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The Journal of Physical Chemistry Letters

Enhanced-Resolution Single-Shot 2DFT Spectroscopy by Spatial Spectral Interferometry

Austin P. Spencer, Boris Spokoyny, Elad Harel

Published Feb 25, 2015• 10 citations
Publisher

Abstract

We demonstrate use of spatial interference for the complete electric field reconstruction of two-dimensional (2D) coherent spectroscopic signals generated through four-wave mixing (4WM) in a single laser shot. Until now, the amplitude and phase characterization of 4WM signals has relied primarily on Fourier transform spectral interferometry (FTSI), which limits the measurement's sensitivity and resolution. We show that spatial spectral interferometry (SSI) is a generalized approach to 4WM signal detection that eliminates these inherent limitations of FTSI without introducing additional experimental complexity. SSI is used to measure the 2D photon echo spectra of two systems with dramatically different line widths, the coupled D line transitions in rubidium vapor and the energy-transfer dynamics in the light-harvesting protein LH2.

DOI
10.1021/acs.jpclett.5b00273

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We demonstrate use of spatial interference for the complete electric field reconstruction of two-dimensional (2D) coherent spectroscopic signals generated through four-wave mixing (4WM) in a single laser shot. Until now, the amplitude and phase characterization of 4WM signals has relied primarily on Fourier transform spectral interferometry (FTSI), which limits the measurement's sensitivity and resolution. We show that spatial spectral interferometry (SSI) is a generalized approach to 4WM signal detection that eliminates these inherent limitations of FTSI without introducing additional experimental complexity. SSI is used to measure the 2D photon echo spectra of two systems with dramatically different line widths, the coupled D line transitions in rubidium vapor and the energy-transfer dynamics in the light-harvesting protein LH2.
Four-quadrature spectral interferometry using balanced coherent detection enables single-shot full-field characterization of complex-shaped optical waveforms with near quantum-limited sensitivity. A 90 degrees optical hybrid places a waveform in four-quadrature-phases with a stronger, well-characterized reference pulse. Measurement of the four spectra with an integrating two-dimensional detector array followed by balanced detection uniquely determines the signal field. Balanced coherent detection provides common-mode noise rejection and coherent gain enabling near quantum-limited sensitivity. The single-shot waveform was temporally gated from a 100 ps periodic train of arbitrary optical waveforms generated using line-by-line pulse shaping on a 10 GHz optical frequency comb. The measurements show arbitrary waveforms with 200-ps record lengths, 500 GHz optical bandwidths and only 1200 detected photons.
The theory for temporally multidimensional, electronically resonant four-wave-mixing (FWM) spectroscopy based on broadband light interferometry is developed. Both homodyne and heterodyne detection are considered. Upon spectrally resolving the signal, the electronic Bohr frequency is seen to be extremely down-converted, even to zero frequency, but only with homodyne detection. These very low frequency fringes, referred to as radiation difference oscillations, are well known in the interferometric coherent Raman broadband light spectroscopies. Such low frequency fringes permit interferometry in the optical region using Nyquist criteria corresponding to far infrared sampling rates. Possible applications are illustrated by simulations of the two-dimensional third order signals from an electronic two-level system in a variety of ``baths.'' It is seen how homogeneous and inhomogeneous line-shaping mechanisms manifest themselves differently and revealingly in the free induction decay, the photon echo decay and their cross term components of the FWM signal.
Electronic structure and dynamics are captured by optical 2D-Fourier-transform (2DFT) spectroscopy, which tracks the phase of the nonlinear signal during two time delays of a multi-pulse excitation sequence. These Fourier-transformed spectra separate and isolate overlapping and competing contributions to the coherent response. We have developed an ultra-stable platform consisting of nested interferometers with active phase control, allowing for exploration of single- and two-quantum coherences. Phase-resolved spectra are retrieved by all-optical determination of experimental phase ambiguities. GaAs quantum wells show suppression of many-body interactions in cross-linear polarized 2DFT spectra and many-body two-quantum coherences. Potassium vapor also shows unexpected two-quantum coherences.
We employ two-dimensional (2D) coherent, nonlinear spectroscopy to investigate couplings within individual InAs quantum dots (QDs) and QD molecules. Swapping pulse ordering in a two-beam sequence permits one to distinguish between rephasing and nonrephasing four-wave mixing (FWM) configurations. We emphasize the nonrephasing case, allowing one to monitor two-photon coherence dynamics. Respective Fourier transform yields a double quantum 2D FWM map, which is corroborated with its single quantum counterpart, originating from the rephasing sequence. We introduce referencing of the FWM phase with the one carried by the driving pulses, overcoming the necessity of its active stabilization, as required in 2D spectroscopy. Combining single and double quantum 2D FWM provides a pertinent tool in detecting and ascertaining coherent coupling mechanisms between individual quantum systems, as exemplified experimentally.
Recent advances in techniques for generating quantum light have stimulated research on novel spectroscopic measurements using quantum entangled photons. One such spectroscopy technique utilizes non-classical correlations among entangled photons to enable measurements with enhanced sensitivity and selectivity. Here, we investigate the spectroscopic measurement utilizing entangled three photons. In this measurement, time-resolved entangled photon spectroscopy with monochromatic pumping [A. Ishizaki, J. Chem. Phys. 153, 051102 (2020)] is integrated with the frequency-dispersed two-photon counting technique, which suppresses undesired accidental photon counts in the detector and thus allows one to separate the weak desired signal. This time-resolved frequency-dispersed two-photon counting signal, which is a function of two frequencies, is shown to provide the same information as that of coherent two-dimensional optical spectra. The spectral distribution of the phase-matching function works as a frequency filter to selectively resolve a specific region of the two-dimensional spectra, whereas the excited-state dynamics under investigation are temporally resolved in the time region longer than the entanglement time. The signal is not subject to Fourier limitations on the joint temporal and spectral resolution, and therefore, it is expected to be useful for investigating complex molecular systems in which multiple electronic states are present within a narrow energy range.