We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.
We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.
We investigate the quantum tunneling of Bose-Einstein condensates in optical lattices under gravity in the "Wannier-Stark localization" regime and "Landau-Zener tunneling" regime. Our results agree with experimental data [B. P. Anderson et al., Science 282, 1686 (1998); F. S. Cataliotti et al., Science 293, 843 (2001)]. We obtain the total decay rate which is valid over the entire range of temperatures, and show how it reduces to the appropriate results for the classical thermal activation at high temperatures, the thermally assisted tunneling at intermediate temperatures, and the pure quantum tunneling at low temperatures. We design an experimental protocol to observe this new phenomenon in further experiments.
Abstract In quantum tunneling a particle with energy E can pass through a high potential barrier V(E) due to the wave character of the particle. Bose\|Einstein condensates can display very strong tunneling depending on the structure of the trap, which may be a double\|well or optical lattices. We employed for the first time to our knowledge the periodic instanton method to investigate tunneling of Bose\|Einstein condensates in optical lattices. Our results show that there are two kinds of tunneling in this system, Landau\|Zener tunneling between extended states of the system and Wannier\|Stark tunneling between localized states of the system, and that the latter is 1000 times faster than the former. We also obtain the total decay rate for a wide range of temperature, including classical thermal activation, thermally assisted tunneling and quantum tunneling. Our results agree with experimental data in references[1, 2].Finally, we propose an experimental protocol to observe this new phenomenon in future experiments. periodic instanton, Wannier\|Stark localization, Landau\|Zener tunneling, Wannier\|Stark tunneling
We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which incorporates the non-Abelian Josephson effect and has very different density and spin tunneling characteristics compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.
We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which contains non-Abelian Josephson effect and has very different density and spin tunneling characters compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, respectively, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.
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.
This dissertation describes our experimental investigations of quantum transport and atomic motion control using optical potentials.The system we study consists of ultracold sodium atoms under the influence of light forces.First, we introduce the dynamics of neutral atoms in a periodic optical potential.The system resembles the textbook problem of an electron inside the crystalline lattice, and we review the main characteristics of the interaction for the atom optics case.In particular, atoms trapped in a lattice subject to large accelerations undergo Landau-Zener tunneling, process which makes the system unstable.The number of atoms trapped in the potential shows the characteristic exponential decay over time.However, deviations from this law are predicted by quantum mechanics.We use the experimental access to the non-exponential time to demonstrate the Quantum Zeno and Anti-Zeno effects.These effects show the influence of frequent observations on the decay rate of a quantum unstable system.The second part of the dissertation introduces a new system we plan to study, namely, the quantum interaction between sodium atoms in the ground ix state and a conductive surface.We are interested in the measurement of the Casimir-Polder potential with a precision of better than 1%.In order to do this, we have chosen to launch the atoms towards the surfaces at very small incident velocities (a few mm/s), and measure the influence of the interaction on the reflection probability.Atoms reflect from the purely attractive potential due to quantum reflection, an effect with no classical analogy.The experimental observation of quantum reflection requires atomic distributions with temperatures below 1 µK.For this purpose, we have produced and studied a Bose-Einstein condensate (BEC) with sodium atoms.The region where the BEC is created is separated spatially form the surfaces by a distance of 10 cm, vertically.In order to bring the atoms close to the surfaces prior to their launching, we have developed an optical elevator.The elevator uses a moving optical lattice in the regime where tunneling is negligible.Results of the macroscopic optical transport technique, and current progress towards a measurement of the Casimir-Polder interaction, are reported.