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Molecular Physics

Self-entanglement and the dissociation of homonuclear diatomic molecules

Antonios Gonis, X.-G. Zhang, D. M. C. Nicholson, G. Malcolm Stocks

Published Jan 14, 2014• 7 citations
Publisher

Abstract

The concept of self-entanglement is introduced to describe a mixed state or ensemble density as a pure state in an augmented Hilbert space formed by the products of the individual states forming a mixed state (or ensemble). We use this representation of mixed states to show that upon dissociation a neutral homonuclear diatomic molecule will separate into two neutral atoms.

DOI
10.1080/00268976.2013.836610

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The concept of self-entanglement is introduced to describe a mixed state or ensemble density as a pure state in an augmented Hilbert space formed by the products of the individual states forming a mixed state (or ensemble). We use this representation of mixed states to show that upon dissociation a neutral homonuclear diatomic molecule will separate into two neutral atoms.
High-fidelity entanglement of neutral cold atoms can be achieved by combining several already available techniques such as the creation or dissociation of neutral diatomic molecules, manipulating atoms with microfabricated structures (atom chips), and detecting single atoms with almost 100% efficiency. The fidelity of the resulting entanglement is robust against the details of dissociation process. Manipulating this entanglement with integrated or linear atom optics will open a perspective for quantum-information processing with neutral atoms.
In this contribution to Abraham Nitzan's Festschrift, we present a perspective of theoretical research over the years that has pointed to the potential of molecular processes to act as quantum information resources. Under appropriate control, homonuclear dimer (diatom) dissociation (half-collision) and the inverse process of atom-pair collisions are shown to reveal translational (EPR-like) entanglement that enables molecular wave packet teleportation. When such processes involve electronic-state excitation of the diatom, the fluorescence following dissociation can serve as an entanglement witness that unravels the molecular-state characteristics and evolution. Such entangling processes can also exhibit anomalous quantum thermodynamic features, particularly temperature enhancement of a cavity field that interacts with dissociated entangled diatoms.
This article investigates entanglement of the motional states of massive coupled oscillators. The specific realization of an idealized diatomic molecule in one-dimension is considered, but the techniques developed apply to any massive particles with two degrees of freedom and a quadratic Hamiltonian. We present two methods, one analytic and one approximate, to calculate the interatomic entanglement for Gaussian and non-Gaussian pure states as measured by the purity of the reduced density matrix. The cases of free and trapped molecules and hetero- and homonuclear molecules are treated. In general, when the trap frequency and the molecular frequency are very different, and when the atomic masses are equal, the atoms are highly-entangled for molecular coherent states and number states. Surprisingly, while the interatomic entanglement can be quite large even for molecular coherent states, the covariance of atomic position and momentum observables can be entirely explained by a classical model with appropriately chosen statistical uncertainty.
We propose a method for producing entangled spin and orbital states in pairs of atoms resulting from the dissociation of diatomic molecules. The method employs the interference between a one-photon and a two-photon process to break the backward-forward symmetry of the dissociation processes. The spin entanglement of distant atom pairs makes use of excited spin-orbit-coupled (molecular) intermediate states. When the dissociating molecules are confined to a one-dimensional optical lattice, the method can be used to generate long sequences of (spin- and orbit-) entangled pairs of atoms.