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arXiv:2505.06871 · Physical Review Letters

Observation of Modulation-Induced Feshbach Resonance

Tongkang Wang, Yuqi Liu, Jundong Wang, Youjia Huang, Wenlan Chen, Zhendong Zhang, Jiazhong Hu

Published Nov 13, 2025• 1 citation
arXivHTMLPDF

Abstract

In this Letter, we observe a novel resonant mechanism, namely, the modulation-induced Feshbach resonance. By applying a far-detuned laser to the cesium D_{2} transition with intensity modulation, we periodically modulate the energy levels of atomic collisional states. This periodic modulation connects the free-scattering states to shallow molecular states. At specific frequencies, significant atom loss is observed, which corresponds to the resonant coupling between these two types of states. This precisely corresponds to a form of Feshbach resonance, yet in the frequency domain rather than the magnetic-field domain. Using this method, we can directly scan the energy spectrum of molecular bound states without synthesizing any molecules. In addition to these bound states, we can also probe the molecular states embedded in the continuum, which are typically very difficult to detect by the conventional methods based on molecular synthesis. Moreover, by using a far-detuned laser instead of a magnetic field, it enables spatially dependent control over atomic interactions, coupling multiple levels simultaneously and inducing new Feshbach resonances for those atoms that do not have conventional magnetic resonances. Therefore, we believe that this new resonant mechanism offers new opportunities for controlling atomic and molecular interactions in quantum simulations.

DOI
10.1103/qrz6-gjp6

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In this Letter, we observe a novel resonant mechanism, namely, the modulation-induced Feshbach resonance. By applying a far-detuned laser to the cesium D_{2} transition with intensity modulation, we periodically modulate the energy levels of atomic collisional states. This periodic modulation connects the free-scattering states to shallow molecular states. At specific frequencies, significant atom loss is observed, which corresponds to the resonant coupling between these two types of states. This precisely corresponds to a form of Feshbach resonance, yet in the frequency domain rather than the magnetic-field domain. Using this method, we can directly scan the energy spectrum of molecular bound states without synthesizing any molecules. In addition to these bound states, we can also probe the molecular states embedded in the continuum, which are typically very difficult to detect by the conventional methods based on molecular synthesis. Moreover, by using a far-detuned laser instead of a magnetic field, it enables spatially dependent control over atomic interactions, coupling multiple levels simultaneously and inducing new Feshbach resonances for those atoms that do not have conventional magnetic resonances. Therefore, we believe that this new resonant mechanism offers new opportunities for controlling atomic and molecular interactions in quantum simulations.
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.
In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism that does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the transition frequency between the scattering atoms and a two-atom bound state. The real part of the resulting s-wave scattering length a is resonantly enhanced when the oscillation frequency is close to the transition frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a, which arises because the oscillating field converts atom pairs into molecules. The real part of a can be made much larger than the background scattering length without introducing catastrophic atom losses from the imaginary part. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.
We observe magnetically tuned collision resonances for ultracold Cs2 molecules stored in a CO2-laser trap. By magnetically levitating the molecules against gravity, we precisely measure their magnetic moment. We find an avoided level crossing which allows us to transfer the molecules into another state. In the new state, two Feshbach-like collision resonances show up as strong inelastic loss features. We interpret these resonances as being induced by Cs4 bound states near the molecular scattering continuum. The tunability of the interactions between molecules opens up novel applications such as controlled chemical reactions and synthesis of ultracold complex molecules.
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.
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.
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.