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Physical Review A

Preparation of a pure atomic state

Miguel Orszag, J. C. Retamal, C. Saavedra

Published Feb 1, 1992• 34 citations
Publisher

Abstract

We study the resonant interaction of a two-level atom with one mode of the electromagnetic field. We calculate the entropy associated with the atomic state evolving from arbitrary initial conditions. We show that pure atomic states can be generated from an arbitrary initial mixed atomic state. Also, we observe and discuss a significant difference in the long-time behavior of the entropy for an initial number state and a coherent state.

DOI
10.1103/physreva.45.2118

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•Jan 1, 2002•2 citations
We study the resonant interaction of a two-level atom with one mode of the electromagnetic field. We calculate the entropy associated with the atomic state evolving from arbitrary initial conditions. We show that pure atomic states can be generated from an arbitrary initial mixed atomic state. Also, we observe and discuss a significant difference in the long-time behavior of the entropy for an initial number state and a coherent state.
The resonant interaction of two nonidentical two-level atoms with one mode of the electromagnetic field has been considered. The pure-state evolution of the atomic states for field initially in the coherent state and atoms in the ground state has been investigated. It has been shown that for intermediate values of the relative differences of two coupling constants the atoms as well as the field are returned most closely to a pure state at the revival time. The possibility of the maximally entangled states at the beginning of the collapse time has been discussed.
Under on-resonance condition and far-off-resonance condition, at first, we used the full quantum theory to educe the wave function of the system. Secondly, we utilized entropy theory, in virtue of the wave function, to discuss the effects of the initial mean photon number?the atomic motion and the field-mode structure on the evolution of the field(atom) entropy at length in the interaction of a three-level moving atom with field. The results show that the atomic motion leads to the periodic evolution of the field entropy, this periodicity does not depend on the statistical distribution and the intensity of the initial field mode, but depend on the atomic motion and the field-mode structure parameters ep. Both on-resonance condition and far-off-resonance condition, when making a suitable choice for parameter ep (this choice is experimentally possible),we can get pure field state for a long time.
The atomic decay for a two level atom interacting with a single mode of electromagnetic field is considered. In particular for a coherent state or statistical mixture (SM) of two opposite coherent states as initial field states, the exact solution of the master equation is found. Effect of the atomic damping on the partial entropies of the atom or the field and the total entropy as a measures of the purity loss is investigated. The degree of entanglement by the negativity and the mutual information and the atomic coherence through the master equation is studied.
An exact solution for the problem of two two-level atoms interacting with a single-mode detuned quantized radiation field is presented. On resonance, an asymptotic result is derived for large coherent initial fields. It is shown that when the atoms are initially prepared in one of the semiclassical eigenstates, the atom-plus-field wavefunction remains almost factored into an atomic and a field part throughout the interaction. Under certain conditions, the atomic part evolves into a unique pure state at half-revival time. The effects of the cavity detuning on the dynamics of the atomic level occupation probabilities and emission spectra are studied. It is found, for non-symmetrical excitation, that far off-resonance the field acts like a virtual level by means of which the energy is transferred between the atoms. Due to non-zero detuning, nine-peaked spectra are observed and are given a clear explanation from the dressed-state viewpoint. It is established that in the case of symmetrical excitation, the intensity of the emission spectrum is two times larger than that in the case of non-symmetrical excitation.
In the first part of this thesis,we examine the preparation of a single- mode radiation field in arbitrary pure quantum states via resonant inter- action with a sequence of two-level atoms.The preparation is achieved by choosing an appropriate (in general entangled)initial state of the atomic sequence,and does neither require a final state measurement of the atoms,nor a control of the atom-field interaction.Furthermore,the method is applicable also when starting from mixed initial field states. We show how to determine the optimal initial atomic state which pre- pares the desired field state with the maximum fidelity,and prove the feasibility of our state preparation method by numerical calculations. In the second part,we demonstrate the noise-induced control of quantum jumps in a fundamental open quantum system.Here,in addition to the subsequent interaction with a flux of two-level atoms,the quantized field is also coupled to a thermal environment.Under certain experimental conditions,the photon field exhibits a bistable behavior,with quantum jumps between two metastable states.In the presence of a small peri- odic signal (i.e.,a modulation of the initial state of the two-level atoms crossing the single-mode resonator),the best synchronization of these quantum jumps with the signal is achieved at an optimal,nonvanishing temperature of the environment.This stochastic resonance e ffect can be observed in di fferent components of the atomic Bloch vector on exit from the cavity. The third part treats a speci fic problem concerning the characterization of entanglement between two quantum mechanical two-level systems. We consider the optimal decomposition of a two-qubit state into an en- tangled and a separable part,with maximal weight of the latter,and derive necessary and su fficient conditions for the optimality of the de- composition.