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Physical Review A

Collective emission in a resonant cavity in the dependence on an external electric field

D. Bartholdtsen, T. Becker, R.-H. Rinkleff

Published Nov 1, 1992• 7 citations
Publisher

Abstract

Collective emission in a resonant cavity was observed between high-lying levels in Sr and Ba. These transitions react very sensitively to a static external electric field. The square root of the maximum of the intensity of the superfluorescent pulse decreases linearly with the second power of the electric field strength. The behavior of the maximum of the intensity, of the characteristic superfluorescent time, and of the delay time of the superfluorescent pulse was described in the framework of modified Maxwell-Bloch equations and explained by a change of the characteristic time constant of the superfluorescent pulse.

DOI
10.1103/physreva.46.5801

Related papers

Superfluorescent transitions between high-lying levels in an external electric field

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The occurrence of superfluorescence in the near-infrared regime has been investigated between high-lying levels of Sr, Ba, and Na under the influence of a static homogeneous external electric field. The time inequalities for single-pulse superfluorescence were fulfilled. The measurements show for all the investigated superfluorescent transitions that the square root of the peak intensity of the superfluorescent pulse decreases with the square of the electric-field strength. If one takes into account the dependence of the number of excited atoms, the wavelengths, and the line strengths of the superfluorescent pulses on the electric-field strengths, the experimental findings cannot be explained by well-known theories of superfluorescence.

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A superfluorescence effect in a V-type medium with initial Raman inversion, driven by a strong coherent field on one of the transitions, is studied analytically and numerically. It is shown that the collective spontaneous emission evolves in the presence of a minor population of an upper state of a superfluorescent transition. In the limit of the Rabi frequency of a driving field large compared to that of a superfluorescent pulse, the system of two equations for the fields and density-matrix equations for three states of the medium is reduced to Maxwell-Bloch equations for an effective two-level system. The shape of a superfluorescent pulse is perfectly described in terms of a slowly varying envelope function (which is a solution of the Maxwell-Bloch equations), filled with fast oscillations associated with Rabi floppings on the driving transition. In the average, i.e., after integrating over a period of Rabi oscillations, the upper superfluorescent state is populated less than other states, such that the phenomenon may be called ``superfluorescence without inversion'' by analogy with lasing without inversion.

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Superfluorescence in a continuously pumped medium

Eric L. Bolda, R. Y. Chiao, J. C. Garrison

Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.

Physical Review A•Oct 1, 1995•20 citations

Three-dimensional theory of initiation of superfluorescence

Jan Mostowski, Božena Sobolewska

We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers $F \ensuremath{\ge} 1$. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.

Physical Review A•Sep 1, 1984•15 citations
Collective emission in a resonant cavity was observed between high-lying levels in Sr and Ba. These transitions react very sensitively to a static external electric field. The square root of the maximum of the intensity of the superfluorescent pulse decreases linearly with the second power of the electric field strength. The behavior of the maximum of the intensity, of the characteristic superfluorescent time, and of the delay time of the superfluorescent pulse was described in the framework of modified Maxwell-Bloch equations and explained by a change of the characteristic time constant of the superfluorescent pulse.
The occurrence of superfluorescence in the near-infrared regime has been investigated between high-lying levels of Sr, Ba, and Na under the influence of a static homogeneous external electric field. The time inequalities for single-pulse superfluorescence were fulfilled. The measurements show for all the investigated superfluorescent transitions that the square root of the peak intensity of the superfluorescent pulse decreases with the square of the electric-field strength. If one takes into account the dependence of the number of excited atoms, the wavelengths, and the line strengths of the superfluorescent pulses on the electric-field strengths, the experimental findings cannot be explained by well-known theories of superfluorescence.
For a pencil-shaped extended medium with Fresnel number equal to 1, we have quantum mechanically derived a description of the initiation of superfluorescence in terms of Maxwell-Bloch equations with a fluctuating source due to the zero-point fluctuations of the vacuum field. By the introduction of classical behavior, these equations are extended to include nonlinear behavior due to decreasing atomic inversion. The principal assumption in the derivation is that the main features of superfluorescence are governed by the interaction of atoms with field modes inside two small solid angles around the pencil axis. The delay ${\ensuremath{\tau}}_{D}$, defined as the time at which the mean-squared tipping angle of the collective Bloch vector attains the value 1, turns out to be given by ${\ensuremath{\tau}}_{D}=(\frac{{\ensuremath{\tau}}_{R}}{4}){[\mathrm{ln}{(2\ensuremath{\pi}N)}^{\frac{1}{2}}]}^{2}$, where ${\ensuremath{\tau}}_{R}$ is the radiation time for collective decay and NNN is the number of atoms. The corresponding effective initial tipping angle roughly equals 2(N)12\frac{2}{{(N)}^{\frac{1}{2}}}(N)21​2​. A Fokker-Planck equation is derived to describe the statistics of the initial development of the tipping angle. The variance $\ensuremath{\Delta}{\ensuremath{\tau}}_{D}$ of the delay of the superfluorescence pulse satisfies approximately $\ensuremath{\Delta}{\ensuremath{\tau}}_{D}=\frac{2.3}{\mathrm{ln}N}$. A brief comparison with previous treatments of superfluorescence is given.
A superfluorescence effect in a V-type medium with initial Raman inversion, driven by a strong coherent field on one of the transitions, is studied analytically and numerically. It is shown that the collective spontaneous emission evolves in the presence of a minor population of an upper state of a superfluorescent transition. In the limit of the Rabi frequency of a driving field large compared to that of a superfluorescent pulse, the system of two equations for the fields and density-matrix equations for three states of the medium is reduced to Maxwell-Bloch equations for an effective two-level system. The shape of a superfluorescent pulse is perfectly described in terms of a slowly varying envelope function (which is a solution of the Maxwell-Bloch equations), filled with fast oscillations associated with Rabi floppings on the driving transition. In the average, i.e., after integrating over a period of Rabi oscillations, the upper superfluorescent state is populated less than other states, such that the phenomenon may be called ``superfluorescence without inversion'' by analogy with lasing without inversion.
Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.
We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers $F \ensuremath{\ge} 1$. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.