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 the Physical Society of Japan

Coherence Properties of a Radiation Field in the Dicke Model Hamiltonian

Michiyoshi Nagashima

Published May 1, 1978• 2 citations
Publisher

Abstract

A normalized variance of a radiation field is introduced to study the coherence properties of spontaneous and induced emissions in the Dicke model Hamiltonian. It is shown that a superradiant emission from an atomic Dicke state cannot be in a coherent state, though the Dicke state emits photons in a Poisson distribution for the photon number. In the case of the induced omission for an initially intense coherent radiation field, the time evolution of the normalized variance is calculated to see to what extent the initially coherent state remains coherent. We obtain the time evolution of the expectation values of the atomic operators and the photon number operator. These solutions are then compared with semi-classical solutions obtained by taking the diagonal coherent state representation.

DOI
10.1143/jpsj.44.1647

Related papers

Quantum theory of coherent spontaneous and stimulated emissions

Martin E. Smithers, Eugene Y. C. Lu

Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.

Physical Review A•Feb 1, 1974•25 citations

Photon Statistics and Coherence of Stimulated Superradiant Pulses

Y. C. Lx, Arthur Holly Compton

A system of many #we-level atoms or molecules in a collective Dieke state (1) interacting with a single resonant mode of the quantized radiation field has often been adopted as a quantum-mechanical model for a point laser (2). In a previous paper (3) we reported exact dosed-form solutions and photon statistics of coherent spontaneous emission for the model atom-field state in the l imit of infinitely large co-operation number. The purpose of this paper is to report more general results based on this modeI. We give the exact closed-form solutions and photon statistics of coherent emission in the presence of an applied field for the model atom-field state in the same limit. For an initial atomic Dicke state interacting with an applied field in a coherent (Glauber) state (a), the emitted pulse can be desoribed in terms of Glauber states only when the levels of excitation of the initial Dicke states are (~ superradiant ~ (~). For an initially highly inverted system or low excited system, the photon distributions undergo large fluctuations. The model interaction Hamil tonian is given by

•Jan 1, 2007•0 citations

Coherent States and Photon Dynamics in the Dicke Model Hamiltonian

Shôzô Takeno, Michiyoshi Nagashima, Jun Sugimto

Coherent states and dynamics of a photon mode in the Dicke model Hamiltonian are studied by using a method of diagonal coherent-state representation. It is shown that under a strong coupling condition the ground state of the model Hamiltonian is characterized by simultaneous appearance of a photon coherent state and that due to atomic polarization. The energy eigenvalue of such a combined coherent state is shown to be lower than that of the in which all atoms in a matter system are in their ground state while no photon is present. An exact solution for the time evolution of the coherent-state representation of the photon number operator is obtained in terms of the Jacobi elliptic functions. It is shown that periodic, pulse-like and stationary solutions exist under various initial conditions.

Journal of the Physical Society of Japan•Sep 15, 1976•6 citations

Quantum statistics of single-mode radiation emitted by superradiant Dicke states

Anirudh Yadav, Deniz D. Yavuz

We study the quantum statistics of single-mode radiation emitted by an atomic ensemble when the ensemble is initially prepared in a superradiant Dicke state. We show that while the radiation is well approximated by the Glauber coherent state at early times in the evolution, the emission can be truly quantum at later times. In particular, one can observe a large amount of photon-number squeezing in the emission under certain conditions; even a Fock state can be produced. We discuss the quantum statistics of the emission for various parameters, including different initial conditions for the atomic ensemble. To obtain these results, we have developed a formalism where we are able to calculate the quantum statistics of the emission over long time scales even when the number of atoms in the ensemble is quite large.

