Quenched magneto-association of ultracold Feshbach molecules

Kirk Waiblinger, Jason R. Williams, and José P. D'Incao

Phys. Rev. A 104, 033310 – Published 8 September 2021

Abstract

We study enhanced magneto-association of atoms into weakly bound molecules near a Feshbach resonance using a quench preparatory stage. In anticipation of experiments with NASA's Cold Atom Laboratory aboard the International Space Station, we assume as a baseline a dual-species $({}^{87}{Rb} and {}^{41}K)$ gas in a parameter regime enabled by a microgravity environment. It includes subnanokelvin temperatures and dual-species gases at densities as low as $10^{8} / {cm}^{3}$ . Our studies indicate that, in such a regime, traditional magneto-association schemes are inefficient due to the weak coupling between atomic and molecular states at low densities, thus requiring extremely long magnetic field sweeps. To address this issue we propose a modified scheme in which atoms are quenched to unitarity before proceeding with magneto-association. This modified scheme substantially improves molecular formation, allowing for up to $80 %$ efficiency within timescales much shorter than those associated with atomic and molecular losses. We show that this scheme also applies at higher densities, therefore proving to be of interest in ground-based experiments as well.

Received 10 May 2021
Accepted 16 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.033310

Physics Subject Headings (PhySH)

Atomic & molecular collisions Bose gases Cold and ultracold molecules Ultracold collisions

Atomic, Molecular & Optical

Authors & Affiliations

Kirk Waiblinger ¹, Jason R. Williams², and José P. D'Incao ^1,3

¹Department of Physics, University of Colorado, Boulder, 80309 Colorado, USA
²Jet Propulsion Laboratory, California Institute of Technology, Pasadena, 91011 California, USA
³JILA, University of Colorado and NIST, Boulder, 80309 Colorado, USA

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Vol. 104, Iss. 3 — September 2021

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Images

Figure 1
Scattering length (in units of the Bohr radius $a_{0}$ ) as a function of applied $B$ field near the ${}^{87}{Rb} − {}^{41}K$ Feshbach resonance at $B_{0} \approx 39.4 G$ . This resonance is characterized by a width $Δ B \approx 37 G$ and background scattering length $a_{bg} \approx 284 a_{0}$ [42]. Both ${}^{87}{Rb}$ and ${}^{41}K$ atoms are in the $| f = 1, m_{f} = 1 〉$ hyperfine state. $B_{i}$ and $B_{f}$ indicate, respectively, the initial and final values of the $B$ field in a hypothetical magneto-association scheme.
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Figure 2
The energy levels of two atoms in a harmonic trap parameterized by $1 / k_{n} a$ and orbital angular momentum $l = 0$ (see text). In the limit of large $1 / | k_{n} a |$ , the spectrum consists of pure harmonic oscillator levels, whose energies are plotted as dashed lines. Positive energies correspond to atomic states, and negative energies represent molecular states. Note that the expected Feshbach molecular state for large positive $a$ , having binding energy $E_{b} = ℏ^{2} / 2 μ a^{2}$ , is shifted slightly due to the oscillator potential. The gray region indicate the values in which the system is found in the unitary regime, $1 / | k_{n} a | < 1$ .
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Figure 3
Schematic of magnetic field vs time in the traditional and quenched magneto-association schemes. (a) In the traditional magneto-association (TMA) $B$ field is swept from $B_{i}$ to $B_{f}$ at a constant rate during a time $t_{sw}$ . (b) In the quenched magneto-association (QMA) the $B$ field is instantaneously quenched from $B_{i}$ to $B_{0}$ , remaining at $1 / | k_{n} a | = 0$ for a dwell time $t_{dw}$ , followed by a linear sweep from $B_{0}$ to $B_{f}$ . This schematic figure is not to scale, and $B_{i}$ and $B_{f}$ will not, in general, be equidistant from $B_{0}$ , nor will $t_{sw}$ and $t_{dw}$ bear any particular relationship to each other. Here, $t_{u}$ and $t_{u}^{*}$ represent the interaction time, i.e., the time in which $1 / | k_{n} a | < 1$ , for TMA and QMA, respectively.
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Figure 4
Analysis of the relevant timescales for magneto-association. For TMA, the values for $τ_{u} / t_{u}$ calculated from the lifetimes due to RbRbK losses at $T = 100 pK$ (black dashed curves) for various densities and a broad range of sweeping times. As $n$ increases, the values of $t_{sw}$ in which $τ_{u} / t_{u} > 1$ becomes quickly more restrictive. For QMA we display the values for $τ_{u}^{*} / t_{u}^{*}$ (solid curves) for various values of $t_{dw}$ . Regardless of the density, a broad range of $t_{sw}$ satisfies the favorable condition for magneto-association, $τ_{u}^{*} / t_{u}^{*} > 1$ .
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Figure 5
Fraction of molecules produced as a function of $t_{sw}$ for various densities. The dashed curve represents results for TMA, while solid curves are those for QMA at different dwelling times $t_{dw}$ . In all cases the initial and final states are characterized by $a_{i} = - 2 r_{vdW}$ and $a_{f} = 100 r_{vdw}$ , respectively. Note that at $t_{sw} = 0$ , TMA results are identical to those from QMA at $t_{sw} = t_{dw} = 0$ . (See the text for more discussions of these results and comparisons). Each panel displays the corresponding values for $E_{n}$ and $t_{n}$ .
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Figure 6
Fraction of molecules produced as a function of $t_{sw}$ for $n = 10^{13} / {cm}^{3}$ . The dashed curve represents results for TMA, while solid curves are those for QMA at different dwelling times $t_{dw}$ . In all cases the initial and final states are characterized by $a_{i} = - 2 r_{vdW}$ and $a_{f} = 10 r_{vdw}$ , respectively.
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