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

Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of anM-level equidistant radiator in the presence of a thermal electromagnetic field

N. A. Enaki, V. I. Koroli

Published Aug 28, 1998• 8 citations
Publisher

Abstract

We study the spontaneous emission of a multilevel equidistant excited quantum oscillator (nuclei, atoms, molecules) in the case in which the symmetry of the dynamical transitions between the levels is submitted to the SU (1,1) symmetry group and compare our results with those well known for the SU (2) symmetry. It is shown that the equidistant radiator in the process of spontaneous decay in the case of SU (1,1) symmetry exhibits either only acceleration or only a decrease in spontaneous emission rates, while in the case of SU (2) symmetry the radiation pulse is similar to that for the Dicke super-radiance. The exact steady-state solution for the atomic density operator for an equidistant radiator driven by a totally incoherent broad-band (chaotic) field for a SU (1,1) symmetry group is obtained using the Fokker-Planck equation. It is found that for a strong-field limit in the case of SU (1,1) symmetry the fluctuations in the atomic population increase with increasing intensity of the external field and do not achieve their maximal value as in the case of SU (2) symmetry. Moreover, in the case of SU (1,1) transition symmetry we find that there is a superbunching effect for certain values of group parameter I , while in the case of SU (2) symmetry only bunching and antibunching occur. It is found that for vanishing values of the external field intensity the second-order intensity correlation function achieves negative values.

DOI
10.1088/0953-4075/31/16/012

Related papers

Incoherently driven Dicke model

Saad S. M. Hassan, G. P. Hildred, Ravinder Rupchand Puri +1 more

The exact steady-state solution for the reduced atomic density operator for a model system of N identical two-level atoms confined to a single site (the Dicke model) and driven by a totally incoherent broad-band (chaotic) field is derived through the equivalent Fokker-Planck equation of the system. Steady-state values of the atomic observables, higher moments and atomic fluctuations are calculated for an arbitrary N and an arbitrary field strength. It is shown that when the chaotic field is a thermal (black-body) field the atomic system is driven into a steady relative occupation number that obeys the Boltzmann distribution law only for N=1. (The same result for N>1 atoms can be reached only if the cooperative interactions between the atoms are ignored.) In the thermodynamic limit N to infinity there is no critical behaviour in contrast to the resonant coherently driven case. It is also shown that semiclassical (direct) factorisation of the equations of motion does not lead to the correct results for the N to infinity limit of the exact quantum case. Within the exact theory numerical results for finite N (<or=100) are presented for the time-dependent expectation values of the atomic operators, the intensity and the intensity autocorrelation function. Superradiant pulses are emitted by N initially inverted atoms but as the incident intensity is increased this superradiant behaviour is obscured. The steady-state fluorescence spectrum is a single Lorentzian of width proportional to N in the weak-field case. In the strong-field case the spectrum is insensitive to the number of atoms and the result is similar to the one-atom situation. Photon bunching and antibunching effects are investigated for the weak- and strong-field limits. When the chaotic driving field is simply a single-mode thermal field the approach to atomic saturation is delayed in comparison with the case of the broad-band chaotic field.

Journal of Physics B Atomic and Molecular Physics•Aug 28, 1982•38 citations

Cavity Steady-State Behaviors for a Single Equidistant Three-Level Emitter

P. Bardetski, Mihai Macovei

The interaction of a single equidistant three-level radiator (same transition frequencies, dipole moments, and decay rates for both one-photon transitions) with a leaky optical cavity mode that at the same time is driven by an external coherent field is investigated via a generalized Fokker–Planck equation. It is shown that the steady-state behaviors of such an equidistant three-level sample differ from the corresponding ones of a general three-level system. We suppose that this difference appears due the fact that a single equidistant three-level radiator is equivalent to a pair of indistinguishable two-level atoms, provided that the separation between the pair is smaller than the wavelength of the cavity field.

Physica Scripta•Jan 1, 2003•2 citations

Superradiant Intensity Fluctuations in Neoclassical Radiation Theory

Andrzej Zardecki

The fluctuation properties of a system of two level atoms are investigated by introducing a random precession term into the equations of motion of the atomic super Bloch vector. Starting from the assumptions of neoclassical radiation theory a general formula for the dipole field of a small system of atoms is derived. The intensity fluctuations are calculated in the narrowing limit for two extreme cases of very large and very small atomic to thermal energy ratios. The former case, describing a true superradiant emission, involves asymptotic solutions to the Fokker-Planck equation. The latter case, treated by perturbation theory, corresponds to spontaneous emission in the presence of incoherent pumping.

Canadian Journal of Physics•Dec 15, 1974•1 citation

Master-Equation Approach to Spontaneous Emission

G. S. Agarwal

Spontaneous emission from a system of $N$ identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state $|{z}_{0}〉$.

Physical Review A•Nov 1, 1970•232 citations

Spontaneous Emission by a System of Identical Atoms

Demosthenes Dialetis

The spontaneous emission of a set of $N$ identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.

Physical Review A•Sep 1, 1970•42 citations

Theory of emission of radiation from an assembly of N two-level atoms

Ranjana Prakash, Naresh Chandra

Interaction with a multimode quantized radiation field of an assembly of $N$ two-level atoms contained in a small volume is considered for the special cases of (i) highly excited, (ii) weakly excited, and (iii) superradiant atomic assemblies, and solutions of equations of motion are obtained in closed form. For (i) and (ii) we show that, if the atomic assembly is in the Dicke state $|r,m>$, the spontaneously emitted radiation is Lorentzian, and its spectral width and the numerical value of the Lamb shift are $r+|m|$ times that for a single excited atom. For (i) the sign of Lamb shift is opposite to that for (ii) and for a single excited atom. Change in the frequency shift gives chirping in the pulse radiation emitted spontaneously by an assembly of atoms. We obtain the reduced density operator for a single mode and for the complete spontaneous emitted radiation, and discuss its characteristic function, weight function in diagonal representation, coherence functions, and normalized variance. We find that the emitted radiation is chaotic if all atoms are excited or if the assembly is weakly excited and is in thermal equilibrium. For a superradiant assembly, the radiation is coherent; it is only amplitude coherent if the initial atomic density operator is nondiagonal. We also study stimulated emission and scattering for the cases (i) and (ii). For case (iii) these phenomena do not take place.

