Multidimensional Coherent Spectroscopy

Multidimensional electronic and infrared spectroscopies represent important experimental techniques for probing the structural and dynamical properties of molecules. Insight into events such as the energy transfer dynamics in photosynthetic complexes as well as the structural changes in the hydrogen bond network of liquid water have been instrumental for increasing our understanding of the fundamental aspects of bonding and structural evolution. Information concerning electronic and vibrational couplings, transition moments, timescales for spectral diffusion and chemical exchange may all be discerned by implementing multidimensional spectroscopies. These techniques will continue to develop in sophistication in order to extract as much information as possible from the system of interest.
The principles of multidimensional spectroscopy have been applied to nuclear magnetic resonance (NMR) experiments decades ago by Ernst and coworkers. The use of complicated pulse sequences to excite various spin coherences and populations in samples has given us unprecedented information concerning the structure and dynamics in systems as complicated as large proteins. Even the interconversion between two species can be observed with multidimensional NMR whereby it is documented in the appearance of crosspeaks in the 2D spectra. Unfortunately, NMR has limited time resolution (microseconds at best) and as a result cannot access ultrafast timescales (fs – ps). It is at these timescales that important events occur like electron and proton transfer, hydrogen bond dissociation, molecular reorientation and intramolecular energy redistribution. The surroundings in particular may be intimately involved with chemical reactions as reactants cross the transition state to form products [see Figure 1]. As the barrier is being crossed, molecules reorient, interactions with the solvent change and energy is funneled to or from the reacting system. These events can only be accessed by optical methods that utilize ultrafast laser pulses.

Figure 1. The generalized reaction coordinate is used to describe the energetics of a chemical reaction. The surroundings of the reactant species may influence the barrier height of the reaction as well as add 'friction' as reactants traverse the barrier.

Ultrafast optical spectroscopies have developed more slowly than NMR mostly due to technological challenges. From an NMR standpoint, all proton NMR transitions have the same dipole moment, all samples are optically thin and exhibit no propagation effects, NMR transmitters are perfectly stable monochromatic radiation sources, and the entire spectrum has a small bandwidth. From an optical standpoint, molecules contain many different energy levels and generating short controllable laser pulses to excite these transitions is difficult to accomplish. This renders these experiments more complicated since a two-level system is insufficient to describe the system dynamics like for protons in NMR. A major technological hurdle was overcome with the advent of the Ti:Sapphire laser which is now capable of emitting pulses as short as ~5 fs! This laser system has been used in many applications to generate short pulses at different frequencies. These pulses can then stimulate different transitions (electronic or vibrational) on different molecules although sometimes this may require significant modifications to the experimental apparatus. Despite the complexity of the physics of optical spectroscopy as well as experimental implementation, time-delayed ultrafast laser pulses have been used to measure the ground and excited state dynamics occurring in many different molecules. These studies have illustrated the importance of understanding processes occurring on the fastest timescales!

For multidimensional optical spectroscopies time-delayed laser pulses are used to excite and subsequently probe the time dependent dynamics of the system. This is readily observed in a pump-probe experiment whereby only two pulses are used. The first pulse excites a chromophore at a particular frequency and the probe pulse is used to interrogate the system at some time later. The signals may be measured as a function of the laser pulse frequencies as well as the time between the interactions as shown in Figure 2A. A multidimensional spectrum may be generated to examine radiative and nonradiative relaxation processes present in the sample of interest. The pump-probe experiment may be generalized by incorporating three excitation pulses [Figure 2B]. In this experiment, the first two pulses may be viewed as a ‘pump’ pulse and by virtue of their time delay they create a frequency grating (modulated laser spectrum). The third pulse acts as a ‘probe’ pulse that can monitor excited state dynamics as well as spectral diffusion processes since the frequency grating degrades with time. The latter relaxation process is a reflection of the dynamics of the local environment around a chromophore. This is typically referred to as a stimulated echo experiment (analogous to NMR) since an echo pulse is emitted at some time after the third pulse has interacted with the sample. This pulse sequence has the effect of removing inhomogeneous broadening in a spectrum, that is, static contributions to the signal relative to the timescale of the experiment (fs – ps).

Coherent 2D spectroscopies have emerged only recently in the optical domain. These experiments utilize the pulse sequence described above, and consequently Fourier transform the preparation and detection time variables (τ and t) to generate 2D spectra. Figure 3 displays how most experiments have been conducted to date. Beam-splitters are used to generate multiple pulses that are subsequently recombined in the sample in a particular geometry. Phase matching criteria dictate where the sample will emit the echo pulse. A local oscillator pulse is used to amplify as well as determine the phase of the emitted signal. In this experiment, the signal oscillates at optical frequencies and as a result it takes a long time to acquire the interferrograms that are used to construct the 2D spectra. Another useful way to do the experiment is to take advantage of a pulse shaping

apparatus in order to generate several pulses from one with well defined interpulse delays and phase relationships as shown in Figure 4. The echo signal has a -Φ1+2Φ2 dependence for a 2-pulse sequence (pulses 2 and 3 are superimposed in Figure 2B). For the 3-pulse sequence it has a phase dependence of -Φ1+Φ2+Φ3. By phase cycling the pulses in the sequence, all other signals that have different phase dependencies may be subtracted away. This scheme is readily realized with a pulse shaper that utilizes an acousto-optic modulator (AOM) to generate pulse sequences capable of being updated at MHz frequencies. A phase coherent collinear pulse train is generated that can interact with the sample and generate a polarization that oscillates at the difference frequency between the optical cycle and the transition frequency. As a result, a single experiment may only take seconds to acquire as opposed to hours.

Figure 5 displays a 2D spectrum of Rubidium atoms in the gas phase. This model system consists of two accessible excited states that may be reached using an amplified Ti:Sapphire laser system. Transitions to these excited states are shown on the antidiagonal which essentially represents what a linear spectrum would look like. The peaks off the diagonal represent a coupling between these states. The lineshapes in 2D spectra are sensitive to the local environment around the chromophore. Inhomogeneities may be readily observed in the lineshapes depicted in the 2D spectra. The sensitivity of the spectra to the local environment suggests an important application of this technique to optical imaging in tissue. Local inhomogeneities inside cells may be readily probed using the above pulse sequences and this may be exploited to provide new contrast in imaging applications.