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arXiv:1605.08572 · Physical review. B./Physical review. B

Coherent two-dimensional spectroscopy of a Fano model

Daniel Finkelstein‐Shapiro, Felipe Poulsen, Tõnu Pullerits, Thorsten Hansen

Published Nov 23, 2016• 11 citations
arXivHTMLPDF

Abstract

The Fano line shape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the line shapes of many one-dimensional spectroscopies---absorption, emission, scattering, conductance, photofragmentation---applied to very varied systems---atoms, molecules, semiconductors, and metals. Unraveling 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 paper, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the system parameters that become accessible.

DOI
10.1103/physrevb.94.205137

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The Fano line shape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the line shapes of many one-dimensional spectroscopies---absorption, emission, scattering, conductance, photofragmentation---applied to very varied systems---atoms, molecules, semiconductors, and metals. Unraveling 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 paper, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the system parameters that become accessible.
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Summary form only given.Fano resonances arise due to quantum mechanical coupling of a discrete state to a degenerate continuum. The line shape in optical absorption spectra is characterized by an intrinsic broadening of the line, strong asymmetry, and a reduced absorption at one side of the peak falling well below the pure continuum level. Intensive theoretical investigations predicted Fano resonances as a general feature of a large variety of low-dimensional semiconductors. We present the observation of Fano resonances in semiconductor superlattices (SL). In SL, discrete excitonic states of the Wannier-Stark ladder are in resonance with subband continua of lower ladder states. The coupling between discrete and continuous states is mediated by Coulomb interaction, which is also responsible for the formation of the discrete excitonic states. As a unique feature of Fano resonances in SL, the Fano coupling strength can be continuously changed in the experiment by tuning the applied electric field. We have also performed time-integrated four-wave-mixing experiments to investigate the influence of Fano coupling on the polarization decay of a Wannier-Stark exciton. We have been able to resolve the polarization decay of a Fano resonance in the time-integrated signal and to follow its changes with field.
Two-dimensional (2D) line shapes derived from four types of coherent third-order nonlinear spectroscopies as a function of two independent time or frequency variables are compared. The signals scattered into two wave-vector-matching directions in the limits of high-time or high-frequency resolution are calculated for an inhomogeneously broadened ensemble of two-level systems with phenomenological dephasing and population relaxation times. While one-dimensional (1D) line shape analysis for this model is ambiguous, the contours of these 2D line shapes are shown to be characteristic of the relative time scales of the three relevant line-broadening parameters. These broadening mechanisms are also apparent by comparing 2D spectral profiles along the diagonal and antidiagonal frequency axes. For time domain experiments, in analogy with NMR correlation spectroscopy, the radiated signal is observed as a function of the two coherence periods and is 2D Fourier transformed to obtain a line shape. For experiments based on the photon echo, the ellipticity of the absolute value 2D line shape is related to the ratio of the inhomogeneous width to the dephasing rate, whereas experiments based on the transient grating method are shown to be functionally 1D. For frequency domain experiments, the contours of the 2D line shape can yield information on static and both dynamic broadening mechanisms. While the addition of spectral diffusion to such calculations will modify these results for frequency domain experiments, characterizing these dynamics in the time domain naturally leads to a 3D experiment analogous to the spin diffusion experiment in NMR.
The coherent dynamics of continuum states and their interplay with excitons at the direct gap of germanium (T=1.8 K) is studied by femtosecond four-wave mixing. In order to unambiguously distinguish between the contribution of continuum states and excitons, we spectrally resolve the diffracted wave as a function of time delay for different excitation photon energies. For excitation many binding energies above the direct gap, the spectra exhibit two clearly separated maxima, one narrow line at the exciton and a much broader contribution of the continuum states. Surprisingly, the continuum contribution persists to longer time delays than the exciton. The experimental results are explained in the framework of the semiconductor Bloch equations.
Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase φ of the time-dependent dipole response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also demonstrate the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism uses quantum-phase control to amplify extreme-ultraviolet light resonantly interacting with He atoms. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with applications in many branches of spectroscopy.