Quadratic Open Quantum Harmonic Oscillator

Abstract

We study the quantum open system evolution described by a Gorini-Kossakowski-Sudarshan-Lindblad generator with creation and annihilation operators arising in Fock representations of the $s{l}_2$ Lie algebra. We show that any initial density matrix evolves to a fully supported density matrix and converges towards a unique equilibrium state. We show that the convergence is exponentially fast and we exactly compute the rate for a wide range of parameters. We also discuss the connection with the two-photon absorption and emission process.

25 pages

References in corpus (6)

• Generators of KMS Symmetric Markov Semigroups on B(h) Symmetry and Quantum Detailed Balance
• Quadratic bosonic and free white noises
• Uncertainty functions of the open quantum harmonic oscillator in the Lindblad theory
• The quadratic Fock functor
• Quadratic exponential vectors
• Self-adjointness and boundedness in quadratic quantization

Cited by in corpus (1)

• Quantum Zeno effect for open quantum systems