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Journal of Modern Optics

Quantum logic with channelled atomic particles

Erika Andersson, Stig Stenholm

Published May 1, 2001• 2 citations
Publisher

Abstract

This paper discusses the time-dependent quantum description of logical operations based on channelled atomic particles. We envisage particle traps in the form of grooves which steer atoms or ions, make them switch potential channels or interact with each other. Thus the presence of a particle can act as a control bit steering a target particle from one course into another. This phenomenon may be used to effect conditional logic operations. We discuss the quantum dynamics of the system using a simple analytic model whose proposed behaviour is verified by wave packet calculation.

DOI
10.1080/09500340010017479

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This paper discusses the time-dependent quantum description of logical operations based on channelled atomic particles. We envisage particle traps in the form of grooves which steer atoms or ions, make them switch potential channels or interact with each other. Thus the presence of a particle can act as a control bit steering a target particle from one course into another. This phenomenon may be used to effect conditional logic operations. We discuss the quantum dynamics of the system using a simple analytic model whose proposed behaviour is verified by wave packet calculation.
Summary form only given. A quantum computer is composed of quantum bits that can support superposition states and hence allow parallel processing for certain problems such as factorization. All quantum computations can, in principle, be reduced to a series of two-bit quantum logic gates accompanied by simple single-bit rotations. An example of a two-bit quantum logic gate is the controlled-NOT (CN) gate, which rotates one quantum bit by 180 dependent on the state of a second quantum bit. We demonstrate operation of a two bit CN quantum logic gate on a trapped ion.
We study control of wave packets with a finite accuracy, approaching it as quantum information processing. For a given control resolution, we define the analogs of several quantum bits within the shape of a single wave packet. These bits are based on wave packet symmetries. Analogs of one- and two-bit gates can be implemented using only free wave packet evolution and coordinate-dependent ac Stark shifts applied at the moments of fractional revivals. As in quantum computation, the gates form a logarithmically small set of basis operations which can be used to approximate any unitary transformation desired for quantum control of the wave packet dynamics. Numerical examples show the application of this approach to control vibrational wave packet revivals.
Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting nonclassical properties. We describe a simple quantum logic gate, the quantum controlled-NOT, and analyze some of its applications. We discuss two possible physical realizations of the gate, one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole-dipole interaction.
Ultracold collisions of ions with neutral atoms in traps are studied. Recently, ultracold atom-ion systems have become available in experimental setups, where their quantum states can be coherently controlled. This control allows for an implementation of quantum information processing, combining the advantages of charged and neutral particles. The state-dependent dynamics that is a necessary ingredient for quantum computation schemes is provided in this case by the short-range interaction forces that depend on the hyperfine states of both particles. In this work, a theoretical description of spin-state-dependent trapped atom-ion collisions is developed in the framework of a multichannel quantum-defect theory and an effective single-channel model is formulated that reduces the complexity of the problem. Based on this description, a two-qubit phase gate between a 135Ba^{135}\mathrm{Ba}135Ba+{}^{+}+ ion and a 87Rb^{87}\mathrm{Rb}87Rb atom is simulated using a realistic combination of the singlet and triplet scattering lengths. The gate process is optimized and accelerated with the help of optimal control techniques. The result is a gate fidelity of $1\ensuremath{-}{10}^{\ensuremath{-}3}$ within 350350350 $\ensuremath{\mu}$s.