Coherent spectroscopies on ultrashort time and length scales

T. Brixner, M. Aeschlimann, A. Fischer, P. Geisler, S. Goetz, B. Hecht, J.-S. Huang, T. Keitzl, C. Kramer, P. Melchior, W. Pfeiffer, G. Razinskas, C. Rewitz, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany Fachbereich Physik and Research Center OPTIMAS, TU Kaiserslautern, Erwin-SchrödingerStr. 46, 67663 Kaiserslautern, Germany Nano-Optics and Biophotonics Group, Experimentelle Physik 5, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan Fakultät für Physik, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld


Introduction
The investigation of ultrafast phenomena in nanoscale systems calls for spectroscopic techniques that combine ultrahigh spatial with ultrahigh temporal resolution. In ultrafast nanooptics [1], several methods were developed to analyze and manipulate the dynamics of individual nanoobjects. The challenges are to realize simultaneously and independently the required spatial and temporal degrees of freedom within one method. Propagation along spatial coordinates may be relevant and the properties of electromagnetic near-fields in the vicinity of the object have to be taken into account. This leads to additional complications but also to new exploitable degrees of freedom like longitudinal field variations below the diffraction limit. Here three coherent spectroscopies that we have recently developed are discussed. They all offer spatial and temporal resolution and are suitable for investigating nanooptical ultrafast phenomena.

Space-time-resolved microscopy using spectral interferometry
In the first method (Fig. 1a), we use a confocal microscope in which the excitation is raster-scanned over the sample, and the detection can be chosen independently with help of an additional piezoscanning mirror (PSM) and selection through a pinhole (PH) [2]. Thus we have measured the plasmon group velocity and dispersion in chemically grown Ag nanowires [3]. We also analyzed single-crystal Au samples in which artificial nanoantennas were structured by focused ion-beam (FIB) milling (Fig. 1b). Analysis of reflection versus emission ( Fig. 1c) with spectral interferometry (Fig. 1d) provides the time-domain data (Fig. 1e). Our method opens the possibility to construct and analyze complex nanoplasmonic "circuits".

Space-time-resolved spectroscopy below the diffraction limit using coherent control
In the second method, we aim at spatially separated excitation and detection with a resolution below the optical diffraction limit. This is achieved with coherent control concepts employing femtosecond (polarization) pulse shaping in connection with photoemission electron microscopy (PEEM) for spatial resolution (Fig. 2a). Using the proper pulse shape enables ultrafast excitation sequences in which the first pulsed interaction ("excitation") is spatially separated from the second pulsed interaction ("probe") below the diffraction limit [4]. This concept can be used for selective excitation of photoemission "hot spots" on a corrugated Ag surface (Fig. 2b) [5]. The optimal polarization-shaped pulse with 400 fs duration is quite long (Fig. 2c) and hence points at surprisingly long electronic coherence lifetimes (see Section 4). For spectroscopic applications, the adaptive control approach with a learning loop may be too cumbersome because of separate optimization for each particular target. We show that recently derived analytic control rules can also be employed experimentally and provide the desired nanooptical excitation in a direct fashion (Fig. 2d) [6].

Coherent two-dimensional nanoscopy
In the third method, we generalize coherent two-dimensional (2D) spectroscopy such that it provides additional spatial resolution below the diffraction limit [7]. While in conventional 2D spectroscopy, three input fields create a third-order polarization that is then radiated off as a signal field (Fig. 3a), our scheme for 2D nanometer-resolved spectroscopy ("nanoscopy") employs four optical input fields and no optical output (Fig. 3b). In that way, the diffraction limit can be avoided. We detect the emitted photoelectrons with PEEM after interaction with a four-pulse sequence as generated with a pulse shaper (Fig. 3c). Then 2D spectra can be obtained with 50 nm spatial resolution (Fig. 3d). With the corrugated Ag surface from Figs. 2b,c it is thus possible to map out the coherence lifetimes via modeling and analysis of the 2D lineshapes [7]. Preliminary results have been recorded for other nanostructured systems such as thin-film solar cells in which local lifetimes, as revealed by coherent 2D nanoscopy, are relevant for the cell's efficiency. Fig. 3. Coherent 2D nanoscopy [7]. (a) Conventional four-wave mixing (FWM) with three input and one optical output field is analogous to (b) the new scheme with four input and zero optical output fields. (c) A sequence of four femtosecond pulses excites the sample in a spot larger than the diffraction limit, but PEEM provides 50-nm spatial resolution. (d) An exemplary 2D nanospectrum is shown for a corrugated Ag surface.

Conclusion
The nanoscopic realm is made accessible on an ultrafast timescale by a number of new spectroscopic methods. They all offer information on the coherent evolution of a quantum system via phasesensitive analysis. This is achieved in a combination of concepts from three different research communities: ultrafast nano-optics, coherent control, and coherent two-dimensional spectroscopy. We expect broad applicability to many different nanoscopic systems in the future.