## Cooperative radiation from atoms in different geometries: decay rate and frequency shift |

Advances in Optics and Photonics, Vol. 4, Issue 2, pp. 108-156 (2012)

http://dx.doi.org/10.1364/AOP.4.000108

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### Abstract

A landmark in the development of quantum electrodynamics was the discovery that emission–reabsorption of virtual photons modifies the value of energy levels in an atom from those computed by using Dirac’s equation (Lamb shift). An early result of statistical quantum electrodynamics was that the exchange of virtual photons in an ensemble of identical atoms leads as well to a change in the frequency of the radiation emitted from this system (cooperative Lamb shift). Dicke’s discovery that coherence effects lead to the shortening of the emission lifetime from a small sample by a factor equal to the number of atoms in the ensemble (superradiance or cooperative decay rate) was an early landmark in quantum optics. Both cooperative decay rate and cooperative Lamb shift were shown to have the same physical origin—the exchange of virtual photons, a process described by the Lienard–Wiechert dipole–dipole interaction. This effective potential is the kernel of the integral equation describing the dynamics of the system. This complex long-range kernel gives, for both cooperative quantities, strong dependence on the geometry of the atomic cloud. I summarize the known expressions for the initial cooperative decay rate and the cooperative Lamb shift in different geometries. The results for both the scalar photon and the vector photon (electrodynamics) theories for experimentally realizable systems of either uniform or phased polarization are given.

© 2012 OSA

**OCIS Codes**

(270.5580) Quantum optics : Quantum electrodynamics

(270.6630) Quantum optics : Superradiance, superfluorescence

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 16, 2012

Revised Manuscript: May 21, 2012

Manuscript Accepted: May 21, 2012

Published: June 26, 2012

**Virtual Issues**

(2012) *Advances in Optics and Photonics*

**Citation**

Jamal T. Manassah, "Cooperative radiation from atoms in different geometries: decay rate and frequency shift," Adv. Opt. Photon. **4**, 108-156 (2012)

