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International Journal of the Physical Sciences

The strength of the atom localization coupling with the standing-wave field under the dephasing rate influence

Abd El Nabi S

Published Apr 16, 2013• 0 citations
Publisher

Abstract

We investigate the localization of the four-level V-type atom inside a classical standing-wave field through the absorption spectrum of the weak probe field. The expression of the probe absorption spectrum is derived analytically via perturbation treatment of a weak probe field. Numerical results and discussion of the probe susceptibility spectrum behaviour via non-perturbation treatment of the density matrix elements to all orders of fields are obtained. We have shown that the precision of localization of the atom is dependent on the dephasing rates of atomic coherence as well as on some parameters of the driving and standing-wave fields. A strong localization through sharply peak is achieved at a certain value for the dephasing rates in resonance detunings. Key words: Quantum optics, atomic system, atom localization.

DOI
10.5897/ijps09.186

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We investigate the localization of the four-level V-type atom inside a classical standing-wave field through the absorption spectrum of the weak probe field. The expression of the probe absorption spectrum is derived analytically via perturbation treatment of a weak probe field. Numerical results and discussion of the probe susceptibility spectrum behaviour via non-perturbation treatment of the density matrix elements to all orders of fields are obtained. We have shown that the precision of localization of the atom is dependent on the dephasing rates of atomic coherence as well as on some parameters of the driving and standing-wave fields. A strong localization through sharply peak is achieved at a certain value for the dephasing rates in resonance detunings. Key words: Quantum optics, atomic system, atom localization.
We propose a scheme for localizing an atom in a four-level configuration inside a classical standing wave field, conditioned upon the measurement of frequency of a weak probe field. In the classical standing wave field, the interaction between the atom and the field is position dependent due to the Rabi-frequency of the driving field. Hence, as the absorption frequency of the probe field is measured the position of the atom inside the classical standing wave field will be determined. Localizing of the atom via the absorption spectrum occurs during its motion in the standing wave field. The investigation of the probe field absorption shows that the degree of localization depends on the interaction parameters such as detuning, and Rabi-frequency of the driving field.
The localization of atom is studied in two-dimensional (2D) in a four-level V-type atomic system by using the Gaussian field. The atom localization is investigated through the absorption spectrum of the weak probe field inside two orthogonal standing-wave fields. We consider three hypotheses for the interaction between the atom and fields (standing-wave and Gaussian fields), each hypothesis is considered individually. We obtain the expression for the first-order approximation of the absorption of the probe field mathematically for the hypothesis (I). The Gaussian field parameter plays an important role in the precision of the atom localization. The 2D atom localization can be dependent on the detuning of the probe field (resonance and off-resonance), the Rabi frequencies and the phase shifts.
We propose a scheme to localize an atom in a three-level A-type configuration inside a classical standing wave field conditioned upon the measurement of frequency of a weak probe field. Inside the classical standing wave field, the interaction between atom and the field is position-dependent due to the Rabi frequency of the driving field; hence, as the absorption frequency of the probe field is measured, the position of an atom inside the classical standing wave field will be determined. Localizing of an atom via absorption spectrum occurs during its motion inside the standing wave field. An investigation of the probe field frequency shows that the degree of localization depends on interaction parameters such as detuning, phase difference between applied fields, and Rabi frequency of the driving field.
We propose a scheme to localize a two-level atom inside a classical standing wave field conditioned upon the measurement of the frequency of a weak probe field at resonance excitation of a two-level atomic system. Inside the classical standing wave field, the interaction between the atom and the field is position-dependent due to the Rabi frequency of the driving field; hence, as the absorption frequency of the probe field is measured, the position of an atom inside the classical standing wave field will be determined. The effects of atomic parameters on atom localization are then discussed.
It is shown, using density matrix calculation, that high precision two-dimensional (2D) atom localization in V-type system can be achieved by applying an additional microwave coupling field between the excited states. In the present scheme, two lasers, probe and pump, form a V-type system by coupling the ground state to the excited states while an additional 2D standing microwave field is used to couple the excited states. The solutions of the density matrix equations reveal that the off-diagonal density matrix element ρ31ρ_{31}ρ31​, which signify the coherence between the states connected by the probe laser, is position dependent. As the imaginary part of ρ31ρ_{31}ρ31​ is proportional to the imaginary part of the susceptibility, the probe absorption also becomes position dependent and in this situation one can readily obtain information about the atom position from the probe absorption spectra. Perfect 2D atom localization can be achieved by carefully selecting different system parameters such as detuning, relative phase, dephasing and field strength. It is found that the atom localization is highly dependent on the probe and coupling field detuning values. In view of this, a systematic study is performed on the system parameters and different zones have been identified which give rise to different absorption shapes, e.g. "dip", "wall", "peak" as well as negative absorption or amplification. Probe absorption spectrum is also found to be dependent on relative phase between the applied fields. The dependence of the dephasing parameter on the probe absorption is investigated and found to be detrimental to atom localization. The effect of the microwave coupling strength on "wall" type absorption shape is also studied and the results are discussed. Finally, a possible practical realization of the present scheme is discussed in Conclusion section.
We propose a scheme for subwavelength localization of an atom conditioned upon the absorption of a weak probe field at a particular frequency. Manipulating atom-field interaction on a certain transition by applying drive fields on nearby coupled transitions leads to interesting effects in the absorption spectrum of the weak probe field. We exploit this fact and employ a four-level system with three driving fields and a weak probe field, where one of the drive fields is a standing-wave field of a cavity. We show that the position of an atom along this standing wave is determined when probe-field absorption is measured. We find that absorption of the weak probe field at a certain frequency leads to subwavelength localization of the atom in either of the two half-wavelength regions of the cavity field by appropriate choice of the system parameters. We term this result as sub-half-wavelength localization to contrast it with the usual atom localization result of four peaks spread over one wavelength of the standing wave. We observe two localization peaks in either of the two half-wavelength regions along the cavity axis.