arXiv:2508.09962•Physical Review A•Nov 17, 2025•0 citations

Different types of coherence: Young-type interference versus Dicke superradiance

Daniel Bhatti, Manuel Bojer, Joachim von Zanthier

Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with a nonvanishing dipole moment. We find that the two configurations produce similar far-field intensity patterns, although they stem from fundamentally distinct types of coherence: while in the second case the atoms display coherence among the individual particles, leading to Young-type interference like that known from classical dipoles, atoms in Dicke states possess collective quantum coherence stemming from entanglement and quantum correlations of the state, leading to an interference pattern resulting from enhanced spontaneous emission. This demonstrates that the radiation generated by synchronized dipoles and Dicke superradiance---even if they do produce the same interference pattern---are fundamentally distinct phenomena and have to be interpreted in different ways.

arXiv:2105.04892•Physical Review A•Nov 1, 2021•5 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
A normalized variance of a radiation field is introduced to study the coherence properties of spontaneous and induced emissions in the Dicke model Hamiltonian. It is shown that a superradiant emission from an atomic Dicke state cannot be in a coherent state, though the Dicke state emits photons in a Poisson distribution for the photon number. In the case of the induced omission for an initially intense coherent radiation field, the time evolution of the normalized variance is calculated to see to what extent the initially coherent state remains coherent. We obtain the time evolution of the expectation values of the atomic operators and the photon number operator. These solutions are then compared with semi-classical solutions obtained by taking the diagonal coherent state representation.
Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.
A system of many #we-level atoms or molecules in a collective Dieke state (1) interacting with a single resonant mode of the quantized radiation field has often been adopted as a quantum-mechanical model for a point laser (2). In a previous paper (3) we reported exact dosed-form solutions and photon statistics of coherent spontaneous emission for the model atom-field state in the l imit of infinitely large co-operation number. The purpose of this paper is to report more general results based on this modeI. We give the exact closed-form solutions and photon statistics of coherent emission in the presence of an applied field for the model atom-field state in the same limit. For an initial atomic Dicke state interacting with an applied field in a coherent (Glauber) state (a), the emitted pulse can be desoribed in terms of Glauber states only when the levels of excitation of the initial Dicke states are (~ superradiant ~ (~). For an initially highly inverted system or low excited system, the photon distributions undergo large fluctuations. The model interaction Hamil tonian is given by
Coherent states and dynamics of a photon mode in the Dicke model Hamiltonian are studied by using a method of diagonal coherent-state representation. It is shown that under a strong coupling condition the ground state of the model Hamiltonian is characterized by simultaneous appearance of a photon coherent state and that due to atomic polarization. The energy eigenvalue of such a combined coherent state is shown to be lower than that of the in which all atoms in a matter system are in their ground state while no photon is present. An exact solution for the time evolution of the coherent-state representation of the photon number operator is obtained in terms of the Jacobi elliptic functions. It is shown that periodic, pulse-like and stationary solutions exist under various initial conditions.
We study the quantum statistics of single-mode radiation emitted by an atomic ensemble when the ensemble is initially prepared in a superradiant Dicke state. We show that while the radiation is well approximated by the Glauber coherent state at early times in the evolution, the emission can be truly quantum at later times. In particular, one can observe a large amount of photon-number squeezing in the emission under certain conditions; even a Fock state can be produced. We discuss the quantum statistics of the emission for various parameters, including different initial conditions for the atomic ensemble. To obtain these results, we have developed a formalism where we are able to calculate the quantum statistics of the emission over long time scales even when the number of atoms in the ensemble is quite large.
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with a nonvanishing dipole moment. We find that the two configurations produce similar far-field intensity patterns, although they stem from fundamentally distinct types of coherence: while in the second case the atoms display coherence among the individual particles, leading to Young-type interference like that known from classical dipoles, atoms in Dicke states possess collective quantum coherence stemming from entanglement and quantum correlations of the state, leading to an interference pattern resulting from enhanced spontaneous emission. This demonstrates that the radiation generated by synchronized dipoles and Dicke superradiance---even if they do produce the same interference pattern---are fundamentally distinct phenomena and have to be interpreted in different ways.
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.