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Physical Review A

Coherent multichannel optical theorem: Quantum control of the total scattering cross section

Adrien Devolder, Timur V. Tscherbul, Paul W. Brumer

Published May 18, 2022• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.105.052808

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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 85Rb\ensuremath-85Rb^{85}\mathrm{Rb}\text{\ensuremath{-}}^{85}\mathrm{Rb}85Rb\ensuremath-85Rb collisions, promising systems for the experimental demonstration of the quantum interference control of the total scattering cross section.
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 generalized 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 85Rb-85Rb collisions, promising systems for the first experimental demonstration of the quantum interference control of the total scattering cross section.
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 show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics that is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying the relative populations and phases of initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold s-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O_{2}+O_{2} collisions, showing extensive control over s-wave spin-exchange cross sections and product branching ratios over many orders of magnitude.
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.
Intriguing quantum effects that result from entangled molecular rovibrational states are shown to provide a novel means for controlling both differential and total collision cross sections in identical particle diatom-diatom scattering. Computational results on elastic and inelastic scattering of para--H2_22​ and para--H2_22​ are presented, with the collision energy ranging from 400 cm−1^{-1}−1 to the ultracold regime. The experimental realization and possible extension to other systems are discussed.
We propose a single-photon router using a single atom with an inversion center coupled to quantum multichannels made of coupled-resonator waveguides. We show that the spontaneous emission of the atom can direct single photons from one quantum channel into another. The on-demand classical field perfectly switches off the single-photon routing due to the quantum interference in the atomic amplitudes of optical transitions. Total reflections in the incident channel are due to the photonic bound state in the continuum. Two virtual channels, named the scatter-free and controllable channels, are found, which are coherent superpositions of quantum channels. Any incident photon in the scatter-free channel is totally transmitted. The propagating states of the controllable channel are orthogonal to those of the scatter-free channel. Single photons in the controllable channel can be perfectly reflected or transmitted by the atom.