Bloch space structure, the qutrit wave function and atom-field entanglement in three-level systems

Abstract

We have given a novel formulation of the exact solutions for the lambda, vee and cascade three-level systems where the Hamiltonian of each configuration is expressed in the SU(3) basis. The solutions are discussed from the perspective of the Bloch equation and the atom-field entanglement scenario. For the semiclassical systems, the Bloch space structure of each configuration is studied by solving the corresponding Bloch equation and it is shown that at resonance, the eight-dimensional Bloch sphere is broken up into two distinct subspaces due to the existence of a pair of quadratic constants. Because of the different structure of the Hamiltonian in the SU(3) basis, the non-linear constants are found to be distinct for different configurations. We propose a possible representation of the qutrit wave function and show its equivalence with the three-level system. Taking the bichromatic cavity modes to be in the coherent state, the amplitudes of all three quantized systems are calculated by developing an Euler angle based dressed state scheme. Finally following the Phoenix-Knight formalism, the interrelation between the atom-field entanglement and population inversion for all configurations is studied and the existence of collapses and revivals of two different types is pointed out for the equidistant cascade system in particular.

33 pages, 6 figures, revised version

References in corpus (6)

• Sudden Death of Entanglement
• Measures and dynamics of entangled states
• Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment
• Qutrit state engineering with biphotons
• Entanglement sudden death in qubit-qutrit systems
• Quantum information transfer for qutrits

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• Geometry of a two-spin quantum state in evolution
• Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution
• Resonance fluorescence in $\Lambda$, $V$ and $\Xi$ -- type three-level configurations
• A note on the Bloch representation of absolutely maximally entangled states
• A unified approach to $\Lambda$-, $\Xi$- and $V$-type systems with one continuum
• Collapse and Revival Oscillation in Double Jaynes-Cummings Model
• SU(4) based classification of four-level systems and their semiclassical solution
• An Inequality for Entangled Qutrits in SU(3) basis
• Bimodal phase transition in a periodically modulated $\Lambda$-type three-level system