Multi-quantum eigenstates of a linear chain of coupled qubits

Details Multi-quantum eigenstates of a linear chain of coupled qubits Multi-quantum eigenstates of a linear chain of coupled qubits

2005-05-27

arxiv.org/abs/quant-ph/0505206v2

Phys. Rev. A 71, 060311 (2005)

Physics

Quantum Physics

4 pages, accepted for publication in Physical Review A; New version incorporates a minor correction made in the published pape

Scientific paper

10.1103/PhysRevA.71.060311

We present a technique to identify exact analytic expressions for the multi-quantum eigenstates of a linear chain of coupled qubits. A choice of Hilbert subspaces is described which allows an exact solution of the stationary Schr\"{o}dinger equation without imposing periodic boundary conditions and without neglecting end effects, fully including the dipole-dipole nearest-neighbor interaction between the atoms. The treatment is valid for an arbitrary coherent excitation in the atomic system, any number of atoms, any size of the chain relative to the resonant wavelength and arbitrary initial conditions of the atomic system. The procedure we develop is general enough to be adopted for the study of excitation in an arbitrary array of atoms including spin chains and one-dimensional Bose-Einstein condensates.

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