Coherent Nonlinear Spectroscopy Research Articles

Controlled coherent-coupling and dynamics of exciton complexes in a MoSe2 monolayer

Quantifying and controlling the coherent dynamics and couplings of optically active excitations in solids is of paramount importance in fundamental research in condensed matter optics and for their prospective optoelectronic applications in quantum technologies. Here, we perform ultrafast coherent nonlinear spectroscopy of a charge-tunable MoSe2 monolayer. The experiments show that the homogeneous and inhomogeneous line width and the population decay of exciton complexes hosted by this material can be directly tuned by an applied gate bias, which governs the Fermi level and therefore the free carrier density. By performing two-dimensional spectroscopy, we also show that the same bias-tuning approach permits us to control the coherent coupling strength between charged and neutral exciton complexes.

Ab initio simulation of laser-induced electronic and vibrational coherence

The atomistic resolution recently achieved by ultrafast spectroscopies demands corresponding theoretical advances. Real-time time-dependent density-functional theory (RT-TDDFT) with Ehrenfest dynamics offers an optimal trade-off between accuracy and computational costs to study electronic and vibrational dynamics of laser-excited materials in the sub-picosecond regime. However, this approach is unable to account for thermal effects or zero-point energies which are crucial in the physics involved. Herein, we adopt a quantum-semiclassical method based on RT-TDDFT+Ehrenfest to simulate laser-induced electronic and vibrational coherences in condensed matter. With the example of carbon-conjugated molecules, we show that ensemble-averaging with initial configurations from a nuclear quantum distribution remedies many shortcomings of single-trajectory RT-TDDFT+Ehrenfest, damping electronic coherence and introducing ultrafast non-adiabatic coupling between excited states. As the number of sampled configurations decreases with size and rigidity of the compounds, computational costs remain moderate for large systems for which mean-field approaches shine. The explicit inclusion of a time-dependent pulse in the simulations makes this method a prime advance for first-principles studies of coherent nonlinear spectroscopy as an independent counterpart to experimental results.

High-gain harmonic generation with temporally overlapping seed pulses and application to ultrafast spectroscopy.

Collinear double-pulse seeding of the High-Gain Harmonic Generation (HGHG) process in a free-electron laser (FEL) is a promising approach to facilitate various coherent nonlinear spectroscopy schemes in the extreme ultraviolet (XUV) spectral range. However, in collinear arrangements using a single nonlinear medium, temporally overlapping seed pulses may introduce nonlinear mixing signals that compromise the experiment at short time delays. Here, we investigate these effects in detail by extending the analysis described in a recent publication (Wituschek et al., Nat. Commun., 11, 883, 2020). High-order fringe-resolved autocorrelation and wave packet interferometry experiments at photon energies > 23 eV are performed, accompanied by numerical simulations. It turns out that both the autocorrelation and the wave-packet interferometry data are very sensitive to saturation effects and can thus be used to characterize saturation in the HGHG process. Our results further imply that time-resolved spectroscopy experiments are feasible even for time delays smaller than the seed pulse duration.

Phase cycling of extreme ultraviolet pulse sequences generated in rare gases

The development of schemes for coherent nonlinear time-domain spectroscopy in the extreme-ultraviolet regime (XUV) has so far been impeded by experimental difficulties that arise at these short wavelengths. In this work we present a novel experimental approach, which facilitates the timing control and phase cycling of XUV pulse sequences produced by harmonic generation in rare gases. The method is demonstrated for the generation and high spectral resolution characterization of narrow-bandwidth harmonics (≈14 eV) in argon and krypton. Our technique simultaneously provides high phase stability and a pathway-selective detection scheme for nonlinear signals—both necessary prerequisites for all types of coherent nonlinear spectroscopy.

Coherent dynamics and mapping of excitons in single-layer MoSe2 and WSe2 at the homogeneous limit

We perform coherent nonlinear spectroscopy of excitons in single-layers of MoSe$_2$ and WSe$_2$ encapsulated between thin films of hexagonal boron nitride. Employing four-wave mixing microscopy we identify virtually disorder free areas, generating exciton optical response at the homogeneous limit. Focussing on such areas, we measure exciton homogeneous broadening as a function of environmental factors, namely temperature and exciton density. Exploiting FWM imaging, we find that at such locations, nonlinear absorption of the exciton excited states and their coherent couplings can be observed. Using the WSe$_2$ heterostructure, we infer coherence and density dynamics of the exciton 2S state. Owing to its increased radiative lifetime, at low temperatures, the dephasing of the 2S state is longer than of the 1S transition. While scanning various heterostructures across tens of micrometers, we conclude that the disorder, principally induced by strain variations, remain to be present creating spatially varying inhomogeneous broadening.

Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses

The recent development of ultrafast extreme ultraviolet (XUV) coherent light sources bears great potential for a better understanding of the structure and dynamics of matter. Promising routes are advanced coherent control and nonlinear spectroscopy schemes in the XUV energy range, yielding unprecedented spatial and temporal resolution. However, their implementation has been hampered by the experimental challenge of generating XUV pulse sequences with precisely controlled timing and phase properties. In particular, direct control and manipulation of the phase of individual pulses within an XUV pulse sequence opens exciting possibilities for coherent control and multidimensional spectroscopy, but has not been accomplished. Here, we overcome these constraints in a highly time-stabilized and phase-modulated XUV-pump, XUV-probe experiment, which directly probes the evolution and dephasing of an inner subshell electronic coherence. This approach, avoiding any XUV optics for direct pulse manipulation, opens up extensive applications of advanced nonlinear optics and spectroscopy at XUV wavelengths.

Enhanced screening and spectral diversity in many-body elastic scattering of excitons in two-dimensional hybrid metal-halide perovskites

In two-dimensional hybrid organic-inorganic metal-halide perovskites, the intrinsic optical lineshape reflects multiple excitons with distinct binding energies, each dressed differently by the hybrid lattice. Given this complexity, a fundamentally far-reaching issue is how Coulomb-mediated many-body interactions --- elastic scattering such as excitation-induced dephasing, inelastic exciton bimolecular scattering, and multi-exciton binding --- depend upon the specific exciton-lattice coupling. We report the intrinsic and density-dependent exciton pure dephasing rates and their dependence on temperature by means of a coherent nonlinear spectroscopy. We find exceptionally strong screening effects on multi-exciton scattering relative to other two-dimensional single-atomic-layer semiconductors. Importantly, the exciton-density dependence of the dephasing rates is markedly different for distinct excitons. These findings establish the consequences of particular lattice dressing on exciton many-body quantum dynamics, which critically define fundamental optical properties that underpin photonics and quantum optoelectronics in relevant exciton density regimes.

Using Coherent Spectroscopy to Determine the Presence of Nanoparticles in Colloidal Solutions

A review is presented of using nonlinear coherent spectroscopy to monitor the state of colloidal solutions of nanoparticles (Ti, Ni, and Ag) employed to improve the performance of supercapacitors, and to determine the effect nanosilver has on the hepatitis C virus. Examples of the spectra of a colloidal silver solution in two phase states (nanosilver and silver in the finely dispersed phase) are given.

Stable interferometric platform for phase modulation of seeded free-electron lasers.

We present a compact phase modulation setup designed for high laser intensities sufficient to drive highly nonlinear processes, such as high-gain harmonic generation in seeded free-electron lasers. This paves the way for all-extreme-ultravioloet coherent nonlinear spectroscopy. The high linearity, phase stability, and sensitivity of the setup are demonstrated by probing the quantum interference of electronic wave packets in the deep ultraviolet region (268nm) combined with photoion time-of-flight mass spectrometry.

Tri-comb spectroscopy

Multi-dimensional coherent spectroscopy (MDCS)1,2 is a powerful method for optical spectroscopy that has become an important tool for studying ultrafast dynamics in a wide range of systems. It is an optical analog of multidimensional nuclear magnetic resonance spectroscopy that enables the measurement of homogeneous linewidths in inhomogeneously broadened systems, many-body interactions, and coupling between excited resonances, all of which are not simultaneously accessible by any other linear or non-linear method. Current implementations of MDCS require a bulky apparatus and suffer from resolution and acquisition speed limitations that constrain their applications outside the laboratory3-5. Here we propose and demonstrate an approach to nonlinear coherent spectroscopy that utilizes three frequency combs with slightly different repetition rates. Unlike traditional nonlinear methods, tri-comb spectroscopy uses only a single photodetector and no mechanical moving elements to enable faster acquisition times, while also providing comb resolution. As a proof of concept, a multidimensional coherent spectrum with comb cross-diagonal resolution is generated using only 365 ms of data. These improvements make multidimensional coherent spectroscopy relevant for systems with narrow resonances (especially cold atomic and molecular systems). In addition the method has the potential to be field deployable for chemical sensing applications.

