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PROPERTIES OF COHERENT MATTER-WAVE BUBBLES

O. Zobay, B. M. Garraway

Published Jan 1, 2000• 4 citations
OpenAlex

Abstract

Recently we have proposed a method to create thin matter-wave bubbles from coherent atoms trapped in a magnetic potential. In this article we discuss in detail some properties of these states. In particular, we numerically and analytically investigate the Wigner function to demonstrate their non-classical nature. Furthermore, we study the energy and lifetime of the bubbles, which are long-lived resonances in a radio frequency-induced adiabatic potential, and illustrate how they can be transformed into excited eigenstates of the original harmonic trapping potential.

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•Jan 1, 2007•4 citations
Recently we have proposed a method to create thin matter-wave bubbles from coherent atoms trapped in a magnetic potential. In this article we discuss in detail some properties of these states. In particular, we numerically and analytically investigate the Wigner function to demonstrate their non-classical nature. Furthermore, we study the energy and lifetime of the bubbles, which are long-lived resonances in a radio frequency-induced adiabatic potential, and illustrate how they can be transformed into excited eigenstates of the original harmonic trapping potential.
We discuss a method to create two-dimensional (2D) traps as well as atomic shell, or bubble, states for a Bose-Einstein condensate initially prepared in a conventional magnetic trap. The scheme relies on the use of time-dependent, radio-frequency-induced adiabatic potentials. These are shown to form a versatile and robust tool to generate interesting trapping potentials. Our shell states take the form of thin, highly stable matter-wave bubbles and can serve as stepping stones to prepare atoms in highly excited trap eigenstates or to study ``collapse and revival phenomena.'' Their creation requires gravitational effects to be compensated by applying additional optical dipole potentials. However, in our scheme gravitation can also be exploited to provide a route to two-dimensional atom trapping. We demonstrate the loading process for such a trap and examine experimental conditions under which a 2D condensate may be prepared.
Adiabatic dressed state potentials are created when magnetic substates of trapped atoms are coupled by a radio-frequency field. We discuss their theoretical foundations and point out fundamental advantages over potentials purely based on static fields. The enhanced flexibility enables one to implement numerous configurations, including double wells, Mach-Zehnder, and Sagnac interferometers which even allows for internal state-dependent atom manipulation. These can be realized using simple and highly integrated wire geometries on atom chips.
We investigate a classical phase-space approach of matter-wave propagation based on the truncated Wigner equation (TWE). We show that such a description is suitable for ideal matter waves in quadratic time-dependent confinement as well as for harmonically trapped Bose-Einstein condensates in the Thomas-Fermi regime. In arbitrary interacting regimes, the TWE combined with the moment method yields the low-energy spectrum of a condensate as predicted by independent variational methods. TWE also gives the right breathing-mode frequency for long-ranged interactions decaying as 1/r21/{r}^{2}1/r2 in three dimensions and for a contact potential in two dimensions. Quantum signatures, beyond the TWE, may only be found in the condensate dynamics beyond the regimes of classical phase-space propagation identified here.
Abstract Within the many different models, that appeared with the use of cold atoms to create BECs, the bubble trap shaped potential has been of great interest. However, the relationship between the physical parameters and the resulting manifold geometry remains yet to be fully understood for the anisotropic bubble trap physics in the thin-shell limit. In this paper, we work towards this goal by showing how the parameters of the system must be manipulated in order to allow for a non-collapsing thin-shell limit. In such a limit, a dimensional compactification takes place, thus leading to an effective 2D Hamiltonian which relates to up-to-date bubble trap experiments. At last, the resulting Hamiltonian is perturbatively solved for both the ground-state wave function and the excitation frequencies in the leading order of deviations from a spherical bubble trap.
During this thesis a novel trapping and manipulation technique for neutral atoms on atom chips has been developed and experimentally implemented. Radio-frequency (rf) coupling of internal states of magnetically trapped atoms results in versatile microscopic potentials, which overcome various limitations of static magnetic traps. An extensive experimental analysis of this new technique has been carried out, exploring the state-dependency of the rf potentials and the possible realization of non-trivial trapping geometries. Based on these results, the first coherent matter wave beam splitter on an atom chip has been realized, demonstrating for the first time the all-magnetic coherent splitting of a condensate. This new atom optical tool has then been applied to investigate the phase-properties of one-dimensional Bose-Einstein condensates. The potential configuration developed during this thesis provides direct access to the phase fluctuations in the system and has allowed the first time-resolved study of equilibrium properties and non-equilibrium dynamics in a one-dimensional Bose gas.