Delocalized excitons and interaction effects in extremely dilute thermal ensembles

Double-quantum spectroscopy of dense atomic vapors: Interplay between Doppler and self-broadenings

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.

Pulse overlap artifacts and double quantum coherence spectroscopy

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.

Pulse overlap ambiguities in multiple quantum coherence spectroscopy

Coherent two-dimensional electronic spectroscopy probes ultrafast dynamics using femtosecond pulses. In the case where the time scale of the studied dynamics become comparable to the pulse duration, pulse overlap effects may compromise the experimental data. Here, we perform one-dimensional coherence scans and study pulse overlap effects in clean two-level systems. We find parasitic multiple-quantum coherences as a consequence of the arbitrary time ordering during the temporal pulse overlap. Surprisingly, the coherence lifetimes exceed the pulse coherence time by a factor of 1.85. These findings have important implications for the interpretation of higher-order coherent two-dimensional and related spectroscopy experiments.

Two-dimensional electronic spectroscopy of an ultracold gas

Femtosecond coherent multidimensional spectroscopy is demonstrated for an ultracold gas.  A setup for phase modulation spectroscopy is used to probe the 3²S_1/2-2²P_1/2,3/2 transition in an 800μK-cold sample of ⁷Li atoms confined in a magneto-optical trap. The observation of a double quantum coherence response, a signature of interparticle interactions, paves the way for detailed investigations of few- and many-body effects in ultracold gases using this technique. The experiment combines a frequency resolution of 3 GHz with a potential time resolution of 200 fs, which allows for high-resolution studies of ultracold atoms and molecules both in the frequency and in the time domain.

High-resolution two-dimensional electronic spectroscopy reveals the homogeneous line profile of chromophores solvated in nanoclusters

Doped clusters in the gas phase provide nanoconfined model systems for the study of system-bath interactions. To gain insight into interaction mechanisms between chromophores and their environment, the ensemble inhomogeneity has to be lifted and the homogeneous line profile must be accessed. However, such measurements are very challenging at the low particle densities and low signal levels in cluster beam experiments. Here, we dope cryogenic rare-gas clusters with phthalocyanine molecules and apply action-detected two-dimensional electronic spectroscopy to gain insight into the local molecule-cluster environment for solid and superfluid cluster species. The high-resolution homogeneous linewidth analysis provides a benchmark for the theoretical modelling of binding configurations and shows a promising route for high-resolution molecular two-dimensional spectroscopy.

Understanding the interaction of single chromophores with nanoparticles remains a challenging task in nanoscience. Here the authors provide insight into the interaction between isolated base-free phthalocyanine molecules and He and Ne nanoclusters in the gas phase using high-resolution two-dimensional spectroscopy.

Collective Resonance of D States in Rubidium Atoms Probed by Optical Two-Dimensional Coherent Spectroscopy

Collective resonance of interacting particles has important implications in many-body quantum systems and their applications. Strong interactions can lead to a blockade that prohibits the excitation of a collective resonance of two or more nearby atoms. However, a collective resonance can be excited with the presence of weak interaction and has been observed for atoms in the first excited state (P state). Here, we report the observation of collective resonance of rubidium atoms in a higher excited state (D state) in addition to the first excited state. The collective resonance is excited by a double-quantum four-pulse excitation sequence. The resulting double-quantum two-dimensional (2D) spectrum displays well-isolated peaks that can be attributed to collective resonances of atoms in P and D states. The experimental one-quantum and double-quantum 2D spectra can be reproduced by a simulation based on the perturbative solutions to the optical Bloch equations, confirming collective resonances as the origin of the measured spectra. The experimental technique provides a new approach for preparing and probing collective resonances of atoms in highly excited states.

Double-quantum-zero-quantum 2D coherent spectroscopy reveals quantum coherence between collective states in an atomic vapor

We report a novel, to the best of our knowledge, double-quantum-zero-quantum two-dimensional coherent spectroscopy (2DCS) that allows direct detection of the quantum coherence between multiparticle collective states. Through correlating the double-quantum coherence and the zero-quantum coherence, signatures for coherence between collective states can be well isolated as side peaks and readily identified in the 2D spectrum. The experiment is implemented in a vapor of rubidium atoms in a collinear 2DCS setup. Good agreement with a theoretical simulation using density matrix confirms the essential role of the interatomic correlation effect in generating the side peak signals. This 2D spectrum technique paves a new avenue for studying the coherent coupling of highly excited states and many-body properties.

A flexible and scalable, fully software-based lock-in amplifier for nonlinear spectroscopy

We demonstrate a cost-effective, fully software-based lock-in amplifier (LIA) implemented on a commercial computer. The device is designed for application in nonlinear spectroscopy, such as transient absorption and coherent multidimensional spectroscopy, but may also be used in any other application. The performance of our device is compared to a state-of-the-art commercial LIA with nearly identical results for both devices. Advantages of our device over commercial hardwired electronic LIAs are the improved flexibility in the data analysis and the possibility of arbitrary up-scaling of the number of LIA channels.

Pulse area dependence of multiple quantum coherence signals in dilute thermal gases

In the general framework of open quantum systems, we assess the impact of the pulse area on single and double quantum coherence (1QC and 2QC) signals extracted from fluorescence emitted by dilute thermal gases. We show that 1QC and 2QC signals are periodic functions of the pulse area, with distinctive features that reflect the particles' interactions via photon exchange, the polarizations of the laser pulses, and the observation direction.

