This lab is located at 2-067.
Diffraction based pulse shaping, developed by the Nelson group, can produce multiple and arbitrarily shaped coherent femtosecond pulses, with excellent phase stability and high temporal resolution. The spatial and temporal control afforded by this method provides a unique platform for staging phase-matched degenerate four-, six-, and eight-wave mixing experiments; as well as two- and three-dimensional Fourier Transform optical spectroscopy (FTOPT).
Figure 1. In the FTOPT measurement, a laser pulse first enters the beam shaper (blue box), consisting of a spatial light modular (SLM 1) at the focus of a telescope. A phase pattern is applied that generates the desired spatial beam geometry. The beams then enter the pulse shaper (green box). A telescope first inverts the beams, which then impinge upon a grating G, spectrally dispersing the beams. A cylindrical lens CL focuses the spectrum onto SLM 2. The phase pattern applied in the horizontal dimension controls the temporal (spectral) phase and the sawtooth pattern in the vertical dimension diffracts the beams (d). The diffracted beams return through the pulse-shaping apparatus, hitting a pick off mirror that sends the beams to the sample. The signal is generated in a phase-matched direction given by the specified beam geometry. The full amplitude and phase of the emitted signal is retrieved via heterodyne detection and spectral interferometry.
We are currently utilizing this novel pulse shaping scheme for χ(3), χ(5), and χ(7) multi-dimensional optical spectroscopy experiments of semiconductor quantum wells embedded in an optical microcavity and organic semiconductor J-aggregate double-walled nanotubes and thin films. The excellent phase stability allows us to probe the coupling and dynamics of multiple electronic states, including those of single- and multi-exciton states. Moreover, the nonlinear signal of interest is detected in the rotating frame, analogous to 2D FT NMR methods developed for radio-frequency pulses.
Inorganic semiconductor quantum wells and microcavities
Figure 2: A quantum well sample (no optical cavity) contains 10 layers of 10 nm thick GaAs, separated by 10 nm thick barriers of Al0.3Ga0.7As. Quantum confinement splits the degeneracy of the valence band into what is termed the heavy hole and light hole bands. They couple through the conduction band to form a three-level single particle energy level system, shown in (a), with resonances at 372.5 and 374 THz, respectively. (Higher-lying biexciton levels are not shown.) In two separate measurements, the conjugate field, Ec and the non-conjugate field, Ea, were scanned over the time range 0 to -4 ps in 15 fs steps. These pulse sequences are depicted schematically in (b) and (c) The mixing time, T, was zero. The spectral fringes created between the signal and LO fields were analyzed to extract the full signal amplitude and phase information. The resulting 2D spectra for the non-rephasing and rephasing pulse sequences are shown in spectra A and B, respectively. Here, we use the term non-rephasing to denote a pulse sequence where a non-conjugate field arrives first at the sample (virtual echo) and the term rephasing to denote a pulse sequence where the conjugate field arrives first (photon echo).
J-aggregate thin films
J-aggregates are a class of molecular aggregates that exhibit a wide variety of enhanced nonlinear properties due to very strong intermolecular coupling. They can self-assemble into a variety of nanometer-scale structures, depending on the properties of the molecule. We've begun studies on BIC molecular J-aggregates, which are thought to assemble into two-dimensional brickwork structures (see below). Due to the strong coupling, an optical excitation is coherently shared among many molecules forming a delocalized exciton. The size of the exciton depends on the strength of the coupling and disruptions to the coupling due to disorder. 2D FTOPT can elucidate the mechanisms behind disorder because it separates homogeneous dephasing (dynamic disorder, i.e. exciton-phonon scattering) from inhomogeneous dephasing (static disorder, i.e. energetic disorder). By studying the temperature dependence of the disorder, we can determine which type of disorder controls the delocalization for different temperatures.
Figure 3: (LEFT) Cartoon of brickwork structure for BIC J-aggregates, showing exciton delocalization at different temperatures controlled by different types of disorder. The static disorder imposed localization (dotted line) doesn't change with temperature whereas the localization imposed by dynamic disorder (solid line) does change with temperature. (MIDDLE) 2D FTOPT photon echo showing the inhomogeneous nature of the optical transition at low temperature. (RIGHT) 2D FTOPT photon echo showing an increase in dynamic disorder with an increase in temperature.
All-optical manipulation of exciton-polariton condensates
Exciton-polaritons are composite particles resulting from strong interactions between exciton states in quantum wells and photon modes in the semiconductor microcavity (see below). They have already been used to successfully demonstrate Bose-Einstein condensation and superfluidity in the past decade. We are currently working on the all-optical manipulation of polariton condensates by using novel two-dimensional potentials. The potential profiles are generated from the high-density exciton reservoir by exploiting the repulsive interactions between excitons. Future work will concentrate on the all-optical dynamic modulation and control of polariton condensates.
