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Journal of the Optical Society of America B

Raman emission versus dopplerons in a two-level atomic cell

Andree A. Tallet

Published Aug 1, 1994• 5 citations
Publisher

Abstract

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.

DOI
10.1364/josab.11.001336

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Journal of Mathematical Physics•May 1, 1985•7 citations
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.
We have observed a new type of sub-Doppler laser cooling with neither polarization gradients nor magnetic fields. All known sub-Doppler laser cooling methods require one of these two to resdistribute the atomic population among the energy levels. This allows the irreversible processes of optical pumping vels. This allows the irreversible processes of optical pumping (OP) to manipulate the conservative force of light shifts (e.g. resonant exchange between the two beams comprising a standing wave) into a damping force. Our scheme employs stimulated Raman transitions between ground state hyperfine levels of Rb with a bichromatic standing wave, accompanied by a momentum change of {Delta}p = 2{h_bar}k. OP, with {Delta}p = 1{h_bar}k, creates a population imbalance allowing repetition of the Raman process. When the detuning of the light from Raman resonance {delta} is properly chosen, the net momentum exchange damps the atomic motion. Changing {delta} by only {gamma}/6(1 MHz) replaces cooling by heating. This process separates the velocity selective Raman resonance and OP processes differently from others, and helps clarify the role of these different mechanisms.
We investigate theoretically the amplification of a laser beam propagating through a collection of Doppler-broadened two-level atoms driven by an intense counterpropagating laser beam. Large amplification of the beam is predicted when the pump-beam Rabi frequency is comparable to the Doppler width of the atomic transition, even without including the effects of atomic recoil. The microscopic origin of the gain can be attributed to the coherent driving of the atomic dipole moment, suggesting that amplification and lasing due to collective atomic recoil may be influenced by this process.
We report computational results for the time evolution of the velocity distribution P(V,t) for two-level and multilevel ``Doppler'' laser cooling. We compare results obtained from the semiclassical (SC) Fokker-Planck equation and from generalized optical Bloch equations applied to density matrices over a basis of products of internal and quantized translational states (QDM). Computer memory requirements are optimized to make large-scale QDM calculations feasible. QDM and SC agree well except for two cases: (a) atoms in the wells of the light-shift potential (with kinetic energy less than the well depth, U0{\mathit{U}}_{0}U0​), and (b) atoms with recoil energy ER{\mathit{E}}_{\mathit{R}}ER​ comparable to or greater than the natural linewidth \ensuremath{\Elzxh}\ensuremath{\Gamma}. Transient dips occur in P(V,t) at V=0 in QDM results due to slow cooling of atoms in the light-shift potential wells. Dips in P(V,t) occur at velocity-tuned-resonance (Doppleron) velocities but disappear over long interaction times as atoms accumulate near points where the force is zero. When ER{\mathit{E}}_{\mathit{R}}ER​\ensuremath{\approxeq}\ensuremath{\Elzxh}\ensuremath{\Gamma}, sharp peaks occur in P(V,T) at V=\ifmmode\pm\else\textpm\fi{}VR{\mathit{V}}_{\mathit{R}}VR​ from velocity-selective population quasitrapping not previously found in a two-level transition. Sharp features in P(V,t) occur also for J\ensuremath{\rightarrow}J+1 transitions with J>0, small U0{\mathit{U}}_{0}U0​/ER{\mathit{E}}_{\mathit{R}}ER​, and sufficiently large detuning, from transitions between individual quantum states in the periodic potential.
Previous theoretical results on the influence of a laser on the line shape of a coupled transition-laser-induced line narrowing-have been restricted to the case where the laser is detuned from the center of its atomic gain profile or is in the form of a traveling wave. This paper extends those results to include the case where the laser is an intense standing-wave field tunable to the center of its atomic gain profile (conditions for Lamb dip). The effect may be observed either in transmission, by probing the coupled transition with a weak traveling-wave field coaxial with the laser field, or else in spontaneous emission from the coupled transition viewed along the axis of the laser field. It is now well known that for a laser detuned from the center of its atomic gain profile, two narrow Lorentzian resonances of different widths appear superimposed upon the broad background signal at frequencies symmetrically located about the corresponding line center. When the laser is tuned to the center of its gain profile, however, additional fine structure develops. This structure, which is particularly significant when the laser field is intense, may have important applications in highresolution spectroscopy and laser-frequency stabilization. In this paper the laser frequency may be smaller or larger than the frequency of the coupled transition. In the latter case an intense laser introduces additional splitting effects, even when the laser is detuned. Splitting effects due to weakly saturating laser fields are also discussed. The problem is formulated by expanding elements of the ensemble-averaged density matrix in an infinite series of spatial Fourier components. A perturbation technique is employed, valid for a weak probe field and a standing-wave field of arbitrary intensity. One obtains an expression for emission induced by the probe field due to atoms moving with one velocity, written in terms of continued fractions in the general case and with Bessel functions in an important special case. This expression is integrated over the atomic velocity distribution by means of a computer to obtain the total emission due to atoms moving with all velocities. In some cases the integrated expressions may be written in closed algebraic form. A detailed discussions of line shapes and of the physical processes involved is included.
We have considered the excitation spectra for a three-level atom interacting simultaneously with a strong pump field and a weak signal field. The atom consists of an upper excited state ‖2〉 and two lower states ‖1〉 and ‖3〉 where the transition ‖1〉↔‖3〉 is electric-dipole forbidden from parity considerations. The pump field, whose frequency mode ωb is initially populated, operates near resonance between the states ‖2〉 and ‖3〉, ‖2〉↔‖3〉, while the signal field describes the radiative decays ‖2〉→‖3〉 and ‖2〉→‖1〉, respectively. Using the Green function method, the spectral functions for the signal field have been calculated in the limit of high photon densities of the pump field describing the following processes: (i) one-photon process; the spectra consist of a main peak at the signal frequency ω=ω21 and a pair of sidebands at ω=ω21±Ω−(ω23−ωb)/2, where Ω2=Ω2b/2+(ω23−ωb)2/4 with Ωb and (ω23−ωb) being the Rabi frequency and the detuning of the pump field, respectively. The intensity of the main peak at ω=ω21 is positive indicating signal-field absorption while those of the sidebands are always negative implying amplification (stimulated emission) of the signal field. The sum of the intensities (in absolute value) of the sidebands is twice that of the main peak at resonance while in the off-resonance case it depends on the value of the ratio (ω23−ωb)/2Ω. (ii) Stimulated three-photon process; the spectra consists of a pair of sidebands peaked at ω=ω21−2ωb±Ω−(ω23−ωb)/2 whose intensity is negative indicating amplification. At resonance the sidebands have equal intensities but at finite detuning asymmetry arises enhancing one peak while diminishing the intensity of the other. (iii) Stimulated two-photon process; the stimulated Raman spectra consist of a peak at ω=ω31, which has a delta function distribution, and a pair of strongly amplified sidebands at ω=ω31±Ω+(ω23−ωb)/2. The computed spectra for the three processes are presented graphically for different values of Rabi frequencies and detunings.