© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:physics/9611028 · Physical Review A

Interference of resonance fluorescence from two four-level atoms

T. Wong, S. M. Tan, Matthew J. Collett, Daniel F. Walls

Published Feb 1, 1997• 34 citations

Abstract

In a recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)], polarization-sensitive measurements of the fluorescence from two four-level ions driven by a linearly polarized laser were made. Depending on the polarization chosen, different degrees of interference were observed. We carry out a theoretical and numerical study of this system, showing that the results can largely be understood by treating the atoms as independent radiators which are synchronized by the phase of the incident laser field. The interference and its loss may be described in terms of the difference between coherent and incoherent driving of the various atomic transitions in the steady state. In the numerical simulations, which are carried out using the Monte Carlo wave-function method, we remove the assumption that the atoms radiate independently and consider the photodetection process in detail. This allows us to see the total interference pattern build up from individual photodetections and also to see the effects of superfluorescence, which become important when the atomic separation is comparable to an optical wavelength. The results of the calculations are compared with the experiment. We also carry out simulations in the non-steady-state regime and discuss the relationship between the visibility of the interference pattern and which-path considerations.

DOI: 10.1103/physreva.55.1288

Related papers

Interference pattern with a dark center from two atoms driven by a coherent laser field

Terry Rudolph, Z. Ficek

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.

Physical Review A•Jul 1, 1998•15 citations

Interference and collective behavior in atomic fluorescence

J.C. Robinson, F.L. Moore, Patrick R. Morrow +2 more

The study of collective atomic behavior is an important problem which has attracted much interest in recent years. Motivated by recent advances in ion trapping technology,1 and by a calculation of interference in the fluorescence from two atoms,2 we have investigated the effects of collective behavior on the interference fringe visibility. Interference in the fluorescence from two atoms separated by a fixed distance is examined as a function of driving laser and cavity parameters. The fringe visibility, a measure of the coherence of the atomic radiation, is calculated for the system of two driven atoms and the cavity mode. In free space, as the atoms are driven towards saturation, the visibility drops due to loss of coherence. The visibility goes from unity, at weak field, to 10% at saturation and falls off to zero asymptotically at higher fields. Dramatic improvement in visibility is found in the presence of the atom-cavity coupling, with the largest enhancement at intermediate driving field. This result indicates that induced coherence is a sensitive measure of collective behavior. Our progress in the experimental realization of this system with laser cooled beryllium ions confined in a linear trap is described, and directions for future work are indicated.

Annual Meeting Optical Society of America•Jan 1, 1993•0 citations

Complementarity and Young’s interference fringes from two atoms

W. M. Itano, Jonas Bergquist, J. J. Bollinger +3 more

The interference pattern of the resonance fluorescence from a $J=1/2$ to $J=1/2$ transition of two identical atoms confined in a three-dimensional harmonic potential is calculated. The thermal motion of the atoms is included. Agreement is obtained with experiments [U. Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)]. Contrary to some theoretical predictions, but in agreement with the present calculations, a fringe visibility greater than 50% can be observed with polarization-selective detection. The dependence of the fringe visibility on polarization has a simple interpretation, based on whether or not it is possible in principle to determine which atom emitted the photon.

arXiv:quant-ph/9711041•Physical Review A•Jun 1, 1998•76 citations

Intensity-intensity correlations as a probe of interferences under conditions of noninterference in the intensity

G. S. Agarwal, Joachim von Zanthier, C. Skornia +1 more

The different behavior of first-order interferences and second-order correlations are investigated for the case of two coherently excited atoms. For intensity measurements this problem is in many respects equivalent to Young's double-slit experiment and was investigated in an experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)] and later analyzed in detail by Itano et al. [Phys. Rev. A 57, 4176 (1998)]. Our results show that in cases where the intensity interferences disappear the intensity-intensity correlations can display an interference pattern with a visibility of up to 100%. The contrast depends on the polarization selected for the detection and is independent of the strength of the driving field. The nonclassical nature of the calculated intensity-intensity correlations is also discussed.

arXiv:quant-ph/0111126•Physical Review A•May 16, 2002•36 citations

Quantum interference in the fluorescence of a molecular system

Jin Wang, Howard M. Wiseman, Z. Ficek

It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys. Rev. Lett. 77, 1032 (1996)] that quantum interference between two molecular transitions can lead to a suppression or enhancement of spontaneous emission. This is manifest in the fluorescent intensity as a function of the detuning of the driving field from the two-photon resonance condition. Here we present a theory that explains the observed variation of the number of peaks with the mutual polarization of the molecular transition dipole moments. Using master equation techniques we calculate analytically as well as numerically the steady-state fluorescence, and find that the number of peaks depends on the excitation process. If the molecule is driven to the upper levels by a two-photon process, the fluorescent intensity consists of two peaks regardless of the mutual polarization of the transition dipole moments. If the excitation process is composed of both a two-step, one-photon process and a one-step, two-photon process, then there are two peaks on transitions with parallel dipole moments and three peaks on transitions with antiparallel dipole moments. This latter case is in excellent agreement with the experiment.

