Quantum Behavior of a <inline-formula> <mml:math id="mm8001" display="block"> <mml:semantics> <mml:mi mathvariant="script">PT</mml:mi> </mml:semantics> </mml:math> </inline-formula>-Symmetric Two-Mode System with Cross-Kerr Nonlinearity

Abstract

Quantum behavior of two oscillator modes, with mutually balanced gain and loss and coupled via linear coupling (including energy conserving as well as energy non-conserving terms) and nonlinear cross-Kerr effect, is investigated. Stationary states are found and their stability analysis is given. Exceptional points for PT -symmetric cases are identified. Quantum dynamics treated by the model of linear operator corrections to a classical solution reveals nonclassical properties of individual modes (squeezing) as well as their entanglement.

Keywords

• nonlinearly coupled oscillators
• PT symmetry
• cross-Kerr nonlinearity
• stability analysis
• quantum properties