Modeling the adiabatic creation of ultracold polar ${}^{23}{\mathrm{Na}}^{40}\mathrm{K}$ molecules

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Modeling the adiabatic creation of ultracold polar $^{23} {Na}^{40} K$ molecules

Frauke Seeßelberg, Nikolaus Buchheim, Zhen-Kai Lu, Tobias Schneider, Xin-Yu Luo, Eberhard Tiemann, Immanuel Bloch, and Christoph Gohle

Phys. Rev. A 97, 013405 – Published 12 January 2018

Abstract

In this work we model and realize stimulated Raman adiabatic passage (STIRAP) in the diatomic $^{23} {Na}^{40} K$ molecule from weakly bound Feshbach molecules to the rovibronic ground state via the $|v_{d} = 5, J = Ω = 1〉$ excited state in the $d^{3} Π$ electronic potential. We demonstrate how to set up a quantitative model for polar molecule production by taking into account the rich internal structure of the molecules and the coupling laser phase noise. We find excellent agreement between the model predictions and the experiment, demonstrating the applicability of the model in the search for an ideal STIRAP transfer path. In total we produce 5000 fermionic ground-state molecules. The typical phase-space density of the sample is 0.03 and induced dipole moments of up to 0.54 D can be observed.

Received 4 September 2017

DOI:https://doi.org/10.1103/PhysRevA.97.013405

Physics Subject Headings (PhySH)

Coherent control Cold and ultracold molecules Dipolar gases Fine & hyperfine structure Molecular spectra Stark effect Zeeman effect

Feshbach resonance

Atomic, Molecular & Optical

Authors & Affiliations

Frauke Seeßelberg^1,*, Nikolaus Buchheim¹, Zhen-Kai Lu¹, Tobias Schneider¹, Xin-Yu Luo¹, Eberhard Tiemann², Immanuel Bloch^1,3, and Christoph Gohle¹

¹Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
²Institut für Quantenoptik, Leibniz Universität Hannover, 30167 Hannover, Germany
³Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 München, Germany

^*frauke.seesselberg@mpq.mpg.de

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Vol. 97, Iss. 1 — January 2018