http://www.opticsinfobase.org/aop/abstract.cfm?URI=aop-4-2-108

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### References

- E. Fermi, “Quantum theory of radiation,” Rev. Mod. Phys. 4, 87–132 (1932). [CrossRef]
- W. E. Lamb and R. C. Retherford, “Fine structure of the atom by a microwave method,” Phys. Rev. 72, 241–243 (1947). [CrossRef]
- H. A. Bethe, “The electromagnetic shift of energy levels,” Phys. Rev. 72, 339–341 (1947). [CrossRef]
- R. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954). [CrossRef]
- V. M. Fain, “On the theory of the coherent spontaneous emission,” Sov. Phys. JETP 9, 562–565 (1959).
- R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two level atoms,” Phys. Rep. 7, 101–179(1973). [CrossRef]
- J. T. Manassah, “Statistical quantum electrodynamics of resonant atoms,” Phys. Rep. 101, 359–427(1983). [CrossRef]
- M. J. Stephen, “First order dispersion forces,” J. Chem. Phys. 40, 669–673 (1964). [CrossRef]
- R. H. Lehmberg, “Radiation from an N-atom system. 1. general formalism,” Phys. Rev. A 2, 883–888 (1970). [CrossRef]
- R. H. Lehmberg, “Radiation from an N-atom system. 2. emission from a pair of atoms,” Phys. Rev. A 2, 889–896 (1970). [CrossRef]
- N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke superradiance in optically pumped HF gas,” Phys. Rev. Lett. 30, 309–312 (1973). [CrossRef]
- R. Roehlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Ruffer, “Collective Lamb shift in single photon superradiance,” Science 328, 1248–1251 (2010). [CrossRef] [PubMed]
- R. Roehlsberger, “The collective Lamb shift in nuclear γ-ray superradiance,” J. Mod. Opt. 57, 1979–1992 (2010). [CrossRef]
- W. R. Garrett, R. C. Hart, J. E. Wray, I. Datskou, and M. G. Payne, “Large multiple collective line shifts observed in three-photon excitation of Xe,” Phys. Rev. Lett. 64, 1717–1720 (1990). [CrossRef] [PubMed]
- R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shift in three-photon resonance,” Phys. Rev. A 39, 93–94 (1989). [CrossRef] [PubMed]
- R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Three-photon frequency shift on non-collinear excitation,” J. Phys. B 22, 2211–2222 (1989). [CrossRef]
- R. Friedberg and J. T. Manassah, “Eigenfunctions and eigenvalues in superradiance with x–y translational symmetry,” Phys. Lett. A 372, 2787–2801 (2008). [CrossRef]
- R. Friedberg and J. T. Manassah, “Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory,” Phys. Lett. A 372, 2514–2521 (2008). [CrossRef]
- A. A. Svidzinsky, J. T. Chang, and M. O. Scully, “Cooperative spontaneous emission of N atoms: many-body eigenstates, the effect of virtual Lamb shift processes and analogy with radiation of N classical oscillators,” Phys. Rev. A 81, 053821 (2010). [CrossRef]
- J. Keaveney, A. Sargsyan, U. Krohn, I. G. Hughes, D. Sarkisyan, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012). [CrossRef] [PubMed]
- S. Prasad and R. J. Glauber, “Coherent radiation by a spherical medium of resonant atoms,” Phys. Rev. A 82, 063805 (2010). [CrossRef]
- R. Friedberg and J. T. Manassah, “The decay dynamics of a slab of two-level atoms excited by an ultrashort resonant pulse,” Opt. Commun. 281, 3755–3761 (2008). [CrossRef]
- R. Friedberg and J. T. Manassah, “Time-dependent directionality of cooperative emission after short pulse excitation,” Opt. Commun. 281, 4391–4397 (2008). [CrossRef]
- R. Friedberg and J. T. Manassah, “Electromagnetic decay modes in a spherical sample of two-level atoms,” Phys. Lett. A 372, 6833–6842 (2008). [CrossRef]
- R. Friedberg and J. T. Manassah, “The dynamical CLS in a system of two-level atoms in a slab-geometry,” Phys. Lett. A 373, 3423–3429 (2009). [CrossRef]
- R. Friedberg and J. T. Manassah, “The metamorphosis in the emission angular profile from an inverted two-level atom system,” Opt. Commun. 282, 3089–3099 (2009). [CrossRef]
- J. T. Manassah, “The metastable states in the cooperative emission from a system of two-level atoms in a sphere,” Laser Phys. 20, 1397–1403 (2010). [CrossRef]
- R. Friedberg and J. T. Manassah, “Electromagnetic modes of an infinite cylindrical sample of two-level atoms,” J. Math. Phys. 52, 042107 (2011). [CrossRef]
- R. Friedberg and J. T. Manassah, “Non-Dicke decay in a small spherical sample with radially varying density,” Phys. Rev A 85, 013834 (2012). [CrossRef]
- A. Svidzinsky and M. O. Scully, “Evolution of collective N-atom states in single photon superradiance: effect of virtual Lamb shift processes,” Opt. Commun. 282, 2894–2897 (2009). [CrossRef]
- R. Friedberg, “Refinement of a formula for decay after weak coherent excitation of a sphere,” Annal. Phys. 325, 345–358 (2010). [CrossRef]
- R. Friedberg and J. T. Manassah, “The Eikonal-SVEAS analytic closed forms for single photon superradiance,” Laser Phys. 20, 250–258 (2010). [CrossRef]
- R. Friedberg, “Nonradiative transfer of excitation in coherent decay from a Gaussian atomic distribution,” J. Phys. B 44, 175505 (2011). [CrossRef]
- R. Friedberg and J. T. Manassah, “The CLS in an ellipsoid,” Phys. Rev. A 81, 063822 (2010). [CrossRef]
- R. Friedberg and J. T. Manassah, “Cooperative Lamb shift and the cooperative decay rate for an initially detuned phased state,” Phys. Rev. A 81, 043845 (2010). [CrossRef]
- J. T. Manassah, “Giant cooperative Lamb shift in a density-modulated slab of two-level atoms,” Phys. Lett. A 374, 1985–1988 (2010). [CrossRef]
- J. T. Manassah, “The dynamical cooperative Lamb shift in a system of two-level atoms in a sphere in the scalar photon theory,” Laser Phys. 20, 259–269 (2010). [CrossRef]
- A. Svidzinsky and M. O. Scully, “On the evolution of N-atom state prepared by absorption of a single photon,” Opt. Commun. 283, 753–757 (2010). [CrossRef]
- R. Friedberg and J. T. Manassah, “Analytic expressions for the initial cooperative decay rate and cooperative Lamb shift for a spherical sample of two-level atoms,” Phys. Lett. A 374, 1648–1659 (2010). [CrossRef]
- R. Friedberg and J. T. Manassah, “Initial cooperative decay rate and cooperative Lamb shift of resonant atoms in an infinite cylindrical geometry,” Phys. Rev. A 84, 023839 (2011). [CrossRef]
- D. C. Burnham and R. Y. Chiao, “Coherent resonance fluorescence excited by short light pulses,” Phys. Rev. 188, 667–675 (1969). [CrossRef]
- R. Friedberg and S. Hartmann, “Pulse induced radiation in the linear regime,” Opt. Commun. 2, 301–304 (1970). [CrossRef]
- J. T. Manassah, “Emission from a slab of resonant two-level atoms induced by a delta-pulse excitation,” Laser Phys. 22, 559 (2012). [CrossRef]
- J. T. Manassah, “Analytic approximate expression for the spectral distribution of the emission from a slab of resonant two-level atoms prepared by an ultrashort δ pulse,” Phys. Rev. A 85, 055801 (2012). [CrossRef]
- J. T. Manassah, “The Purcell–Dicke effect in the emission from a coated small sphere of resonant atoms placed inside a matrix cavity,” Laser Phys. 22, 738–744 (2012). [CrossRef]
- A. Svidzinsky, “Nonlocal effects in single photon superradiance,” Phys. Rev. A 85, 013821 (2012). [CrossRef]
- V. I. Yukalov and E. P. Yukalova, “Possibility of superradiance by magnetic nanoclusters,” Laser Phys. Lett. 8, 804–813 (2011); and references to earlier work cited therein. [CrossRef]

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