Measurement and extinction of vector light shifts using interferometry of spinor condensates

A. A. Wood, L. D. Turner, and R. P. Anderson

Phys. Rev. A 94, 052503 – Published 2 November 2016

Abstract

We use differential Ramsey interferometry of ultracold atoms to characterize the vector light shift (VLS) from a far-off-resonance optical dipole trap at $λ = 1064$ nm. The VLS manifests as a “fictitious” magnetic field, which we perceive as a change in the Larmor frequency of two spinor condensates exposed to different intensities of elliptically polarized light. We use our measurement scheme to diagnose the light-induced magnetic field and suppress it to $2.1 (8) \times 10^{- 4}$ of its maximum value by making the trapping light linearly polarized with a quarter-wave plate in each beam. Our sensitive measurement of the VLS-induced field demonstrates high-precision, in vacuo interferometric polarimetry of dipole-trapping light and can be adapted to measure vector shifts from other lasers, advancing the application of optically trapped atoms to precision metrology.

Received 22 July 2016

DOI:https://doi.org/10.1103/PhysRevA.94.052503

Physics Subject Headings (PhySH)

Angular momentum of light Atom & ion trapping & guiding Atom interferometry Bose-Einstein condensates Electronic transitions Quantum description of light-matter interaction Quantum measurements

Atomic, Molecular & Optical

Authors & Affiliations

A. A. Wood^1,2, L. D. Turner¹, and R. P. Anderson¹

¹School of Physics & Astronomy, Monash University, Victoria 3800, Australia
²School of Physics, University of Melbourne, Victoria 3010, Australia

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Issue

Vol. 94, Iss. 5 — November 2016

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Images

Figure 1
Top: The scalar light shift from a focused laser beam (orange) creates a spin-independent trapping potential, proportional to the (inverted) intensity profile. Gravity acts to tilt and shallow the potential (blue), with a trap minimum offset from the intensity maximum. Bottom: A BEC (circle) trapped in this potential experiences a greater intensity variation than at the beam center, accentuating the gradient of the vector light shift. For the beam power (550 mW) and waist $(67 μ m)$ shown here—similar to those used in our experiment—gravity shifts the trap minimum by $10 μ m$ , where the effective field magnitude is $B_{vls} = 0.3$ mG for a polarization circularity of $C = 0.07$ . The effective field gradient at the trap minimum is $\partial B_{vls} / \partial z = 24$ mG/cm due to the tightly focused beam.
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Figure 2
(a) Schematic of the experimental apparatus and (b),(c) different configurations to measure vector light shifts. The position and amplitude of each dipole-trapping beam is controlled by an AOM; introducing a second rf frequency to an AOM allows independent control of two dipole beams propagating along the same direction. Splitting either the $x^{'}$ - or $z^{'}$ -oriented dipole beams into two beams $A$ and $B$ allows us to position two BECs along the axial extent of a third, orthogonal beam $C$ . We measure the difference in VLS-induced fields at the location of each condensate using two distinct methods: (b) Delayed drop method. By turning beams $A$ and $B$ off at different times, each BEC falls a different distance prior to the interrogation, sampling a different intensity of beam $C$ alone. (c) In-trap interferometry. Higher precision is achieved by keeping the BECs in trap. We vary the relative intensity of beams $A$ and $B$ (which share a common polarization), and measure the intensity dependence of the VLS-induced field. For each method, we vary the magnitude of the VLS-induced field and its gradient by rotating a QWP in each beam path.
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Figure 3
Differential Ramsey interferometry and elliptical data reduction. (a) Representative Stern-Gerlach absorption images after time of flight for each stage of the Ramsey pulse sequence. (b) We measure the spin projection of each condensate $F_{z}$ ; varying the second $π / 2$ -pulse phase for each iteration of the experiment traces out phase domain Ramsey fringes. (c) Shot-to-shot field fluctuations scramble the phase of each interferometer, but plotting the output of one interferometer against the other yields an ellipse, from which we can extract the relative phase $Δ ϕ$ .
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Figure 4
Magnetic field difference (right axis) and gradient (left axis) induced by the vector light shift from the $z^{'}$ -oriented dipole beam (circles) and $x^{'}$ beam (squares), for variable polarization circularity. The VLS magnetic field difference $| Δ B_{vls} | < 1$ mG at two locations of each dipole beam (separated by $Δ y = 41.7 μ m$ ) is probed using differential interferometry. Rotating a quarter-wave plate placed in the path of each beam changes the vector light shift and thus the light-induced field gradient $Δ B_{vls} / Δ y$ . Biasing the measurement with three linearly independent background magnetic fields allows us to determine the direction of $B_{vls}$ for each beam $[cos φ$ in Eq. (7)]. Solid ( $z^{'}$ -beam) and dashed ( $x^{'}$ -beam) lines are a phenomenological fit from which we determine the peak gradient induced by each beam [Eq. (7)].
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Figure 5
In-trap measurement and cancellation of VLS field difference. Top: The variation of the VLS field difference $Δ B_{vls}$ with intensity difference, for six quarter-wave plate angles over a 10 arcmin range. The single error bar is representative of typical uncertainty reported from ellipse fits, $u (Δ ϕ) \approx 0.011 π$ . The gradient of each line is an intensity normalized VLS field, as shown vs wave-plate angle in the lower plot. Vertical error bars represent the uncertainty in each fitted gradient $\partial B_{vls} / \partial I$ ; horizontal error bars represent the resolution of the QWP rotation stage. The slope of this line can be used to impute the vector polarizability [Eq. (10)] and a suppression ratio of $2.1 (8) \times 10^{4}$ [Eqs. (16) and (17)] corresponding to the minimum achieved intensity normalized VLS field.
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Figure 6
Spin-mixing dynamics of a spinor BEC with the VLS approximately nulled (top) and when set to 132(6) mG $cm^{- 1}$ (bottom): fractional population evolution (left) and centroid displacement, relative to the $ρ_{0}$ centroid position (right). The VLS induces an effective magnetic field gradient along the gravitational direction $(y)$ , driving strong component separation (shown in the inset Stern-Gerlach absorption image, taken 15 ms after the $π / 2$ pulse). Separation reduces spatial overlap of the three Zeeman sublevels and suppresses spin mixing from the $m_{F} = \pm 1$ states into the $m_{F} = 0$ state.
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