Ultrafast Dephasing and Collective Effects in the Quantum Hall Effect Regime

Abstract

Dedicated to Professor Dr. Roland Zimmermann on the occasion of his 60th birthday Using time resolved four-wave-mixing (FWM) spectroscopy and many-body theory we investigate the role of non-instantaneous collective and correlation effects in the dynamics of the cold two dimensional electron gas (2DEG) in large magnetic fields. We find a strong non-Markovian magnetoexciton dephasing and a strong time-dependent Coulomb coupling between the Landau levels (LL), governed by the dynamics of the inter-LL magnetoplasmon (MP) excitations. Our results show that ultrafast spectroscopy is a powerful tool for studying collective and strong correlation effects on the nanoscale. IntroductionCollective effects on the nanometer and femtosecond scale present a frontier problem of condensed matter physics [1-6]. Well-established pictures need to be revised, such as the semiclassical Boltzmann picture of dephasing and relaxation [2, 5-7] and the Random Phase Approximation (RPA) description of the interactions among the photoexcited quasiparticles [1,2]. Transient wave-mixing spectroscopy is ideally suited for exploring such correlation effects, as fluctuations beyond the RPA generate a FWM signal with distinct time and frequency dependence [1, 2]. In undoped semiconductors, the lowest electronic excitations of the ground state electrons are the high energy interband e-h pair excitations, which can adjust almost instantaneously to the dynamics of the photoexcited carriers. The latter then behave as quasiparticles with mutual interactions, while the ground state can be considered as rigid: the many-body nature of the system only affects the different parameters associated with the band structure and the dielectric screening. As a result, the role of the Coulomb correlations can be studied by using theoretical approaches such as the ''dynamics-controlled truncation scheme" (DCTS) [8], which assume that all Coulomb interactions occur between photoexcited e-h pairs and are thus dynamically generated by the optical excitation.The DCTS, however, assumes the absence of free carriers in the ground state [8], a condition that does not hold in modulation-doped quantum wells (MDQWs) with a cold 2DEG in the ground state. The almost unexplored dynamics of strongly correlated systems, whose ground state electrons interact unadiabatically with the photo-excited

Ultrafast nonlinear optical response of the quantum Hall system

“…Here we focus on photoexcitation of the LL0 and LL1 optical transitions only, which are dynamically coupled by the LL0 → LL1 inter-LL MPs [25,38,[40][41][42][43]. These MPs are the lowest-energy neutral charge excitations of the ν = 1 quantum Hall ferromagnet, where the intra-LL charge excitations are suppressed since all spin-↑ LL0 states are occupied in the ground state [107][108][109].…”

“…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.…”

Theory of ultrafast exciton dynamics in the Quantum Hall system

“…Recent time-resolved four-wave-mixing experiments shed new light into the dynamics of this strongly correlated system, and opened a new field of nonequilibrium Quantum Hall physics [5,6,7,8,9,10,11,12,13,14]. The interband optical absorption spectrum of the 2DEG is dominated by LL exciton peaks [5,8].…”

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

“…We conclude that the vertex (rescattering) corrections affect the FWM profile in a significant way.In particular, the non-exponential time-dependence of the {1-LL0-e + 1-LL1-h + LL0→LL1 MP} correlation manifests itself in the symmetric temporal profile of the ∆t 13 signal, which is not adequately described by the Born approximation or by the average polarization model used to inerpret the 2DEG FWM experiments. [20,84,88,89,90,91] We now turn to the population relaxation. 5.7(a) and (b) show the time evolution of the LL0 (n 0 ) and LL1 (n 1 )total carrier populations, photoexcited at t=0 by a single optical pulse, and their different contributions, 5.…”

“…[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.…”