Physical Review A•Apr 1, 1980•10 citations
We study the spontaneous emission of a multilevel equidistant excited quantum oscillator (nuclei, atoms, molecules) in the case in which the symmetry of the dynamical transitions between the levels is submitted to the SU (1,1) symmetry group and compare our results with those well known for the SU (2) symmetry. It is shown that the equidistant radiator in the process of spontaneous decay in the case of SU (1,1) symmetry exhibits either only acceleration or only a decrease in spontaneous emission rates, while in the case of SU (2) symmetry the radiation pulse is similar to that for the Dicke super-radiance. The exact steady-state solution for the atomic density operator for an equidistant radiator driven by a totally incoherent broad-band (chaotic) field for a SU (1,1) symmetry group is obtained using the Fokker-Planck equation. It is found that for a strong-field limit in the case of SU (1,1) symmetry the fluctuations in the atomic population increase with increasing intensity of the external field and do not achieve their maximal value as in the case of SU (2) symmetry. Moreover, in the case of SU (1,1) transition symmetry we find that there is a superbunching effect for certain values of group parameter I , while in the case of SU (2) symmetry only bunching and antibunching occur. It is found that for vanishing values of the external field intensity the second-order intensity correlation function achieves negative values.
The exact steady-state solution for the reduced atomic density operator for a model system of N identical two-level atoms confined to a single site (the Dicke model) and driven by a totally incoherent broad-band (chaotic) field is derived through the equivalent Fokker-Planck equation of the system. Steady-state values of the atomic observables, higher moments and atomic fluctuations are calculated for an arbitrary N and an arbitrary field strength. It is shown that when the chaotic field is a thermal (black-body) field the atomic system is driven into a steady relative occupation number that obeys the Boltzmann distribution law only for N=1. (The same result for N>1 atoms can be reached only if the cooperative interactions between the atoms are ignored.) In the thermodynamic limit N to infinity there is no critical behaviour in contrast to the resonant coherently driven case. It is also shown that semiclassical (direct) factorisation of the equations of motion does not lead to the correct results for the N to infinity limit of the exact quantum case. Within the exact theory numerical results for finite N (<or=100) are presented for the time-dependent expectation values of the atomic operators, the intensity and the intensity autocorrelation function. Superradiant pulses are emitted by N initially inverted atoms but as the incident intensity is increased this superradiant behaviour is obscured. The steady-state fluorescence spectrum is a single Lorentzian of width proportional to N in the weak-field case. In the strong-field case the spectrum is insensitive to the number of atoms and the result is similar to the one-atom situation. Photon bunching and antibunching effects are investigated for the weak- and strong-field limits. When the chaotic driving field is simply a single-mode thermal field the approach to atomic saturation is delayed in comparison with the case of the broad-band chaotic field.
The interaction of a single equidistant three-level radiator (same transition frequencies, dipole moments, and decay rates for both one-photon transitions) with a leaky optical cavity mode that at the same time is driven by an external coherent field is investigated via a generalized Fokker–Planck equation. It is shown that the steady-state behaviors of such an equidistant three-level sample differ from the corresponding ones of a general three-level system. We suppose that this difference appears due the fact that a single equidistant three-level radiator is equivalent to a pair of indistinguishable two-level atoms, provided that the separation between the pair is smaller than the wavelength of the cavity field.
The fluctuation properties of a system of two level atoms are investigated by introducing a random precession term into the equations of motion of the atomic super Bloch vector. Starting from the assumptions of neoclassical radiation theory a general formula for the dipole field of a small system of atoms is derived. The intensity fluctuations are calculated in the narrowing limit for two extreme cases of very large and very small atomic to thermal energy ratios. The former case, describing a true superradiant emission, involves asymptotic solutions to the Fokker-Planck equation. The latter case, treated by perturbation theory, corresponds to spontaneous emission in the presence of incoherent pumping.
Spontaneous emission from a system of NNN identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state ∣z0〉|{z}_{0}〉∣z0​〉.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
Interaction with a multimode quantized radiation field of an assembly of NNN two-level atoms contained in a small volume is considered for the special cases of (i) highly excited, (ii) weakly excited, and (iii) superradiant atomic assemblies, and solutions of equations of motion are obtained in closed form. For (i) and (ii) we show that, if the atomic assembly is in the Dicke state ∣r,m>|r,m>∣r,m>, the spontaneously emitted radiation is Lorentzian, and its spectral width and the numerical value of the Lamb shift are r+∣m∣r+|m|r+∣m∣ times that for a single excited atom. For (i) the sign of Lamb shift is opposite to that for (ii) and for a single excited atom. Change in the frequency shift gives chirping in the pulse radiation emitted spontaneously by an assembly of atoms. We obtain the reduced density operator for a single mode and for the complete spontaneous emitted radiation, and discuss its characteristic function, weight function in diagonal representation, coherence functions, and normalized variance. We find that the emitted radiation is chaotic if all atoms are excited or if the assembly is weakly excited and is in thermal equilibrium. For a superradiant assembly, the radiation is coherent; it is only amplitude coherent if the initial atomic density operator is nondiagonal. We also study stimulated emission and scattering for the cases (i) and (ii). For case (iii) these phenomena do not take place.