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

Europhysics Letters (EPL)

Inhibition of cooperative quantum jumps due to fast spontaneous decay

C. Skornia, Joachim von Zanthier, G. S. Agarwal, E. Werner, HERBERT WALTHER

Published Dec 1, 2001• 6 citations
Publisher

Abstract

\n \nA Quantum Monte Carlo wave function approach is used to rule out the\npossibility of cooperative effects in the quantum jump statistics of\nadjacent three-level ions of the type discussed in a series of\nexperiments and theoretical investigations. By deriving analytical\nresults and examining quantum jumps in various subspaces, we track this\noutcome to the fact that a fast spontaneous decay inhibits\ndipole-dipole-induced entanglement between the ions developing on a\nmuch slower time scale. This inhibition is demonstrated even for weak\npumping of the fast transition. The Quantum Monte Carlo calculation\nthus sheds new light on the controversy arising from the findings of\ntwo recent conflicting experiments by Block et al. (Eur. Phys. J. D, 7 \n(1999) 461) and Donald et al. (Europhys. Lett., 51 (2000) 388).\n\n

DOI
10.1209/epl/i2001-00572-5

Related papers

Simplified approach to double jumps for fluorescing dipole-dipole interacting atoms

Volker Hannstein, Gerhard C. Hegerfeldt

A simplified scheme for the investigation of cooperative effects in the quantum jump statistics of small numbers of fluorescing atoms and ions in a trap is presented. It allows the analytic treatment of three dipole-dipole interacting four-level systems which model the relevant level scheme of Ba+ ions. For the latter, a huge rate of double and triple jumps was reported in a former experiment and the huge rate was attributed to the dipole-dipole interaction. Our theoretical results show that the effect of the dipole-dipole interaction on these rates is at most 5% and that for the parameter values of the experiment there is practically no effect. Consequently it seems that the dipole-dipole interaction can be ruled out as a possible explanation for the huge rates reported in the experiment.

•Feb 2, 2006•4 citations

Cooperative quantum jumps for three dipole-interacting atoms

Volker Hannstein, Gerhard C. Hegerfeldt

We investigate the effect of the dipole-dipole interaction on the quantum jump statistics of three atoms. This is done for three-level systems in a $\mathsf{V}$ configuration and in what may be called a $\mathsf{D}$ configuration. The transition rates between the four different intensity periods are calculated in closed form. Cooperative effects are shown to increase by a factor of 2 compared to two of either three-level systems. This results in transition rates that are, for distances of about one wavelength of the strong transition, up to 100% higher than for independent systems. In addition the double and triple jump rates are calculated from the transition rates. In this case cooperative effects of up to 170% for distances of about one wavelength and still up to 15% around 10 wavelengths are found. Nevertheless, for the parameters of an experiment with ${\mathrm{Hg}}^{+}$ ions the effects are negligible, in agreement with the experimental data. For three ${\mathrm{Ba}}^{+}$ ions this seems to indicate that the large cooperative effects observed experimentally cannot be explained by the dipole-dipole interaction.

arXiv:quant-ph/0401050•Physical Review A•Aug 30, 2004•6 citations

Monte Carlo simulation of the atomic master equation for spontaneous emission

Ralph Dum, P. Zoller, Helmut Ritsch

A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.

Physical Review A•Apr 1, 1992•656 citations

Dynamics of spontaneous emission

P. L. Knight

A number of interpretations of the origins of spontaneous emission are examined. In particular, the idea of quantum jumps in the recorded fluorescence from excited atoms and their theoretical treatment is reviewed using recent Monte-Carlo simulation approaches to spontaneous emission. These are illustrated for pure spontaneous emission and for the telegraphic quantum jump signal in the fluorescence from three-level atoms.

Physica Scripta•Jan 1, 1997•5 citations

Analytical treatment of quantum jumps in a system of two interacting two-level atoms

Q. V. Lawande, B. N. Jagatap, S. V. Lawande

We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.

Physical Review A•Oct 1, 1990•11 citations

Quantum jumps in a system of few trapped ions

G. S. Agarwal, W.V. Lawande, Richard D’Souza

A theory of quantum jumps in a system of few trapped ions is formulated. The V configuration of the energy levels and incoherent pumping are assumed. The master equation is derived in terms of the SU(3) collective operators for the V system. Numerical results for the intensity-intensity correlations for up to five ions are presented. Analytical results for a system of two ions are derived separating out dynamics at two difference time scales and by eliminating adiabatically the fast variables. From the analytical results, the underlying three-state Markov process that can be used to characterize the quantum jumps in the two-ion system is identified. Probability distributions for various off-on time intervals are presented.>

IEEE Journal of Quantum Electronics•Jul 1, 1988•10 citations
\n \nA Quantum Monte Carlo wave function approach is used to rule out the\npossibility of cooperative effects in the quantum jump statistics of\nadjacent three-level ions of the type discussed in a series of\nexperiments and theoretical investigations. By deriving analytical\nresults and examining quantum jumps in various subspaces, we track this\noutcome to the fact that a fast spontaneous decay inhibits\ndipole-dipole-induced entanglement between the ions developing on a\nmuch slower time scale. This inhibition is demonstrated even for weak\npumping of the fast transition. The Quantum Monte Carlo calculation\nthus sheds new light on the controversy arising from the findings of\ntwo recent conflicting experiments by Block et al. (Eur. Phys. J. D, 7 \n(1999) 461) and Donald et al. (Europhys. Lett., 51 (2000) 388).\n\n
A simplified scheme for the investigation of cooperative effects in the quantum jump statistics of small numbers of fluorescing atoms and ions in a trap is presented. It allows the analytic treatment of three dipole-dipole interacting four-level systems which model the relevant level scheme of Ba+ ions. For the latter, a huge rate of double and triple jumps was reported in a former experiment and the huge rate was attributed to the dipole-dipole interaction. Our theoretical results show that the effect of the dipole-dipole interaction on these rates is at most 5% and that for the parameter values of the experiment there is practically no effect. Consequently it seems that the dipole-dipole interaction can be ruled out as a possible explanation for the huge rates reported in the experiment.
We investigate the effect of the dipole-dipole interaction on the quantum jump statistics of three atoms. This is done for three-level systems in a V\mathsf{V}V configuration and in what may be called a D\mathsf{D}D configuration. The transition rates between the four different intensity periods are calculated in closed form. Cooperative effects are shown to increase by a factor of 2 compared to two of either three-level systems. This results in transition rates that are, for distances of about one wavelength of the strong transition, up to 100% higher than for independent systems. In addition the double and triple jump rates are calculated from the transition rates. In this case cooperative effects of up to 170% for distances of about one wavelength and still up to 15% around 10 wavelengths are found. Nevertheless, for the parameters of an experiment with Hg+{\mathrm{Hg}}^{+}Hg+ ions the effects are negligible, in agreement with the experimental data. For three Ba+{\mathrm{Ba}}^{+}Ba+ ions this seems to indicate that the large cooperative effects observed experimentally cannot be explained by the dipole-dipole interaction.
A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.
We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.
A theory of quantum jumps in a system of few trapped ions is formulated. The V configuration of the energy levels and incoherent pumping are assumed. The master equation is derived in terms of the SU(3) collective operators for the V system. Numerical results for the intensity-intensity correlations for up to five ions are presented. Analytical results for a system of two ions are derived separating out dynamics at two difference time scales and by eliminating adiabatically the fast variables. From the analytical results, the underlying three-state Markov process that can be used to characterize the quantum jumps in the two-ion system is identified. Probability distributions for various off-on time intervals are presented.>