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arXiv:0902.3797 · Physical Review A

Coherent bimolecular reactions with quantum-degenerate matter waves

Hui Jing, Jing Cheng, Pierre Meystre

Published Feb 20, 2009• 3 citations
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Abstract

We demonstrate theoretically that the abstraction reaction $A+{B}_{2}\ensuremath{\rightarrow}AB+B$ can be driven coherently and efficiently with quantum-degenerate bosonic or fermionic matter waves. We show that the initial stages of the reaction are dominated by quantum fluctuations, resulting in the appearance of macroscopic nonclassical correlations in the final atomic and molecular fields. The dynamics associated with the creation of bosonic and of fermionic dimer-atom pairs is also compared. This study opens up a promising regime of quantum-degenerate matter-wave chemistry.

DOI
10.1103/physreva.79.023622

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We demonstrate theoretically that the abstraction reaction A+B2\ensuremath→AB+BA+{B}_{2}\ensuremath{\rightarrow}AB+BA+B2​\ensuremath→AB+B can be driven coherently and efficiently with quantum-degenerate bosonic or fermionic matter waves. We show that the initial stages of the reaction are dominated by quantum fluctuations, resulting in the appearance of macroscopic nonclassical correlations in the final atomic and molecular fields. The dynamics associated with the creation of bosonic and of fermionic dimer-atom pairs is also compared. This study opens up a promising regime of quantum-degenerate matter-wave chemistry.
Chemical reactions in a statistical ensemble are conventionally regarded as incoherent processes driven by thermodynamics. In the classical regime, reactions are expected to proceed faster at high temperatures and slow to a halt in the zero-temperature limit according to Arrhenius kinetics. In the quantum degenerate regime, where bosonic atoms and molecules form coherent matter waves, reactions are instead described by nonlinear mixing of matter-wave fields, leading to collectively-enhanced reaction rates and coherent amplification. This raises the question: how does the matter-wave phase evolve during a reaction, and how can it influence reaction dynamics? In the quantum regime, the matter-wave phases of the reactants and products are expected to match through wave mixing, analogous to phase matching of photonic fields in nonlinear optics.\par We report the observation of phase coherent reaction dynamics of Bose-condensed atoms and molecules near a Feshbach resonance. Using matter wave diffraction with optical lattices, we verify spatial coherence of both reactants and products and observe phase doubling when atomic waves combine into molecular waves - the matter-wave analogue of second-harmonic generation. The diffraction patterns also reveal distinct signatures of entanglement generated between reacting particles as the reaction is initiated. Our observations establish phase coherence and entanglement as two essential features of "quantum many-body chemistry" where macroscopic quantum fields govern the reaction dynamics.
Chemical reactions in a statistical ensemble are conventionally regarded as incoherent processes driven by thermodynamics. In the classical regime, reactions are expected to proceed faster at high temperatures and slow to a halt in the zero-temperature limit according to Arrhenius kinetics. In the quantum degenerate regime, where bosonic atoms and molecules form coherent matter waves, reactions are instead described by nonlinear mixing of matter-wave fields, leading to collectively-enhanced reaction rates and coherent amplification. This raises the question: how does the matter-wave phase evolve during a reaction, and how can it influence reaction dynamics? In the quantum regime, the matter-wave phases of the reactants and products are expected to match through wave mixing, analogous to phase matching of photonic fields in nonlinear optics.\par We report the observation of phase coherent reaction dynamics of Bose-condensed atoms and molecules near a Feshbach resonance. Using matter wave diffraction with optical lattices, we verify spatial coherence of both reactants and products and observe phase doubling when atomic waves combine into molecular waves - the matter-wave analogue of second-harmonic generation. The diffraction patterns also reveal distinct signatures of entanglement generated between reacting particles as the reaction is initiated. Our observations establish phase coherence and entanglement as two essential features of "quantum many-body chemistry" where macroscopic quantum fields govern the reaction dynamics.
Chemical reactions in a statistical ensemble are conventionally regarded as incoherent processes driven by thermodynamics. In the classical regime, reactions are expected to proceed faster at high temperatures and slow to a halt in the zero-temperature limit according to Arrhenius kinetics. In the quantum degenerate regime, where bosonic atoms and molecules form coherent matter waves, reactions are instead described by nonlinear mixing of matter-wave fields, leading to collectively-enhanced reaction rates and coherent amplification. This raises the question: how does the matter-wave phase evolve during a reaction, and how can it influence reaction dynamics? In the quantum regime, the matter-wave phases of the reactants and products are expected to match through wave mixing, analogous to phase matching of photonic fields in nonlinear optics.\par We report the observation of phase coherent reaction dynamics of Bose-condensed atoms and molecules near a Feshbach resonance. Using matter wave diffraction with optical lattices, we verify spatial coherence of both reactants and products and observe phase doubling when atomic waves combine into molecular waves - the matter-wave analogue of second-harmonic generation. The diffraction patterns also reveal distinct signatures of entanglement generated between reacting particles as the reaction is initiated. Our observations establish phase coherence and entanglement as two essential features of "quantum many-body chemistry" where macroscopic quantum fields govern the reaction dynamics.
Chemical reactions in a statistical ensemble are conventionally regarded as incoherent processes driven by thermodynamics. In the quantum degenerate regime, where atoms and molecules form coherent matter waves, reactions are theoretically described by nonlinear mixing of matter-wave fields. In this scenario, we expect phase matching between reactants and products, analogous to the mixing of photonic fields in nonlinear optics. Here we report on the observation of phase coherent reaction dynamics of Bose-condensed atoms and molecules near a Feshbach resonance. Using matter-wave diffraction with optical lattices, we verify spatial coherence of both atoms and molecules and observe phase doubling when atomic waves combine into molecular waves, the matter-wave analogue of optical frequency doubling. The diffraction patterns further reveal two-atom entanglement generated during the reaction. Our observations establish phase coherence and entanglement generation as two essential features of "quantum many-body chemistry". Moreover, our work opens a pathway to control of reaction dynamics by manipulation of matter-wave phases.
We formulate and exactly solve a model for coherent association and dissociation of fermionic heteronuclear dimers in the deep-lattice Mott regime. Starting from the onsite three-component atom--molecule Hamiltonian, we show how the single-site model maps to the paradigmatic Jaynes--Cummings Hamiltonian from quantum optics. In this mapping, the fermionic molecular/free-atom sector forms an effective two-level system, while the bosonic atomic mode plays the role of the oscillator degree of freedom. We fix the conserved number of fermionic constituent atoms to one but allow an arbitrary conserved number NNN of bosonic constituent atoms. The accessible doublet is then ∣e,N−1⟩↔∣g,N⟩|e,N-1\rangle\leftrightarrow|g,N\rangle∣e,N−1⟩↔∣g,N⟩, and the coherent conversion coupling is bosonically enhanced to χNχ\sqrt{N}χN​. Exact analytic expressions are derived for molecular dissociation, atom-pair association, mode populations, and boson--fermion correlation dynamics. The model provides a transparent matter-wave realization of Jaynes--Cummings physics in a heteronuclear Bose--Fermi system and an exactly solvable setting for understanding coherent atom--molecule conversion and bosonic enhancement in lattice systems.