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Physical Review A

Nonlinear frequency conversion with short laser pulses and maximum atomic coherence

L. Deng, M. G. Payne, W. R. Garrett

Published Jul 1, 1998• 22 citations
Publisher

Abstract

A perturbation treatment for Raman generation with a combination of long, short, and delayed laser pulses is presented. When the coupling and probe lasers are applied in a counterintuitive sequence, the fast oscillatory contributions to populations and coherence are eliminated by robust adiabatic passage, allowing a much simpler solution to the problem. Such counterintuitive and on-resonance operation allows effective electromagnetically induced transparency to evolve so that the probe laser photons will experience no absorption yet still fully participate in the nonlinear frequency conversion. Consequently, better conversion efficiency should be possible.

DOI
10.1103/physreva.58.707

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A perturbation treatment for Raman generation with a combination of long, short, and delayed laser pulses is presented. When the coupling and probe lasers are applied in a counterintuitive sequence, the fast oscillatory contributions to populations and coherence are eliminated by robust adiabatic passage, allowing a much simpler solution to the problem. Such counterintuitive and on-resonance operation allows effective electromagnetically induced transparency to evolve so that the probe laser photons will experience no absorption yet still fully participate in the nonlinear frequency conversion. Consequently, better conversion efficiency should be possible.
We present experimental data on adiabatically driven frequency conversion with ultrashort (picosecond) laser pulses towards the vacuum-ultraviolet regime, enhanced by coherent population return and preparation of maximal atomic coherences. We generate the sum frequency of an intense pump pulse and a probe pulse via a two-photon resonance in xenon. When we slightly detune the pump laser from two-photon resonance, the atomic populations are adiabatically driven forth and back from the atomic ground state to an excited state. This coherent population return (CPR) prepares the medium in a transient state of maximal atomic coherence, which enhances frequency mixing with a probe laser. We thoroughly study the variation of CPR-enhanced frequency conversion with experimental parameters and compare CPR with conventional, resonantly enhanced frequency conversion. In particular, we investigate the temporal evolution of the atomic coherence and the effect of inevitable ac Stark shifts. We find that ac Stark shifts induce an asymmetry in the spectral characteristics of CPR, which nevertheless permits enhanced frequency conversion. For the case of resonantly enhanced frequency conversion, we show that the atomic coherences are maintained for several tens of picoseconds after the pump pulse, which permits time-delayed frequency conversion. Moreover, we analyze the pressure dependence of the atomic coherence' lifetime and observe a free induction decay at the two-photon coherence with the generation of a second harmonic field. These findings shall push applications of adiabatic light-matter interactions also to the regime of nonlinear optics, driven by intense laser pulses.
We theoretically study nonlinear optical frequency conversion with time-frequency entangled paired photons whose sum frequency is on two-photon resonance of an atomic ensemble. Assisted by a strong coupling laser, two paired photons with wide spectrum are converted into a single monochromatic photon. The on-resonance nonlinear process is made possible due to the electromagnetically induced transparency that not only eliminates the on-resonance absorption but also enhances the nonlinear interaction between the single photons and atoms. Compared to this quantum-nonlinear conversion, the classical corresponding single-photon counts from accidental two-photon coincidence has a wide spectrum and experiences large absorption. As a result, the system can be used as an efficient two-photon quantum correlator in which the classical accidental coincidences can be suppressed. We perform numerical simulations basing on a Rb atomic vapor cell with realistic operating parameters.
We derive an analytic solution for pulsed frequency conversion based on electromagnetically induced transparency or maximum coherence in resonant atomic vapors. In particular, drive-field and coherence depletion are taken into account. The solutions are obtained with the help of a Hamiltonian approach, which in the adiabatic limit allows one to reduce the full set of Maxwell-Bloch equations to simple canonical equations of Hamiltonian mechanics for the field variables. Adiabatic integrals of motion can be obtained and general expressions for the spatiotemporal evolution of field intensities derived. Optimum conditions for maximum conversion efficiency are identified and the physical mechanism of nonlinear conversion in the limit of drive-field and coherence depletion discussed.
We present a time-dependent calculation for four-wave mixing using a combination of long, short, and time delayed laser pulses in the context of electromagnetically induced transparency. Two transform limited nanosecond lasers are used to create a highly coherent mixture of the ground state and an excited state via a two-photon process. Once the induced transparency is established, a laser with short pulse length is injected after a suitable delay to generate four-wave mixing. We show that the wave mixing process is phase matched for all detunings, and with appropriately selected atomic coherence and populations, near 100% photon flux conversion efficiency can be obtained, independent of the intensity of the short pulse laser. In addition, we show that for small detunings for the short pulse laser, the four-wave mixing field travels with the speed of light in vacuum and suffers no pulse distortion even though the medium is highly dispersive at the frequency of the generated wave. These advantages open a door for future applications of the scheme for highly efficient, very stable UV generation.
The spatial and temporal dynamics of two short pulses propagating in an optically dense medium of resonant three-level Λ-atoms is investigated numerically and analytically. The maximum coherence for the Raman transition due to coherent population trapping. It is shown that, at the initial stage of propagation, the waveforms of such pulses only slightly change along the length of the medium, which may considerably exceed the length of linear absorption for a single weak pulse. As the length of the absorbing medium increases, the energy of the probe (first) pulse is completely transferred into the second (control) pulse.
The features of spatial propagation of two partially overlapping short resonant pulses (counterintuitive pulse sequencing) in an absorbing medium of three-level atoms under conditions of adiabatic population transfer are investigated. We find that pulses can propagate with practically constant amplitudes in a medium with length much higher than the absorption length. It is shown that adiabatic population transfer creates full population inversion on a dipole-forbidden (Raman) transition over the way of pulses' propagation. We suggest use of this technique for conversion of picosecond laser pulses into tunable coherent anti-Stokes radiation.