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Additional info for Highly Nonclassical Quantum States and Environment Induced Decoherence
8), or in other words it turns into an entangled state. According to the summary in Sec. 1, the rate of entanglement can be obtained as A= k=0,l=0 | ϕk (0)| Φl (0)| V |ϕ0 (0) |0 |2 . 4) Using the explicit form of the interaction Hamiltonian V in Eq. , in our system the rate of entanglement is the normally ordered correlation function of the operators J+ and J− . Let us turn to the case of finite temperatures, when the total system has to be represented by a mixed state even at t = 0. 6) can be regarded as a relevant measure of decoherence [26,27].
Due to the dissipation all these lobes will move slowly downwards. The initial interference pattern (Figs. 6 a) and b)) has the regularity of the tetrahedron, there are equally pronounced oscillations along all the edges, representing the quantum coherence between the coherent states. Figs. 6 c) and d) depict the situation after a time which is short in the sense that the 46 TWO-LEVEL ATOMS AND DECOHERENCE the shapes of the lobes of the coherent states are not appreciably affected (no dissipation), but the interference is already negligible between them, except for the single pair along the vertical edge of the tetrahedron.
Librium position, the anharmonic effects become apparent. The collapse and revival in X (t) and P (t) can be explained by referring to the various Bohr frequencies that determine their time dependence: dephasing of these frequencies leads to the collapse of the expectation value, and we observe revival when they rephase again. 5, the original phase of the eigenstates is restored [68, 80] around the full revival time trev = 110 t0 , where t0 is the period of the small oscillations in the potential.