arXiv:quant-ph/9909059•Physical Review A•Jun 16, 2000•27 citations

Quantum interference effects in spontaneous atomic emission: Dependence of the resonance fluorescence spectrum on the phase of the driving field

M. A. G. Martinez, Peter R. Herczfeld, Charles Samuels +2 more

We discuss quantum interference effects in the resonance fluorescence spectrum of a \ensuremath{\Lambda} three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.

Physical Review A•Jun 1, 1997•122 citations

In a recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)], polarization-sensitive measurements of the fluorescence from two four-level ions driven by a linearly polarized laser were made. Depending on the polarization chosen, different degrees of interference were observed. We carry out a theoretical and numerical study of this system, showing that the results can largely be understood by treating the atoms as independent radiators which are synchronized by the phase of the incident laser field. The interference and its loss may be described in terms of the difference between coherent and incoherent driving of the various atomic transitions in the steady state. In the numerical simulations, which are carried out using the Monte Carlo wave-function method, we remove the assumption that the atoms radiate independently and consider the photodetection process in detail. This allows us to see the total interference pattern build up from individual photodetections and also to see the effects of superfluorescence, which become important when the atomic separation is comparable to an optical wavelength. The results of the calculations are compared with the experiment. We also carry out simulations in the non-steady-state regime and discuss the relationship between the visibility of the interference pattern and which-path considerations.

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.

The study of collective atomic behavior is an important problem which has attracted much interest in recent years. Motivated by recent advances in ion trapping technology,1 and by a calculation of interference in the fluorescence from two atoms,2 we have investigated the effects of collective behavior on the interference fringe visibility. Interference in the fluorescence from two atoms separated by a fixed distance is examined as a function of driving laser and cavity parameters. The fringe visibility, a measure of the coherence of the atomic radiation, is calculated for the system of two driven atoms and the cavity mode. In free space, as the atoms are driven towards saturation, the visibility drops due to loss of coherence. The visibility goes from unity, at weak field, to 10% at saturation and falls off to zero asymptotically at higher fields. Dramatic improvement in visibility is found in the presence of the atom-cavity coupling, with the largest enhancement at intermediate driving field. This result indicates that induced coherence is a sensitive measure of collective behavior. Our progress in the experimental realization of this system with laser cooled beryllium ions confined in a linear trap is described, and directions for future work are indicated.

The interference pattern of the resonance fluorescence from a

J=1/2

to

J=1/2

transition of two identical atoms confined in a three-dimensional harmonic potential is calculated. The thermal motion of the atoms is included. Agreement is obtained with experiments [U. Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)]. Contrary to some theoretical predictions, but in agreement with the present calculations, a fringe visibility greater than 50% can be observed with polarization-selective detection. The dependence of the fringe visibility on polarization has a simple interpretation, based on whether or not it is possible in principle to determine which atom emitted the photon.

The different behavior of first-order interferences and second-order correlations are investigated for the case of two coherently excited atoms. For intensity measurements this problem is in many respects equivalent to Young's double-slit experiment and was investigated in an experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)] and later analyzed in detail by Itano et al. [Phys. Rev. A 57, 4176 (1998)]. Our results show that in cases where the intensity interferences disappear the intensity-intensity correlations can display an interference pattern with a visibility of up to 100%. The contrast depends on the polarization selected for the detection and is independent of the strength of the driving field. The nonclassical nature of the calculated intensity-intensity correlations is also discussed.

It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys. Rev. Lett. 77, 1032 (1996)] that quantum interference between two molecular transitions can lead to a suppression or enhancement of spontaneous emission. This is manifest in the fluorescent intensity as a function of the detuning of the driving field from the two-photon resonance condition. Here we present a theory that explains the observed variation of the number of peaks with the mutual polarization of the molecular transition dipole moments. Using master equation techniques we calculate analytically as well as numerically the steady-state fluorescence, and find that the number of peaks depends on the excitation process. If the molecule is driven to the upper levels by a two-photon process, the fluorescent intensity consists of two peaks regardless of the mutual polarization of the transition dipole moments. If the excitation process is composed of both a two-step, one-photon process and a one-step, two-photon process, then there are two peaks on transitions with parallel dipole moments and three peaks on transitions with antiparallel dipole moments. This latter case is in excellent agreement with the experiment.

We discuss quantum interference effects in the resonance fluorescence spectrum of a \ensuremath{\Lambda} three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.