide, and a Larmor clock to measure the tunneling time. Delta-kick cooling is used to achieve the extremely low temperatures required for the tunneling time experiments. A 2.4x reduction in the atomic velocity spread is demonstrated, reducing the rms velocity spread to \SI{0.46(5)}{mm/s}. This corresponds to cooling to an effective temperature of \SI{2.0(4)}{nK}. The thin optical barrier opens up the possibility to study the decay of quasi-bound condensates via tunneling. We develop a novel trapping configuration for this purpose, in which the barrier acts as one of the walls of the trap. Inter-atomic interactions strongly dictate the escape dynamics of the condensate out of this trap, giving rise to three distinct regimes--- classical over the barrier spilling, quantum tunneling driven by interactions, and decay dominated by background losses. We show that in the tunneling regime, the decay rate depends exponentially with the chemical potential of the condensate. Experimental results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.
Quantum tunneling is a quantum phenomenon in which a microscopic object crosses through a potential barrier even if its energy cannot overcome the barrier. A general belief is that tunneling occurs only when the barrier width is comparable to, or smaller than the de Broglie’s wavelength of the object. Here, we study the tunneling of an ultracold atom among N far-separated trapping potentials in a state-selective optical lattice and present a mechanism to realize long-range tunneling. We find that, mediated by the propagating matter wave emitted from the atom, coherent tunneling of the atom to the remote lattices occurs as long as bound states are present in the energy spectrum of the system formed by the atom and its matter-wave. Going beyond the Markovian approximation, and breaking through the conventional distance constraint, our result opens another avenue to realizing tunneling and gives a guideline for developing tunneling devices. It is generally believed that quantum tunneling cannot occur when the distance is larger than the particle’s wavelength. This paper reveals that a long-range quantum tunneling of the atom to the remote trapping potentials mediated by its emitted matter wave occurs as long as bound states are present in the energy spectrum of the total system formed by the atom and its matter-wave.