Phase-modulated harmonic light spectroscopy.

By combining phase-modulated nonlinear spectroscopy with second harmonic generation, the concept of phase-modulated harmonic light spectroscopy is introduced. Simultaneous spectroscopy with different harmonics of the light is demonstrated and linear and nonlinear excitation of the spectroscopic sample is investigated. Sum frequency generation and stray light effects during temporal pulse overlap have been evaluated in detail, accompanied by simulations. The presented work provides a promising concept to facilitate coherent nonlinear time-domain spectroscopy in the extreme ultraviolet wavelength regime and contributes valuable insights for future studies in this direction.

Harvesting, Coupling, and Control of Single-Exciton Coherences in Photonic Waveguide Antennas.

We perform coherent nonlinear spectroscopy of individual excitons strongly confined in single InAs quantum dots (QDs). The retrieval of their intrinsically weak four-wave mixing (FWM) response is enabled by a one-dimensional dielectric waveguide antenna. Compared to a similar QD embedded in bulk media, the FWM detection sensitivity is enhanced by up to 4 orders of magnitude, over a broad operation bandwidth. Three-beam FWM is employed to investigate coherence and population dynamics within individual QD transitions. We retrieve their homogenous dephasing in a presence of low-frequency spectral wandering. Two-dimensional FWM reveals off-resonant Förster coupling between a pair of distinct QDs embedded in the antenna. We also detect a higher order QD nonlinearity (six-wave mixing) and use it to coherently control the FWM transient. Waveguide antennas enable us to conceive multicolor coherent manipulation schemes of individual emitters.

Few-photon coherent nonlinear optics with a single molecule

The pioneering experiments of linear spectroscopy were performed using flames in the 1800s, but nonlinear optical measurements had to wait until lasers became available in the twentieth century. Because the nonlinear cross section of materials is very small, usually macroscopic bulk samples and pulsed lasers are used. Numerous efforts have explored coherent nonlinear signal generation from individual nanoparticles or small atomic ensembles with millions of atoms. Experiments on a single semiconductor quantum dot have also been reported, albeit with a very small yield. Here, we report on coherent nonlinear spectroscopy of a single molecule under continuous-wave single-pass illumination, where efficient photon-molecule coupling in a tight focus allows switching of a laser beam by less than a handful of pump photons nearly resonant with the sharp molecular transition. Aside from their fundamental importance, our results emphasize the potential of organic molecules for applications such as quantum information processing, which require strong nonlinearities.

Frequency comb transferred by surface plasmon resonance

Frequency combs, millions of narrow-linewidth optical modes referenced to an atomic clock, have shown remarkable potential in time/frequency metrology, atomic/molecular spectroscopy and precision LIDARs. Applications have extended to coherent nonlinear Raman spectroscopy of molecules and quantum metrology for entangled atomic qubits. Frequency combs will create novel possibilities in nano-photonics and plasmonics; however, its interrelation with surface plasmons is unexplored despite the important role that plasmonics plays in nonlinear spectroscopy and quantum optics through the manipulation of light on a subwavelength scale. Here, we demonstrate that a frequency comb can be transformed to a plasmonic comb in plasmonic nanostructures and reverted to the original frequency comb without noticeable degradation of <6.51 × 10−19 in absolute position, 2.92 × 10−19 in stability and 1 Hz in linewidth. The results indicate that the superior performance of a well-defined frequency comb can be applied to nanoplasmonic spectroscopy, quantum metrology and subwavelength photonic circuits.

Stimulated X-ray Raman scattering - a critical assessment of the building block of nonlinear X-ray spectroscopy.

With the invention of femtosecond X-ray free-electron lasers (XFELs), studies of light-induced chemical reaction dynamics and structural dynamics reach a new era, allowing for time-resolved X-ray diffraction and spectroscopy. To ultimately probe coherent electron and nuclear dynamics on their natural time and length scales, coherent nonlinear X-ray spectroscopy schemes have been proposed. In this contribution, we want to critically assess the experimental realisation of nonlinear X-ray spectroscopy at current-day XFEL sources, by presenting first experimental attempts to demonstrate stimulated resonant X-ray Raman scattering in molecular gas targets.

