A note on the geometry of the quantum states of a two-level atom in external radiation fields

Rabi oscillations, entanglement and teleportation in the anti-Jaynes-Cummings model

“…2 determined using the approach in [4] agrees precisely with that determined using the semi-classical approach in [11] corresponding to a 2-dimensional subspace of C 2 Span {|e , |g }. In the approach [11], at resonance where detuning δ = 0 the atomic population is inverted from |e to |g and the Bloch-vector r = (sin(θ) cos(φ) , sin(θ) sin(φ) , cos(θ)) describes a path along the yz -plane on the Bloch-sphere. For other values of detuning, the atom evolves from |e to a linear superposition of |e and |g and back to |e and the Bloch-vector r describes a circle about the north pole of the Bloch-sphere.…”

“…The geometric configuration of the state space demonstrated on the Bloch-sphere in Fig. 2 determined using the approach in [4] agrees precisely with that determined using the semi-classical approach in [11] corresponding to a 2-dimensional subspace of C 2 Span {|e , |g }. In the approach [11], at resonance where detuning δ = 0 the atomic population is inverted from |e to |g and the Bloch-vector r = (sin(θ) cos(φ) , sin(θ) sin(φ) , cos(θ)) describes a path along the yz -plane on the Bloch-sphere.…”

Effects of Frequency Detuning and Excitation Quantum Number on the Dynamics of Entanglement in the Jaynes-Cummings Polariton Model

“…1 determined using the approach in [6] agrees precisely with that determined using the semi-classical approach in [20] corresponding to a 2-dimensional subspace of C 2 Span {|e , |g }. In the approach [20], at resonance where detuning δ = 0 the atomic population is inverted from |e to |g and the Bloch-vector r = (sin(θ) cos(φ) , sin(θ) sin(φ) , cos(θ)) describes a path along the yz -plane on the Bloch-sphere. For other values of detuning, the atom evolves from |e to a linear superposition of |e and |g and back to |e and the Bloch-vector r describes a circle about the North pole of the Bloch-sphere.…”

“…The geometric configuration of the state space demonstrated on the Bloch-sphere in Fig. 1 determined using the approach in [6] agrees precisely with that determined using the semi-classical approach in [20] corresponding to a 2-dimensional subspace of C 2 Span {|e , |g }. In the approach [20], at resonance where detuning δ = 0 the atomic population is inverted from |e to |g and the Bloch-vector r = (sin(θ) cos(φ) , sin(θ) sin(φ) , cos(θ)) describes a path along the yz -plane on the Bloch-sphere.…”

Rabi Oscillations, Entanglement and Teleportation in the Anti-Jaynes-Cummings Model

“…3) an interesting feature that appears at resonance specified by We note that the qubit state transitions described by the Bloch vector in the AJC process ( Figure 1) are blue-side band transitions characterized by the sum frequency The geometric configuration of the state space demonstrated on the Bloch-sphere in Figure 2 determined using the approach in [5] agrees precisely with that determined using the semi-classical approach in [28]…”