Precise control of magnetic fields and optical polarization in a time-orbiting potential trap

A. J. Fallon, S. J. Berl, E. R. Moan, and C. A. Sackett

Phys. Rev. A 102, 023108 – Published 10 August 2020

Abstract

A time-orbiting potential trap confines neutral atoms in a rotating magnetic field. The rotation of the field can be useful for precision measurements, since it can average out some systematic effects. However, the field is more difficult to characterize than a static field, and it makes light applied to the atoms have a time-varying optical polarization relative to the quantization axis. These problems can be overcome by using stroboscopic techniques, where either a radio-frequency field or a laser is applied in pulses that are synchronized to the rotating field. By using these methods, the magnetic field can be characterized with a precision of 10 mG and light can be applied with a polarization error of $5 \times 10^{- 5}$ .

Received 20 March 2020
Accepted 10 July 2020

DOI:https://doi.org/10.1103/PhysRevA.102.023108

Physics Subject Headings (PhySH)

Atom & ion trapping & guiding Bose-Einstein condensates

Atomic, Molecular & Optical

Authors & Affiliations

A. J. Fallon , S. J. Berl, E. R. Moan , and C. A. Sackett

Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 102, Iss. 2 — August 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Radio-frequency spectra of trapped condensate atoms. The vertical axis shows the fraction of atoms remaining in the trap after rf is applied at the indicated frequency. (a) Spectrum obtained by using a single long pulse of 200 ms duration. (b) Spectrum obtained by using a train of 250 pulses each with $10 μ s$ duration. The pulses are synchronized to the 12.8 kHz bias rotation frequency, so that the magnetic field has the same value during each pulse. At the delay time shown, the field magnitude happens to take on nearly its largest value. The curve is a Lorentzian fit.
Reuse & Permissions
Figure 2
Time dependence of the magnetic-field magnitude during TOP field oscillation, as measured by the center frequency of spectra such as in Fig. 1. Error bars are one- $σ$ errors from the fit. Solid curves are fits to the form of Eq. (10). (a) Initial variation in a trap using nominal driver current amplitudes. (b) Variation after adjusting the oscillating terms in Eq. (10) to be zero. The residual oscillation corresponds to field variations of less than 10 mG.
Reuse & Permissions
Figure 3
Using trap motion to determine the $B_{E y}$ background field. In the main graph, data points are the observed trap positions as the DC gradient $B_{Q}^{'}$ is slowly varied. The curve is a fit to Eq. (14) yielding $B_{E y} = 0.56 (2)$ G. The inset shows measured $B_{E y}$ values as a function of current $I_{y}$ through a pair of DC bias coils. The red point corresponds to the data in the main graph.
Reuse & Permissions
Figure 4
Level diagram for polarization testing. Atoms are trapped in the $F = 2, m = 2$ state, where they cannot scatter $σ_{+}$ polarized light. Any contamination by $π$ or $σ_{-}$ light leads to scattering and loss from the trap; the diagram shows $π$ light for illustration. Because of the scattering, a small population can be temporarily established in the $F = 2, m = 1$ state, where the strong excitation to $m^{'} = 2$ can destructively interfere with the excitation amplitude from $m = 2$ . This leads to a suppression of scattering at high optical intensity.
Reuse & Permissions
Figure 5
(a) Experimental measurements of atom loss. Data points show the fraction of atoms $P$ remaining in the trap after 1280 pulses of laser light at the indicated total intensity, relative to the saturation intensity $I_{S}$ . (b) Numerical calculation of the survival probability after $N$ pulses ${(1 - ε)}^{N}$ for $N = 1280$ . The solid curve shows the result from the optical Bloch equations for a polarization impurity $E_{π} = 2 \times 10^{- 4}$ . The dashed curve shows the behavior that would be expected in the absence of dark-state formation. The inset shows that the loss $ε$ depends linearly on the polarization impurity, here calculated at $I = 100 I_{S}$ . The slope $d ε / d | E_{π} |^{2}$ is approximately 9.5 at the first minimum.
Reuse & Permissions
Figure 6
Dependence of polarization error on beam alignment. Points show the fraction of $π$ polarized light at the atoms, determined as described in the text. The angle $θ$ between the laser beam and the rotating field is varied by adjusting the time $t$ at which the light pulse is centered. The curve is a parabolic fit giving $| E_{π} |^{2} = 0.61 (3) \times Ω_{1}^{2} t^{2}$ , in reasonable agreement with the expectation $| E_{π} |^{2} = θ^{2} / 2$ .
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information