Two-photon Fourier spectroscopy with femtosecond light pulses

Improving Spectral, Spatial, and Mechanistic Resolution Using Fourier Transform Nonlinear Optics: A Tutorial Review

Fourier transform nonlinear optics (FT-NLO) is a powerful experimental physical chemistry tool that provides insightful spectroscopic and imaging data. FT-NLO has revealed key steps in both intramolecular and intermolecular energy flow. Using phase-stabilized pulse sequences, FT-NLO is employed to resolve coherence dynamics in molecules and nanoparticle colloids. Recent advances in time-domain NLO interferometry using collinear beam geometries makes determination of molecular and material linear and nonlinear excitation spectra, homogeneous line width, and nonlinear excitation pathways straightforward. When combined with optical microscopy, rapid acquisition of hyperspectral images with the information content of FT-NLO spectroscopy is possible. With FT-NLO microscopy, molecules and nanoparticles colocated within the optical diffraction limit can be distinguished based on their excitation spectra. The suitability of certain nonlinear signals for statistical localization present exciting prospects for using FT-NLO to visualize energy flow on chemically relevant length scales. In this tutorial review, descriptions of FT-NLO experimental implementations are provided along with theoretical formalisms for obtaining spectral information from time-domain data. Select case studies that illustrate the use of FT-NLO are presented. Finally, strategies for extending super-resolution imaging capabilities based on polarization-selective spectroscopy are offered.

Achieving sub-diffraction spatial resolution using combined Fourier transform spectroscopy and nonlinear optical microscopy

Fourier transform nonlinear optical microscopy is used to perform nonlinear spectroscopy of single gold nanorods in an imaging platform, which enables sub-diffraction spatial resolution. The nonlinear optical signal is detected as a function of the time delay between two phase-locked pulses, forming an interferogram that can be used to retrieve the resonant response of the nanoparticles. Detection of the nonlinear signal through a microscopy platform enables wide-field hyperspectral imaging of the longitudinal plasmon resonances in individual gold nanorods. Super-resolution capabilities are demonstrated by distinguishing multiple nanorods that are co-located within the optical diffraction limit and are spatially separated by only tens of nanometers. The positions and resonance energies obtained through Fourier transform nonlinear optical microscopy agree with the relative positions and aspect ratios deduced from electron microscopy.

Phase-modulated electronic wave packet interferometry reveals high resolution spectra of free Rb atoms and Rb*He molecules

Phase-modulated wave packet interferometry is combined with mass-resolved photoion detection to investigate rubidium atoms attached to helium nanodroplets in a molecular beam experiment. The spectra of atomic Rb electronic states show a vastly enhanced sensitivity and spectral resolution when compared to conventional pump-probe wave packet interferometry. Furthermore, the formation of Rb*He exciplex molecules is probed and for the first time a fully resolved vibrational spectrum for transitions between the lowest excited 5Π3/2 and the high-lying electronic states 2(2)Π, 4(2)Δ, 6(2)Σ is obtained and compared to theory. The feasibility of applying coherent multidimensional spectroscopy to dilute cold gas phase samples is demonstrated in these experiments.

Quantum focusing and coherent control of nonresonant two-photon absorption in frequency domain

We theoretically investigate the nonresonant two-photon absorption (TPA) process in a two-level atom induced by a weak chirped pulse in the frequency domain. According to the extremum condition of the two-photon transition probability (TPTP) at the transition center frequency, we propose a Fresnel-inspired pulse tailoring scheme for TPA that is significantly different from that of Broers et al. [Phys. Rev. A46, 2749 (1992)]. Using this scheme, the TPTP can be focused or eliminated completely by constructively or destructively modulating various pathways of the quantum interference. Our results are a significant improvement on those obtained by Broers et al. and will have potential applications in selective two-photon microscopy and spectroscopy.

Temporal coherent control of superfluorescent pulses

We demonstrate that collective atomic interferences can be investigated by measuring the superfluorescence (SF) time delay. A pair of broadband (≈20  nm), ultrashort (≈80  fs), collinear pulses with a variable delay coherently excites rubidium (Rb) atoms. The generated superfluorescent pulses at 420 nm on the cascade transition are recorded by a picosecond streak camera. Both intensity and SF time delay of the 420 nm pulse are altered as the delay between input pulses varies. In particular, the SF time delay of the normalized 420 nm pulse exhibits oscillations with different periods. This can be understood in terms of atomic and quantum interferences due to two possible two-photon excitation pathways through the intermediate levels (Rb D-lines).

