Optical Control of Magnetic Feshbach Resonances by Closed-Channel Electromagnetically Induced Transparency

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Optical Control of Magnetic Feshbach Resonances by Closed-Channel Electromagnetically Induced Transparency

A. Jagannathan, N. Arunkumar, J. A. Joseph, and J. E. Thomas

Phys. Rev. Lett. 116, 075301 – Published 17 February 2016

Abstract

We control magnetic Feshbach resonances in an optically trapped mixture of the two lowest hyperfine states of a ${}^{6}{Li}$ Fermi gas, using two optical fields to create a dark state in the closed molecular channel. In the experiments, the narrow Feshbach resonance is tuned by up to 3 G. For the broad resonance, the spontaneous lifetime is increased to 0.4 s at the dark-state resonance, compared to 0.5 ms for single-field tuning. We present a new model of light-induced loss spectra, employing continuum-dressed basis states, which agrees in shape and magnitude with loss measurements for both broad and narrow resonances. Using this model, we predict the trade-off between tunability and loss for the broad resonance in ${}^{6}{Li}$ , showing that our two-field method substantially reduces the two-body loss rate compared to single-field methods for the same tuning range.

Received 4 November 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.075301

Physics Subject Headings (PhySH)

Electromagnetically induced transparency

Feshbach resonance

Atomic, Molecular & Optical

Authors & Affiliations

A. Jagannathan^1,2, N. Arunkumar¹, J. A. Joseph¹, and J. E. Thomas^1,*

¹Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
²Department of Physics, Duke University, Durham, North Carolina 27708, USA

^*Corresponding author. jethoma7@ncsu.edu

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Issue

Vol. 116, Iss. 7 — 19 February 2016

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Images

Figure 1
Level scheme for the two-field optical technique. Optical fields of frequencies $ω_{1}$ (detuning $Δ_{1}$ ) and $ω_{2}$ (detuning $Δ_{2}$ ), respectively, couple two singlet ground molecular states $| g_{1} ⟩$ and $| g_{2} ⟩$ to the singlet excited molecular state $| e ⟩$ ; $V_{HF}$ is the hyperfine coupling between the incoming atomic pair state in the open triplet channel $| T, k ⟩$ and $| g_{1} ⟩$ , and it is responsible for a magnetically controlled Feshbach resonance.
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Figure 2
Single-field-induced shift of the narrow Feshbach resonance at 543.2 G. The large loss peak on the right arises from the broad resonance. The left loss peak arises from the shifted narrow resonance. Vertical dashed line, position of the unshifted narrow resonance. The background (nonoptical) three-body loss near 543.2 G has been suppressed for clarity. Pulse duration $τ = 5.0 ms$ ; $T = 5.4 μ K$ ; $Δ_{L} = Δ_{1} = 30.2 MHz$ . (a) $Ω_{1} = 2.00 γ_{e}$ ; $B_{res}^{'} = 541.9 G$ . (b) $Ω_{1} = 2.65 γ_{e}$ ; $B_{res}^{'} = 541.0 G$ . (c) $Ω_{1} = 3.10 γ_{e}$ ; $B_{res}^{'} = 540.2 G$ ; $γ_{e} = 2 π \times 11.8 MHz$ . Blue dots, experiment; solid red curves, continuum-dressed-state model [16].
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Figure 3
Loss suppression using the two-field optical technique. The $ω_{1}$ beam shifts the narrow Feshbach resonance. The frequency of the $ω_{2}$ beam is chosen to suppress loss from (a) the broad resonance and (b) the shifted narrow Feshbach resonance. (c) Expanded view of (b) near the loss suppression region. Pulse duration $τ = 5.0 ms$ ; $T = 4.5 μ K$ ; $Ω_{1} = 2.6 γ_{e}$ ; $Ω_{2} = 0.8 γ_{e}$ ; $Δ_{L} = Δ_{1} = 30.2 MHz$ ; $B_{res}^{'} = 541.1 G$ . Vertical dashed line, position of the unshifted narrow resonance. Solid red curves, continuum-dressed-state model [16].
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Figure 4
Loss suppression near the broad resonance at 832.2 G, for $B = 840 G$ , as a function of single photon detuning by sweeping the $ω_{1}$ laser frequency. Pulse duration $τ = 5.0 ms$ ; $T = 14.8 μ K$ ; $Ω_{1} = 1.36 γ_{e}$ ; $Ω_{2} = 0.9 γ_{e}$ ; $Δ_{2} = 10.0 MHz$ . Maximum suppression occurs for $Δ_{e} = Δ_{2} = 10.0 MHz$ , where $δ_{e} = 0$ . Solid red curve, continuum-dressed-state model [16].
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Figure 5
Number of atoms in state $| 1 ⟩$ vs time with $Ω_{1} = 0.65 γ_{e}$ and $ω_{1}$ tuned to cause loss at 841 G. $Ω_{2} = 0.9 γ_{e}$ , and $ω_{2}$ is tuned to suppress loss near 841 G. With $Ω_{1} = 0.65 γ_{e}$ and $Ω_{2} = 0$ , the corresponding decay time is $≃ 0.5 ms$ . $γ_{e} = 2 π \times 11.8 MHz$ is the radiative decay rate; $T = 4.5 μ K$ . Solid green curve, $N (t) = N (0) / (1 + γ t)$ , where $γ = 2.5 s^{- 1}$ .
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Figure 6
Level schemes in (a) bare-state and (b) continuum-dressed-state bases. $| g_{1} ⟩$ , $| g_{2} ⟩$ , and $| e ⟩$ are the bare molecular states in the energetically closed (singlet) channel. $| T, k ⟩$ is a bare continuum state in the open (triplet) channel. The hyperfine interaction $V_{HF}$ couples the bare molecular state $| g_{1} ⟩$ and the continuum states $| T, k ⟩$ , creating the continuum-dressed bound state $| E ⟩$ and the (Feshbach resonance) scattering state $| E_{k} ⟩$ .
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