Two-dimensional electronic spectroscopy

[1] The term electronic refers to the fact that the optical frequencies in the visible spectral range are used to excite electronic energy states of the system; however, such a technique is also used in the IR optical range (excitation of vibrational states) and in this case the method is called two-dimensional infrared spectroscopy (2DIR).

[2] This technique records the signal which is emitted from a system after an interaction with a sequence of 3 laser pulses.

The main result of this technique is a two-dimensional absorption spectrum that shows the correlation between excitation and detection frequencies.

[3] 2DES has been combined with photoelectrochemical recordings (PEC2DES) to study charge separation in the photosynthetic complex photosystem I, which is the physiological output signal in contrast to fluorescence.

[clarification needed] The interaction with the pulses creates a third-order nonlinear response function

of the system from which it is possible to extract two-dimensional spectra as a function of excitation and detection frequencies.

[6][7][8] A possible way to recover an analytical expression of the response function is to consider the system as an ensemble and deal with the light-matter interaction process by using the density matrix approach.

[5] Such a result shows that the response function is proportional to the product of the three pulses' electric fields.

the wave vectors of the three pulses, the nonlinear signal will emit in several directions

An interpretation of these signals is possible by considering the system to be composed of many electric dipoles.

When the first pulse interacts with the system, the dipoles start to oscillate in phase.

The interaction with the third pulse, in the case of rephasing, generates a signal which has an opposite temporal evolution with respect to the previous one.

the oscillations are in-phase again and the new signal generated is called photon echo.

In the other case, there is no creation of a photon echo and the signal is called non-rephasing.

From these signals is possible to extract the pure absorptive and dispersive spectra which are usually shown in literature.

The time-domain nonlinear response of the system interferes with another pulse called local oscillator (LO) which allows measurement of both amplitude and phase.

Such a signal is usually acquired with a spectrometer which separates the contribution of each spectral components (detection frequencies

Once the scan ends, the detector has acquired a signal as a function of coherence time per each detection frequency

The time evolution of the system can be measured by repeating the procedure described before for different values of

The boxcar geometry is a configuration where all the pulses arrive at the system from different directions

The partially collinear geometry is another implementation of this technique where the first and the second pulse coming from the same direction

When a cross peak appears means that two electronic states of the system are coupled because when the pulses pump an electronic state, the system responds with emission from a different energy level.

[5] Thanks to the high spectral resolution, this technique acquires information based on the two dimensional shape of the peaks.

is close to zero the diagonal peaks show an elliptical lineshape as is shown in the figure on the right.

[13] The width along the diagonal line represents the inhomogeneous broadening which contains information about interactions between the environment and the system.

The value of the linewidth will be close to the one calculated in the linear absorption spectrum.

On the other hand, the linewidth along the off-diagonal shows a smaller value with respect to the diagonal one.

fs, the shape of the peaks becomes circular and the width along diagonal and off-diagonal line are similar.

[16][17] In this case the positions of the maximum values in the 2D spectra per each detection frequency are considered.

The same approach can also be used by considering the positions of the maximum values per each excitation frequency (y axis) and the slope will be 45° at