^{1}and Peter Hamm

^{1,a)}

### Abstract

We demonstrate a method to collect purely absorptive three-dimensional (3D) fifth-order vibrational spectra on the model system in . The six beam interferometer is described, as well as a method to experimentally determine the phase of the 3D spectrum. The measured spectra agree very well with simulations of the data based on the cumulant expansion. There are five peaks corresponding to different paths up and down the vibrational ladder. The positions, signs, and amplitudes of the peaks agree with theoretical predictions, and the intensities of the peaks scale linearly with concentration. Based on the concentration dependence and agreement between the simulations and measurements, we conclude that cascaded lower order signals contribute negligibly to the observed signal.

The work was supported by the Swiss Science Foundation under Grant No. 200020-107492/1. S.G.-R. was partially supported by the National Science Foundation (USA) under Grant No. OISE-0601907.

I. INTRODUCTION

II. MATERIALS AND METHODS

III. PHASING OF FIFTH-ORDER SIGNALS

IV. ABSORPTIVE FIFTH-ORDER SIGNALS

V. RESULTS

VI. CASCADING THIRD-ORDER SIGNALS DO NOT CONTRIBUTE TO THE FIFTH-ORDER IR SPECTRUM

VII. CONCLUSIONS

### Key Topics

- Absorption spectra
- 20.0
- Carbon dioxide
- 12.0
- Infrared spectra
- 9.0
- Absorption spectroscopy
- 8.0
- Coherence
- 8.0

## Figures

(a) Fifth-order, 3D spectroscopy has five strong pump pulses which generate a fifth-order polarization, which interferes with a local oscillator, LO. (b) The four double-sided Feynman diagrams for the phase matching direction for a two-level system. (c) The signal from each of these diagrams alone has a phase-twisted lineshape. (d) Adding these four diagrams generates an absorptive fifth-order spectrum.

(a) Fifth-order, 3D spectroscopy has five strong pump pulses which generate a fifth-order polarization, which interferes with a local oscillator, LO. (b) The four double-sided Feynman diagrams for the phase matching direction for a two-level system. (c) The signal from each of these diagrams alone has a phase-twisted lineshape. (d) Adding these four diagrams generates an absorptive fifth-order spectrum.

Schematic of the six beam interferometer for 3D-IR spectroscopy. (a) interferometer layout, (b) phase matching geometry, and (c) balanced detection.

Schematic of the six beam interferometer for 3D-IR spectroscopy. (a) interferometer layout, (b) phase matching geometry, and (c) balanced detection.

Absorption spectrum of in ; the sample path length is .

Absorption spectrum of in ; the sample path length is .

Phasing fifth-order signals. (a) Each pair of beams that creates a coherence in the sample also creates (b) a spatial grating in the focus. (c) A small pinhole, diameter, diffracts some of these gratings in the direction of the detector, converting the spatial grating to an interferogram. (d) The phases from the Fourier transforms of these interferograms can be used to calculate the phase of the 3D-IR spectrum.

Phasing fifth-order signals. (a) Each pair of beams that creates a coherence in the sample also creates (b) a spatial grating in the focus. (c) A small pinhole, diameter, diffracts some of these gratings in the direction of the detector, converting the spatial grating to an interferogram. (d) The phases from the Fourier transforms of these interferograms can be used to calculate the phase of the 3D-IR spectrum.

(a) The experimental absorptive 3D spectrum of gives five peaks . (b) Simulations based on the cumulant expansion accurately reproduce the data. (c) The five peaks come from the various pathways up and down the vibrational ladder. Above each column in gray are the relative amplitude and sign of each peak accounting for the various pathways through population states and harmonic scaling of the transition dipole moments.

(a) The experimental absorptive 3D spectrum of gives five peaks . (b) Simulations based on the cumulant expansion accurately reproduce the data. (c) The five peaks come from the various pathways up and down the vibrational ladder. Above each column in gray are the relative amplitude and sign of each peak accounting for the various pathways through population states and harmonic scaling of the transition dipole moments.

The intensity of the measured signal is linear with concentration, . Direct fifth-order signal should be linear with , whereas cascaded third-order signals should scale like . This indicates that cascaded third-order signals do not contribute to the 3D-IR.

The intensity of the measured signal is linear with concentration, . Direct fifth-order signal should be linear with , whereas cascaded third-order signals should scale like . This indicates that cascaded third-order signals do not contribute to the 3D-IR.

The double-sided Feynman diagrams for cascaded third-order signals. The left column gives the diagrams for direct fifth-order processes which generate the five peaks in the 3D-IR spectrum. The middle column gives the sequential cascaded processes in which one chromophore emits a field which acts as a pump for another third-order process on another chromophore. The right column gives the parallel cascades, in which a third-order process on one chromophore stimulates the emission of a third-order process on another chromophore. [(a) and (b)] For these two peaks cascaded processes exist to generate signals. [(c) and (d)] For these two peaks there is a sequential cascade (but no parallel cascade) which could potentially generate a signal at these frequencies. It will be suppressed by the frequency mismatch between the and coherences, which are circled. (e) There is no cascade which can generate this peak because it requires walking up the vibrational ladder.

The double-sided Feynman diagrams for cascaded third-order signals. The left column gives the diagrams for direct fifth-order processes which generate the five peaks in the 3D-IR spectrum. The middle column gives the sequential cascaded processes in which one chromophore emits a field which acts as a pump for another third-order process on another chromophore. The right column gives the parallel cascades, in which a third-order process on one chromophore stimulates the emission of a third-order process on another chromophore. [(a) and (b)] For these two peaks cascaded processes exist to generate signals. [(c) and (d)] For these two peaks there is a sequential cascade (but no parallel cascade) which could potentially generate a signal at these frequencies. It will be suppressed by the frequency mismatch between the and coherences, which are circled. (e) There is no cascade which can generate this peak because it requires walking up the vibrational ladder.

## Tables

A comparison of the amplitude of the five detected peaks with the analytical results assuming a harmonic scaling of the transition dipole moments, simulation, and experiment. The simulation of the signals uses the cumulant expansion and the same time grid as the experiment. The coherence pathways correspond to reading the bra-ket pairs going up the double-sided Feynman diagrams of Fig. 5.

A comparison of the amplitude of the five detected peaks with the analytical results assuming a harmonic scaling of the transition dipole moments, simulation, and experiment. The simulation of the signals uses the cumulant expansion and the same time grid as the experiment. The coherence pathways correspond to reading the bra-ket pairs going up the double-sided Feynman diagrams of Fig. 5.

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