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arXiv:1911.07063 · Physical Review A

Analytic approximations to the strengths of near-threshold optical Feshbach resonances

Mateusz Borkowski

Published Jun 1, 2023• 1 citation
arXivHTMLPDF

Abstract

Optical Feshbach resonances allow one to control cold atomic scattering, produce ultracold molecules, and study atomic interactions via photoassociation spectroscopy. In the limit of ultracold $s$-wave collisions, the strength of an optical Feshbach resonance can be expressed via an energy-independent parameter called the optical length. Here we give fully analytic approximate expressions for its magnitude applicable to near-threshold bound states of an excited molecular state dominated by a single resonant-dipole or van der Waals interaction. We express these magnitudes in terms of intuitive quantities, such as the laser intensity, the excited-state binding energy, the $s$-wave scattering length, and the Condon point. Additionally, we extend the utility of the optical length to associative stimulated Raman adiabatic passage in three-dimensional optical lattices by showing that the free-bound Rabi frequency induced by a laser coupling a pair of atoms in an optical lattice site can be approximately related to the trap frequency and the optical length.

DOI
10.1103/physreva.107.063101

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Optical Feshbach resonances allow one to control cold atomic scattering, produce ultracold molecules, and study atomic interactions via photoassociation spectroscopy. In the limit of ultracold sss-wave collisions, the strength of an optical Feshbach resonance can be expressed via an energy-independent parameter called the optical length. Here we give fully analytic approximate expressions for its magnitude applicable to near-threshold bound states of an excited molecular state dominated by a single resonant-dipole or van der Waals interaction. We express these magnitudes in terms of intuitive quantities, such as the laser intensity, the excited-state binding energy, the sss-wave scattering length, and the Condon point. Additionally, we extend the utility of the optical length to associative stimulated Raman adiabatic passage in three-dimensional optical lattices by showing that the free-bound Rabi frequency induced by a laser coupling a pair of atoms in an optical lattice site can be approximately related to the trap frequency and the optical length.
This thesis reports on the first observation of optical tuning of interactions in an ultracold atomic gas. To control the elastic interactions, we use optically induced scattering resonances. They are realized by coupling pairs of atoms to a bound molecular state with the help of laser light. In comparison to the well-known magnetic Feshbach resonances, these optical Feshbach resonances allow a very fast switching of interactions in a spatially resolved way. This is because laser light can be switched on and off much faster than magnetic fields and because the light intensity can be spatially structured. Our experiments are performed with a Bose-Einstein condensate (BEC) of Rb atoms, which we produce in our new BEC setup. This apparatus has been constructed in the framework of this thesis and offers excellent optical access to the ultracold atom cloud. To investigate the tunability of atomic interactions with single-frequency laser light, we optically couple pairs of free atoms to an electronically excited molecular state. The coupling is achieved with a laser that is tuned close to the respective free-bound photoassociation transition. By changing the laser detuning we are able to adjust the atomic scattering length to any value between 10 a0 and 190 a0, where a0 denotes the Bohr radius. The atomic scattering length is a single quantity that fully describes ultracold elastic interactions. Since laser induced atom losses restrict the duration of our experiments, Bragg spectroscopy is employed as a fast method to measure the scattering length. We also demonstrate that optical Feshbach resonances can be realized with a two-color Raman coupling scheme. To implement this scheme, a second laser is added that couples the excited molecular state to a weakly bound molecular level in a ground state potential. Tuning the second laser results in a modification of the atomic scattering length similar to the one observed with a single laser. In addition, this scheme allows to control the width of the resonance via the detuning of the first laser. For the one-color and two-color coupling schemes, we investigate how the elastic scattering properties depend on the different available parameters, i.e. the laser detunings and intensities. Our experimental findings can successfully be described with an available theoretical model, which treats ultracold collisions in the presence of laser light. Optical Feshbach resonances have the possibility of becoming a valuable tool for fast switching of interactions. This is of special interest in quantum computation schemes with neutral atoms, where interactions between different atomic qubits need to be controlled.
