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AIP conference proceedings

High efficiency four-wave mixing at low power densities and low concentrations: The role of coherence

M. G. Payne

Published Jan 1, 2001• 0 citations
Publisher

Abstract

Two transform limited nanosecond lasers are used in a delayed pulse mode to prepare a highly coherent mixture of the ground state and the upper state of a two-photon transition. A picosecond laser co-propagates through the prepared medium at a delayed time and generates a four-wave mixing field. With a carefully chosen time delay, the wave mixing process is phase matched for all detunings and concentrations, and all of the third laser photons can be converted to the mixing field, independent of the intensity of the short-pulse laser. The condition for optimum conversion efficiency does not usually correspond to maximum atomic coherence. In the case of a near resonance short-pulse laser, the condition for phase matching leads to efficient conversion, with the mixing field propagating at the speed of light in vacuum with no distortion.

DOI
10.1063/1.1405598

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Two transform limited nanosecond lasers are used in a delayed pulse mode to prepare a highly coherent mixture of the ground state and the upper state of a two-photon transition. A picosecond laser co-propagates through the prepared medium at a delayed time and generates a four-wave mixing field. With a carefully chosen time delay, the wave mixing process is phase matched for all detunings and concentrations, and all of the third laser photons can be converted to the mixing field, independent of the intensity of the short-pulse laser. The condition for optimum conversion efficiency does not usually correspond to maximum atomic coherence. In the case of a near resonance short-pulse laser, the condition for phase matching leads to efficient conversion, with the mixing field propagating at the speed of light in vacuum with no distortion.
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.
Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time ${T}_{2}^{\ensuremath{'}}$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102--124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.
We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.
We observed electromagnetically induced transparency-based four-wave mixing (FWM) in the pulsed regime at low light levels. The FWM conversion efficiency of 3.8(9)3.8(9)%3.8(9) was observed in a four-level system of cold 87Rb{}^{87}\mathrm{Rb}87Rb atoms using a driving laser pulse with a peak intensity of $\ensuremath{\approx}80$ $\ensuremath{\mu}\mathrm{W}/{\mathrm{cm}}^{2}$, corresponding to an energy of $\ensuremath{\approx}60$ photons per atomic cross section. Comparison between the experimental data and the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)] showed good agreement. Additionally, a high conversion efficiency of 46(2)46(2)%46(2) was demonstrated when applying this scheme using a driving laser intensity of $\ensuremath{\approx}1.8$ mW/cm2\mathrm{mW}/{\mathrm{cm}}^{2}mW/cm2. According to our theoretical predictions, this FWM scheme can achieve a conversion efficiency of nearly 100100%100 when using a dense medium with an optical depth of 500.
In this study, we extended the observation of the effect of the coherence of a laser field to four-wave mixing interactions in atomic media. These measurements will help us understand quantitatively recent techniques employing broad-band nanosecond laser pulses for measurements of sub-picosecond dipole relaxation lifetimes in a variety of media. The coherence of the laser field in this work is controlled using random phase/frequency modulation techniques, creating a field in the laboratory known as the phase diffusion field. The four-wave mixing signal is generated by an ensemble of two-level atoms (Na) interacting with degenerate broad-band, correlated, pump and probe fields. This two-level system is produced by optically pumping the sodium atoms into a single hyperfine component of the ground state. Data sets were taken without and with noise applied to the optical field. For the latter, we measured the dependence of the power of the four-wave mixing signal on the delay times between the pump and probe beams. These data sets were compared with the computer simulation results.
Efficient frequency conversion of photons has important applications in optical quantum technology because the frequency range suitable for photon manipulation and communication usually varies widely. Recently, an efficient frequency conversion system using a double- Λ four-wave mixing (FWM) process based on electromagnetically induced transparency (EIT) has attracted considerable attention because of its potential to achieve a nearly 100% conversion efficiency (CE). To obtain such a high CE, the spontaneous emission loss in this resonant-type FWM system must be suppressed considerably. A simple solution is to arrange the applied laser fields in a backward configuration. However, the phase mismatch due to this configuration can cause a significant decrease in CE. Here, we demonstrate that the phase mismatch can be effectively compensated by introducing the phase shift obtained by two-photon detuning. Under optimal conditions, we observe a wavelength conversion from 780 to 795 nm with a maximum CE of 91.2 % ± 0.6 % by using this backward FWM system at an optical depth of 130 in cold 87 Rb atoms. The current work represents an important step toward achieving low-loss, high-fidelity quantum frequency conversion based on EIT.