Figure 4: (LEFT) Schematic structre of a 3/2 semiconductor microcavity quantum well. Light in the microcavity is confined as a standing wave. Three sets of four quantum wells are placed at the antinodes of the standing wave. (RIGHT) The black dashed lines show the cavity and bare exciton energy dispersions. WHen the exciton states and cavity photon modes interact strongly, the eigenstates of the system are known as lower polariton (LP) and upper polariton (UP). Their energy dispersions are shown in red and blue, respectively.
Other topics we are interested in investigating in the future include interactions among coupled electronic states in inorganic semiconductor nanocrystals, organic molecular crystals, hybrid J-aggregate/nanocrystal systems, and Bose-Einsten condensation of exciton-polaritons.
 "Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells," K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, Science 324, 1169 (2009). [url]
 "Exciton-exciton correlations revealed by two-quantum, two-dimensional Fourier transform optical spectroscopy," K. W. Stone, D. B. Turner, K. Gundogdu, S. T. Cundiff, and K. A. Nelson, Acc. Chem. Res. 42, 1452 (2009). [url]
 "Three dimensional electronic spectroscopy of excitons in GaAs quantum Wells," D. B. Turner, K. W. Stone, K. Gundogdu, K. A. Nelson, J. Chem. Phys. 131, 144510 (2009). [url]
 "Coherent measurements of high-order electronic correlations in quantum wells," D. B. Turner and K. A. Nelson, Nature 466, 1089 (2010). [url]
 "Invited article: The coherent optical laser beam recombination technique (COLBERT) spectrometer: Coherent multidimensional spectroscopy made easier," D. B. Turner, K. W. Stone, K. Gundogdu, K. A. Nelson, Rev. Sci. Instr. 82, 081301 (2011). [url]
 "Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy," D. B. Turner, P. Wen, D. H. Arias, K. A. Nelson, Phys. Rev. B 84, 165321 (2011). [url]
 "Persistent exciton-type many-body interaction GaAs qunatum wells measured using two-dimensional optical spectroscopy," D. B. Turner, P. Wen, D. H. Arias, K. A. Nelson, H. Li, G. Moody, M. E. Siemens, and S. T. Cundiff, Phys. Rev. B 85, 201303(R) (2012). [url]
 "Thermally-limited exciton delocalization in superradiant molecular aggregates," D. H. Arias, K. W. Stone, S. M. Vlaming, B. J. Walker, M. G. Bawendi, R. J. Silbey, V. Bulovic, and K. A. Nelson, J. Phys. Chem. B 117, 4553-4559 (2012). [url]
 "Selective enhancements in 2D Fourier transform optical spectroscopy with tailored pulse shapes," P. Wen and K. A. Nelson, J. Phys. Chem. A 117, 6380-6397 (2013). [url]
 "Influence of multi-exciton correlations on nonlinear polariton dynamics in semiconductor microcavities," P. Wen, G. Christmann, J. J. Baumberg, K. A. Nelson, New J. Phys. 15 025005 (2013). [url]
 "Robust excitons inhabit soft supramolecular nanotubes," D. M. Eisele, D. H. Arias, X. Fu, E. A. Bloemsma, C. P. Steiner, R. A. Jensen, P. Rebentrost, H. Eisele, A. Tokmakoff, S. Lloyd, K. A. Nelson, D. Nicastro, J. Knoester, and M. G. Bawendi," Proc. Natl. Acad. Sci. 111, E3367-E3375 (2014). [url]
 "Coherent exciton dynamics in supramolecular light harvesting nanotubes reveal by ultrafast quantum process tomography," J. Yuen-Zhou, D. H. Arias, D. M. Eisele, C. P. Steiner, J. J. Krich, M. G. Bawendi, K. A. Nelson, and A. Aspuru-Guzik, ACS Nano, 8, 5527-5534 (2014). [url]
 "Bose-Einstein condensation of long-lifetime polaritons in thermal equilibrium," Y. Sun, P. Wen, Y. Yoon, G. Liu, M. Steger, L. N. Pfeiffer, K. West, D. W. Snoke, and K. A. Nelson, Phys. Rev. Lett. 118, 016602 (2017) [url]
 "Direct measurement of polariton–polariton interaction strength," Y. Sun, Y. Yoon, M. Steger, G. Liu, L. N. Pfeiffer, K. West, D. W. Snoke, and K. A. Nelson, Nat. Phys. 13, 870 (2017), [url]