We investigate the influence of the distribution of atom velocities in a hot rubidium sample on the correlation between field-intensity fluctuations of two independently generated four-wave mixing signals and between the transmission signals. The nonlinear process is driven by a single continuous-wave (cw) laser in a pure two-level system due to the forward geometry with circular and parallel polarization of the input fields. The intensity cross correlations of the four-wave mixing signals and the transmission signals present an oscillatory behavior with a clear dependence on the power of the incident fields, which indicates a connection with Rabi oscillations. A two-level theoretical model using stochastic differential equations to account for the mechanism of conversion of phase noise into amplitude noise shows good agreement with our experimental results. Moreover, we show how the response of the system is affected by the different atomic velocity groups.
We investigate the influence of the distribution of atom velocities in a hot rubidium sample on the correlation between field-intensity fluctuations of two independently generated four-wave mixing signals and between the transmission signals. The nonlinear process is driven by a single continuous-wave (cw) laser in a pure two-level system due to the forward geometry with circular and parallel polarization of the input fields. The intensity cross correlations of the four-wave mixing signals and the transmission signals present an oscillatory behavior with a clear dependence on the power of the incident fields, which indicates a connection with Rabi oscillations. A two-level theoretical model using stochastic differential equations to account for the mechanism of conversion of phase noise into amplitude noise shows good agreement with our experimental results. Moreover, we show how the response of the system is affected by the different atomic velocity groups.
We study the field-intensity fluctuations of two independent four-wave-mixing signals generated in a cold rubidium sample as well as the transmission signals. We employ an experimental setup using a single cw laser to induce the nonlinear process in a forward geometry using either parallel and circular or orthogonal and linear polarizations of the input fields. Even though the spectra of each experimental configuration are significantly different due to the distinct level structures of each scenario, both cases present intensity-intensity cross correlations of the four-wave-mixing signals. We also calculate the cross correlation between the input fields and draft a theoretical model that indicates that resonant phase-noise to amplitude-noise conversion allows the observation of Rabi oscillations in the cross-correlation curves.
In this work, we present a set of experiments involving four-wave mixing processes in rubidium atoms. We employ several experimental configurations exploring two- and three-level systems in cascade or Λ configurations, all of which are in a copropagating geometry, to investigate different physical phenomena present in each scenario. In the first experiment, we combine a cw diode laser and a 1 GHz femtosecond pulse train to generate coherent blue light through the four-wave mixing process in hot rubidium vapor. The generated coherent signal is analyzed by scanning either the diode frequency or the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler- Townes splitting with a wide separation in the doublet structure due to the configuration of copropagating fields. To model these results, we employ the density matrix formalism to write the Bloch equations and solve them numerically. The solutions allow us to explore other cases beyond those involving our experimental setup, comparing the response of the upper-level population and the generated signal coherence for homogeneously and non-homogeneously broadened systems. Moreover, in this same experiment, we also observed an unexpected interference effect between excitation routes of the four-wave mixing process when the repetition rate of the pulse train is scanned. The theoretical model demonstrates that the interfering effect appears only when the repetition rate is carefully chosen to produce a pair of modes of the frequency comb resonant with both one- and two-photon transitions for the same atomic velocity group. In the second experiment, still with a hot rubidium vapor, we explore two symmetrical degenerate four- wave mixing signals induced by two almost copropagating laser beams, with~ka and~kb wave-vectors, and detected simultaneously in the 2~ka −~kb and 2~kb −~ka directions. Each spectrum has a single peak with a short frequency separation between them, which our model indicates is due to the nonlinear behavior of the refractive indexes, a consequence of the high intensity of both input fields. Finally, we use the same experimental setup for the two symmetrical signals to study the field intensity fluctuations of the degenerate four-wave mixing signals and the transmission signals. In this case, the sample is an ensemble of cold rubidium atoms in a magneto-optical trap. There is an intensity- intensity cross-correlation between the signals due to the resonant phase-noise to amplitude-noise conversion. In this type of cold system, we can neglect the Doppler- broadening, allowing a straightforward study of the dependency of the correlations on the laser detuning. In these measurements, we observe a type of oscillation in the correlation curves that the theoretical model indicates to be connected with Rabi oscillations, revealed by the fluctuations long after the transient period.
We extend the study on a four-wave mixing (FWM) scheme of contiuous-wave lasers in a hot rubidium vapor when the probe and coupling fields work in the electromagnetically induced transparency (EIT) regime while the pump and signal fields work in the two-photon Raman regime. Our experimental results show that the generated signal field is well contained in an EIT dip of the incident probe field as a result of efficient FWM. We find, in particular, that an optimal FWM process can only be attained when the coupling and pump fields are well matched in intensity. If the probe intensity is far beyond the EIT condition, however, the nonlinear efficiency of energy transfer from the probe field to the signal field will be greatly reduced.
In this work we describe an experimental investigation on the spatial intensity distribution of the two transmitted beams and the two beams generated in a four-wave mixing (FWM) process, using rubidium vapor as a nonlinear medium. The two FWM signals are detected in the 2⃗kF − ⃗kP and 2⃗kP − ⃗kF directions, where ⃗kF and ⃗kP are the incident beam directions. A diode laser, responsible by the two Ąelds that driven the FWM process, is tuned to the 5S1⇑2(F ≙ 3) Ð→ 5P3⇑2 of the 85Rb. The images of the four beams are obtained using a CMOS camera for a Ąxed atomic density and a Ąxed frequency of the input beams. From each image we can determine the spatial distribution of the intensity of the respective beam. We analyzed the spatial intensity distribution of the signals, as well as the spatial intensity Ćuctuation. The spatial intensity distribution of the transmitted beams shows a decrease of the beam waist for intensities close to the saturation intensity, while for high intensities the spatial proĄle is almost constant. This behavior indicates an autofocusing effect, related to the variation of the refractive index of the medium. The spatial distribution of the intensity Ćuctuation is obtained considering an average surface for each image, and is used to calculate the autocorrelation of the transmitted beams and the two generated FWM beams. Working with the intensity Ćuctuation, we can deĄne a transverse spatial correlation length, which is used to compare the behavior of the four beams with that of a free beam. In this sense, the autocorrelations of intensity Ćuctuations of the transmitted beams show a decrease in the correlation length in the same region of intensities where we observe the self-focusing effect, and as we increase the intensity, the correlation length approaches the value obtained for the free beam. On the other hand, the correlation length for the autocorrelations of the signals generated by FWM increases as the intensity of the incident beams increases.
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)].