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Physical Review A

Subwavelength atom localization via quantum coherence in a three-level atomic system

Fazal Ghafoor

Published Dec 29, 2011• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.84.063849

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Journal of the Optical Society of America B•Dec 6, 2010•75 citations
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.
We present a scheme for two-dimensional (2D) atom localization in a three-level atomic system. The scheme is based on quantum coherence via classical standing wave fields between the two excited levels. Our results show that conditional position probability is significantly phase dependent of the applied field and frequency detuning of spontaneously emitted photons. We obtain a single localization peak having probability close to unity by manipulating the control parameters. The effect of atomic level coherence on the sub-wavelength localization has also been studied. Our scheme may be helpful in systems involving atom-field interaction.
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.
A scheme for one-dimensional localization of a three-level atom is proposed by employing a modified technique for the formation of a standing-wave regime using two standing-wave fields. In the present system, precise position information of the atom can be achieved by measuring the population of the excited state, which can be efficiently controlled by the symmetric and the asymmetric superpositions of two standing-wave fields in the presence of constructive quantum interference. Our results highlight that, depending upon the effect of asymmetric superposition, the proposed scheme may provide a promising way to obtain various types of single-peak and double-peak localizations of the atom either in a one-wavelength range or in a half-wavelength range with appropriate values of the Rabi frequencies, detunings and spatial phase shifts of the coupling fields.
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.
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.
A scheme for two-dimensional (2D) subwavelength atom localization is proposed, in which the atom is in a four-level tripod configuration and driven by two orthogonal standing-wave lasers. Because of the spatial dependence of atom-field interaction, the spontaneously emitted photon carries information about the position of the atom in standing-wave fields. We exploit this fact to 2D atom localization conditioned on the measurement of spontaneously emitted photon at a particular frequency, and obtain a high precision and resolution in the position probability distribution. Moreover, an improvement by a factor of 2 in the detecting probability of an atom can be achieved by initially preparing the atom in the coherent population trapping state. Qualitatively, the high-precision, high-resolution atom localization can be attributed to the quantum interference effect between competitive multiple spontaneous decay channels.