Method for high-resolution frequency measurements in the extreme ultraviolet regime: random-sampling Ramsey spectroscopy

Ramsey-like schemes have been recently introduced in combination with high-order laser harmonic sources for high-resolution spectroscopic studies in the extreme ultraviolet (XUV). Here we demonstrate a novel method, combining measurements only in a limited subset of randomly chosen time-sampling intervals, which lead us to perform the first high-resolution XUV spectroscopy of atomic argon with a simple split-pulse setup. Providing an experimentally simple and convenient solution to the problem of performing high-resolution absolute frequency measurements in the XUV, our approach will help paving new roads into this challenging spectral territory.

Tracking autoionizing-wave-packet dynamics at the 1-fs temporal scale

We present time-resolved studies and Fourier transform spectroscopy of inner-shell excited states undergoing Auger decay and doubly excited autoionizing states, utilizing coherent extreme-ultraviolet (XUV) radiation continua. Series of states spanning a range of ∼4  eV are excited simultaneously. An XUV probe pulse tracks the oscillatory and decaying evolution of the formed wave packet. The Fourier transform of the measured trace reproduces the spectrum of the series. The present work paves the way for ultrabroadband XUV spectroscopy and studies of ultrafast dynamics in all states of matter.

Measurement of two-photon excitation spectra of fluorescent proteins with nonlinear Fourier-transform spectroscopy

We present measurements of two-photon excitation (TPE) spectra of various fluorescent proteins with nonlinear Fourier-transform spectroscopy. By using an ultrabroadband laser pulse with a spectrum ranging from 700 to 1100 nm, the absolute TPE spectra of six typical fluorescent proteins (SeBFP, Sapphire, eGFP, eCFP, Venus, DsRed) were measured with high spectral resolution.

Ramsey spectroscopy of bound atomic states with extreme-ultraviolet laser harmonics

We report the experimental measurement of Ramsey interference fringes in the single-photon excitation to a high-lying bound state of atomic argon by pairs of phase-locked, time-delayed, extreme UV high-order-harmonic pulses at 87 nm. High-visibility Ramsey fringes are observed for delays larger than 100 ps, thus demonstrating a potential resolving power >10(5) at this wavelength.

Quantitative differentiation of dyes with overlapping one-photon spectra by femtosecond pulse shaping

We demonstrate that DiI and Rhodamine B, which are not easily distinguishable to one-photon measurements, can be differentiated and in fact quantified in mixture via tailored two-photon excitation pulses found by a genetic algorithm (GA). A nearly three-fold difference in the ratio of two-photon fluorescence of the two dyes is achieved, without a drop in signal of the favored fluorophore. Implementing an acousto-optic interferometer, we were able to prove that the mechanism of discrimination is second-harmonic tuning by the phase-shaped pulses to the relative maxima and minima of these cross-sections.

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Quantum interference spectroscopy of rubidium-helium exciplexes formed on helium nanodroplets

Femtosecond multiphoton pump-probe photoionization is applied to helium nanodroplets doped with rubidium (Rb). The yield of Rb+ ions features pronounced quantum interference (QI) fringes demonstrating the coherence of a superposition of electronic states on a time scale of tens of picoseconds. Furthermore, we observe QI in the yield of formed RbHe exciplex molecules. The quantum interferogram allows us to determine the vibrational structure of these unstable molecules. From a sliced Fourier analysis one cannot only extract the population dynamics of vibrational states but also follow their energetic evolution during the RbHe formation.

Development of ultrahigh-precision coherent control and its applications

Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.

Real-time observation of phase-controlled molecular wave-packet interference

The quantum interference of two molecular wave packets has been precisely controlled in the B electronic state of the I2 molecule by using a pair of fs laser pulses whose relative phase is locked within the attosecond time scale and its real-time evolution has been observed by another fs laser pulse. It is clearly observed that the temporal evolution changes drastically as a function of the relative phase between the locked pulses, allowing us to read both amplitude and phase information stored in the wave functions of the molecular ensemble.

Fourier transform measurement of two-photon excitation spectra: applications to microscopy and optimal control

We report a novel Fourier transform method for measuring two-photon excitation spectra. We demonstrate this method using simple dye molecules and discuss its applications in two-photon fluorescence microscopy and optimal control. This method facilitates an intuitive interpretation of recent control experiments in terms of tuning the nonlinear spectrum of the exciting laser source.

