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arXiv:quant-ph/0505014 · Journal of Physics B Atomic Molecular and Optical Physics

Subwavelength atom localization via coherent population trapping

G. S. Agarwal, Kishore T. Kapale

Published Aug 14, 2006• 212 citations
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Abstract

We present an atom localization scheme based on coherent population trapping. We consider atomic transitions in a Lambda configuration where the control field is a standing-wave field. The probe field and the control field produce coherence between the two ground states and prepare the atom in a pure state. We show that the population in one of the ground states has the same fringe pattern as produced by a Fabry–Perot interferometer and thus measurement of this population would localize the atom. Interestingly enough the role of the cavity finesse is played by the ratio of the intensities of the pump and probe. This is in fact the reason for obtaining extreme subwavelength localization.

DOI
10.1088/0953-4075/39/17/002

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We present an atom localization scheme based on coherent population trapping. We consider atomic transitions in a Lambda configuration where the control field is a standing-wave field. The probe field and the control field produce coherence between the two ground states and prepare the atom in a pure state. We show that the population in one of the ground states has the same fringe pattern as produced by a Fabry–Perot interferometer and thus measurement of this population would localize the atom. Interestingly enough the role of the cavity finesse is played by the ratio of the intensities of the pump and probe. This is in fact the reason for obtaining extreme subwavelength localization.
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.
We present a simple scheme of atom localization in a subwavelength domain via manipulation of Raman gain process. We consider a four-level system with a pump and a weak probe field. In addition, we apply a coherent field to control the gain process. The system is similar to the one used by Agarwal and Dasgupta [Phys. Rev. A 70, 023802 (2004)] for the superluminal pulse propagation through Raman gain medium. For atom localization, we consider both pump and control fields to be the standing-wave fields of the cavity. We show that a much precise position of an atom passing through the standing-wave fields can be determined by measuring the gain spectrum of the probe field.
Interaction of the internal states of an atom with spatially dependent standing-wave cavity field can impart position information of the atom passing through it leading to subwavelength atom localization. We recently demonstrated a different regime of atom localization [Phys. Rev. A 72, 013820 (2005)], namely sub-half-wavelength localization through phase control of electromagnetically induced transparency. This regime corresponds to extreme localization of atoms within a chosen half-wavelength region of the standing-wave cavity field. Here we present further investigation of the simplified model considered earlier and show interesting features of the proposal. We show how the model can be used to simulate a variety of energy-level schemes. Furthermore, the dressed-state analysis is employed to explain the emergence and suppression of the localization peaks, and the peak positions and widths. The range of parameters for obtaining clean sub-half-wavelength localization is identified.
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 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.