Unlike spontaneous Raman effect, nonlinear Raman scattering generates fields with a well-defined phase, allowing Raman signals from individual scatterers to add up into a highly directional, high-brightness coherent beam. Here, we show that the phase of coherent Raman scattering can be accurately controlled and finely tuned by using spectrally and temporally tailored optical driver fields. In our experiments, performed with spectrally optimized phase-tunable laser pulses, such a phase control is visualized through the interference of the coherent Raman signal with the field resulting from nonresonant four-wave mixing. This interference gives rise to Fano-type profiles in the overall nonlinear response measured as a function of the delay time between the laser pulses, featuring a well-resolved destructive-interference dip on the dark side of the Raman peak. This phase-control strategy is shown to radically enhance the coherent response from weak Raman modes, thus helping confront long-standing challenges in nonlinear Raman imaging and microspectroscopy.
Unlike spontaneous Raman effect, nonlinear Raman scattering generates fields with a well-defined phase, allowing Raman signals from individual scatterers to add up into a highly directional, high-brightness coherent beam. Here, we show that the phase of coherent Raman scattering can be accurately controlled and finely tuned by using spectrally and temporally tailored optical driver fields. In our experiments, performed with spectrally optimized phase-tunable laser pulses, such a phase control is visualized through the interference of the coherent Raman signal with the field resulting from nonresonant four-wave mixing. This interference gives rise to Fano-type profiles in the overall nonlinear response measured as a function of the delay time between the laser pulses, featuring a well-resolved destructive-interference dip on the dark side of the Raman peak. This phase-control strategy is shown to radically enhance the coherent response from weak Raman modes, thus helping confront long-standing challenges in nonlinear Raman imaging and microspectroscopy.
A model of two-level weakly interacting quantum systems is used to demonstrate that the phase of molecular vibrations excited through stimulated Raman scattering can be controlled by the relative phase of time-separated laser pulses, allowing synchronization and amplitude control of coherence excitation in a medium. For transients with a phase relaxation time less than the field cycle, the field half-cycle can serve as a subfemtosecond probe of coherent vibrations. In this regime, the high-frequency field-induced modulation of molecular dipole moments gives rise to a detectable modulation of the optical response of a medium at the frequency $2\ensuremath{\omega}$, $\ensuremath{\omega}$ being the frequency of the laser field.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
Recent adaptive feedback control experiments demonstrated control of transient (i.e. nonimpulsive) Stokes emission from two closely spaced Raman-active modes in liquid methanol [e.g., B. J. Pearson et al., Phys. Rev. A 63, 063412 (2001)]. Optimally shaped pulses were found that selectively excited one of the two Stokes lines alone, optimized emission from both modes together, or completely suppressed all Stokes emission. Here, two general control mechanisms capable of affecting the ratio of intensities of the Stokes lines are identified. The first is operational when the duration of the pump pulse (tp) is on the order of the collisional dephasing time (td). The ratio of the peak heights of the two Stokes lines can then be controlled by simply varying the duration and/or intensity of the pump pulse. The second operates when 1∕tp is on the order of the energy separation of the two Raman modes, and hence when the two Raman modes are coupled due to overlapping nonlinear polarizations that drive the stimulated Raman scattering. In this regime, asymmetry in the spectral amplitudes within the pump pulse can control the asymmetry in the peak heights of the Stokes emission. Both these mechanisms have the same clear physical interpretation: shaping the pump pulse controls the nonlinear optical response of the medium, which in turn controls the stimulated Stokes emission, itself a ${\ensuremath{\chi}}^{(3)}$ nonlinear effect. In neither mechanism does the ratio of peak heights in the Stokes spectrum reflect directly the ratio of excited-state populations associated with the two Raman modes, as was assumed in the experiments, nor does the control involve coherent quantum interference effects.
Phase-and-polarization coherent control is applied to control the nonlinear response of a quantum system. We use it to obtain high-resolution background-free single-pulse coherent anti-Stokes Raman spectra. The ability to control both the spectral phase and the spectral polarization enables measurement of a specific off-diagonal susceptibility tensor element while exploiting the different spectral response of the resonant Raman signal and the nonresonant background to achieve maximal background suppression.
The possibility to manipulate quantum coherence and interference, apart from its fundamental interest in quantum mechanics, is essential for controlling nonlinear optical processes such as high harmonic generation, multiphoton absorption, and stimulated Raman scattering. We show, analytically and numerically, how a nonlinear optical process via resonance Raman scattering (RRS) can be manipulated in a four-level double-Λ system by using pulsed laser fields. We find that two simultaneously excited RRS paths involved in the system can generate an ultimately destructive interference in the broad-bandwidth-limit regime. This, in turn, reduces the four-level system to an equivalent three-level system in a V configuration capable of naturally vanishing RRS effects. We further show that this counterintuitive phenomenon, i.e., the RRS vanishing, can be prevented by transferring a modulated phase of the laser pulse to the system at resonance frequencies. This work demonstrates a clear signature of both quantum destructive and constructive interference by actively controlling resonant multiphoton processes in multilevel quantum systems, and it therefore has potential applications in nonlinear optics, quantum control, and quantum information science.
In this thesis, atomic coherence is used to enhance nonlinear optical processes in multi-level atoms. The multi-photon transitions are driven resonantly, and at the same time without absorptive losses, by using electromagnetically induced transparency (EIT), thereby allowing the study of χ(3) and χ(5) nonlinearities using weak driving fields. The coherently modified probe beam(s) and the atom-radiated signal fields arising from four- and six- wave- mixing (FWM and SWM) processes are measured in the spectral, temporal and spatial domains. In a three-level ladder-type atomic system, multiple peaks having spectral asymmetries are observed in the EIT window as well as in the FWM signal waveforms due to the diverse multiplicities of the participating atomic states. Using phase control tailored in the frequency domain, we demonstrate all-optical methods to control these spectral waveforms and discuss applications involving waveform-shaping and metrology. For the EIT study we demonstrate a switching of multiple dark peaks into bright peaks via phase-control of interferences in the underlying dark-states. In the FWM study we demonstrate all-optical spectral line shape symmetrization, linewidth narrowing and bandwidth switching. In a four-level inverted-Y-type atomic system, we drive and measure coexisting and phase-matched FWM and SWM signals. By using precision control of the relative phase and amplitude between these two processes of different nonlinear orders, we demonstrate phase coherence between them. First, a single-phase measurement is performed in the temporal and spatial domains, and the interferogram is used to measure the resonant frequency of the 5D5/2-5P3/2 atomic transition in 85Rb. Second, the method is extended to realize a capacity for two-phase measurement. In this case, the spectral bandwidth of the signal is modified in order to measure the phase-shift occurring in one Mach-Zehnder interferometer, while the intensity of the total signal waveform measures the phase-shift occurring in a second interferometer. Finally, we demonstrate phase-dependent spatial fusion between two ultra-weak optical fields by using a strong coupling field to first convert the weak fields into bosonic dark-state polaritons, which are then steered into a common all-optical waveguide mode arising due to the coupling field's intensity distribution and the resulting cross-Kerr refractive index gradient.