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Physical Review A

Suppression of potential roughness in atom-chip ac Zeeman traps

Shuangli Du, Austin R. Ziltz, William Miyahira, S. Aubin

Published May 31, 2022• 4 citations
Publisher

Abstract

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 $^{87}\mathrm{Rb}$ 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.

DOI
10.1103/physreva.105.053127

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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\ensuremathμm100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}100\ensuremathμm from the chip and operating on a 6.8 GHz hyperfine transition, is expected to suppress potential roughness by a factor of 4\ifmmode×\else\texttimes\fi1054\ifmmode\times\else\texttimes\fi{}{10}^{5}4\ifmmode×\else\texttimes\fi105 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×\else\texttimes\fi1042\ifmmode\times\else\texttimes\fi{}{10}^{4}2\ifmmode×\else\texttimes\fi104. Conversely, the ac skin effect also slightly exacerbates potential roughness, in ac Zeeman traps, from defects in the sidewall of a wire trace.
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.
Spin-specific trapping and mechanical control of ultracold atoms is difficult with current techniques, but offers the possibility of exploring new physics systems, such as spin-dependent trapped atom interferometers, as well as quantum gates, 1D many-body spin gases, and novel cooling schemes. Microwave near-field potentials based on the AC Zeeman effect provide a mechanism for such spin-specific control of atoms: in principle, independent potentials can be targeted to different spin states simultaneously. A broadband microwave atom chip can be used to generate both AC Zeeman trapping potentials and a microwave lattice for long distance trap positioning. We present recent experimental results on the successful trapping of ultracold rubidium atoms in an AC Zeeman atom chip trap using RF intra-hyperfine manifold transitions. Notably, these traps suppress the potential roughness encountered in traditional micro-magnetic chip traps.
We present a toolbox of microstrip building blocks for microwave atom chips geared towards trapped atom interferometry. Transverse trapping potentials based on the AC Zeeman (ACZ) effect can be formed from the combined microwave magnetic near fields of a pair or a triplet of parallel microstrip transmission lines. Axial confinement can be provided by a microwave lattice (standing wave) along the microstrip traces. Microwave fields provide additional parameters for dynamically adjusting ACZ potentials: detuning of the applied frequency to select atomic transitions and local polarization controlled by the relative phase in multiple microwave currents. Multiple ACZ traps and potentials, operating at different frequencies, can be targeted to different spin states simultaneously, thus enabling spin-specific manipulation of atoms and spin-dependent trapped atom interferometry.
Ultracold atom experiments use a gas of neutral atoms with temperatures less than 100 µK above absolute zero and offer unmatched experimental control of quantum states and coherence, which has allowed ultracold atom-based measurements to be some of the most precise to date. While ultracold atom experiments can control almost all atomic degrees of freedom, spin-dependent trapping and spatial manipulation has remained difficult if not inaccessible. We are developing a method of spin-dependent trapping and spatial manipulation for ultracold neutral atoms using the AC Zeeman force produced by a microwave magnetic near-field gradient generated by an atom chip. We measure the AC Zeeman force on ultracold rubidium atoms by observing its effect on the motion of atoms in free-fall and on those confined in a trap. We have studied the force as a function of microwave frequency detuning from a hyperfine transition at 6.8 GHz at several magnetic field strengths and have observed its characteristic bipolar and resonant features predicted by two-level dressed atom theory. We find that the force is several times the strength of gravity in our setup, and that it can be targeted to a specific hyperfine transition while leaving other hyperfine states and transitions relatively unaffected. We find that our measurements are reasonably consistent with parameter-free theoretical predictions.
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.