Coherent two-dimensional spectroscopy of a Fano model

Abstract

The Fano lineshape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the lineshapes of many one-dimensional spectroscopies -absorption, emission, scattering, conductance, photofragmentation -applied to very varied systems -atoms, molecules, semiconductors and metals. Unravelling a spectroscopy into a second dimension reveals the relationship between states in addition to decongesting the spectra. Femtosecond-resolved two-dimensional electronic spectroscopy (2DES) is a four-wave mixing technique that measures the time-evolution of the populations, and coherences of excited states. It has been applied extensively to the dynamics of photosynthetic units, and more recently to materials with extended band-structures. In this letter, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the new system parameters that become accessible.Whenever a discrete state and a continuum state interact and radiative transitions are allowed from the ground state to both, an interference occurs that gives rise to the Fano lineshape [1][2][3][4]. In the presence of dissipative processes, it has been shown that the generalized Fano equation consisting of a standard Fano plus a Lorentzian term is [1, 2, 5-9]:where q = µ e /nπV µ c and = (ω L − ω e )/γ e , µ e is the transition dipole moment to the discrete excited state, µ c the transition dipole moment to the continuum, V the coupling of the discrete excited state to the continuum, n the density of states of the continuum, ω e is the energy of the discrete state relative to the ground state, ω L is the radiation field frequency, and γ e = nπV 2 is the linewidth of the excited state, induced by its coupling nV 2 to the continuum set of states. C is the weight of the Lorentzian term and is related to the dissipative processes [6][7][8][9][10]. Since its original inception, the 1961 paper has resulted in more than 8,000 citations testifying to its ubiquity in physics, chemistry and materials science. The first Fano profiles were observed more than 80 years ago in atomic spectra, including photoionization of atoms and photodissociation of small molecules [3,4]. The field of study was established around scattering processes where the phenomena of coupling to a thermal bath resulting in dissipation or decoherence is not important, except in a few cases, notably pressure broadening [11][12][13].The synthesis and control of matter at the nanoscale opened up the observation of Fano profiles to dissipative systems [14][15][16][17][18] which in turn spurred a renewed interest in theoretical descriptions that would solve the problem in open quantum systems [8][9][10][19][20][21], and correctly account for the relaxation. Consequent with this desire to measure dissipation, more sophisticated spectroscopies are to be invoked. 2D electronic spectroscopy (2DES) is arguably one of the best spectroscopies to measure decoherence and relaxation between states [22][23]...

Radiative Enhancement of Linear and Third-Order Vibrational Excitations by an Array of Infrared Plasmonic Antennas

“…The interaction between the molecular transition and the plasmon resonance is manifested in the Fano-like asymmetric dip, which is observed in the linear spectrum at the molecular transition frequency, as seen in Figure c. Recently, the studies of Fano line shapes were extended also to nonlinear spectroscopy, which can provide more details on the origin of the plasmon–molecule interaction. ,,, The third-order transient absorption and 2DIR spectra of the polymer films (waiting time 300 fs) with and without plasmonic enhancement are shown in Figure . The negative and positive peaks in the nonenhanced spectra in panels (a) and (b) of the figure correspond to the ground state bleach and stimulated emission and the excited state absorption, respectively.…”

Anomalous Nonlinear Optical Response of Graphene Near Phonon Resonances

“…However, the χ (3) energy dependence can be described by the phenomenological Fano lineshape [30] in order to describe the CARS process. Such methodology has been applied to understand the FWM [31,32] and CARS spectra of atomic systems at high energies [33]. The Fano lineshape can be written as a function of energy E as:…”

Coherent two-dimensional electronic mass spectrometry

“…We adopted the model of ref. 55 for a qualitative comparison with our data and calculated the lineshape of the rephasing contribution for different values of the Fano q parameter, which is inversely proportional to the coupling strength V to the ionic continuum 55 (Fig. 3c ).…”

“…As demonstrated recently, the lineshape can be controlled and converted back to a Lorentzian absorption profile by an additional laser field 54 . In coherent 2D spectroscopy, Fano resonances lead to distorted peak shapes that depend on the coupling strength between a discrete state and a continuum as analyzed theoretically in a recent work 55 and studied experimentally for molecular layers on plasmonic arrays 56 . We adopted the model of ref.…”

“…Furthermore, the measured data comprise positive signal contributions at the edges of the spectrum that are not well described within the 2D Fano model in ref. 55 . While this model treats a single auto-ionizing state, we expect multiple auto-ionizing states in the case of NO 2 .…”