Exploring quasi-probability Husimi-distributions in nonlinear two trapped-ion qubits: intrinsic decoherence effects

The Husimi phase-space distribution is an efficient tool for studying quantum coherent states as it provides information on quantum-state features. The paper investigates the non-classicality and mixedness dynamics of two dipole trapped qubits beyond Lamb-Dicke regime. We analyze the Husimi distribution non-classicality and Wehrl entropy mixedness, which are substantially impacted by several physical characteristics that involve unitary ion-mode interaction, Lamb-Dicke nonlinearity, dipole two-qubit interaction, and intrinsic decoherence. Our results show that when these physical parameters grow, the phase-space information of the trapped-ion-qubit state becomes more sensitive, resulting in more von-Neumann/Wehrl entropy mixedness. The unitary ion-mode interaction, in particular, intensifies the von-Neumann/Wehrl entropy qubit’s mixedness, and the Husimi distribution coincides with the von-Neumann entropy qubit’s mixedness. Furthermore, the dipole interaction of the qubits considerably impacts and delays the emergence of the maximal von-Neumann/Wehrl entropy qubit’s mixedness.