Amplification of laser beams counterpropagating through a potassium vapor: The effects of atomic coherence William J. Brown, Jeff R. Gardner, and Daniel J. Gauthier Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708-0305 R. Vilaseca Departament de Fı `sica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Colom 11, E-08222 Terrassa, Spain Received 21 April 1997 We observe amplification of a linearly polarized laser beam propagating through a Doppler-broadened atomic potassium vapor driven by an intense, linear and orthogonally polarized counterpropagating laser beam. The observed gain spectra are well explained by a model that incoporates only the effects of the coherent driving of the atomic dipole moment and not atomic recoil. Our results suggest that the recently reported observations of amplification and lasing using a laser-driven sodium vapor may not arise from the effects of collective atomic recoil. S1050-29479707210-7 PACS numbers: 42.50.Gy, 42.50.Hz, 42.50.Vk I. INTRODUCTION For many years researchers have exploited the fact that the center-of-mass momentum of an atom changes when it absorbs or emits radiation. This atomic recoil is the basis for laser cooling and trapping of neutral atoms 1 as well as some types of matter-wave interferometers 2 and it gives rise to resonances in the nonlinear spectroscopy of cold at- oms 3. Our understanding of these processes is quite good for weak electromagnetic fields and simple atomic systems but few studies have been performed in the regime where the coupling between the atoms and the radiation field is highly nonlinear or the atomic structure is complex. Recently, Lippi et al. 4 and Hemmer et al. 5 reported the observation of optical amplification and laser oscillation due to collective atomic recoil in a Doppler-broadened, high-temperature ( 600 K sodium vapor. They attribute the gain to an atomic density grating a periodic bunching of the atoms formed by the aggregate effect of atomic recoil. The modu- lation depth of the atomic density grating is expected to be small at such high temperatures 6; however, substantial amplification may occur because of the high atomic number densities. From one point of view, the atoms bunch in re- sponse to the spatially-varying dipole force arising from the interference between the pump and probe fields whose modulation depth grows as the probe beam is amplified 7,8. This mechanism is similar to that occurring in a free-electron laser 9. In this paper, we investigate the amplification of a weak, linearly polarized laser beam propagating through a Doppler- broadened atomic potassium vapor driven by an intense, lin- ear, and orthogonally polarized counterpropagating laser beam. It appears that atomic recoil effects do not contribute significantly to the observed amplification in our experiments even though the conditions are similar to those described in Refs. 4 and 5. Rather, our results strongly suggest that the traditional mechanism of the coherent driving of the atomic dipole moment by the laser beams ‘‘coherence’’ effects can explain our observations. This supports our recent theoretical work regarding the possibility that there might be a complex interplay between atomic recoil and coherence effects in the previous experiments 10. Note that the orthogonal polarizations of the beams used in our experiment preclude the possibility of the two beams interfering, thus eliminating atomic dipole forces as a cause of atom bunching. However, the polarization-gradient force arising from the spatially dependent change in polarization of the optical field is as large in our experiment as the dipole force in the experiments of Refs. 4 and 5. This is due to the fact that the optical pumping rate of the hyperfine sub- levels is comparable to the spontaneous emission rate of the upper state for the intense pump beam used in our experi- ment 11. A large polarization gradient force gives rise to a slight spatial redistribution of atoms in different magnetic sublevels and thus can amplify the probe beam through a mechanism similar to that proposed in Ref. 7. II. OBSERVATION OF LASER BEAM AMPLIFICATION In the experimental setup the potassium vapor is con- tained in an evacuated stainless steel cell length L =4 cm with optical quality windows, into which buffer gases can be introduced. Both the pump and the probe beams are tuned near the 4 S 1/2 →4 P 1/2 ( D 1 ) transition in potassium occurring at  0 =769.9 nm. The pump laser beam frequency  d , maximum power P d =600 mW incident on the atoms is generated by an actively-stabilized Ti:sapphire ring laser and collimated to a radius r d =370  m (1/e field radius as it passes through the cell, resulting in an intensity of I d =2 P d /  r d 2 280 W/cm 2 . A grating-stabilized diode laser is the source of the probe beam frequency  p , power P p =3  W which is collimated to a radius r p =200  m, resulting in an intensity of I p 5 mW/cm 2 . Both beams are incident on the vapor cell at an angle of 20° with respect to the window normal to prevent multiple reflected beams from entering the interaction region and the angle between the pump and probe beams is  0.002 rad. The absolute fre- quencies of the lasers are calibrated using a Lamb-dip refer- PHYSICAL REVIEW A OCTOBER 1997 VOLUME 56, NUMBER 4 56 1050-2947/97/564/32557/$10.00 3255 © 1997 The American Physical Society