Relativistic recoil in radiative atomic transitions (2 pages)

R. Bonifacio, L. De Salvo, William A. Barletta

Hartmut M. Pilkuhn

A modified time-dependent perturbation theory for single-photon emission is proposed, which yields the exact photon energy for a relativistically recoiling atom. The relevant unperturbed ``Hamiltonian'' has stationary eigenvalues ${E}^{2}$. Its form is generalized here to hydrogenic atoms of arbitrary nuclear spins.

Roy H. Garstang

Mary M. Cola, Luca Volpe, N. Piovella

We demonstrate that superradiance and collective atomic recoil lasing from cold atoms can be enhanced using a two-frequency pump with frequency difference twice the two-photon recoil frequency ${\ensuremath{\omega}}_{r}$. In the good-cavity regime the atoms behave as a three-recoil-level system, collectively scattering a single-frequency radiation mode. In the bad-cavity regime, the superradiant cascade through the different recoil momentum states is strongly accelerated. The emitted radiation shows a discrete spectrum whose harmonics are separated by $2{\ensuremath{\omega}}_{r}$ and generated by transitions between adjacent momentum levels.

F. A. Babushkin

Kunnat J. Sebastian

We show that in order to satisfy the condition of relativistic invariance for the one-photon radiative transition amplitudes of a composite system to relative order $\frac{1}{{c}^{2}}$ in an approximately relativistic canonical theory, the position operator in the theory should satisfy a condition which encompasses the world-line condition of Currie, Jordan, and Sudarshan. We also obtain the expression for the $E1$ and the $M1$ single-photon transition amplitudes of the composite system in the center of momentum frame, including the relativistic corrections of leading order. These expressions show that the relativistic corrections are qualitatively different for the electrically charged and neutral composite systems. They also depend, especially in the case of the $M1$ amplitudes, rather sensitively on the binding interaction among the constituent particles. There are also relativistic corrections which depend simultaneously on the recoil momentum of the composite system and on the use of the relativistic center-of-mass variables in the problem and which so far have not been considered in the literature.