In this paper, we investigated the coherent degenerate and nondegenerate four-wave interaction in the propagation of a femtosecond laser pulse in atomic rubidium vapor. In the case of degenerate four-wave interaction, the mechanism for optical switching in an optically dense resonant medium is considered. The third-order nonlinear interaction of the laser beams intersecting in the cell at a small angle leads to a nonlinear response in the form of a fourth beam, which occurs as a result of the interaction between the two pump beams and the third signal laser beam.
In this paper, we investigated the coherent degenerate and nondegenerate four-wave interaction in the propagation of a femtosecond laser pulse in atomic rubidium vapor. In the case of degenerate four-wave interaction, the mechanism for optical switching in an optically dense resonant medium is considered. The third-order nonlinear interaction of the laser beams intersecting in the cell at a small angle leads to a nonlinear response in the form of a fourth beam, which occurs as a result of the interaction between the two pump beams and the third signal laser beam.
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.
Abstract We report experimental and theoretical results of two symmetrical signals of degenerate four-wave mixing generated in rubidium vapor. Both nonlinear signals are induced by two almost copropagating laser beams, with k ⃗ a and k ⃗ b wave-vectors, and detected simultaneously in the 2 k ⃗ a − k ⃗ b and 2 k ⃗ b − k ⃗ a directions. In each direction, we observe a single peak when the two beams are tuned on the closed transition 85 Rb 5 S 1/2 ( F = 3) → 5 P 3/2 ( F = 4). The excitation spectra reveal a small frequency separation between the two peaks, which is explained when propagation effects are taken into account. Furthermore, our theoretical analysis shows that a correct description of the frequency position of each peak is achieved with a variable refractive index for both lasers, in which the scanning laser experiences an anomalous window in the refractive index near resonance.
Nonlinear optical processes, with a particular emphasis on parametric four-wave mixing (PFWM), are studied in rubidium vapor. A theoretical framework is introduced that enables accurate calculations of nonlinear light-matter interactions, and calculations of these interactions using this framework are performed for a broad range of excitation conditions. In particular, the effects of femtosecond pulse parameters such as pulse duration, pulse energy, center wavelength, and chirp are investigated. Simulation results provide insight into the light-matter interactions in rubidium vapor for these conditions. The effects of pump pulse parameters on the production and evolution of atomic wavepackets in the nonlinear medium are investigated. A number of femtosecond-scale phenomena that were elusive or previously unknown are observed, including the observation of quantum beating at pump-probe time delays exceeding 500 ps, quantum beating on the 7s1/2 - 5d3/2 energy defect at 611 cm-1, and the effects of pump pulse chirp on the amplitude and temporal dynamics of quantum beating. Toward the goal of using the nonlinear optical process of PFWM to interrogate the nearest neighbor distribution (NND), a new analytical derivation for the NND in the non-interacting particle approximation is presented, along with the results of molecular dynamics simulations of the NND in rubidium vapor for realistic pair interaction potentials.
We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}krL\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}kr is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}krb\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.
We show that four-wave mixing in optically dense media is very different than in an optically thin medium. In time-resolved degenerate four-wave mixing we experimentally observe ``negative'' time delay response, fast decay rates at short delay times, and broad shoulders at long delays. The observations are explained very well in terms of pulse propagation effects, and a theoretical framework is presented for the analysis of the nonlinear interaction. We treat both the incident and generated fields self-consistently, and solve for the interaction of short pulses with a resonantly absorbing medium. The implications for the extraction of relaxation rates from four-wave-mixing experiments involving ultrashort pulses in optically dense matter are discussed.
We present experimental observations of phase-conjugate degenerate four-wave mixing in a two-level atomic system (the ${3s}^{2}{S}_{1/2}, F=2, {m}_{F}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2}, F=3, {m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of atomic sodium) driven by cw, narrow-band $(\ensuremath{\sim}250 \mathrm{kHz}),$ stabilized pump and probe fields. The primary measurements that we report are of the peak signal strength of the four-wave-mixing interaction and the bandwidth of the four-wave-mixing spectrum (as the laser frequency is tuned through the resonant frequency) as a function of the intensity of the pump field. We compare these measurements with the predictions of a theoretical analysis in which extension to include the effect of the small transverse velocity $(\ensuremath{\sim}3 \mathrm{m}/\mathrm{s}\mathrm{e}\mathrm{c})$ of the atomic beam is critical. These measurements provide a direct verification of the theory of this important nonlinear interaction.