Information processing in parallel through directionally resolved molecular polarization components in coherent multidimensional spectroscopy.

We propose that information processing can be implemented by measuring the directional components of the macroscopic polarization of an ensemble of molecules subject to a sequence of laser pulses. We describe the logic operation theoretically and demonstrate it by simulations. The measurement of integrated stimulated emission in different phase matching spatial directions provides a logic decomposition of a function that is the discrete analog of an integral transform. The logic operation is reversible and all the possible outputs are computed in parallel for all sets of possible multivalued inputs. The number of logic variables of the function is the number of laser pulses used in sequence. The logic function that is computed depends on the chosen chromophoric molecular complex and on its interactions with the solvent and on the two time intervals between the three pulses and the pulse strengths and polarizations. The outputs are the homodyne detected values of the polarization components that are measured in the allowed phase matching macroscopic directions, kl, kl=∑iliki where ki is the propagation direction of the ith pulse and {li} is a set of integers that encodes the multivalued inputs. Parallelism is inherently implemented because all the partial polarizations that define the outputs are processed simultaneously. The outputs, which are read directly on the macroscopic level, can be multivalued because the high dynamical range of partial polarization measurements by nonlinear coherent spectroscopy allows for fine binning of the signals. The outputs are uniquely related to the inputs so that the logic is reversible.

Coherence dynamics and quantum-to-classical crossover in an exciton–cavity system in the quantum strong coupling regime

Interaction between light and matter generates optical nonlinearities, which are particularly pronounced in the quantum strong coupling regime. When a single bosonic mode couples to a single fermionic mode, a Jaynes–Cummings (JC) ladder is formed, which we realize here using cavity photons and quantum dot excitons. We measure and model the coherent anharmonic response of this strongly coupled exciton–cavity system at resonance. Injecting two photons into the cavity, we demonstrate a larger polariton splitting with respect to the vacuum Rabi splitting. This is achieved using coherent nonlinear spectroscopy, specifically four-wave mixing, where the coherence between the ground state and the first (second) rung of the JC ladder can be interrogated for positive (negative) delays. With increasing excitation intensity and thus rising average number of injected photons, we observe spectral signatures of the quantum-to-classical crossover of the strong coupling regime.

