Detection of Long-Lived Complexes in Ultracold Atom-Molecule Collisions

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Detection of Long-Lived Complexes in Ultracold Atom-Molecule Collisions

Matthew A. Nichols, Yi-Xiang Liu, Lingbang Zhu, Ming-Guang Hu, Yu Liu, and Kang-Kuen Ni

Phys. Rev. X 12, 011049 – Published 15 March 2022

See synopsis: Ultracold Molecules Have Staying Power

Abstract

A thorough understanding of molecular scattering in the ultralow temperature regime is crucial for realizing long coherence times and enabling tunable interactions in molecular gases, systems which offer many opportunities in quantum simulation, quantum information, and precision measurement. Of particular importance is the nature of the long-lived intermediate complexes which may be formed in ultracold molecular collisions, as such complexes can dramatically affect the stability of molecular gases, even when exothermic reaction channels are not present. Here, we investigate collisional loss in an ultracold mixture of ${}^{40}K {}^{87}{Rb}$ molecules and ${}^{87}{Rb}$ atoms, where chemical reactions between the two species are energetically forbidden. Through direct detection of the ${KRb}_{2}^{*}$ intermediate complexes formed from atom-molecule collisions, we show that a 1064 nm laser source used for optical trapping of the sample can efficiently deplete the complex population via photoexcitation, an effect which can explain the strong two-body loss observed in the mixture. By monitoring the time evolution of the ${KRb}_{2}^{*}$ population after a sudden reduction in the 1064 nm laser intensity, we measure the lifetime of the complex [0.39(6) ms], as well as the photoexcitation rate for 1064 nm light [ $0.50 (3) μ s^{- 1} (kW / {cm}^{2})^{- 1}$ ]. The observed lifetime, which is $\sim 10^{5}$ times longer than recent estimates based on the Rice-Ramsperger-Kassel-Marcus statistical theory, calls for new theoretical insight to explain its origin.

Received 4 June 2021
Accepted 18 January 2022

DOI:https://doi.org/10.1103/PhysRevX.12.011049

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic & molecular collisions Cold and ultracold molecules Ultracold chemistry Ultracold collisions

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

synopsis

Ultracold Molecules Have Staying Power

Published 15 March 2022

Intermediate, nonreactive atom-molecule complexes last for a surprisingly long time.

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Authors & Affiliations

Matthew A. Nichols ^1,2,3,*, Yi-Xiang Liu ^1,2,3, Lingbang Zhu^1,2,3, Ming-Guang Hu^1,2,3,‡, Yu Liu ^1,2,3,§, and Kang-Kuen Ni^1,2,3,†

¹Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
³Harvard-MIT Center for Ultracold Atoms, Cambridge, Massachusetts 02138, USA

^*matthewnichols@g.harvard.edu
^†ni@chemistry.harvard.edu
^‡Present address: QuEra Computing, 1284 Soldiers Field Road, Boston, Massachusetts 02135, USA.
^§Present address: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.

Popular Summary

Chemical reactions transform molecular reactants into products through the formation of intermediate, loosely bound associations known as complexes. While complexes are typically short-lived, their lifetime can be extended dramatically at ultralow temperatures. A thorough understanding of the dynamics in this regime could enable more refined control over interactions in molecular gases, a potentially useful feature in some quantum-information applications. Here, we report that the lifetime of one molecular complex is 5 orders of magnitude longer than what is expected from a theory that had previously been successfully used to match experimental data.

The duration of complexes at ultralow temperatures is thought to arise from a combination of very deep potential energy wells and a limited number of “quantum channels” that provide a way out. Because of this, the transient complexes can be trapped for a very long time before they exit as products or reactants. This also provides an experimental advantage: It is possible for these long-lived complexes to be photoexcited by the laser light that is typically used as a container to hold the gases of ultracold molecules inside a vacuum chamber. We use this to study ultracold collisions between Rb atoms and KRb molecules, which form ${KRb}_{2}^{*}$ complexes as an intermediary. By monitoring the complex’s photoexcitation by the confining laser light, we measure the ${KRb}_{2}^{*}$ lifetime.

Our results call for a deeper theoretical understanding of molecular collisions at ultracold temperatures.

