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arXiv:quant-ph/0508010 · Physical Review A

Measurement of the separation between atoms beyond diffraction limit

Juntao Chang, Jörg Evers, Marlan O. Scully, Muhammad Suhail Zubairy

Published Mar 10, 2006• 54 citations
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Abstract

Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a standing wave laser field. The information is extracted from the collective resonance fluorescence spectrum, relying entirely on far-field imaging techniques. Both the interatomic separation and the positions of the two particles can be measured with fractional-wavelength precision over a wide range of distances from about $\ensuremath{\lambda}∕550$ to $\ensuremath{\lambda}∕2$.

DOI
10.1103/physreva.73.031803

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•Nov 9, 2004•0 citations
Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a standing wave laser field. The information is extracted from the collective resonance fluorescence spectrum, relying entirely on far-field imaging techniques. Both the interatomic separation and the positions of the two particles can be measured with fractional-wavelength precision over a wide range of distances from about \ensuremathλ∕550\ensuremath{\lambda}∕550\ensuremathλ∕550 to \ensuremathλ∕2\ensuremath{\lambda}∕2\ensuremathλ∕2.
The intensity-intensity correlation function of the resonance fluorescence light of two two-level atoms driven by a resonant standing-wave laser field is examined. Our aim is to gain information on the distance between the two atoms from observables accessible in experiments. For this, we numerically solve the time-evolution equations of the system and calculate the steady-state intensity-intensity correlation by using the Laplace transform and quantum regression theory. By varying the interatomic distance from about half a wavelength down to small fractions of a wavelength, we show that the correlation function exhibits characteristic properties for different distance ranges. Based on these results, we propose a scheme to obtain interatomic distance information from the power spectrum of the correlation function, which allows us to extract the desired distance information over a wide range of distances with high accuracy.
In this Comment we study the resonance fluorescence of a system of two atoms separated by an arbitrary distance RRR in an on-resonance laser field. The steady-state spectrum is calculated in the strong-field limit both for negligible and for non-negligible dipole-dipole interaction. The singlet state of the system is included throughout, even for small interatomic separations. We show that the so-called "scaling factor," or the enhancement of the integrated fluorescence by NNN atoms (above the expected factor of NNN), predicted in the literature by many authors, does not, in fact, exist.
We optically detect the positions of single neutral cesium atoms stored in a standing wave dipole trap with a sub-wavelength resolution of 105 nm. The distance between two simultaneously trapped atoms is measured with an even higher precision of 55 nm. We resolve the discreteness of the interatomic distances due to the 532 nm spatial period of the standing wave potential and infer the exact number of trapping potential wells separating the atoms. Finally, combining an initial position detection with a controlled transport, we place single atoms at a predetermined position along the trap axis to within 300 nm.