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Figure 1
Molecular structure of ${}^{23}{Na} {}^{40}K$ . (a) Potential energy curves according to Ref. [20]. The ground-state potentials $X^{1} Σ$ and $a^{3} Σ$ and the excited-state potentials $D^{1} Π$ and $d^{3} Π$ , which are relevant for the present work, are highlighted by black solid lines. The $B^{1} Π / c^{3} Σ$ system used in Ref. [11] is indicated with dashed lines. The vertical lines symbolize the pump (P) and Stokes (S) lasers used to populate the rovibronic ground state by STIRAP, with the respective Rabi frequencies denoted as $Ω_{P}$ and $Ω_{S}$ . We show the singlet (solid) and triplet (dashed) component of one state in $E$ and $G$ and one spin projection for $|FB〉$ (scaled up by a factor of 100). (b) Schematic of the molecular structure of the levels involved in STIRAP. The experimental data on the upper left shows the spectrum of the excited state $v_{d} = 5$ , $J = Ω = 1$ at 85.5 G recorded with $45^{\circ}$ polarization and starting with the $m_{F} = - 7 / 2$ Feshbach molecules that can be created at this field (lines are a guide to the eye). Three Zeeman $m_{J}$ components are clearly visible, but no hyperfine structure is resolved. The individual hyperfine states of the excited state and the ground state are indicated schematically (circles) as well as the hyperfine components of the Feshbach state (diamonds). Symbols with the same total nuclear spin quantum number $m_{I} = m_{Na} + m_{K}$ ( $- 5 / 2$ , $- 7 / 2$ , $- 9 / 2)$ have the same color (light blue, red, dark blue); white symbols refer to states that are not populated. Exemplary, shown by red and blue lines, is the case of a $π$ -polarized pump beam and a $σ^{+}$ -polarized Stokes beam. In this case, only the two $m_{F} = - 7 / 2$ components of $m_{J} = 1$ contribute to STIRAP. The strengths of the pump and Stokes transitions are different, as indicated by the thickness of the lines. The one-photon detuning $Δ$ and the two-photon detuning $δ$ are also indicated. Note that the energy axis for the excited state (spectrum and schematic) is inverted for clarity.
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Figure 2
EIT spectrum as measured in the experiment (circles) by scanning the pump laser detuning $Δ$ while keeping the Stokes laser resonant with the $m_{J} = 1$ component of the excited state, $δ = Δ$ . Error bars denote standard deviations of several experimental runs. The line is a fit using Eq. (4). From this fit we extract a peak pump Rabi frequency of $Ω_{P} = 2 π \times 3.9$ MHz and a peak Stokes Rabi frequency of $Ω_{S} = 2 π \times 8.4$ MHz. See text for details.
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Figure 3
Hyperfine spectra of the rovibronic ground state. They were recorded with different polarizations at $Δ = 100$ MHz and using a 70- $μ s$ STIRAP pulse duration. Circles (triangles) denote the data recorded with $π (⊥)$ -pump polarization, the Stokes beam being always $⊥$ -polarized. Error bars denote the standard errors of the means of several experimental runs and are mostly smaller than the symbol size. Vertical lines indicate the positions of the lowest hyperfine levels $[m_{F} = - 5 / 2$ , solid; $- 7 / 2$ , dashed; $- 9 / 2$ , dash-dotted; same color convention as in Fig. 1]. Simulation results for the two polarization scenarios are indicated by solid lines, for which the experimentally measured phase noise is included (see text for details). The data and simulation result for the $⊥ / ⊥$ -polarization configuration are offset by −0.1 for clarity.
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Figure 4
STIRAP at different one-photon detunings. (a) STIRAP efficiency as measured in the experiment (symbols). Error bars denoting the standard errors of the means are smaller than the symbol size, and model results without phase noise (dashed lines) and including phase noise (solid lines, averaged over 12 simulations) are also shown. Color and symbol shape encode polarization scenarios. Circles and dark blue lines (triangles and red lines) denote $π (⊥)$ -pump polarization; the Stokes beam is always $⊥$ -polarized. The light blue dashed line refers to the experimentally not realized case of $σ^{+}$ polarization for both pump and Stokes lasers. (b) Optimal STIRAP duration $τ$ as determined for each $Δ$ for the $π / ⊥$ combination. Data (circles) with model prediction including phase noise (solid line).
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Figure 5
STIRAP at high electric fields. Stark shift of the STIRAP transition for various applied electric fields (circles, lower axis). The applied electric field has been calibrated using a dc Stark shift model and the molecular dipole moment determined in Ref. [24]. The corresponding induced electric dipole moment is given on the upper axis, indicating that polar molecules with 0.54 D have been produced.
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Physical Review A

covering atomic, molecular, and optical physics and quantum information

Modeling the adiabatic creation of ultracold polar $^{23} {Na}^{40} K$ molecules

Frauke Seeßelberg, Nikolaus Buchheim, Zhen-Kai Lu, Tobias Schneider, Xin-Yu Luo, Eberhard Tiemann, Immanuel Bloch, and Christoph Gohle

Phys. Rev. A 97, 013405 – Published 12 January 2018

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Physical Review A

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Modeling the adiabatic creation of ultracold polar 23Na40K molecules

Frauke Seeßelberg, Nikolaus Buchheim, Zhen-Kai Lu, Tobias Schneider, Xin-Yu Luo, Eberhard Tiemann, Immanuel Bloch, and Christoph Gohle

Phys. Rev. A 97, 013405 – Published 12 January 2018

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Modeling the adiabatic creation of ultracold polar $^{23} {Na}^{40} K$ molecules