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Scientific Herald of Uzhhorod University Series Physics

Resonant transmition of the quantum information from one atom-qubit to another at large distances

Світлана Іванівна Мигалина

Published Dec 24, 2009• 0 citations
Publisher

Abstract

The feasibility of resonance transfer of quantum information from one double-level atom to another that is at an arbitrary distance from the former one has been proved. Symmetric and antisymmetric combinations of the wave functions of individual atoms are considered. When taking into account the interatomic dipole-dipole interaction, a certain energy corresponds to each wave function. A solution has been found to a system of equations for the amplitudes of the probability that a resonance photon will be absorbed by one of the system atoms. Three types of solution to the system of equations have been investigated for the resonance and nonresonance absorption of photons and different interatomic distances. It has been shown that when atoms are at an infinite distance from one another, so that there is no dipole-dipole interaction of atoms, quantum information can be transferred from one atom to another via the quantum teleportation channel.

DOI
10.24144/2415-8038.2009.25.107-114

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The feasibility of resonance transfer of quantum information from one double-level atom to another that is at an arbitrary distance from the former one has been proved. Symmetric and antisymmetric combinations of the wave functions of individual atoms are considered. When taking into account the interatomic dipole-dipole interaction, a certain energy corresponds to each wave function. A solution has been found to a system of equations for the amplitudes of the probability that a resonance photon will be absorbed by one of the system atoms. Three types of solution to the system of equations have been investigated for the resonance and nonresonance absorption of photons and different interatomic distances. It has been shown that when atoms are at an infinite distance from one another, so that there is no dipole-dipole interaction of atoms, quantum information can be transferred from one atom to another via the quantum teleportation channel.
Purpose. As a standard model for describing the processes of a resonant transmission of quantum information on arbitrary distances is the system of two identical two-level atoms, one of which is under radiation of the field of real photons. Such a system can serve as a basis for the construction of an element basis of quantum computers. The purpose of this paper is to study the different modes of dynamics of a system of two identical two-level atoms when they interacts with the field of real photons. Methods. In this paper, we propose a general approach to the description of the processes for the transfer of quantum information from one atom-qubit to another on the arbitrary interatomic distances, which includes two types of new physical effects: the attenuation of quantum states and the retardation of the dipole-dipole interaction. Results. The optical properties of a system of two identical two-level atoms in collective (symmetric Ψ s and antisymmetric Ψ a ) Bell states at arbitrary interatomic distances are investigated. The closed analytical expressions for the shifts and widths of the considered collective states are considered, taking into account the retarded dipole-dipole interaction of atoms. In calculation of the radial matrix elements of the dipole-dipole interaction, the wave functions of the model Fues potential are used. Conclusions. A detailed study of the mechanisms of resonant transmission of the excitation energy at arbitrary distances between the two-element atoms has an important practical significance for the physical realization of the logical operator CNOT.
Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.
The resonant dipole-dipole interaction between highly excited Rydberg levels dominates the interaction of neutral atoms at short distances scaling as 1/r31/{r}^{3}1/r3. Here we take advantage of the combined effects of strong dipole-dipole interaction and multifrequency driving fields to propose one type of selective Rydberg pumping mechanism. In the computational basis of two atoms ${|00\ensuremath{\rangle},|01\ensuremath{\rangle},|10\ensuremath{\rangle},|11\ensuremath{\rangle}}$, this mechanism allows $|11\ensuremath{\rangle}$ to be resonantly pumped upwards to the single-excited Rydberg states while the transitions of the other three states are suppressed. From the perspective of mathematical form, we achieve an analogous F\"orster resonance for ground states of neutral atoms. The performance of this selective Rydberg pumping is evaluated using the definition of fidelity for a controlled-ZZZ gate, which manifests a characteristic robustness to the deviation of interatomic distance, fluctuation of F\"orster resonance defect, and spontaneous emission of double-excited Rydberg states. As applications of this mechanism, we discuss in detail the preparation of the maximally entangled symmetric state for two atoms via ground-state blockade, and the maximally entangled antisymmetric state via engineered spontaneous emission, within the state-of-the-art experiments, respectively.
The quantum correlations between a qubit and its environment are described quantitatively in terms of interatomic distance. Specifically, considering a realistic system of two two-level atoms and taking into account the dipole-dipole interaction and collective damping, the quantum entanglement and quantum discord are investigated during the dissipative process as functions of the interatomic distance. For atoms that are initially maximally entangled, it turns out that there is a critical distance at which each atom is maximally quantum correlated with its environment. Counterintuitively, the approach of the two atoms can maximize the entanglement between each one and the environment and, even at the same distance, minimize the loss of entanglement between the pair.