Antisymmetric states entanglement

An example of entangled states in a two-atom system are the symmetric and antisymmetric states, which correspond to the symmetric and antisymmetric combinations of the atomic dipole moments, respectively [1,7,21]. These states are created by the dipole-dipole interaction between the atoms and are characterized by different spontaneous decay rates that the symmetric state decays with an enhanced, whereas the antisymmetric state decays with a reduced spontaneous emission rate [7]. For the case of two atoms confined into the region much smaller than the optical wavelength, the antisymmetric state does not decay at all, and therefore can be regarded as a decoherence-free state. 

This result shows that we can relatively easily prepare two nonidentical atoms in the maximally entangled antisymmetric state. The closeness of the prepared state to the ideal one is measured by the fidelity F. Here F is equal to the obtained maximum population in the state —). For il F the fidelity of the... 

Thus, the final state of the system is a product state of the atomic antisymmetric state a) and the vacuum state of the cavity mode. In this scheme the cavity mode is left in the vacuum state, which protects the antisymmetric state against any noise of the cavity. The scheme to entangle two atoms in a cavity, proposed by Cirac and Zoller [28], has been realized experimentally by Hagly et al. [36]. 

Thus, if the cavity field is measured and found in the state a), the atoms are in the antisymmetric state. If the cavity field is found in the state - a), the atoms are in the entangled state ... 

In the section IV.B.2, we have shown that two nonidentical two-level atoms can be prepared in an arbitrary superposition of the maximally entangled antisymmetric state a) and the ground state g)... 

For fit = n the entangled state (84) reduces to a nonmaximally entangled antisymmetric state... 

The first term in Eq. (88) arises from the fluorescence emitted on the e) —> s) —> g) transitions, which involve the symmetric state. The second term arises from the e) —> a) —> g) transitions through the antisymmetric state. These two terms describe two different channels of transitions for which the angular distribution is proportional to [1 cos (/ i2cos0)]. The last term in Eq. (88) originates from interference between these two radiation channels. It is seen from Eq. (1.88) that the angular distribution of the fluorescence field depends on the population of the entangled states. v) and a). Moreover, independent of the interatomic separation rj2, the antisymmetric state does not radiate in the direction perpendicular to the atomic axis, as for 0 = 7i/2 the factor [1 — cos (fcri2cos0)] vanishes. In contrast, the symmetric state radiates in all directions. 

Guo and Yang [53] have analyzed spontaneous decay from two atoms initially prepared in an entangled state. They have shown that the time evolution of the population inversion, which is proportional to the intensity (87), depends on the degree of entanglement of the initial state of the system. Ficek et al. [10] have shown that in the case of two nonidentical atoms, the time evolution of the intensity 7(R, t) can exhibit quantum beats that result from the presence of correlations between the symmetric and antisymmetric states. In fact, quantum beats are present only if initially the system is in a nonmaximally entangled state, and no quantum beats are predicted for maximally entangled as well as unentangled states. 

Note that the states T4), T2) and T3) are the same as for the small sample model, discussed in the preceding section. This means that the presence of the antisymmetric state does not affect the two-photon entangled states, but it can affect the population distribution between the states and the purity of the system. In Fig. 10, we plot the populations P, of the states T,) as a function of the interatomic separation. The figure demonstrates that the atoms are driven into a mixed state composed of two states Tj) and a), and there is a vanishing probability that the system is in the states IT2) and s). 

We have shown in Ref. [19] that if the systems in question have three levels, one can completely eliminate decoherence and disentanglement by imposing a special symmetry using the appropriate modulation. Thus, even if drastic reduction of all the decoherence matrix elements is not possible, then by using local modulations, one may equate the intraparticle elements, eliminate the interparficle elements, and code the QI in the ground and antisymmetric dark state of the two excited levels, and consequently completely preserve coherence and entanglement. 

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