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

Signatures of exciton dynamics and interaction in coherently and fluorescence-detected four- and six-wave-mixing two-dimensional electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) can be realized in increasing nonlinear orders of interaction with the electric field, bringing new information about single- and multi-particle properties and dynamics. Furthermore, signals can be detected both coherently (C-2DES) and by fluorescence (F-2DES), with fundamental and practical differences. We directly compare the simultaneous measurements of four- and six-wave mixing C-2DES and F-2DES on an excitonic heterodimer of squaraine molecules. Spectral features are described in increasing orders of nonlinearity by an explicit excitonic model. We demonstrate that the four-wave-mixing spectra are sensitive to one-exciton energies, their delocalization and dynamics, while the six-wave-mixing spectra include information on bi-exciton and higher excited states including the state energies, electronic coupling, and exciton-exciton annihilation. We focus on the possibility to extract the dynamics arising from exciton-exciton interaction directly from the six-wave-mixing spectra. To this end, in analogy to previously demonstrated fifth-order coherently detected exciton-exciton-interaction 2DES (EEI2D spectroscopy), we introduce a sixth-order fluorescence-detected EEI2D spectroscopy variant.

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.

Molecular Coherent Three-Quantum Two-Dimensional Fluorescence Spectroscopy

We introduce molecular coherent three-quantum (3Q) two-dimensional (2D) fluorescence spectroscopy with phase cycling via shot-to-shot pulse shaping at a 1 kHz repetition rate. This allows us to acquire simultaneously, within a single scan, three fourth-order and six sixth-order signals correlating various one-quantum, two-quantum, and 3Q coherences. We demonstrate the approach on the dye molecule rhodamine 700 and reproduce all nine 2D data sets, including their absolute signal strengths, with simulations using a single, consistent set of model parameters. We observe a linear concentration dependence of all nonlinear signals, evidencing the absence of cascades and many-particle signals of noninteracting molecules. The single-beam, background-free implementation allows direct comparability between various nonlinear signal types and provides information about multiple excited states. Apart from molecules, the method is expected to be applicable to supramolecular systems, polymers, and solid-state materials with the prospect of revealing signatures of bi- and triexcitonic states.

Extended Coherently Delocalized States in a Frozen Rydberg Gas

The long-range dipole-dipole interaction can create delocalized states due to the exchange of excitation between Rydberg atoms. We show that even in a random gas many of the single-exciton eigenstates are surprisingly delocalized, composed of roughly one quarter of the participating atoms. We identify two different types of eigenstates: one which stems from strongly-interacting clusters, resulting in localized states, and one which extends over large delocalized networks of atoms. These two types of states can be excited and distinguished by appropriately tuned microwave pulses, and their relative contributions can be modified by the Rydberg blockade and the choice of microwave parameters.

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.

Rapid multiple-quantum three-dimensional fluorescence spectroscopy disentangles quantum pathways

Coherent two-dimensional spectroscopy is a powerful tool for probing ultrafast quantum dynamics in complex systems. Several variants offer different types of information but typically require distinct beam geometries. Here we introduce population-based three-dimensional (3D) electronic spectroscopy and demonstrate the extraction of all fourth- and multiple sixth-order nonlinear signal contributions by employing 125-fold (1⨯5⨯5⨯5) phase cycling of a four-pulse sequence. Utilizing fluorescence detection and shot-to-shot pulse shaping in single-beam geometry, we obtain various 3D spectra of the dianion of TIPS-tetraazapentacene, a fluorophore with limited stability at ambient conditions. From this, we recover previously unknown characteristics of its electronic two-photon state. Rephasing and nonrephasing sixth-order contributions are measured without additional phasing that hampered previous attempts using noncollinear geometries. We systematically resolve all nonlinear signals from the same dataset that can be acquired in 8 min. The approach is generalizable to other incoherent observables such as external photoelectrons, photocurrents, or photoions.

Long range dipole-dipole interaction in low-density atomic vapors probed by double-quantum two-dimensional coherent spectroscopy

Optical double-quantum two-dimensional coherent spectroscopy (2DCS) was implemented to probe interatomic dipole-dipole interactions in both potassium and rubidium atomic vapors. The dipole-dipole interaction was detected at densities of 4.81×10⁸ cm ^-3 and 8.40×10⁹ cm ^-3 for potassium and rubidium, respectively, corresponding to a mean interatomic separation of 15.8 μm or 3.0×10⁵ a ₀ for potassium and 6.1 μm or 1.2×10⁵ a ₀ for rubidium, where a ₀ is the Bohr radius. The experimental results confirm the long range nature of the dipole-dipole interaction, which is critical for understanding many-body physics in atoms/molecules. The long range interaction also has implications in atom-based applications involving many-body interactions. Additionally, we demonstrated that double-quantum 2DCS is sufficiently sensitive to probe dipole-dipole interaction at densities that can be achieved with cold atom in a magneto-optical trap, paving the way for double-quantum 2DCS studies of cold atoms and molecules. The method can also open a new avenue to study long-range interactions in solid state systems such as quantum dots and color centers in diamonds.

Before Förster. Initial excitation in photosynthetic light harvesting

Electronic 2D spectroscopy allows nontrivial quantum effects to be explored in unprecedented detail. Here, we apply recently developed fluorescence detected coherent 2D spectroscopy to study the light harvesting antenna 2 (LH2) of photosynthetic purple bacteria. We report double quantum coherence 2D spectra which show clear cross peaks indicating correlated excitations. Similar results are found for rephasing and nonrephasing signals. Analysis of signal generating quantum pathways leads to the conclusion that, contrary to the currently prevailing physical picture, the two weakly coupled pigment rings of LH2 share the initial electronic excitation leading to quantum mechanical correlation between the two clearly separate absorption bands. These results are general and have consequences for the interpretation of initially created excited states not only in photosynthesis but in all light absorbing systems composed of weakly interacting pigments where the excitation transfer is commonly described by using Förster theory. Being able to spectrally resolve the nonequilibrium dynamics immediately following photoabsorption may provide a glimpse to the systems' transition into the Förster regime.