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Physical Review A

Experimental study of absorption and gain by two-level atoms in a time-delayed non-Markovian optical field

Michael H. Anderson, Gautam Vemuri, J. Cooper, P. Zoller, Stephen J. Smith

Published Apr 1, 1993• 30 citations
Publisher

Abstract

We have measured the absorption from a weak time-delayed probe field by a two-level atomic system [Na 3${\mathit{s}}_{1/2}$(F=2,${\mathit{m}}_{\mathit{F}}$=2)\ensuremath{\rightarrow}3${\mathit{p}}_{3/2}$(F=3,${\mathit{m}}_{\mathit{F}}$=3)] saturated by a phase-diffusing pump field. The pump and probe, derived from the same artificially-noise-modulated phase-diffusing laser beam, are frequency degenerate and resonant with the atomic transition. The probe is a time-delayed replica of the pump. Our results, carried out in a regime where the field bandwidth and the Rabi frequency are comparable, provide confirmation of recent theoretical predictions [K. Gheri, M. A. M. Marte, and P. Zoller, J. Opt. Soc. Am. B 5, 1559 (1991)] for the atomic response to the non-Markovian composite of a pump and time-delayed probe, valid for arbitrary bandwidths and intensities. Amplification of the probe field is observed for delays comparable to the lifetime of the upper level and again for very long delays, if the bandwidth is less than the decay rate of the upper state.

DOI
10.1103/physreva.47.3202

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We have measured the absorption from a weak time-delayed probe field by a two-level atomic system [Na 3s1/2{\mathit{s}}_{1/2}s1/2​(F=2,mF{\mathit{m}}_{\mathit{F}}mF​=2)\ensuremath{\rightarrow}3p3/2{\mathit{p}}_{3/2}p3/2​(F=3,mF{\mathit{m}}_{\mathit{F}}mF​=3)] saturated by a phase-diffusing pump field. The pump and probe, derived from the same artificially-noise-modulated phase-diffusing laser beam, are frequency degenerate and resonant with the atomic transition. The probe is a time-delayed replica of the pump. Our results, carried out in a regime where the field bandwidth and the Rabi frequency are comparable, provide confirmation of recent theoretical predictions [K. Gheri, M. A. M. Marte, and P. Zoller, J. Opt. Soc. Am. B 5, 1559 (1991)] for the atomic response to the non-Markovian composite of a pump and time-delayed probe, valid for arbitrary bandwidths and intensities. Amplification of the probe field is observed for delays comparable to the lifetime of the upper level and again for very long delays, if the bandwidth is less than the decay rate of the upper state.
We have measured the absorption of a weak, stochastic field in the presence of a strong, degenerate stochastic pump that saturates the 3S1/2(F = 2, m f =2) → 3P3/2(F = 3, m f = 3) transition in atomic sodium. The probe is a time delayed replica of the pump field, and the net field obeys non-Markovian phase diffusing statistics. The absorption (gain) of the probe field was measured as a function of the time delay. We use cw lasers and impose phase diffusing statistics (δ-correlated frequency fluctuations) with a system of electro-optics. The time delay is provided by lengths of optical fiber. Our results agree well with a recent theory for atomic response to non-Markovian fields, valid for arbitrary strengths and bandwidths of the pump field and a weak time delayed probe. For both pump and probe fields resonant with the transition, we observe maximum gain for a probe time delay of approximately 0.8 lifetimes of the upper state (γ−1).
We present results of our experimental investigations of phase-conjugate four-wave mixing in a nearly Doppler-free, collisionless, two-level quantum system with a partially coherent non-Markovian laser field. The two components of the laser field---an intense pump and a weak, time-delayed probe---are derived from a single narrow-band cw laser source on which phase and frequency fluctuations conforming to the phase diffusion model are superimposed. We carry out these measurements using the D2{D}_{2}D2​ transition in an optically pumped diffuse beam of atomic sodium. We vary the pump intensity, laser bandwidth, and temporal delay between the pump and probe, and measure the peak signal strength, the bandwidth, and the asymmetry of the four-wave-mixing spectrum. For comparison with our experimental results of the peak signal strength, we also analyze the same interaction numerically, through direct integration of the optical Bloch equations. The numerical results are in good agreement with the measurements.
We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the 3s2S1∕23s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}3s2S1∕2​, F=2F=2F=2, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, F=3F=3F=3, mF=3{m}_{F}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.
Four-wave mixing in homogeneously broadened, two-level atoms, driven by time-delayed, correlated phase-diffusing optical fields is investigated. The spectrum of the driving field has an arbitrary bandwidth, i.e., it can have a Lorentzian or a Gaussian profile or an intermediate profile (Voigt). A time delay between the strong pump and weak probe field provides a partial correlation between the fields, and this time delay makes the composite field seen by the atoms non-Markovian. It is shown that the calculation of the four-wave-mixing signal reduces to the solution of six coupled Langevin equations with multiplicative noise; Monte Carlo techniques are utilized to study the response of the atoms to non-Markovian fields. A technique for numerically simulating phase-diffusing fields with colored frequency fluctuations is shown. The four-wave-mixing profiles are found to be significantly different from those for which the driving field is chaotic. The profiles show oscillatory behavior as evidence of the Rabi frequency, a feature not seen in previous works. For some parameter values, a revival of the signal is seen for an increasing time delay, analogous to the revivals seen in chaotic field signals [Phys. Rev. A 44, 6009 (1991)].
Abstract : In this research program, the investigators have explored the role of fluctuations of a laser field on coherent interactions between the laser field and simple atomic systems. A key feature of these experiments is their ability to provide measurements of complex nonlinear optical interactions which are sufficient for direct, quantitative comparison with theory. The main thrust of the present work has been the study of non-Markovian field statistics, present in experiments that use multiple, time-delayed input beams to drive the nonlinear system. The specific interaction studied was Phase-Conjugate Four-Wave Mixing in an optically-pumped beam of atomic sodium, which the researchers measured as a function of laser bandwidth, Rabi frequency, and delay time between the pump and probe beams. The investigators have also calculated the expected signal strength through numerical integration of the Optical Bloch Equations. Experimental and numerical results are in very good agreement. The investigators also studied theoretically two-photon absorption with correlated, time-delayed input fields, and provided the first experimental confirmation of the fundamental theory of Phase-Conjugate Four-Wave Mixing with monochromatic fields in a simple atomic system.
We report measurements of the effect of laser fluctuations on a strong-field degenerate four-wave mixing interaction, carried out in a nearly Doppler-free, two-level system using a single laser with statistically well-defined phase fluctuations. The counterpropagating pump beams and the probe beam, each split from this phase-noise-modulated source, were fully correlated. The nonlinear medium was an optically-pumped diffuse beam of atomic sodium. By time-delaying the probe with respect to the pump beams, the composite field becomes non-Markovian. Four-wave mixing results in the generation of a phase-conjugate beam anti-parallel to the probe beam. With the laser field spectrum nearly Lorentzian in shape, and with a field linewidth greater (and, for comparison, much narrower) than the natural linewidth of the sodium, we measured the intensity of the phase-conjugate beam as the pump and probe beams were tuned through the D2 resonance, as a function of intensity of die pump beam (up to intensities several times the saturation intensity), and for varying delay between the pump and probe fields. This experiment provides a cleaner measurement of this interaction than any previously available.