Dynamics within a tunable harmonic plus quartic waveguide

Rudolph N. Kohn, Jr. and James A. Stickney

Phys. Rev. A 102, 033327 – Published 17 September 2020

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.

Received 26 February 2020
Revised 25 August 2020
Accepted 26 August 2020

DOI:https://doi.org/10.1103/PhysRevA.102.033327

Physics Subject Headings (PhySH)

Atom & ion trapping & guiding Atom interferometry Cold atoms & matter waves

Atomic, Molecular & Optical

Authors & Affiliations

Rudolph N. Kohn, Jr.^* and James A. Stickney

Space Dynamics Laboratory, Albuquerque, New Mexico 87106, USA

^*rudy.kohn@sdl.usu.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 102, Iss. 3 — September 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
An illustration showing how an energy-dependent frequency shift results in a gradual approach to pseudoequilibrium, even in the absence of collisions. An initial cloud is produced with parameters $m = 1 kg, ω = 1 s^{- 1}, x_{4}^{2} = 20 m^{2}, x_{D} = 5 m, p_{D} = 0 kg m^{- 1} s^{- 1}$ , and $σ_{x} = σ_{p} = 1.5 m$ . These values are chosen for their compactness and simplicity and not to resemble any realistically achievable system. We allow the cloud to evolve, and snapshots are taken at several times to illustrate the gradual spreading out of the cloud. The particular times illustrated are chosen because they have the center of mass of the cloud near the center of the trap, so that the spreading out of the cloud in space over time is clearly visible. Additionally shown is a phase-space diagram for each point in time showing how the clean 2D Gaussian at $t = 0$ becomes an increasingly long spiral, as atoms with different energies accumulate relative angles in phase space so that atoms that started near each other with different energies drift apart.
Reuse & Permissions
Figure 2
$〈 x 〉$ as a function of time. Most of the decay to quasithermal equilibrium is shown. The plot uses parameters $ξ_{D} = 8, ϕ_{D} = 0, ω = 100 s^{- 1}, σ_{x} (t = 0) = 1 m$ , and $x_{4} = 8 m$ . For these parameters, $Λ ≅ 0.586$ .
Reuse & Permissions
Figure 3
$〈 x^{2} 〉$ as a function of time for the same parameters as used in Fig. 2. Note the more rapid oscillations as well as the more rapid decay of the oscillations.
Reuse & Permissions
Figure 4
The size of the cloud as a function of time, using the same parameters as Figs. 2 and 3.
Reuse & Permissions
Figure 5
Pictured here are the results of a Monte Carlo numerical simulation of sloshing in a harmonic plus quartic trap. Along the vertical axis, the top subplot describes the center-of-mass position of the cloud and the bottom subplot shows the cloud size. The horizontal axis in both subplots describes how long the cloud was allowed to slosh in the trap before turning off the trapping potential for time of flight. The black curves represent the position and size of the cloud without time of flight. The dotted curves (red online) show the position and size of the cloud after a time of flight of 0.015 s. The other simulation parameters are $m = 1 kg, ω = 100 s^{- 1}$ , and $x_{4} = 8 m$ . The value of $k_{B} T$ is 10000 J. The clouds were generated in a harmonic potential, then given a kick by introducing a gradient of $- 2.4 x$ J/m for 0.021 s. These values were chosen to make the results without time of flight similar to the results in Figs. 2, 3, 4, 2, 3, 4, 2, 3, 4, in order to ease comparison between the analytical solution and the simulation.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information