Weak Measurements in Non-Hermitian Systems

Abstract

"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the standard definition of the "weak value" of an observable must be modified. These studies are undertaken in the context of bound state scattering theory, a non-Hermitian formalism for which the Hilbert spaces involved are unambiguously defined and the metric operators can be explicitly computed. Numerical examples are given for a model system.

References in corpus (14)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Introduction to PT-Symmetric Quantum Theory
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Exact PT-Symmetry Is Equivalent to Hermiticity
• Complex weak values in quantum measurement
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• The significance of the imaginary part of the weak value
• PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics
• Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
• Weak and semiweak values in non-ideal spin measurements: an exact treatment beyond the asymptotic regime
• Which Green Functions Does the Path Integral for Quasi-Hermitian Hamiltonians Represent?
• Entanglement in the classical limit: quantum correlations from classical probabilities
• Non-Hermitian quantum mechanics: the case of bound state scattering theory
• Artificial Rydberg Atom

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• Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme
• Field extension of real values of physical observables in classical theory can help attain quantum results