...at JILA, which is a joint institute of the University of Colorado and the National Institute for Standards and Technology
Coherent Phenomena in Semiconductors
Transient Four-Wave Mixing
Matter that has been resonantly excited by coherent laser pulse remembers the phase of the incident light for a length of time. This time, known as the dephasing time, can be tens of nanoseconds (or longer) in a dilute gas of atoms. However, for electron-hole pairs of a typical (intrinsic, bulk) semiconductor the dephasing time is about one picosecond. Due to this timescale, the coherent phenomena in semiconductors has only been accessible with femtosecond laser sources. Consequently, routine studies of coherence in semiconductors were not undertaken until several decades after those in dilute atomic gases.
A typical experiment for probing coherence is transient four-wave mixing (TFWM). In one version this experiment (see figure at right), two ultrashort optical pulses (10-100 femtoseconds in duration) are focused onto a semiconductor sample with small angle between them. The interaction of the two pulses gives rise to a diffraction signal. The signal goes in the direction 2k2-k1, where k1 and k2 are the incident pulses (the subscript denotes time order).
These experiments are yielding insight into the differences between coherent phenomena in semiconductors and dilute atomic gases. The presence of many-body interactions in the semiconductors results in dramatic differences.
Two-dimensional Fourier-Transform Spectroscopy
Typical 2DFT Spectra for a GaAs multiple quantum well at low temperture. These rephasing spectra are acquired with co-linear (left) and cross-linear (right) polarization configurations.
Two-dimensional Fourier-transform (2DFT) spectroscopy is an extension of the standard TFWM technique, and the optical analogue of multidimensional nuclear magnetic resonance spectroscopy. The advantage of this technique comes from correlating the phase (frequency) evolution of the nonlinear polarization field during two independent time periods. A complex two-dimensional spectrum is produced by performing a numerical Fourier-transform.
As shown in the example above, a single two-dimensional spectrum can identify couplings between resonances (cross peaks), separate quantum mechanical pathways, and distinguish among microscopic many-body interactions and biexciton effects. Additionally, the homogeneous and inhomogeneous linewidths of a resonance can be extracted from the diagonal and anti-diagonal slices of the resonance feature. For futher details see the related publication record and other links below.
Recently, we have developed a new 2DFT spectrometer that allows us to capture the complex 2D spectrum for previously unseen polarizations and to examine two-quantum transistions.
< postdocs Alan Bristow, Denis Karaiskaj and Xingcan Dai are currently involved in this research, Tianhao Zhang recently graduated with a thesis on 2DFT spectroscopy>
Characterizing Self-Assembled Quantum Dots
Analogy to a photon echo. Runners = oscillators, with speeds = resonance frequencies, and gun shot = resonant pulse. Click "GO" to create a coherent superposition between the ground and excited state. Watch the runners "dephase" from one another. Then click "TURN" to send in a second conjugate pulse to reverse the dephasing. Wait to see the resulting "echo" of the initial configuration.
Self-assembled quantum dots are small (nanometer scale) islands of low bandgap semiconductor embedded in a higher bandgap material. Dephasing information can be used to understand how light, dot excitons, and the surrounding environment interact with one another. Because of variations in size, however, the excited state of each dot evolves at a slightly different rate, causing the four-wave mixing signal to decay much more rapidly than the dephasing time. Fortunately, an effect called the photon echo can be used to recover the dephasing information. The first pulse excites the dots, and then after a time t the second pulse reverses the evolution of their excited states. After a time 2t, the dot states rephase to form the photon echo. The dephasing time is recovered by measuring the decay of the photon echo signal as t is varied. See the analogy to runners on a track above. Quantum dots show dephasing behavior that is similar to atoms in some respects, but they also reveal more complicated behavior due to closer coupling with the environment.
< postdoc Xingcan Dai is currently involved in this research >