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Coherent Laser-Atom Interactions With Partially Coherent Laser Fields

Daniel S. Elliott

Published Aug 30, 1999• 0 citations
OpenAlex

Abstract

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.

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Coherent signals produced by time delayed, fluctuating optical pulses interacting with atoms in the vapor phase have attracted much interest recently, due to their potential as a source of sub-picosecond time resolution. The theoretical description of such experiments brings into play many profound questions connected with stochastic Bloch equations. For example, even though the noise properties of a single laser beam may be Markovian in nature, in these experiments the atoms are subjected to at least two time-delayed fields which may be correlated. Because the atoms retain some memory of the first field at the time when the second field acts, the entire process becomes non-Markovian. In principle, the variation of such parameters as the homogeneous and inhomogeneous widths, allows the experimenter some degree of control over this memory time associated with the atomic medium.\n&more...

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Overview of experimental investigations of laser bandwidth effects in nonlinear optics

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A number of experimental investigations have been carried out over the past fifteen years which have been used to study the effect of the bandwidth of the laser on various nonlinear optical interactions. These are useful and interesting for a number of reasons. On the technical side laser bandwidth effects can limit the accuracy of measurements of the frequency of atomic transitions as well as the determination of the strength of the interaction. Of a more fundamental interest is the question of the behavior of the nonlinear atomic system when interacting with the non-monochromatic field. In the first experiments carried out to investigate these effects lasers were used which could be operated on a single longitudinal mode or on multiple modes corresponding to the presence or absence of an intra-cavity etalon. Following this a number of techniques were developed to modulate the amplitude phase and/or frequency of the output of a stabilized cw laser with a random (but well-characterized) signal. In this way laser fields could be generated in the laboratory which closely approximate models of laser fields on which theorists have based calculations of laser bandwidth effects. These works allow direct quantitative comparison of results with theory. A number of these field models which can now be generated in the laboratory will be discussed as well as measurements of the role they play in nonlinear interactions.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 1, 1991•1 citation
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 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 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.
Coherent signals produced by time delayed, fluctuating optical pulses interacting with atoms in the vapor phase have attracted much interest recently, due to their potential as a source of sub-picosecond time resolution. The theoretical description of such experiments brings into play many profound questions connected with stochastic Bloch equations. For example, even though the noise properties of a single laser beam may be Markovian in nature, in these experiments the atoms are subjected to at least two time-delayed fields which may be correlated. Because the atoms retain some memory of the first field at the time when the second field acts, the entire process becomes non-Markovian. In principle, the variation of such parameters as the homogeneous and inhomogeneous widths, allows the experimenter some degree of control over this memory time associated with the atomic medium.\n&more...
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)].
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.
A number of experimental investigations have been carried out over the past fifteen years which have been used to study the effect of the bandwidth of the laser on various nonlinear optical interactions. These are useful and interesting for a number of reasons. On the technical side laser bandwidth effects can limit the accuracy of measurements of the frequency of atomic transitions as well as the determination of the strength of the interaction. Of a more fundamental interest is the question of the behavior of the nonlinear atomic system when interacting with the non-monochromatic field. In the first experiments carried out to investigate these effects lasers were used which could be operated on a single longitudinal mode or on multiple modes corresponding to the presence or absence of an intra-cavity etalon. Following this a number of techniques were developed to modulate the amplitude phase and/or frequency of the output of a stabilized cw laser with a random (but well-characterized) signal. In this way laser fields could be generated in the laboratory which closely approximate models of laser fields on which theorists have based calculations of laser bandwidth effects. These works allow direct quantitative comparison of results with theory. A number of these field models which can now be generated in the laboratory will be discussed as well as measurements of the role they play in nonlinear interactions.