It is well-known that cold atoms near sss-wave Feshbach resonances have universal properties that are insensitive to the short-range details of the interaction. What is less known is that atoms near higher partial-wave Feshbach resonances also have remarkable universal properties. We illustrate this with a single atom interacting resonantly with two fixed static centers. At a Feshbach resonance point with orbital angular momentum $L\ensuremath{\ge}1$, we find 2L+12L+12L+1 shallow bound states whose energies behave like 1/R2L+11/{R}^{2L+1}1/R2L+1 when the distance RRR between the two centers is large. We then compute corrections to the binding energies due to other parameters in the effective range expansions. For completeness we also compute the binding energies near sss-wave Feshbach resonances, taking into account the corrections. Afterwards we turn to the bound states at large but finite scattering volumes. For ppp-wave and higher partial-wave resonances we derive a simple formula for the energies in terms of a parameter called ``proximity parameter.'' These results are applicable to a free atom interacting resonantly with two atoms that are localized to two lattice sites of an optical lattice, and to one light atom interacting with two heavy ones in free space. Modifications of the low energy physics due to the long range van der Waals potential are also discussed.
Feshbach resonances play a major role in translationally cold-molecule preparation. In this context, their laser control is of crucial importance. This work is devoted to the depiction of some basic mechanisms of such a control using intense, short laser pulses and referring to nonlinear multiphoton processes. Our goal is to adiabatically transport a Feshbach resonance onto a zero-width resonance, the characteristics of which have already been discussed in the literature. Three processes are then addressed: (i) during the rise of the pulse and its plateau, the preparation of a so-called laser bound molecule (LBM) still stable, but structurally different from the standard chemically bound molecule; (ii) during the pulse switching off, an adiabatic transport of this LBM on a very few excited vibrational levels, and (iii) concomitantly, a filtration strategy to photodissociate all these levels except one, giving thus rise to but a single field-free excited vibrational state. With or without an eventual stimulated Raman adiabatic passage technique to bring all the population to the ground rovibrational state, this opens an alternate for a full optical control of ultracold-molecule formation. The illustrative example, offering the potentiality to be transposed to other diatomics, is H2+{\mathrm{H}}_{2}^{+}H2+​.
We have observed optically induced Feshbach resonances in a cold ( <1 mK) sodium vapor. The optical coupling of the ground and excited-state potentials changes the scattering properties of an ultracold gas in much the same way as recently observed magnetically induced Feshbach resonances, but allows for some experimental conveniences associated with using lasers. The scattering properties can be varied by changing either the intensity or the detuning of a laser tuned near a photoassociation transition to a molecular state in the dimer. In principle this method allows the scattering length of any atomic species to be altered. A simple model is used to fit the dispersive resonance line shapes.
It is possible to tune the scattering length for the collision of ultracold ground-state alkaline-earth-metal atoms using an optical Feshbach resonance. This is achieved with a laser far detuned from an excited molecular level near the frequency of the atomic intercombination transition. Simple resonant-scattering theory, illustrated by the example of , allows an estimate of the magnitude of the effect. Unlike alkali metal species, large changes of the scattering length are possible while atom loss remains small, because of the very narrow linewidth of the molecular photoassociation transition. This raises prospects for control of atomic interactions for a system without magnetically tunable Feshbach resonance levels.
We propose a type of Feshbach resonance occurring when two different ultracold atoms in their ground state undergo an sss-wave collision in the presence of a laser. The collisional levels of the atom pair are coupled by the laser to a rovibrational molecular level of the same electronic ground state: We name it a laser-assisted self-induced Feshbach resonance. This mechanism, valid for all heteronuclear quantum gas mixtures, is analyzed on the example of ultracold 87Rb^{87}\mathrm{Rb}87Rb and 84Sr^{84}\mathrm{Sr}84Sr atoms for which the resonant laser frequency falls in the subterahertz range. The interspecies scattering length can be controlled with the laser frequency and intensity without atom loss. Moreover, chirping slowly, the frequency allows for the adiabatic formation of ultracold 87Rb84Sr^{87}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{84}\mathrm{Sr}87Rb84Sr molecules in a manner very similar to a magnetic Feshbach resonance. A stimulated Raman adiabatic passage follows for stabilizing the molecules in their rovibronic ground state.