Nonlinear optical studies of the transient coherence in the Quantum Hall system

Abstract

We review recent investigations of the femtosecond non-linear optical response of the two-dimensional electron gas (2DEG) in a strong magnetic field. We probe the Quantum Hall (QH) regime for filling factors ν ∼ 1. Our focus is on the transient coherence induced via optical excitation and on its time evolution during early femtosecond timescales. We simultaneously study the interband and intraband coherence in this system by using a nonlinear spectroscopic technique, transient threepulse four wave mixing optical spectroscopy, and a many-body theory. We observe striking differences in the temporal and spectral profile of the nonlinear optical signal between a modulation doped quantum well system (with the 2DEG) and a similar undoped quantum well (without a 2DEG). We attribute these qualitative differences to Coulomb correlations between the photoexcited electron-hole pairs and the 2DEG. We show, in particular, that intraband many-particle coherences assisted by the inter-Landau-level magnetoplasmon excitations of the 2DEG dominate the femtosecond nonlinear optical responce. The most striking effect of these exciton-magnetoplasmon coherences is a large off-resonant four-wave-mixing signal in the case of very low photoexcited carrier densities, not observed in the undoped system, with strong temporal oscillations and unusually symmetric temporal profile.

Ultrafast nonlinear optical response of the quantum Hall system

“…In summary, we discussed a theory [46,114] that can describe the ultrafast non-linear optical response of magnetoexcitons in both doped and undoped semiconductors, including systems with a strongly correlated manyelectron ground state, like the quantum Hall system. We discussed a method for describing the interaction contributions to the density matrix equation of motion, which gives the third-order non-linear polarization measured in pumb-probe and FWM experiments.…”

“…Recent time-resolved four-wave-mixing experiments have shed new light into the dynamics of this strongly correlated system [25,[38][39][40][41][42][43][44][45][46][47][48]. The 2DEG correlations and collective electronic excitations dominate the dephasing of the photoexcited excitons for low photoexcitation intensities [25,[38][39][40][41][42][43][44][45][46][47][48], while the time and frequency dependence of the FWM spectra revealed new dynamical features that could not be explained within the random phase approximation (RPA). Of particular interest is the dynamics of the quantum Hall system during time scales comparable to the characteristic time it takes the cold 2DEG "bath" system to react to the introduction of photoexcited excitons.…”

“…We were able to separate out the correlated contributions, which lead to the incoherent effects, without assuming a Hartree-Fock ground state, as in the case of the DCTS. Although our theory can be used to treat the general case, we are interested is the spin-↑ polarized LL0 2DEG, motivated by recent three-pulse FWM experiments [45][46][47]52]. We derive an average polarization model from the full theoretical formulation to explain the experimental results, and show we can access the interband and intraband dynamics of the system.…”

Ultrafast dynamical properties of strongly interacting systems under nonlinear coherent photoexcitation by multiple ultrashort laser pulses

“…For example, in the samples used in the experiments of Refs. [[85,90]], the LL0 resonance displayed a Lorentzian lineshape while the FWM signal in the case of photoexcitation at the LL0 energy did not produce any unexpected results. On the other hand, these experiments show the emergence, for ν <2, of an asymmetric LL1 resonance with a strong high energy shoulder.…”

“…[81] Ultrarafast nonlinear 1.2 Thesis Structure spectroscopy can shed light into the coherent dynamics of the QHS. [82,83,84,85,86,87,88,89,90,91] The above developments make our theoretical advances, which address transient coherence and relaxation in strongly correlated systems, particularly timely.…”