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Frontiers in Physics

The two-body collision controlled by the magnetic field and laser field near magnetic Feshbach resonance

Bing-Kuan Lyu, Bo-Wen Si, Zong-Han Yu, Gao‐Ren Wang, Shu‐Lin Cong

Published Jul 5, 2023• 0 citations

Abstract

It is crucial to control the collision between ultracold atoms by applying external fields. We developed a theoretical model for investigating the s-wave scattering of ultracold atoms controlled by the magnetic field and laser field. The calculation is performed by using the close-coupling method and mapped Fourier grid method. Due to the interference between the photoassociation and bound-to-bound transitions, the bound state in the continuum, which is a resonance with a vanishing width, occurs at the magnetic field position near the magnetic Feshbach resonance. The widths of resonances in the neighborhood of the bound state in the continuum are narrow. Changing the laser intensity can shift the magnetic field position where the bound state in the continuum occurs through modifying the ground molecular state to induce wide resonances at desired magnetic field positions. By increasing the resonance width, the tunability of the real part of the scattering length at resonances can be significantly improved. Changing the laser intensity can also adjust the coupling between the ground and excited molecular states. When the coupling between the ground and excited molecular states approaches zero, a resonance is induced, and the photoassociation and bound-to-bound transitions are both significantly suppressed at this resonance. Therefore, the atomic loss peak due to spontaneous emission does not appear at this resonance. The magnetic field position of this resonance is stable against the change in laser frequency.

DOI: 10.3389/fphy.2023.1198477

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It is crucial to control the collision between ultracold atoms by applying external fields. We developed a theoretical model for investigating the s-wave scattering of ultracold atoms controlled by the magnetic field and laser field. The calculation is performed by using the close-coupling method and mapped Fourier grid method. Due to the interference between the photoassociation and bound-to-bound transitions, the bound state in the continuum, which is a resonance with a vanishing width, occurs at the magnetic field position near the magnetic Feshbach resonance. The widths of resonances in the neighborhood of the bound state in the continuum are narrow. Changing the laser intensity can shift the magnetic field position where the bound state in the continuum occurs through modifying the ground molecular state to induce wide resonances at desired magnetic field positions. By increasing the resonance width, the tunability of the real part of the scattering length at resonances can be significantly improved. Changing the laser intensity can also adjust the coupling between the ground and excited molecular states. When the coupling between the ground and excited molecular states approaches zero, a resonance is induced, and the photoassociation and bound-to-bound transitions are both significantly suppressed at this resonance. Therefore, the atomic loss peak due to spontaneous emission does not appear at this resonance. The magnetic field position of this resonance is stable against the change in laser frequency.

This thesis reports on a novel scheme for controlling the scattering properties of an ultracold atomic gas with laser light. We show theoretically and experimentally that light near-resonant with a molecular bound-to-bound transition can be used to shift the magnetic field at which a magnetic Feshbach resonance occurs. This makes it possible to tune the interaction strength with laser light and at the same time induce considerably less loss than an optical Feshbach resonance would do. To find an appropriate bound-to-bound transition for this scheme, we perform excited-state spectroscopy. When applying laser light resonant with one such bound-to-bound transition we observe an Autler-Townes splitting of the magnetic Feshbach resonance. We find good agreement between the theoretical model and experimental data. Our scheme can be used for a variety of future applications. For example, light patterns created by holographic masks could serve as a tool for changing the scattering length of ultracold atoms on very short time and length scales.

We study collision of two atoms with formation of Feshbach resonance at combined interaction with the external magnetic field and laser radiation. In cases of one- and two-photon resonances of laser radiation with two discrete vibrational molecular levels, we show that Feshbach resonances appear at interaction of external magnetic field with dressed states formed via Autler-Townes effect. In addition, in case of one-photon resonance the lower vibrational molecular state is coupled by laser radiation with the continuum of the elastic channel and forms laser-induced Feshbach resonance via both Autler-Townes effect and LICS mechanism. We study the combined process of formation of Feshbach resonances; this enables the control of Feshbach resonance by varying the magnetic field and intensity and frequency of laser radiation. We obtain the cross-sections of elastic and inelastic scattering and show that quenching of resonance occurs at the energy equal to that of the systems ground state. Dependence of the cross-sections on the magnetic field and laser intensity is examined in detail. In all considered cases, the scattering length is obtained depending on the magnetic and laser fields are studied. In the absence of magnetic interaction if the hyperfine substates of the quasibound state in the closed channel and those of individual colliding atoms in the open channel are the same, Feshbach resonances may arise via weak interaction between nuclear and electronic motions, which leads to transitions between electronic states. The obtained results can be employed in new studies of collisions of cold atoms, e.g., of alkali metal atoms and for interpretation of new experiments in BECs.

We theoretically investigate the control of a magnetic Feshbach resonance using a bound-to-bound molecular transition driven by spatially modulated laser light. Due to the spatially periodic coupling between the ground and excited molecular states, there exists a band structure of bound states, which can uniquely be characterized by some extra bumps in radio-frequency spectroscopy. With the increasing of coupling strength, the series of bound states will cross zero energy and directly result in a number of scattering resonances, whose position and width can be conveniently tuned by the coupling strength of the laser light and the applied magnetic field (i.e., the detuning of the ground molecular state). In the presence of the modulated laser light, universal two-body bound states near zero-energy threshold still exist. However, compared with the case without modulation, the regime for such universal states is usually small. A unified formula, which embodies the influence of the modulated coupling on the resonance width is given. The spatially modulated coupling also implies a local spatially varying interaction between atoms. Our work proposes a practical way of optically controlling interatomic interactions with high spatial resolution and negligible atomic loss.

We use laser light near resonant with a molecular bound-to-bound transition to control a magnetic Feshbach resonance in ultracold Fermi gases of

{}^{40}

K atoms. The spectrum of excited molecular states is measured by applying a laser field that couples the ground Feshbach molecular state to electronically excited molecular states. Nine strong bound-to-bound resonances are observed below the

{}^{2}{P}_{1/2}+{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

threshold. We use radio-frequency spectroscopy to characterize the laser-dressed bound state near a specific bound-to-bound resonance and show clearly the shift of the magnetic Feshbach resonance using light. The demonstrated technology could be used to modify interatomic interactions with high spatial and temporal resolutions in the crossover regime from a Bose-Einstein condensate to a Bardeen-Cooper-Schrieffer superfluid.

We propose a type of Feshbach resonance occurring when two different ultracold atoms in their ground state undergo an

s

-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

^{87}\mathrm{Rb}

and

^{84}\mathrm{Sr}

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

^{87}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{84}\mathrm{Sr}

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.

We describe two-field optical techniques to control interactions in Feshbach resonances for two-body scattering in ultracold gases. These techniques create a molecular dark state in the closed channel of a magnetically tunable Feshbach resonance, greatly suppressing optical scattering compared to single optical field methods. The dark-state method enables control of the effective range, by creating narrow features that modify the energy dependence of the scattering phase shift, as well as control of the elastic and inelastic parts of the zero-energy

s

-wave scattering amplitude. We determine the scattering length and the effective range from an effective range expansion, by calculating the momentum-dependent scattering phase shift from the two-body scattering state.