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arXiv:0707.0602 · Physical Review A

Limitations of the modulation method to smooth wire-guide roughness

Isabelle Bouchoule, Jean-Baptiste Trebbia, Carlos L. Garrido Alzar

Published Feb 27, 2008• 16 citations
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Abstract

It was recently demonstrated that wire-guide roughness can be suppressed by modulating the wire currents so that the atoms experience a time-averaged potential without roughness [Trebbia et al., Phys. Rev. Lett. 98, 263201 (2007)]. In this paper, we theoretically study the limitations of this technique. At low modulation frequency, we show that the longitudinal potential modulation produces heating of the cloud, and we compute the heating rate. We also give a quantum derivation of the rough conservative potential associated with the micromotion of the atoms. At large modulation frequency, we compute the loss rate due to nonadiabatic spin flip and show that it presents resonances at multiple modulation frequencies. These studies show that the modulation technique works for a wide range of experimental parameters. We also give conditions to realize radio-frequency evaporative cooling in such a modulated trap.

DOI
10.1103/physreva.77.023624

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It was recently demonstrated that wire-guide roughness can be suppressed by modulating the wire currents so that the atoms experience a time-averaged potential without roughness [Trebbia et al., Phys. Rev. Lett. 98, 263201 (2007)]. In this paper, we theoretically study the limitations of this technique. At low modulation frequency, we show that the longitudinal potential modulation produces heating of the cloud, and we compute the heating rate. We also give a quantum derivation of the rough conservative potential associated with the micromotion of the atoms. At large modulation frequency, we compute the loss rate due to nonadiabatic spin flip and show that it presents resonances at multiple modulation frequencies. These studies show that the modulation technique works for a wide range of experimental parameters. We also give conditions to realize radio-frequency evaporative cooling in such a modulated trap.
We present a method to suppress the potential roughness of a wire-based, magnetic atom guide: modulating the wire current at a few tens of kHz, the potential roughness, which is proportional to the wire current, averages to zero. Using ultra-cold 87rmRb^{87}{\\rm Rb}87rmRb clouds, we show experimentally that modulation reduces the roughness by at least of a factor five without measurable heating or atom loss. This roughness suppression results in a dramatic reduction of the damping of center of mass oscillations.
Trapping and manipulating ultracold atoms through the use of atom chips offers the ability to engineer complex electromagnetic field geometries in a compact form factor. One of the primary limitations hindering their use is trap potential roughness which arises as a result of defects in the atom chip wires when atoms are brought close to the chip. This roughness can play a limiting role in atom interferometry and strong 1D confinement experiments. We present an initial experimental demonstration of atom chip potential roughness suppression using radio-frequency (RF) AC Zeeman (ACZ) potentials on an atom chip. Using ∼20 MHz RF magnetic near-fields from the chip to target intra-manifold transitions in the 87Rb ground state, we trap atoms in a spindependent ACZ potential. We compare the axial trapping potential for atoms in comparable 2-wire DC and AC Zeeman traps and show evidence of roughness suppression in the AC trap.
We present several toy models for predicting the character and strength of the roughness of ac Zeeman trapping potentials generated by imperfections in wire traces on an atom chip. An ac Zeeman trapping potential is generated by targeting a microwave or rf magnetic field at hyperfine or Zeeman ground-state transitions, respectively, while a dc Zeeman trap uses a static magnetic field to manipulate an atom via its magnetic moment. We find that an ac Zeeman trap suppresses potential roughness by several orders of magnitude with respect to a comparable dc Zeeman trap. This suppression stems from the inherent differences between an atom's response to dc and ac (namely rf and microwave) magnetic fields, in concert with how the ac skin effect smooths out a current distribution disturbed by a conductivity variation. For chip wires fabricated by evaporation, we find that an ac Zeeman trap for 87Rb^{87}\mathrm{Rb}87Rb atoms, located $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ from the chip and operating on a 6.8 GHz hyperfine transition, is expected to suppress potential roughness by a factor of $4\ifmmode\times\else\texttimes\fi{}{10}^{5}$ compared with a similar dc Zeeman trap. For a comparable ac Zeeman trap operating on a 10 MHz Zeeman transition, the suppression is $2\ifmmode\times\else\texttimes\fi{}{10}^{4}$. Conversely, the ac skin effect also slightly exacerbates potential roughness, in ac Zeeman traps, from defects in the sidewall of a wire trace.
We propose a simple three-wire-based magnetic trap potential for direct forced evaporative cooling of neutral atoms without using induced spin-flip technologies. We have devised a method for controlling the trap depth without sacrificing its frequencies by only varying wire currents and external magnetic fields. By having multiples of these wires on different levels integrated into an atom chip, it is possible to attain Bose-Einstein condensation without the conventional forced evaporation technique.
Recently, we have experimentally demonstrated a continuous loading mechanism for an optical dipole trap from a guided atomic beam [M. Falkenau, V. V. Volchkov, J. R\"uhrig, A. Griesmaier, and T. Pfau, Phys. Rev. Lett. 106, 163002 (2011)]. The observed evolution of the number of atoms and temperature in the trap are consequences of the unusual trap geometry. In the present paper, we develop a model based on a set of rate equations to describe the loading dynamics of such a mechanism. We consider the collision statistics in the nonuniform trap potential that leads to two-dimensional evaporation. The comparison between the resulting computations and experimental data allows to identify the dominant loss process and suggests ways to enhance the achievable steady-state atom number. Concerning subsequent evaporative cooling, we find that the possibility of controlling axial and radial confinement independently allows faster evaporation ramps compared to single beam optical dipole traps.