Double resonance of Raman transitions in a degenerate Fermi gas

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Double resonance of Raman transitions in a degenerate Fermi gas

Moosong Lee, Jeong Ho Han, Jin Hyoun Kang, Min-Seok Kim, and Y. Shin

Phys. Rev. A 95, 043627 – Published 20 April 2017

Abstract

We measure momentum-resolved Raman spectra of a spin-polarized degenerate Fermi gas of ${}^{173}{Yb}$ atoms for a wide range of magnetic fields, where the atoms are irradiated by a pair of counterpropagating Raman laser beams as in the conventional spin-orbit coupling scheme. Double resonance of first- and second-order Raman transitions occurs at a certain magnetic field and the spectrum exhibits a doublet splitting for high laser intensities. The measured spectral splitting is quantitatively accounted for by the Autler-Townes effect. We show that our measurement results are consistent with the spinful band structure of a Fermi gas in the spatially oscillating effective magnetic field generated by the Raman laser fields.

Received 28 February 2017

DOI:https://doi.org/10.1103/PhysRevA.95.043627

Physics Subject Headings (PhySH)

Fermi gases Spin-orbit coupling

Spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Moosong Lee, Jeong Ho Han, Jin Hyoun Kang, Min-Seok Kim, and Y. Shin^*

Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea and Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea

^*yishin@snu.ac.kr

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Vol. 95, Iss. 4 — April 2017

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Images

Figure 1
(a) Schematic diagram of the experimental apparatus. ${}^{173}{Yb}$ atoms are collected with a Zeeman slower and a magneto-optical trap (MOT), loaded into a 1070-nm optical dipole trap (ODT), and transported to a small hexagonal chamber by moving the ODT. Images of atoms after optical Stern-Gerlach spin separation [21, 22]: (b) equal mixture of the six spin components of the $F = 5 / 2$ hyperfine ground state and (c) fully polarized sample in the $m_{F} = - 5 / 2$ spin state.
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Figure 2
Raman spectroscopy of a degenerate Fermi gas (DFG). (a) Raman coupling setup with a pair of counterpropagating laser beams, whose frequency difference is denoted by $δ ω$ . (b) Energy diagram of the ${}^{3}P_{1}$ state of ${}^{173}{Yb}$ and the relative detuning of the Raman laser. Exemplary time-of-flight images of Fermi gases after applying a pulse of the Raman beams for (c) $δ ω / 2 π = 14.8$ kHz and (d) 29.6 kHz. The vertical dashed lines indicate the center of the unperturbed sample. (e) and (f) One-dimensional momentum distributions $n (k_{x})$ of the samples (yellow dashed curve) obtained by integrating the images along the $y$ direction. The normalized Raman spectra $S_{R} (k_{x})$ (red solid curve) are measured as $S_{R} (k_{x}) = [n (k_{x}) - n_{ref} (k_{x})] / n_{ref} (0)$ , where $n_{ref} (k_{x})$ is the reference distribution (blue dash-dotted curve) obtained without applying the Raman beam pulse.
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Figure 3
Raman spectra measured by scanning various experimental parameters, including Raman beam pulse duration $t$ , frequency difference $δ ω$ , magnetic field $B$ , and Raman beam power $P$ : (a) $δ ω = 4 E_{R} / ℏ, B = 16.6$ G, $P = 0.47$ mW; (b) $t = 2$ ms, $B = 0$ G, $P = 1.1$ mW; (c) $t = 2$ ms, $δ ω = 13.4 E_{R} / ℏ, P = 0.21$ mW; and (d) $t = 2$ ms, $δ ω = 13.4 E_{R} / ℏ, B = 133$ G (see the text for details of the sample condition and the polarization configuration of the Raman beams). The dashed lines in (b) indicate $k = k_{R} (\frac{ℏ}{4 E_{R}} δ ω - n)$ for $n = - 2, - 1, 1$ , and 2, and those in (c) and (d) are guides for the eyes with slopes of $\frac{d k}{d B} = - \frac{k_{R}}{4 B_{R}}$ and $\frac{d k}{d P} = - 0.3 k_{R} / mW$ . Each spectrum was obtained by averaging more than three measurements.
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Figure 4
Double resonance of Raman transitions. Raman spectra of an $m_{F} = - 5 / 2$ spin-polarized sample as a function of the magnetic field $B$ for $δ ω = 8 E_{R} / ℏ$ and various Raman beam powers: (a) $P = 0.13$ mW, (b) 0.21 mW, and (c) 0.36 mW. As the Raman coupling strength increases with higher $P$ , a spectral doublet splitting develops at $B = 4 B_{R} \approx 72$ G, where the $(r, Δ m_{F}) = (1, 1)$ and $(2, 0)$ transitions are doubly resonant. (d) The same spectrum as in (c) with the guide lines (solid) indicating the resonant momentum positions for various Raman transitions, which are calculated from Eq. (3) without including the ac Stark shift. The dashed lines are the corresponding final momentum positions. (e)–(h) Diagrams of the Raman transitions observed in the spectra.
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Figure 5
Spectral splitting at double resonance. (a) Three atomic states involved in the double resonance at $B = 4 B_{R}$ . For a ${}^{173}{Yb}$ atom in the $m_{F} = - 5 / 2$ state, $Ω_{-} = 5.3 Ω_{+}$ , and the upper two states are more strongly coupled. (b) Raman spectrum for $δ ω = 8 E_{R} / ℏ$ and $B = 4 B_{R}$ as a function of the Raman coupling strength $Ω_{-}$ . The dashed lines are the theoretical prediction of $k_{α, β} = \pm \frac{k_{R}}{8 \sqrt{2}} \frac{ℏ Ω_{-}}{E_{R}}$ , which is calculated in the limit of $Ω_{+} / Ω_{-} \to 0$ (see text).
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Figure 6
Energy band structures of a SO-coupled spin-1/2 atom under the Raman laser dressing: $Ω_{-} = 5.3 Ω_{+}$ in (a)–(c) and $Ω_{-} = Ω_{+}$ in (d)–(f), and $ℏ δ = 3 E_{R}$ in (a) and (d), $4 E_{R}$ in (b) and (e), and $5 E_{R}$ in (c) and (f). The color of the solid lines indicates the bare spin fractions of the energy eigenstates: blue for spin up and red for spin down. The dashed lines represent the energy spectrum for $Ω_{\pm} = 0$ . The gray shaded areas in (a)–(c) indicate the region corresponding to the momentum states occupied by the sample in the experiment.
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