Speaker
Description
Two-Dimensional Optical Spectroscopy (2DOS) is a third-order nonlinear optical spectroscopic technique capable of correlating excitations between states in molecular and material systems (1, 2). The technique makes use of three light pulses, two pump pulses and a probe pulse, which when incident on the system generates a third-order signal that can be heterodyne detected by the probe pulse or a local oscillator. In short, the interaction of the system with the first pump pulse generates coherences within the system, which are projected onto a population state by the second pump pulse. Following this, the interaction of the system with the probe pulse generates secondary coherences within the system, whose decay leads to the emission of the signal field. This time-domain signal field is Fourier transformed over the two coherence periods to generate the 2DOS spectrum, where the spectral features on the corresponding spectrum vary over the delay between the pump-pulse pair and probe pulse. This delay, generally known as the waiting time or population time, is scanned to capture dynamic processes within the system of interest.
A 2DOS spectrum comprises of diagonal and off-diagonal cross peak features. Diagonal peaks track individual excited states or transitions, whereas cross peaks relate two individual excited states. These cross peak features are generally assigned to direct bilinear coupling or population transport between states (1, 2). In addition, the lineshapes of the peaks can be analyzed to extract a wealth of information on system-bath interactions. The system-bath interactions can be classical or quantum in nature and dephase the coherences induced by the light fields in the third-order technique. Recently, we reported on the theoretical possibility of a new source of cross peak spectral features which arise on considering quantum system-bath interactions (3).
To theoretically simulate the 2DOS spectra, the system’s response to the incident light fields is calculated perturbatively, where the dephasing induced by the system-bath interaction is treated in the interaction picture. Following this, the second-order cumulant approximation is invoked, where the fluctuation in transition energies of the states are assumed to follow a gaussian distribution (4). This reduces the information on the system-bath interaction to a two-point energy-gap correlation function between the states of the system. The diagonal peaks are described using correlation functions relating a single transition’s frequency-gap over a time-interval t, i.e., $C_{ii}(t)=\left\langle \delta\omega_{ig}(t)\delta\omega_{ig}(0)\right\rangle$, whereas, cross peaks are described using correlation functions which relate the frequency-gaps of two distinct transitions over the interval t, i.e., $C_{ji}(t)=\left\langle \delta\omega_{jg}(t)\delta\omega_{ig}(0)\right\rangle$, where $i \neq j$. In our previous theoretical demonstration (3), we proved that on considering quantum energy-gap cross correlation functions $C_{ji}(t)$, i.e., $C_{ji}(t)$ defined using a quantum mechanical model yielding a complex valued function, such as the Displaced Harmonic Oscillator (DHO), new cross peak spectral features can be observed on the 2DOS spectrum of systems where direct bilinear coupling and population transport between states are absent.
In addition to the new cross peak spectral features, “intra-band coherences” manifest beating features over the waiting time, both along the diagonals and cross peaks of the 2DOS spectrum. These features only arise when quantum frequency-gap correlation functions $C_{ji}(t)$ are used. A classical description of $C_{ji}(t)$ would result in zero cross peak contributions and the inter-state coherence beating features would be absent. We analyze these new cross peak spectral and beating features and describe its potential applications in furthering the 2DOS field along with the physical implication of these features.
References
(1) Mukamel, S. Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations. Ann. Rev. Phys. Chem. 2000, 51, 691–729.
(2) Fresch, E.; Camargo, F. V.; Shen, Q.; Bellora, C. C.; Pullerits, T.; Engel, G. S.; Cerullo, G.; Collini, E. Two-dimensional electronic spectroscopy. Nat. Rev. Methods Primers 2023, 3, 84.
(3) Prasad, S.; Gelin, M. F.; Tan, H.-S. Cross Peaks on Two-Dimensional Optical Spectra Arising from Quantum Cross-Correlation Functions. J. Phys. Chem. Lett. 2024, 15, 11485–11495.
(4) Mukamel, S. Principles of nonlinear optical spectroscopy; Oxford University Press, 1995.
