Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Distilling two-atom distance information from intensity-intensity correlation functions

Juntao Chang, Jörg Evers, Muhammad Suhail Zubairy

Published Oct 31, 2006• 36 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.74.043820

Related papers

Two-atom resonance fluorescence in running- and standing-wave laser fields

Terry Rudolph, Z. Ficek, Bryan J. Dalton

Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.

Physical Review A•Jul 1, 1995•56 citations

Measurement of the separation between atoms beyond diffraction limit

Juntao Chang, Jörg Evers, Marlan O. Scully +1 more

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 $\ensuremath{\lambda}∕2$.

arXiv:quant-ph/0508010•Physical Review A•Mar 10, 2006•54 citations

Quantum beats in two-atom resonance fluorescence

Z. Ficek, Barry C. Sanders

We study the resonance fluorescence emitted by two laser-driven coupled identical two-level atoms and allow for an arbitrary separation between the atoms and an arbitrary orientation of the interatomic axis in the laser field. Quantum beats arise in the resonance fluorescence intensity profile when an interatomic axis orientation is not perpendicular to the driving field propagation direction and are well resolved for an interatomic separation comparable to the resonant wavelength. These beats vanish for noninteracting atoms as well as for atoms separated by distances much smaller than the resonant wavelength. We also consider the time-dependent resonance fluorescence photon statistics that also exhibit quantum beats. Sub-Poissonian photon statistics occur for large interatomic separations and, for small separations, sub- and super-Poissonian statistics arise depending on the atomic orientation in the external driving field.

Physical Review A•Jan 1, 1990•39 citations

Power Broadening and Two-photon Correlations in Two-atom Resonance Fluorescence

Thomas Richter

The cooperative resonance fluorescence radiation from two atoms separated by an arbitrary distance and driven by a coherent laser field is studied, taking into account the dipole-dipole near-field interaction. The steady-state total scattering intensity, as a function of laser frequency and field strength, differs considerably from the single-atom one for sufficiently small distances. Photon bunching and antibunching occur in the scattered radiation depending on the laser frequency. Practically a full antibunching effect is found, especially if the laser is tuned to resonance with a transition frequency of the two-atom system. This is in contrast to a recent result of Agarwal et al., who studied the two-atom system but neglected the frequency splitting due to the dipole-dipole near-field interaction.

Optica Acta International Journal of Optics•Mar 1, 1982•25 citations

Resonance fluorescence with squeezed-light excitation

Reeta Vyas, Surendra Singh

Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak-field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. Heisenberg equations of motion are solved in the steady-state and analytic expressions for the fluorescent-light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed, and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation, the second-order intensity correlation function does not factorize. This and other differences are discussed, and curves are presented to illustrate the behavior of various quantities. We also present results for thermal excitation of the atom.

Physical Review A•Jun 1, 1992•33 citations

Intensity correlations in resonance fluorescence from coupled two-level atoms

Marco Wiegand

The normalised intensity correlation function of resonance fluorescence radiation from two-level atoms is studied in various respects. In the first part of the paper the author discusses only interference effects for several uncoupled, linearly arranged, atoms. It is shown that, depending on the distance between the atoms, the direction of observation and the strength of the driving field, an antibunching effect as well as a very big bunching effect may be observed. In the second part of the paper he studies for the case of two atoms and weak external fields the influence of the interaction between the atoms by means of a perturbation theory. It is shown that the coupling between the atoms strongly modifies the normalised intensity correlation function in comparison with the case of uncoupled atoms. He takes as the driving field a coherent external field as well as laser light and thermal light.

Journal of Physics B Atomic and Molecular Physics•Apr 14, 1983•10 citations
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.
Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.
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 $\ensuremath{\lambda}∕2$.
We study the resonance fluorescence emitted by two laser-driven coupled identical two-level atoms and allow for an arbitrary separation between the atoms and an arbitrary orientation of the interatomic axis in the laser field. Quantum beats arise in the resonance fluorescence intensity profile when an interatomic axis orientation is not perpendicular to the driving field propagation direction and are well resolved for an interatomic separation comparable to the resonant wavelength. These beats vanish for noninteracting atoms as well as for atoms separated by distances much smaller than the resonant wavelength. We also consider the time-dependent resonance fluorescence photon statistics that also exhibit quantum beats. Sub-Poissonian photon statistics occur for large interatomic separations and, for small separations, sub- and super-Poissonian statistics arise depending on the atomic orientation in the external driving field.
The cooperative resonance fluorescence radiation from two atoms separated by an arbitrary distance and driven by a coherent laser field is studied, taking into account the dipole-dipole near-field interaction. The steady-state total scattering intensity, as a function of laser frequency and field strength, differs considerably from the single-atom one for sufficiently small distances. Photon bunching and antibunching occur in the scattered radiation depending on the laser frequency. Practically a full antibunching effect is found, especially if the laser is tuned to resonance with a transition frequency of the two-atom system. This is in contrast to a recent result of Agarwal et al., who studied the two-atom system but neglected the frequency splitting due to the dipole-dipole near-field interaction.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak-field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. Heisenberg equations of motion are solved in the steady-state and analytic expressions for the fluorescent-light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed, and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation, the second-order intensity correlation function does not factorize. This and other differences are discussed, and curves are presented to illustrate the behavior of various quantities. We also present results for thermal excitation of the atom.
The normalised intensity correlation function of resonance fluorescence radiation from two-level atoms is studied in various respects. In the first part of the paper the author discusses only interference effects for several uncoupled, linearly arranged, atoms. It is shown that, depending on the distance between the atoms, the direction of observation and the strength of the driving field, an antibunching effect as well as a very big bunching effect may be observed. In the second part of the paper he studies for the case of two atoms and weak external fields the influence of the interaction between the atoms by means of a perturbation theory. It is shown that the coupling between the atoms strongly modifies the normalised intensity correlation function in comparison with the case of uncoupled atoms. He takes as the driving field a coherent external field as well as laser light and thermal light.