# Introduction

The Multidimensional Molecular Spectroscopy group is a team of experimental physicists and physical chemists. We measure, analyze and simulate time-resolved optical signals of molecules and molecular complexes. Our experimental toolbox contains techniques like pump-probe, heterodyned and homodyned transient grating, [1] photon echo peakshift and, as the most important method, two-dimensional electronic spectroscopy, both in single- and double-quantum variants. [2, 3]

## Pump-Probe

Pump-probe or transient absorption spectroscopy is the by far most wide spread of ultrafast techniques. The transmission of a probe pulse through the investigated sample is recorded with and without the presence of a preceding pump-pulse. By scanning the delay of the probe with respect to the pump, transient molecular species like electronic excited states or vibrational modes can be monitored in their time behavior. We use pump-probe as a first view on molecular dynamics and to determine lifetimes of electronically excited states. It is also a reference technique for our central method, two-dimensional electronic spectroscopy.

## Two-dimensional electronic spectroscopy

Two-dimensional electronic spectroscopy (2D-ES) and pump-probe are directly related techniques with many similarities.[4] From a theoretical point of view, 2D-ES and pump-probe share the same non-linear signal, but differ in its representation: in pump-probe one integrates over all excitation frequencies and plots the resulting signal in its time dependence. In 2D-ES on the other hand, the signal gets resolved in excitation frequency. What used to be a simple transient in pump-probe, becomes a time-dependent energy landscape in 2D-ES. In simple terms, the coordinates of these landscapes are excitation and emission frequencies. This increase in dimensionality leads to a much richer data basis for model building. Specifically, 2D-ES highlights energy transfer and coherence pathways which could remain elusive in excitation frequency-integrated techniques like pump-probe.

[1] A. Nemeth, J. Sperling, J. Hauer, H. F. Kauffmann, and F. Milota, "Compact Phase-Stable Design for Single- and Double-Quantum Two-Dimensional Electronic Spectroscopy," Opt Lett **34**, 3301-3303 (2009).

[2] N. Christensson, F. Milota, A. Nemeth, I. Pugliesi, E. Riedle, J. Sperling, T. Pullerits, H. Kauffmann, and J. Hauer, "Electronic Double-Quantum Coherences and Their Impact on Ultrafast Spectroscopy: The Example of beta-Carotene," J Phys Chem Lett **1**, 3366-3370 (2010).

[3] A. Nemeth, F. Milota, T. Mancal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, "Double-quantum two-dimensional electronic spectroscopy of a three-level system: Experiments and simulations," J Chem Phys **133**, 094505 (2010).

[4] J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, "Two-dimensional electronic spectroscopy," Chem Phys Lett **297**, 307-313 (1998).

## Experiments

2D-ES is a nonlinear optical four-wave mixing experiment. Three laser pulses interact with a sample to generate a nonlinear signal field, radiating along a pre-determined direction, the so-called phase matching direction. In addition to the three excitation pulses, our type of 2D-ES experiment also requires a fourth pulse, the local oscillator. The local oscillator is needed to determine the complete signal field, as compared to just the signal’s intensity. The 2D experiment is carried out by recording the radiated signal field as a function of the delay between the first two pulses. Via subsequent Fourier transform, we generate spectral maps of the system’s dynamics. These maps change in time as a function of the delay between the second and third pulse. The crucial part in every 2D-ES experiment is phase stability, as required for the Fourier transformation step. If the phase between the excitation pulses fluctuates randomly, the signal cannot be split up in its desired real and imaginary parts any more. We have already constructed two setups achieving this aim and are currently building a third one. The first setup is based on previously published designs. [1, 2] After a beamsplitter, a diffractive optical element (DOE) produces two pairs of phase-stable beams. After the DOE, the beams are steered by common optics only. The delay between the pulses in the first pair (t_{1}) is introduced by fused-silica wedges.

**2D-ES experiment**

Click inside the image for 3D-mode.

The advantage of this setup is that the population time t_{2} is introduced by a translational stage, allowing for up to 300 ps delay times. Disadvantages are that pulses separated by t_{2} are not phase stable, making a Fourier transformation along this delay unfeasible. Additionally, the two pulse pairs separated by t_{2} have to be precisely overlapped at the sample position, which is far from trivial for pulses of equal spot size. As a major improvement, in 2009 we introduced a wedge-only setup, working with a double-grating as a DOE. [3] Instead of working with two phase-stable pairs, the double grating allows us to use four phase-stable beams. The fact that after the DOE all excitation beams traverse the focusing mirror via a central hole allows focusing under 0° angle of incidence. This avoids astigmatism at the sample position. It was shown by Nelson and co-workers that in such geometry, beams overlap over their full aperture. [4]

Another key advantage beside alignment-free perfect beam overlap is the fact that in this setup, depending on employed phase-matching geometry, one can choose between experiments like pump-probe, heterodyned and homodyned transient grating, photon echo peakshift and single- and double quantum 2D-spectroscopy. (1Q- and 2Q-2D). 2Q-2D [5, 6] means that the Fourier-transformation step is not performed along t_{1} like in 1Q-2D, but along t_{2}. The advantage of such a signal is its simplicity: it only consists of two instead of eight (1Q-2D) excitation pathways. 2Q-2D reaches its full potential in combination with its more conventional single quantum variant: 2Q-2D defines the investigated energy level system, while 1Q-2D describes the dynamics on these energy levels. This combination of 1Q- and 2Q-2D yields a richer, more profound data basis for subsequent modeling than pump-probe or any excitation-frequency-integrated technique.

**2D-ES experiment**

Click inside the image for 3D-mode.

[1] T. Brixner, T. Mancal, I. V. Stiopkin, and G. R. Fleming, "Phase-stabilized two-dimensional electronic spectroscopy," J Chem Phys **121**, 4221-4236 (2004).

[2] M. L. Cowan, J. P. Ogilvie, and R. J. D. Miller, "Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes," Chem Phys Lett **386**, 184-189 (2004).

[3] A. Nemeth, J. Sperling, J. Hauer, H. F. Kauffmann, and F. Milota, "Compact Phase-Stable Design for Single- and Double-Quantum Two-Dimensional Electronic Spectroscopy," Opt Lett **34**, 3301-3303 (2009).

[4] A. A. Maznev, T. F. Crimmins, and K. A. Nelson, "How to make femtosecond pulses overlap," Opt Lett **23**, 1378-1380 (1998).

[5] S. Mukamel, R. Oszwaldowski, and L. Yang, "A coherent nonlinear optical signal induced by electron correlations," J Chem Phys **127** (2007).

[6] A. Nemeth, F. Milota, T. Mancal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, "Double-quantum two-dimensional electronic spectroscopy of a three-level system: Experiments and simulations," J Chem Phys **133**, 094505 (2010).