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Vol. 12, Iss. 1 — January - March 2022

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Figure 1
Ultracold atom-molecule collisions in an optical dipole trap (ODT). Inset: a diagram of the ODT configuration used to confine the mixture of KRb molecules and Rb atoms. The $H$ and $V$ ODTs are formed from 1064 nm Gaussian beams with $1 / e^{2}$ diameters of 70 and $200 μ m$ , respectively. The purple arrow represents the UV ionization laser pulse, which has a duration of 7 ns, used for photoionization of ${KRb}_{2}^{*}$ complexes. Electric ( $E$ ) and magnetic ( $B$ ) fields are applied to extract the ions and to maintain nuclear spin quantization, respectively. (b) Schematic illustration of the potential energy surface for collisions between KRb and Rb. The incident energy of one free electronic ground state Rb atom and one free KRb molecule in its rovibronic ground state is defined as the zero of energy. Because the ${Rb}_{2} + K$ reaction channel is energetically forbidden at ultralow temperatures, the collision must proceed through one of two pathways: $KRb + Rb \leftrightarrow {KRb}_{2}^{*}$ or $KRb + Rb \to {KRb}_{2}^{*} \to {KRb}_{2}^{* *}$ , where ${KRb}_{2}^{* *}$ is an electronically excited state of the complex. The formation, dissociation, and photoexcitation rates of ${KRb}_{2}^{*}$ , as defined in Eq. (1), are labeled as $γ$ , $τ_{c}^{- 1} n_{c}$ , and $Γ (I_{tot}) n_{c}$ , respectively, and the density of states (DOS) of the complex near the incident energy is written as $ρ_{c}$ . The ground-state energies of KRb [39] and ${Rb}_{2}$ [43] are obtained from spectroscopic data, whereas that of ${KRb}_{2}$ is calculated [20].
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Figure 2
Two-body collisional loss in an ultracold mixture of KRb molecules and Rb atoms. (a) Normalized molecule number versus hold time for a pure molecular sample (black circles) and for a representative atom-molecule mixture (red triangles). Each data point is an average of 10 repetitions. Error bars represent the standard error of the mean, the black solid line is a fit to the two-body decay arising from molecule-molecule collisions [12], and the red solid line is a fit using the function $N_{m} (t) = \exp (- k_{m, a} n_{a} t)$ . (b) Dependence of the molecular loss rate on the atomic density. A linear fit (black solid line) yields $k_{m, a} = 6.8 (7) \times 10^{- 11} {cm}^{3} s^{- 1}$ , which is consistent with the predicted universal loss rate [44]. Vertical and horizontal error bars represent the $1 σ$ statistical uncertainty in the measured loss rate and in the calibrated value of $n_{a}$ , respectively. All data shown in (a) and (b) are taken with $B = 542 G$ in a continuously operated ODT of intensity $I_{tot} = 11.3 kW / {cm}^{2}$ .
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Figure 3
Photoexcitation loss of ${KRb}_{2}^{*}$ collision complexes in a 1064 nm optical trap. (a) Steady-state ${KRb}_{2}^{+}$ ion counts measured for different initial atom number densities $n_{a}$ and normalized by the number of experimental cycles ( $\sim 100$ for each data point). Vertical error bars represent shot noise, and horizontal error bars represent the $1 σ$ statistical uncertainty in the calibrated value of $n_{a}$ . The inset shows the timing diagram used for the measurement. The red curve is the total ODT intensity and the blue dashed line is its time average. (b) Steady-state ${KRb}_{2}^{+}$ ion counts measured at different total ODT intensities with $n_{a} = 4.1 (3) \times 10^{11} {cm}^{- 3}$ , and normalized by the number of experimental cycles ( $\sim 50$ for each data point). Error bars represent shot noise, and the solid line is a fit to the data using Eq. (2). The inset shows the timing diagram used for the measurement. The red curve is the intensity of the $V$ ODT, where the intensity during the “high” phase of the modulation period is $I^{'}$ , and that during the “low” phase is $I$ . To control $I_{tot}$ , we vary the $V$ ODT modulation depth while keeping the time-averaged intensity fixed at the continuously operated level, $5.6 kW / {cm}^{2}$ (blue dashed line). The red dashed line is the intensity profile at full modulation depth. The $H$ ODT, not shown here, follows the $V$ ODT timing, but is always modulated at full depth with a time-averaged intensity equal to its continuously operated level, $5.7 kW / {cm}^{2}$ . All data shown in (a) and (b) are taken with $B = 30 G$ and $E = 17 V / cm$ .
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Figure 4
Lifetime of the ${KRb}_{2}^{*}$ collision complex. (a) Time evolution of the ${KRb}_{2}^{*}$ population (measured via the ${KRb}_{2}^{+}$ ion signal) after a rapid change in the 1064 nm intensity, for different values of $I_{tot}$ . Data are normalized by the corresponding number of experimental cycles ( $\sim 100$ for each data point). The time-averaged value of the total intensity is fixed at $11.3 kW / {cm}^{2}$ across all datasets. Error bars represent shot noise, and the solid lines are fits using the function $A (1 - e^{- R t})$ . (b) Characteristic growth rate $R$ of the complex population, as obtained from the fits in (a), versus the corresponding total ODT intensity. Error bars represent the $1 σ$ statistical uncertainty in the fitted value of $R$ , and the solid line is a linear fit to the data. All data shown in (a) and (b) are taken with $B = 30 G$ and $E = 17 V / cm$ .
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