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arXiv:2002.09064 · Physical Review A

Dynamics within a tunable harmonic plus quartic waveguide

Rudolph N. Kohn, James Stickney

Published Sep 17, 2020• 0 citations
arXivHTMLPDF

Abstract

We present a method for measuring nonharmonic contributions to the trapping potential of a cold atomic gas by measuring the dynamics of the cloud. This method can be used to minimize the anharmonicity of a trap, or to tune the quartic anharmonicity to some desired level in a sufficiently tunable trap. We present an approximate solution to the dynamics of a classical noninteracting cloud of thermal atoms in a cigar-shaped harmonic trap with a quartic perturbation along the weakly confined axis which is analytical and closed form. We calculate the first and second moments of position along the weak axis as functions of time, which is sufficient to characterize the trap. The dynamics of the thermal cloud differ notably from those of a single particle, with an offset to the oscillation frequency that persists even as the oscillation amplitude approaches zero. We also present some numerical results that describe the effects of time of flight on the behavior of the cloud in order to better understand the results of a hypothetical experimental realization of this system.

DOI
10.1103/physreva.102.033327

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We present a method for measuring nonharmonic contributions to the trapping potential of a cold atomic gas by measuring the dynamics of the cloud. This method can be used to minimize the anharmonicity of a trap, or to tune the quartic anharmonicity to some desired level in a sufficiently tunable trap. We present an approximate solution to the dynamics of a classical noninteracting cloud of thermal atoms in a cigar-shaped harmonic trap with a quartic perturbation along the weakly confined axis which is analytical and closed form. We calculate the first and second moments of position along the weak axis as functions of time, which is sufficient to characterize the trap. The dynamics of the thermal cloud differ notably from those of a single particle, with an offset to the oscillation frequency that persists even as the oscillation amplitude approaches zero. We also present some numerical results that describe the effects of time of flight on the behavior of the cloud in order to better understand the results of a hypothetical experimental realization of this system.
A combined gravitomagnetic trap was used to measure how the anharmonicity of a trapping potential affects the dynamics of a cold atomic cloud. A displacement of the effective potential minimum as a function of the ensemble temperature was observed. The effect is a direct consequence of the thermal nature of the atomic sample. The results of both a theory approach to the dynamical evolution of the atomic cloud and a numerical simulation are in very good agreement with the experimental observations. The effect can be exploited to devise a novel measurement technique for the temperature of a trapped atomic cloud, as well as to separate thermal and condensed phases in Bose-Einstein condensation experiments.
We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap center. The temperature after excitation exhibits resonance as a function of the driving frequency. We measure these resonances at several different trap frequencies. In order to interpret the experiments, we develop a simple model that incorporates both collisions between atoms and the anharmonicity of the real three-dimensional trapping potential. As well as providing a precise connection between the transverse harmonic oscillation frequency and the temperature resonance frequency, this model gives insight into the heating and loss mechanisms and into the dynamics of driven clouds of cold trapped atoms.
We describe the physical properties of a Bose-Einstein condensate (BEc) confined by a three-dimensional harmonic plus cubic and quartic trap. To this end, we solve the time-dependent Gross–Pitaevskii (GP) equation within a variational approach in order to obtain a set of second ordinary differential equations for the condensate widths. We then discuss in detail the low-lying oscillation modes, in an anharmonic trap where the anharmonicity of the confining potential leads to significant effect on the collective excitations of the system.
A Bose-Einstein condensation (BEC) production machine has been assembled and operated, using two vacuum chambers isolated from each other by a thin tube. A magnetooptical trap (MOT) is operated in the first chamber, where atoms are captured out of a thermal vapor and cooled to about 200 µK. The atoms are then transferred to a magnetic trap which is mounted on to a movable stage. A programmable motor moves the stage about half a meter, carrying the atoms to the second vacuum chamber where they are evaporatively cooled in a time-orbiting potential trap. We successfully used this apparatus to observe the first BEC's at the University of Virginia. We have also implemented a novel atom trap for BEC's of 87 Rb to be used in atom interferometry experiments. The trap is based on a time-orbiting potential waveguide. It supports the atoms against gravity while providing weak confinement to minimize interaction effects. We have loaded a condensate into the waveguide, and removed all other confinement fields. Up to 2 ×10 4 condensate atoms have been loaded into the trap, at estimated temperatures as low as 850 pK. We expect this novel type of trap will be useful for a variety of applications in condensate interferometry. Finally, we have characterized our trap by perturbing the atomic cloud with a sudden change in the confinement field. We subsequently obtain harmonic oscillation frequencies vi (ω x ,ω y ,ω z ) as low as 2π×(6.0, 1.2, 3.3) Hz. We have developed a mathematical description of the waveguide fields to account for the residual fields from the trap leads, obtaining good agreement between the measured and predicted trap behavior. The weak confinement of our guide should greatly reduce the limiting effects of atomic interactions. We anticipate that interferometer measurement times of 1 s or more should be achievable in this device. With suitable modifications, our waveguide could be used to precisely measure electric polarizability, gravitational forces, rotations, and other phenomena. We expect that the trap design presented here will play an essential role in allowing condensate interferometry to realize its potential. Note: Abstract extracted from PDF text
We study the evolution of a trapped atomic cloud subject to a trapping frequency jump for two cases: stationary and moving center of mass. In the first case, the frequency jump initiates oscillations in the cloud's momentum and size. At certain times we find the temperature is significantly reduced. When the oscillation amplitude becomes large enough, local density increases induced by the anharmonicity of the trapping potential are observed. In the second case, the oscillations are coupled to the center of mass motion through the anharmonicity of the potential. This induces oscillations with even larger amplitudes, enhancing the temperature reduction effects and leading to nonisotropic expansion rates while expanding freely.