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Chinese Optics Letters

Precision position measurement of single atom

Ziauddin Ziauddin, Rahmatullah Rahmatullah, Almas Khan Almas Khan

Published Jan 1, 2012• 10 citations
Publisher

Abstract

Atom localization in a five-level atomic system under the effect of three driving fields and one standing wave field is suggested.A spontaneously emitted photon from the proposed system is measured in a detector.Precision position measurement of an atom is controlled via phase and vacuum field detuning without considering the parity violation.

DOI
10.3788/col201210.102701

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Atom localization in a five-level atomic system under the effect of three driving fields and one standing wave field is suggested.A spontaneously emitted photon from the proposed system is measured in a detector.Precision position measurement of an atom is controlled via phase and vacuum field detuning without considering the parity violation.
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.
We propose a three-level atomic system where quantum coherence is generated by a classical standing-wave field coupled to the two upper excited decaying levels. Quantum coherence results in cancellation of the spontaneously emitted spectral lines depending on the choice of the phase of the standing wave. We exploit this phenomenon for precision measurement of the atomic position in the standing wave. Measurement of the conditional position probability distribution shows one to eight peaks per unit wavelength of the standing wave. Only one controllable parameter, that is, the phase of the driving standing wave, is enough to control these atomic positions. Along with the other results, the result of obtaining a single peak is remarkable as it enhances the efficiency of our system by a factor of 8.
A simple scheme for one-dimensional atom localization is proposed by employing a technique for the formation of the standing-wave regime using two unidirectional standing-wave fields. We consider a four-level atomic system similar to the one used by Paspalakis and Knight [Phys. Rev. Lett. 1998, 81, 293–296], with travelling-wave fields for the study of the phase control of emission in the presence of vacuum-induced interference between two spontaneous decay channels. In the present system precise position information of the atom can be achieved by measuring the frequency of spontaneous emission, which can be efficiently controlled by different system parameters and also by adjustment of the relative phase in the presence of the decay interference effect. The proposed scheme provides a potential technique to attain 100% detection probability of the atom in one wavelength range with generation of a sharp localization peak at low light level.
We demonstrate the behavior of three-dimensional (3D) atom localization in a four-level Y-type atomic system driven by a microwave field. The position information of the atom can be obtained by measuring the position-dependent probe absorption when the atom interacts with three orthogonal standing-wave fields. It is found that the precision of the atom localization depends sensitively on the probe detuning and the strength of the microwave field. Remarkably, the localization precision can be significantly improved by increasing the amplitude of the microwave field, and the localization position will be changed by adjusting the relative phase between the standing-wave, microwave, and control fields.
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.
The high-precision position measurement scheme of a single atom in two-dimensions and three-dimensions is investigated in a four-level tripod-type system. The atom interacts with the two orthogonal standing wave fields (OSWFs) and three OSWFs for two- and three-dimensional (2D, 3D) atom localization. The high-precision position of the atom is observed by adjusting the suitable system parameters. We achieve a high-precision single localized peak in the 2D plane and a single localized sphere smaller than the cubic optical wavelength in 3D volume space. We also see the impact of the Doppler shift on atom localization in 2D and 3D. We show that the Doppler shift dramatically deteriorates the precision of spatial information. The proposed high-precision atom localization scheme has applications in laser cooling and Bose–Einstein condensation phenomena.