Quasi-Bell states in a strongly coupled qubit–oscillator system and their delocalization in the phase space

Abstract

We study the evolution of bipartite entangled quasi-Bell states in a strongly coupled qubitoscillator system in the presence of a static bias, and extend it to the ultra-strong coupling regime. Using the adiabatic approximation the reduced density matrix of the qubit is obtained for the strong coupling domain in closed form that involves linear combinations of the Jacobi theta functions. The reduced density matrix of the oscillator yields the phase space Husimi Q-distribution. In the strong coupling regime the Q-function evolves to uniformly separated macroscopically distinct Gaussian peaks representing 'kitten' states at certain specified times that depend on multiple time scales present in the interacting system. For the ultra-strong coupling realm the delocalization in the phase space of the oscillator is studied by using the Wehrl entropy and the complexity of the quantum state. For a small phase space amplitude the entangled quasi-Bell state develops, during its time evolution, squeezing property and nonclassicality of the photon statistics which are measured by the quadrature variance and the Mandel parameter, respectively.

Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

“…An exact invariant for a simple superconducting qubit-oscillator was evaluated. An adiabatic invariant for a nanoresonator coupled to a superconducting resonator was also obtained as shown in (21). The invariant̂for the latter case is more complicated than the former̂.…”

“…The accuracy of conservation for invariant quantities is crucial for securing the validity of the associated analyses of classical and quantum mechanical characteristics of the system fulfilled on the basis of such invariants [16]. In this research,̂given in (6) is an exact invariant whilêgiven in (21) is an adiabatic invariant valid under the condition that ( ) is a slowly varying function. Both invariants are useful for investigating the classical and the quantum properties of each respective system.…”

“…Let us consider a simple superconducting qubit-oscillator of which the effective reduced Hamiltonian is given by Equation (2.2) of [21]. Typically, the two lowest energy levels of quantized states in the anharmonic LC resonator are regarded as a set of a qubit.…”

“…Typically, the two lowest energy levels of quantized states in the anharmonic LC resonator are regarded as a set of a qubit. In this case, the system is described by the Hamiltonian of the form [21]…”

The Test of Entanglement of Polarization States of a Semi-Classical Optical Parametric Oscillator

“…Chakrabarti R. and Jenisha J. (2015) [11] studied the evolution of a bipartite entangled quasi-bell state in a strongly coupled qubit oscillator system in the presence of a static bias, and extended it to the ultra-strong coupling regime. Adiabatic approximation was used to obtain reduced density matrix of the qubit for the strong coupling domain in closed form involving linear combinations of the Jacobi theta functions.…”