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Chinese Journal of Quantum Electronics

Atomic-position localization in optical cavity

Guiping Cheng, Fang Li-ming, Dongmei Liu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The localization of a two-level atom placed in an optical cavity containing a standing wave is investigated,and the single atomic-position can be well-localized by the way of quadrature-field measurement. According to the Rayleigh limit when two two-level atoms are put in the cavity,it is difficult to distinguish between the two atoms if they are very close to each other.Also,the two atoms can be still well-distinguished by quadrature-field measurement.However,if the cavity damping is taken into account, the two-atom relative position localization will be damaged.The larger damping rate of the cavity become, the worse the two-atom relative position localization will be.

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The localization of a two-level atom placed in an optical cavity containing a standing wave is investigated,and the single atomic-position can be well-localized by the way of quadrature-field measurement. According to the Rayleigh limit when two two-level atoms are put in the cavity,it is difficult to distinguish between the two atoms if they are very close to each other.Also,the two atoms can be still well-distinguished by quadrature-field measurement.However,if the cavity damping is taken into account, the two-atom relative position localization will be damaged.The larger damping rate of the cavity become, the worse the two-atom relative position localization will be.
Entanglement of the atom and field leads towards the measurement of the state of the atom or field depending on the kind of measurement made. Taking advantage of this fact, we propose spectroscopic methods for the single atom localization within the subwavelength domain of the optical standing wave field. \n \nWhen a two-level atom interacts with some intense radiation field the spectrum of the scattered light signal exhibits a three-peak Mollow spectrum. We propose a scheme of atom localization based on the resonance fluorescence from a two-level atom interacting with a standing wave field. The Rabi frequency is considered to be position dependent and therefore, the spontaneously emitted photon carries the information about the center-of-mass motion of the atom. This leads to the localization of the single atom by measuring the frequency of the spontaneously emitted photon even during the passage of the atom through the standing wave field. We predict a spatial resolution in position information of up to λ/60 where λ is the optical wavelength. \n \nDetuning of the coherent field with the atomic transition plays an important role in the characterization of the peaks present in the Autler- Townes spectrum of a three-level atom. Strong line narrowing is observed in one of the peaks of the Autler- Townes doublet depending on the choice of the detuning. We investigate how this detuning effects the position information of the atom inside the standing wave field in upper-level and lower-level coupling schemes of Autler- Townes microscopy. We show an enhancement in precision position measurement by factor of at least 4 in upper-level coupling scheme due to the quantum interference phenomenon. This enhancement is not observed in lower-level coupling scheme where the quantum interference is not taking place. \n \nWe also consider a system where a three-level atom is interacting with a monochromatic radiation field in such a way that the decay takes place from upper level to the intermediate level with a rate T and from intermediate level to lower level at a rate γ. This type of system exhibits a non stationary scattered light signal. We report the results of the spontaneous emission spectrum for non stationary scattered light signal by using the definition of time-dependent physical spectrum. This is a rare example of problems where time-dependent physical spectrum can be calculated exactly. We study the characteristics of the spontaneous spectrum for a resonant and off-resonant case and show that this physical spectrum recovers the results of earlier work quite successfully. We also show that the decay rate r disturbs the atomic coherence and finally eliminates the dark line from the center of the spontaneous spectrum. Here we only consider upper-level coupling case for the time-dependent spontaneous spectrum because in lower-level coupling case the system automatically evolved a pumping mechanism due to the coupling of ground level to the upper level via radiation field. Thus a steady-state limit exists in lower-level coupling scheme. \n \nWe investigate the phenomenon of atom localization by using the non stationary Autler-Townes microscopy. The decay rate T reduces the precision in position measurement which is consistent with the results of the non stationary spontaneous emission spectrum. This is due to the fact that for the upper-level coupling case, the standing wave field is coupled to atomic transition and it induces a coherence in the upper-level atomic transition but the spontaneous decay from the upper level to the intermediate level disturbs this coherence. When the effect of the spontaneous decay dominates the coherence effect the quantum interference phenomenon vanishes and thus the precision in localization reduces.
Coherent interaction of an atom with a position-dependent standing-wave cavity field can impart position information of a moving atom through the cavity leading to subwavelength atom localization. We show that the position of the atom along the standing-wave field is determined when the probe-field absorption is measured. We find out 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. In addition, we demonstrate that the position information of a three-level V-shaped moving atom strongly depends on the relative phase of applied fields. By appropriate choice of the relative phase, it is shown that the scheme can be used for localizing an atom flying through the standing-wave field to the sub-half-wavelength domain.
A scheme is proposed to achieve one-dimensional localization of a two-level atom moving through a standing wave regime constructed by two classical standing-wave fields. Precise position information of the atom can be obtained by measuring resonant absorption of a weak coherent field probing the transition strongly driven by the resonant standing-wave fields. Behavior of atomic localization has been shown for symmetric superposition of the standing-wave fields arranged in two distinct configurations: (i) parallel and (ii) cross. In the cross-configuration, we have shown 100% detection probability of the atom within one wavelength range with the evolution of single localization peak in the sub-half-wavelength range due to the variation of spatial phase shift of one of the standing-wave fields. In case of nonresonant coupling of the atom with the standing-wave fields, a single localization peak in the sub-half-wavelength range can be obtained by changing the relative detuning of frequency of the probe field. For achieving high resolution single-peak localization of a two-level atom, the present scheme would be of great interest from the experimental point of view.
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.
Two- and three-dimensional atom localization in a two-level atom–field system via resonance fluorescence is suggested. For the two-dimensional localization, the atom interacts with two orthogonal standing-wave fields, whereas for the three-dimensional atom localization, the atom interacts with three orthogonal standing-wave fields. The effect of the detuning and phase shifts associated with the corresponding standing-wave fields is investigated. A precision enhancement in position measurement of the single atom can be noticed via the control of the detuning and phase shifts.