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Physical Review A

Atom localization via phase and amplitude control of the driving field

Fazal Ghafoor, Sajid Qamar, Muhammad Suhail Zubairy

Published Apr 5, 2002• 156 citations
Publisher

Abstract

Control of amplitude and phase of the driving field in an atom-field interaction leads towards the strong line narrowing and quenching in the spontaneous emission spectrum. We exploit this fact for the atom localization scheme and achieve a much better spatial resolution in the conditional position probability distribution of the atom. Most importantly the quenching in the spontaneous emission manifests itself in reducing the periodicity in the conditional position probability distribution and hence the uncertainty in a particular position measurement of the single atom by a factor of 2.

DOI
10.1103/physreva.65.043819

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Control of amplitude and phase of the driving field in an atom-field interaction leads towards the strong line narrowing and quenching in the spontaneous emission spectrum. We exploit this fact for the atom localization scheme and achieve a much better spatial resolution in the conditional position probability distribution of the atom. Most importantly the quenching in the spontaneous emission manifests itself in reducing the periodicity in the conditional position probability distribution and hence the uncertainty in a particular position measurement of the single atom by a factor of 2.
We propose a scheme for two-dimensional (2D) atom localization based on the controlled spontaneous emission, in which the atom interacts with two orthogonal standing-wave fields. Due to the spatially dependent atom-field interaction, the position probability distribution of the atom can be directly determined by measuring the resulting spontaneously emission spectrum. The phase sensitive property of the atomic system leads to quenching of the spontaneous emission in some regions of the standing-waves, which significantly reduces the uncertainty in the position measurement of the atom. We find that the frequency measurement of the emitted light localizes the atom in half-wavelength domain. Especially the probability of finding the atom at a particular position can reach 100% when a photon with certain frequency is detected. By increasing the Rabi frequencies of the driving fields, such 2D sub-half-wavelength atom localization can acquire high spatial resolution.
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.
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 scheme for realizing two-dimensional (2D) atom localization is proposed based on controllable spontaneous emission in a coherently driven cycle-configuration atomic system. As the spatial-position-dependent atom-field interaction, the frequency of the spontaneously emitted photon carries the information about the position of the atom. Therefore, by detecting the emitted photon one could obtain the position information available, and then we demonstrate high-precision and high-resolution 2D atom localization induced by the quantum interference between the multiple spontaneous decay channels. Moreover, we can achieve 100% probability of finding the atom at an expected position by choosing appropriate system parameters under certain conditions.
We present a simple scheme of two-dimensional (2D) atom localization controlled by spontaneously generated coherence (SGC) and incoherent pump in a closed Λ-type three-level atomic system. Due to the position-dependent atom-field interaction, the conditional position probability distribution of the atom passing through the standing waves can be directly determined by measuring the phase-sensitive probe absorption-gain spectrum. The role of the SGC and incoherent pump in the precision and spatial resolution of 2D atom localization is studied. It is found that the probability of finding the atom at a particular position in one period of the standing waves can reach 100% via properly adjusting the parameters of the system.