Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution

Alexander I. Nesterov

Symmetry, integrability and geometry: methods and applications, Tome 5 (2009)

Résumé

Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian $\mathcal{PT}$-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state $|\psi_i\rangle$ into a specific final state $|\psi_f\rangle$ can be made arbitrarily small. Additionally, it has been shown that finding the shortest possible time requires only the solution of the two-dimensional problem for the quantum system governed by the effective Hamiltonian acting in the subspace spanned by $|\psi_i\rangle$ and $|\psi_f\rangle$. In this paper, we study a similar problem for the generic non-Hermitian Hamiltonian, focusing our attention on the geometric aspects of the problem.

Détail

Keywords: non-Hermitian quantum systems; quantum brachistochrone problem.

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