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Journal of Modern Optics

Entropy Evolution of the Bimodal Field Interacting with an Effective Two-level Atom Via the Raman Transition

Mao Fa Fang

Published Jul 1, 1994• 10 citations
Publisher

Abstract

The properties of entropy evolution of the bimodal field interacting with an effective two-level atom via the Raman transition are studied. The influences of the initial average photon number and of the atomic coherence on the evolution of the bimodal field entropy are examined. It is shown that the bimodal field is in a pure state only under certain conditions in the early stages of time evolution and later tends to a statistical mixture state with maximum entropy values; the bimodal field remains strongly entangled with the atom.

DOI
10.1080/09500349414551271

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The properties of entropy evolution of the bimodal field interacting with an effective two-level atom via the Raman transition are studied. The influences of the initial average photon number and of the atomic coherence on the evolution of the bimodal field entropy are examined. It is shown that the bimodal field is in a pure state only under certain conditions in the early stages of time evolution and later tends to a statistical mixture state with maximum entropy values; the bimodal field remains strongly entangled with the atom.
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According to the complete quantum theory,the quantum field-entropy evolution properties in a system of the two coupled two-level atoms interacting with a single-mode odd-coherent state light field are studied.Through numerical calculation the influence of the initial mean photon number n_0,the coupled intensity g of interaction between the single-mode field and atoms,and the coupled intensity g_a of dipole-dipole interaction between the two coupled atoms on the quantum field-entropy evolving while the initial state of the light field is a single-mode odd-coherent and the two coupled two-level atoms lay in different Einstein Poclolsky Rosen(EPR) entangled state respectively.The results indicate that the time evolving of quantum field-entropy is closely related to the initial atoms state.The quantum field-entropy evolution can display the phenomena of entanglement and disentanglement while they are periodically under the condition of intensity field(n_01). Meanwhile the phenomena of quantum interference is also discovered.The periodicity of the quantum field-entropy anomalous oscillation decreases gradually with the increasing of g values.When g_a is an especial constant,it is shown that the phenomena of period collapse-reversion can present.
An exact solution of the problem of two two-level atoms with degenerate Raman two-photon transitions interacting with one-mode coherent or thermal radiation field in cavity is presented. Asymptotic solution for system state vector is obtained in the approximation of large initial coherent fields. The atom-field is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived. The atom-atom entanglement is investigated with using negativity. The possibility of sudden death and birth of atom-atom entanglement is predicted for a coherent field with large mean photon numbers.
Starting from a three-level atom coupled to two modes of a radiation field, we derive a Raman-coupled Hamiltonian. The exact results are employed to carry out a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, with the privileged field modes being in a coherent state. We invoke the mathematical concept of the maximum variation of a function to construct a measure for entropy fluctuations. It is shown that when the individual modes of the field are far detuned from the intermediate atomic level, there is a dynamical Stark shift induced by the Kerr-like medium. The results show that the Kerr effect creates the superstructure of atomic Rabi oscillation and changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The dynamic behavior of the mean atomic level occupation probabilities are investigated numerically as functions of time. A number of novel phenomena are discovered and discussed.
The field entropy time evolution in Bell state|β_(01) and |β_(11) interacting with the two-mode entangled coherent field is investigated by means of full quantum theory. The effects of the atoms initial state,mean photon numbers of field,the degree of the entanglement for the entangled coherent fields,and the coupling strength of interaction between atoms on the entropy evolution properties of the field are discussed. The results shows that the entropy will forever be zero when the initial state is |β_(11) . For the state |β(01) the oscillation of the field entropy presents periodicity with the increasing of the mean photon number. And the coupling strength of interaction between atoms plays a major role in the entropy evolution properties.
The property of the field entropy in degenerate Raman coupling Jaynes-Jummings models with a linear time-dependent atom-field coupling is investigated.The influence of different initial field and time-dependent atom-field coupling coefficient on the field entropy is discussed at length.The results show that:(1) All the evolutions of field entropies have periodicity whatever the initial field states are.The increase of the mean number of photon does not change evolution periodicity;(2) The different statistical properties of the initial fields will give great effects on the values of the maximum field entropy and the variational range the highest value of field entropy;(3) the perfect periodicity of field entropy will be destroyed due to the linear modulation.When the atom-field coupling coefficient changes slowly,the speed of atoms′ entering the statistical state is slowered;when the atomfield coupling coefficient changes rapidly,the oscillating periodicity of the curve of the evolution of field entropy is shortened,the oscillating frequency of the evolution of field entropy is fastened,and the moments of the atom-field disentanglement are manifolded.