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Physical Review A

Deviation from the sech2 superradiant emission law in a two-level atomic system

Antonio Edson Gonçalves, Salomon Sylvain Mizrahi, B. M. Pimentel

Published Sep 1, 1990• 0 citations
Publisher

Abstract

The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the ${\mathrm{sech}}^{2}$ law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results.

DOI
10.1103/physreva.42.3129

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The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the sech2{\mathrm{sech}}^{2}sech2 law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results.
The superradiant emission is considered for a radiating system constituted by N dressed spin-1/2 magnetic dipoles, described by a nonlinear single particle Hamiltonian that is derived under a mean field approximation. This Hamiltonian describes adequately the transient regime of the emission process: The intensity of the radiation follows the sech2 law and its peak is proportional to N2. Then, one considers the application of a periodic time-dependent transverse magnetic field and we study the behavior of the emission that becomes periodically pulsed.
We study the radiative emission due to the self-dressing of a two-level atom, initially in its bare ground state, interacting with the zero-point electromagnetic field. Evolution in time leads to the formation of a dressed ground state of lower energy. This energy difference between bare and dressed ground state is taken into account by the emission of real photons. In order to describe this aspect of the self-dressing process we study the transition probability amplitude from the initial bare state to an asymptotic state consisting of the atom in its dressed ground state plus some real photons. Adopting nonperturbative techniques based on the resolvent method we find that the bare-dressed transition occurs at the lowest order with the emission of two photons. The spectral distribution obtained shows that there is a probability for emission of photons at frequency of the order of the atom's transition frequency.
We report the experimental observation of a superradiant emission emanating from an elongated dense ensemble of laser cooled two-level atoms, with a radial extent smaller than the transition wavelength. In the presence of a strong driving laser, we observe that the system is superradiant along its symmmetry axis. This occurs even though the driving laser is orthogonal to the superradiance direction. This superradiance modifies the spontaneous emission, and, resultantly, the Rabi oscillations. We also investigate Dicke superradiance in the emission of an almost fully inverted system as a function of the atom number. The experimental results are in qualitative agreement with ab-initio, beyond-mean-field calculations.
Coherence properties of the single-mode electromagnetic radiation emitted by a system of identical two-level atoms which is initially in the superradiant state are determined approximately. The approximation is valid only for short times when the state of the atomic system does not differ appreciably from the superradiant state. The electromagnetic field radiated spontaneously possesses full coherence in the sense of Glauber's definition, its density operator having the form of that for the ideal laser radiation. This coherence disappears when, because of external radiation, stimulated and spontaneous emission both take place.
The collective nature of light emission by atomic ensembles yields fascinating effects such as superradiance and radiation trapping even at the single-photon level.Light emission is influenced by virtual transitions and the collective Lamb shift which yields peculiar features in temporal evolution of the atomic system.We study how two-dimensional atomic structures collectively emit a single photon.Namely, we consider spherical, cylindrical, and spheroidal shells with two-level atoms continuously distributed on the shell surface and find exact analytical solutions for eigenstates of such systems and their collective decay rates and frequency shifts.We identify states which undergo superradiant decay and states which are trapped and investigate how size and shape of the shell affects collective light emission.Our findings could be useful for quantum information storage and the design of optical switches.
The collective nature of light emission by atomic ensembles yields fascinating effects such as superradiance and radiation trapping even at the single-photon level. Light emission is influenced by virtual transitions and the collective Lamb shift which yields peculiar features in temporal evolution of the atomic system. We study how two-dimensional atomic structures collectively emit a single photon. Namely, we consider spherical, cylindrical, and spheroidal shells with two-level atoms continuously distributed on the shell surface and find exact analytical solutions for eigenstates of such systems and their collective decay rates and frequency shifts. We identify states which undergo superradiant decay and states which are trapped and investigate how size and shape of the shell affects collective light emission. Our findings could be useful for quantum information storage and the design of optical switches.