We consider the coherent control of ultracold molecule-molecule scattering, impacted by a dense set of rovibrational resonances. To characterize the resonance spectrum, a rudimentary model based on multichannel quantum defect theory has been used to study the control of the scattering cross section and the reaction rate. Complete control around resonance energies is shown to be possible, but thermal averaging over a large number of resonances significantly reduces the extent of control of reaction rates related to the random distribution of optimal control parameters between resonances. We show that measuring the extent of coherent control could be used to extract meaningful information about the relative contribution of direct scattering versus collision complex formation, as well as about the statistical regime.
We consider the coherent control of ultracold molecule-molecule scattering, impacted by a dense set of rovibrational resonances. To characterize the resonance spectrum, a rudimentary model based on multichannel quantum defect theory has been used to study the control of the scattering cross section and the reaction rate. Complete control around resonance energies is shown to be possible, but thermal averaging over a large number of resonances significantly reduces the extent of control of reaction rates related to the random distribution of optimal control parameters between resonances. We show that measuring the extent of coherent control could be used to extract meaningful information about the relative contribution of direct scattering versus collision complex formation, as well as about the statistical regime.
Ultracold chemistry operates in a regime where thermal motion is suppressed to the microkelvin scale, allowing quantum mechanics to dictate every aspect of molecular interaction. This paper reviews the theoretical foundations and experimental breakthroughs that now make coherent control of ultracold reactions possible. It first outlines the separation of short- and long-range physics through quantum defect theory, emphasizing why short-range dynamics remain intractable and why universal loss emerges naturally. It then examines how long-range potentials, resonances, and quantum interference enable tunable scattering behavior. Two major milestones anchor this discussion: phase-coherent atom–atom–molecule coupling, which confirms the transfer and control of reaction phase, and the experimental resolution of long-range atom–molecule Feshbach resonances using a Fabry–P´erot interferometer model. Finally, it highlights the recent observation of a magnetically tunable molecule–molecule Feshbach resonance in NaLi, overturning long-held assumptions about the impossibility of resonance control in complex molecular systems. Together, these results demonstrate that ultracold molecules can be engineered to undergo fully coherent, interference-driven reactions, establishing a framework for quantum-controlled chemistry and laying the groundwork for applications in quantum simulation and computation.
The optical theorem is a fundamental aspect of quantum scattering theory. Here, we generalize this theorem to the case where the incident scattering state is a superposition of internal states of the collision partners, introducing additional interference contributions and, e.g., providing a route to control the total integral cross section. As in its standard form, forward scattering plays an essential role in the multichannel optical theorem, but with interference terms being related to the inelastic forward scattering amplitudes between states in the initial superposition. Using the resultant control index, we show that extensive control is possible over ultracold collisions of oxygen molecules in their rovibrational ground states, and of $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{85}\mathrm{Rb}$ collisions, promising systems for the experimental demonstration of the quantum interference control of the total scattering cross section.
Compared to purely atomic collisions, ultracold molecular collisions potentially support a much larger number of Fano-Feshbach resonances due to the enormous number of rovibrational states available. In fact, for alkali-metal dimers we find that the resulting density of resonances cannot be resolved at all, even on the sub-$\ensuremath{\mu}$K temperature scale of ultracold experiments. As a result, all observables become averaged over many resonances and can effectively be described by simpler, nonresonant scattering calculations. Two particular examples are discussed: nonchemically reactive RbCs and chemically reactive KRb. In the former case, the formation of a long-lived collision complex may lead to the ejection of molecules from a trap. In the latter case, chemical reactions broaden the resonances so much that they become unobservable.
At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.
Compared to purely atomic collisions, ultracold collisions involving molecules have the potential to support a much larger number of Fano-Feshbach resonances due to the huge amount of ro-vibrational states available. In order to handle such ultracold atom-molecule collisions, we formulate a theory that incorporates the ro-vibrational Fano-Feshbach resonances in a statistical manner while treating the physics of the long-range scattering, which is sensitive to such things as hyperfine states, collision energy, and any applied electromagnetic fields, exactly within multichannel quantum defect theory. Uniting these two techniques, we can assess the influence of highly resonant scattering in the threshold regime, and in particular its dependence on the hyperfine state selected for the collision. This allows us to explore the onset of Ericson fluctuations in the regime of overlapping resonances, which are well known in nuclear physics but completely unexplored in the ultracold domain.
Coherent control of atomic and molecular scattering relies on the preparation of colliding particles in superpositions of internal states, establishing interfering pathways that can be used to tune the outcome of a scattering process. However, the incoherent addition of different partial wave contributions to the integral cross-sections, commonly encountered in systems with complex collisional dynamics, poses a significant challenge, often limiting the control. This work demonstrates that time-reversal symmetry can be used to overcome these limitations by constraining the relation between the S-matrix elements. For example, the preparation of a superposition of two states related by the time-reversal superposition can provide extensive control for transitions to a time-reversal invariant final state, such as the J = 0, M = 0. Using the example of ultracold O 2 –O 2 scattering, we show that for such states coherent control is robust against short-range dynamical complexity. Furthermore, the time-reversal symmetry also protects the control against a distribution of collisional energies. Beyond the ultracold regime, we observe significant differences in the controllability of crossed-molecular beam vs trap experiments with complete control achievable in the former case at any temperature, emphasizing the cooperative role of time-reversal and permutation symmetries in maintaining control at any temperature. These results open new avenues for the coherent control of complex inelastic collisions and chemical reactions both in and outside of the ultracold regime.