Time-symmetric quantum mechanics questioned and defended

The article by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen is stimulating and raises some interesting and profound issues regarding the foundations of quantum mechanics and quantum measurements. One point the authors make is that a measurement of spin component √2‾/2 of a spin-1⁄2 particle is unphysical and can be attributed only to errors in weak measurements performed on a collection of N spins. I offer a more mundane interpretation that does not require the introduction of any error or postselection concepts. The physical, textbook picture of spin-1⁄2 is a vector of length √S(S + 1) = √3‾/2 with some distribution of orientations (that is, polar coordinates θ and φ). A conventional single measurement of Sz can yield only one of the eigenvalues ±1⁄2. This may be interpreted in the classical vector model by envisioning that the spin lies on a cone with θ defined by cosθ = √3‾/3. The expectation value of Sx then vanishes due to the uniform distribution of φ. Having some control over φ can yield a finite value of Sx . Thus I would argue that only an expectation value greater than √3‾/2 is unphysical; a value of √2‾/2 is quite physical and can even be interpreted classically in terms of some distribution of φ and θ.I would phrase the important observation of Aharonov and coauthors in a different way. While spin-1⁄2 has a magnitude of √3‾/2, a fundamental limitation of conventional single-point quantum measurements is that they can yield only the values +1⁄2 and −1⁄2 and any expectation value must therefore lie between those two extremes. Classically, therefore, the spin may not be fully aligned along the z-axis with θ = 0. Such alignment is impossible since it would yield well-defined values of the three noncommuting variables Sz = √3‾/2 and Sx = Sy = 0. However, once multiple time measurements are performed, one can define a reduced distribution of some of the measurements that is conditional on the outcome in the other measurements; such a distribution can be interpreted in terms of Sz greater than 1⁄2 but less than or equal to √3‾/2. That interpretation does not violate any of quantum mechanics’ fundamental rules, which do not usually consider such quantities.Rather than a new, time-symmetric formulation of quantum mechanics that involves pre- and postselection, one can simply treat the scheme of the authors’ figure 1b as a three-point correlation function, whereas figures 2a and 2b show a four-point correlation function, each panel having its own set of conditional probabilities. Error, time reversal, and postselection need not be invoked. Instead, one may think in multiple dimensions and develop the right language for the interpretation of the observables.The combination of pre- and postselection is an attempt to create an artificial ensemble that reproduces the results of multiple-point measurements in a single one-point measurement. As shown by Aharonov and coauthors, that is possible by introducing errors. An alternative physical picture is obtained by retaining the multipoint analysis. Multidimensional thinking is well developed in coherent nonlinear spectroscopy, where a system of spins or optical chromophores are subjected to sequences of short impulsive pulses.11. R. R. Ernst G. Bodenhausen A. Wokaun Principles of Nuclear Magnetic Resonance in One and Two Dimensions Clarendon Press, New York (1978) . , 22. S. Mukamel Annual Review of Physical Chemistry 51 1 691 (2000). https://doi.org/10.1146/annurev.physchem.51.1.691 ; Physical Review A 61 2 21804 (2000). https://doi.org/10.1103/PhysRevA.61.021804 ; Principles of Nonlinear Optical Spectroscopy Oxford U. Press, New York (1995) . Similar ideas may be applied for the interpretation of multiple measurements. One can think of various types of n-point observables obtained by combining n − m perturbations and m measurements. The nonlinear n-point response functions in spectroscopy represent n − 1 impulsive perturbations followed by a single measurement. The objects Aharonov and colleagues considered correspond to n = m. Proper multiple-distribution functions could then be naturally used for the interpretation of such generalized measurements.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. R. Ernst G. Bodenhausen A. Wokaun Principles of Nuclear Magnetic Resonance in One and Two Dimensions Clarendon Press, New York (1978) . Google Scholar2. S. Mukamel Annual Review of Physical Chemistry 51 1 691 (2000). https://doi.org/10.1146/annurev.physchem.51.1.691 ; Google ScholarCrossref, ISI Physical Review A 61 2 21804 (2000). https://doi.org/10.1103/PhysRevA.61.021804 ; , Google ScholarCrossref, ISI Principles of Nonlinear Optical Spectroscopy Oxford U. Press, New York (1995) . , Google Scholar© 2011 American Institute of Physics.

Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system

In spite of their different natures, light and matter can be unified under the strong-coupling regime, yielding superpositions of the two, referred to as dressed states or polaritons. After initially being demonstrated in bulk semiconductors and atomic systems, strong-coupling phenomena have been recently realized in solid-state optical microcavities. Strong coupling is an essential ingredient in the physics spanning from many-body quantum coherence phenomena, such as Bose-Einstein condensation and superfluidity, to cavity quantum electrodynamics. Within cavity quantum electrodynamics, the Jaynes-Cummings model describes the interaction of a single fermionic two-level system with a single bosonic photon mode. For a photon number larger than one, known as quantum strong coupling, a significant anharmonicity is predicted for the ladder-like spectrum of dressed states. For optical transitions in semiconductor nanostructures, first signatures of the quantum strong coupling were recently reported. Here we use advanced coherent nonlinear spectroscopy to explore a strongly coupled exciton-cavity system. We measure and simulate its four-wave mixing response, granting direct access to the coherent dynamics of the first and second rungs of the Jaynes-Cummings ladder. The agreement of the rich experimental evidence with the predictions of the Jaynes-Cummings model is proof of the quantum strong-coupling regime in the investigated solid-state system.

Multidimensional pump-probe spectroscopy with entangled twin-photon states.

We show that entangled photons may be used in coherent multidimensional nonlinear spectroscopy to provide information on matter by scanning photon wave function parameters (entanglement time and delay of twin photons), rather than frequencies and time delays, as is commonly done with classical pulses. Signals are expressed and interpreted intuitively in terms of products of matter and field correlation functions using a diagrammatic close time path loop formalism which reveals the entangled quantum pathways of the fields and matter. The pump-probe signal measured when the pump and the probe are in a twin entangled state shows two-photon resonant contributions which scale linearly rather than quadratically with the incident beam intensity and reveal frequencies of off-resonant transitions. Two-dimensional spectrograms obtained by double Fourier transform of the signal with respect to the entanglement time and delay of the twins could provide detailed information on correlations among states and dynamical processes with high temporal resolution. The analogy with multidimensional time-domain optical techniques which use sequences of short classical pulses and pulse shaping algorithms is pointed out.