We report the first direct observation of the effect of Doppleron resonances on the velocity distribution of atoms in an intense optical standing wave. These observations are in reasonable agreement with the simulations based on a continued-fraction solution for the force.
Atoms moving in an intense, near resonant standing wave (SW) experience a force along the direction of the SW. This force has been investigated by observing its effect on the transverse velocities of atoms in a thermal beam. When the standing wave is tuned above resonance the atomic beam is collimated and has an increased intensity at the center of the beam. Below resonance, the SW anti-collimates the atomic beam, reducing the central intensity. These effects are due to the interaction between the induced atomic dipole and the inhomogeneous field of the SW. Further investigation shows structure in the transverse velocity distribution of the atomic beam. This structure is due to multiphoton (Doppleron) resonances in the force. Calculations reproduce the dipole force and multiphoton resonance effects and are in good agreement with the data.
Dopplerons are the signature of the nonlinear response of moving atoms driven by a continuous standing-wave laser beam. They display maxima on the velocity-dependent atomic population difference at velocities nearly equal to ±(c/ω)[(δ(ω2 + 2Ω2)1/2/(2p + 1)], where Ω is the Rabi frequency associated with an individual beam field and δω is the detuning between the driving frequency and the center of the Doppler linewidth. Probing the device with a weak signal yields gain for Doppler broadenings of the magnitude of the detuning, exclusively on the atomic-resonance-frequency side, with a maximum shifted from the driving frequency by the generalized Rabi frequency associated with a standing wave, defined by (δω2 + 4Ω2)1/2. The existence of dopplerons is demonstrated by peaks occurring at frequencies shifted from the driving frequency by even harmonics of doppleron frequencies. The intensity of the peaks is shown to depend on the Doppler width, and the complexity of the gain curve is shown to increase as the pump intensity does.
Multi-photon Doppleron resonances are investigated for the diffraction of atoms by a classical standing-wave optical field in the regime where energy conservation limits the diffraction orders. In this regime, atomic recoil is incorporated into the description, and consideration of the dynamical shift of the resonance condition from the purely kinematic results becomes critical to observing the desired diffraction of the atomic wave function. Special attention is given to the development of a technique for evaluating the resonances which constitutes a significant simplification of the usual degenerate perturbation theory approach for a quantum-mechanical Hamiltonian. Also developed is a specialized off-resonant atom-field interaction which is shown to be maximally efficient at producing high-order diffraction of the atomic wave function. Suggestions for its implementation are given.