Deep-Ultraviolet Quantum Interference Metrology with Ultrashort Laser Pulses

Precision spectroscopy at ultraviolet and shorter wavelengths has been hindered by the poor access of narrow-band lasers to that spectral region. We demonstrate high-accuracy quantum interference metrology on atomic transitions with the use of an amplified train of phase-controlled pulses from a femtosecond frequency comb laser. The peak power of these pulses allows for efficient harmonic upconversion, paving the way for extension of frequency comb metrology in atoms and ions to the extreme ultraviolet and soft x-ray spectral regions. A proof-of-principle experiment was performed on a deep-ultraviolet (2 x 212.55 nanometers) two-photon transition in krypton; relative to measurement with single nanosecond laser pulses, the accuracy of the absolute transition frequency and isotope shifts was improved by more than an order of magnitude.

High-precision molecular wave-packet interferometry with HgAr dimers

Molecular wave-packet (WP) interferometry has been demonstrated in the A electronic state of the HgAr van der Waals complex with two time-delayed UV fs pulses at 254 nm. The interferograms of three vibrational levels in the WP's display almost 100% fringe contrast as a function of the interpulse delay tau, which is tuned with sub-10 as stability and resolution. It is clearly observed that the three interferograms show their dephasing and rephasing within a single vibrational period, allowing us to prepare arbitrary relative populations of the three levels by adjusting a single parameter tau.

Laser characterization of ultrasonic wave propagation in random media

Lasers can be used to excite and detect ultrasonic waves in a wide variety of materials. This allows the measurement of absolute particle motion without the mechanical disturbances of contacting transducers. In an ultrasound transmission experiment, the wave field is usually accessible only on the boundaries of a sample. Using optical methods, one can measure the surface wave field, in effect, within the scattering region. Here, we describe noncontacting (laser source and detector) measurements of ultrasonic wave propagation in randomly heterogeneous rock samples. By scanning the surface of the sample, we can directly visualize the complex dynamics of diffraction, multiple scattering, mode conversion, and whispering gallery modes. We will show measurements on rock samples that have similar elastic moduli and intrinsic attenuation, but different grain sizes, and hence, different scattering strengths. The intensity data are well fit by a radiative transfer model, and we use this fact to infer the scattering mean free path.

Two-dimensional femtosecond spectroscopy

The simplest two-dimensional (2D) spectra show how excitation with one (variable) frequency affects the spectrum at all other frequencies, thus revealing the molecular connections between transitions. Femtosecond 2D Fourier transform (2D FT) spectra are more flexible and share some of the remarkable properties of their conceptual parent, 2D FT nuclear magnetic resonance. When 2D FT spectra are experimentally separated into real absorptive and imaginary refractive parts, the time resolution and frequency resolution can both reach the uncertainty limit set for each resonance by the sample itself. Coherent four-level contributions to the signal provide new molecular phase information, such as relative signs of transition dipoles. The nonlinear response can be picked apart by selecting a single coherence pathway (e.g., specifying the relative signs of energy level difference frequencies during different time intervals as in the photon echo). Because molecules are frozen on the femtosecond timescale, femtosecond 2D FT experiments can separate a distribution of instantaneous molecular environments and intramolecular geometries as inhomogeneous broadening. This review provides an introduction to two-dimensional Fourier transform experiments exploiting second- and third-order vibrational and electronic nonlinearities.

Ramsey-type spectroscopy with high-order harmonics

We present an experiment where Ramsey-type spectroscopy is applied to autoionizing states of krypton by using the ninth harmonic (88 nm) of a femtosecond Ti:sapphire laser. The ionization process, detected by an electron-energy spectrometer, shows the characteristic quantum interference pattern. The behavior of the fringe contrast compares favorably with a simple essential-state model, whose parameters have been taken from the literature. The experiment shows the feasibility of high-resolution spectroscopy in the extreme ultraviolet by using high-order laser harmonics.

Phase-locked, time-delayed harmonic pulses for high spectral resolution in the extreme ultraviolet

We present experiments in the time and frequency domains aimed at confirming the measured mutual phase coherence of time-delayed, collinear harmonic pulses. We show that pairs of phase-locked harmonic pulses of medium order can be generated for peak intensities up to ~1.5 10(14)W/cm(2) in xenon, demonstrating the possibility of performing high-resolution spectroscopy in the extreme ultraviolet with Ramsey-like techniques.

Fourier-transform sum-frequency surface vibrational spectroscopy with femtosecond pulses

We present a Fourier-transform spectroscopic technique for investigation of surfaces and interfaces based on IR-visible sum-frequency generation with femtosecond light pulses. The observed spectrum has a resolution that is independent of the input pulse characteristics.