The coherent control of scattering processes is considered, with electron impact dissociation of used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies.
The coherent control of scattering processes is considered, with electron impact dissociation of used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies.
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.
The theory of quantum information constitutes the functional value of the quantum entanglement, i.e., quantum entanglement is essential for high fidelity of quantum protocols, while fundamental physical processes behind the formation of quantum entanglement are less relevant for practical purposes. In the present work, we explore physical mechanisms leading to the emergence of quantum entanglement in the initially disentangled system. In particular, we analyze spin entanglement of outgoing electrons in a nonrelativistic quantum (e,2e) collision on a target with one active electron. Our description exploits the time-dependent scattering formalism for typical conditions of scattering experiments, and contrary to the customary stationary formalism operates with realistic scattering states. We quantify the spin entanglement in the final scattering channel through the pair concurrence and express it in terms of the experimentally measurable spin-resolved (e,2e) triple differential cross sections. Besides, we consider Bell's inequality and inspect the regimes of its violation in the final channel. We address both the pure and the mixed initial spin state cases and uncover kinematical conditions of the maximal entanglement of the outgoing electron pair. The numerical results for the pair concurrence, entanglement of formation, and violation of Bell's inequality obtained for the (e,2e) ionization process of atomic hydrogen show that the entangled electron pairs indeed can be formed in the (e,2e) collisions even with spin-unpolarized projectile and target electrons in the initial channel. The positive entanglement balance---the difference between entanglements of the initial and final electron pairs---can be measured in the experiment.
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.
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.
Abstract The generation of quantum entanglement through scattering processes is a fundamental mechanism in quantum information science. In this work, we investigate how coherent-state superpositions, represented as spatial Gaussian wave-packet superpositions, modify nonclassical phase-space features and enhance entanglement production during the scattering of a single particle from a localized spin impurity governed by a Heisenberg-type interaction. We construct even and odd superpositions of coherent states and analyze their time evolution using Fourier-space propagation. The corresponding Wigner distributions are computed analytically, revealing os-cillatory interference fringes and negative-valued regions that quantify nonclassicality. Using the nonclassical volume as a metric, we show that increasing the spatial separation between the Gaussian components enhances nonclassicality, eventually saturating at a stable asymptotic maximum. By incorporating these superposed states as incident wave packets, we compute the post-scattering spin entanglement between the reflected particle and the impurity using the negativity measure. Our results demonstrate that the symmetry of the initial coherent-state superposition fundamentally governs the stability of the generated entanglement: while the even superposition exhibits parameter-sensitive, oscillatory entanglement as the wave-packet separation increases, the odd superpo-sition yields a robust, decay-resistant entanglement plateau across all separation scales. These findings highlight the critical role of engineered nonclassical initial states in optimizing scattering-based quantum technologies
Fundamental entanglement related challenges have prevented quantum-interference-based control (i.e., coherent control) of collisional cross sections from being implemented in the laboratory. Here, differential cross sections for reactive scattering at low temperatures are shown to provide a unique opportunity to display such interference-based control by forming coherent superpositions of degenerate rotational states of reactant molecules $|jm\ensuremath{\rangle}$ with different m. In particular, we identify and quantify a unique signature of coherent control in reactive scattering with applications to $\mathrm{F}+ {\mathrm{H}}_{2}\ensuremath{\rightarrow}$ H +HF and HF + D $\ensuremath{\leftarrow}$ F $+\mathrm{HD} \ensuremath{\rightarrow}\mathrm{HD} +$ F at 11K. Control is shown to be extensive.