Generalized Delta Functions and Their Use in Quantum Optics

Abstract

The Dirac delta function is widely used in many areas of physics and mathematics. Here we consider the generalization of a Dirac delta function to allow the use of complex arguments. We show that the properties of a generalized delta function are very different from those of a Dirac delta function and that they behave more like a pole in the complex plane. We use the generalized delta function to derive the Glauber-Sudarshan P-function for a Schrödinger cat state in a surprisingly simple form. Aside from their potential applications in classical electromagnetism and quantum optics, these results provide insight into the ability of the diagonal P-function to describe density operators with off-diagonal elements.

11 pages, 5 figures

References in corpus (1)

• Quantum limits on phase-preserving linear amplifiers

Cited by in corpus (8)

• Quantum magnonics: when magnon spintronics meets quantum information science
• Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian
• Parametric approximation as open quantum systems problem
• Nonlocal modification of the Kerr metric
• Bi-coherent states as generalized eigenstates of the position and the momentum operators
• Variational analysis of driven-dissipative bosonic fields
• Dirac delta as a generalized holomorphic function
• Electron dynamics induced by quantum cat-state light