Ultrafast dephasing in strongly correlated systems

Abstract

Using projection techniques we derive the equation of motion for the third-order nonlinear optical polarization of a strongly correlated system. We do not assume a Hartree-Fock ground state, but include the ground state correlations via time-independent interaction parameters and energies. Our theory can be used to describe the ultrafast nonlinear optical response of a strongly correlated cold electron gas, such as the two-dimensional electron gas in the quantum Hall effect regime. For this system, we show that the collective electronic excitations lead to a time-dependent coupling of the Landau level magnetoexcitons and a strong non-Markovian exciton dephasing. We discuss the signatures in the transient four-wave-mixing spectrum. . Most efforts so far have focussed on undoped semiconductors, where the lowest electronic excitations are the high energy interband e-h pair excitations that behave as quasiparticles with mutual interactions. In the absence of low lying electronic excitations, the ground state can be considered as rigid, and is usually described within the Hartree-Fock approximation. As a result, in undoped semiconductors, the role of the Coulomb correlations in the ultarafast nonlinear response can be studied in an exact fashion by using, e.g., the ''dynamics-controlled truncation scheme" (DCTS) [2].The DCTS considers a system with a Hartree-Fock ground state and assumes the absence of free carriers prior to the optical excitation [2]. Here we are interested in systems such as modulation-doped quantum wells (MDQWs) in a strong magnetic field, where a strongly correlated two-dimensional electron gas (2DEG) is already present in the ground state. The almost unexplored dynamics of strongly correlated systems, whose ground state electrons interact unadiabatically with the photo-excited e-h pairs, raises very fundamental questions. In MDQWs, the direct exciton-exciton interactions are screened. In the absence of magnetic field, the coherent nonlinear optical response was studied in Refs. [3,4] and shown to be strongly influenced by the interactions between the photoexcited carriers and the Fermi sea excitations.The role of the Coulomb correlations becomes more pronounced when a magnetic field is applied to the 2DEG in MDQWs, in a direction perpendicular to the quantum well plane. The energy

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].…”

“…The interband optical absorption spectrum of the 2DEG is dominated by LL exciton peaks [5,8]. In the QHE system, the 2DEG correlations and collective electronic excitations dominate the dephasing of the photoexcited excitons (X) for low photoexcitation intensities [5,6,7,8,9,10,11,12,13,14]. Of particular interest is the dynamics of the QHE system during time scales comparable to the characteristic time it takes the cold 2DEG "bath" system to react to the introduction of photoexcited Xs.…”

“…Therefore, T M P is of the order of a few hundreds of femtoseconds, longer than the duration of the ∼100fs optical pulses used to probe this system and tunable by changing the magnetic field. Strong quantum kinetic effects in the ultrafast non-linear optical dynamics are expected in this regime, explored for the first time in [5,6,7,8,9,10,11,12,13,14]. In order to study time scales comparable to the duration of the X-2DEG scattering events, well-established pictures such as the semiclassical Boltzmann picture of dephasing and relaxation (which assumes instantaneous X-2DEG scattering) and the Markov approximation need to be revisited [15,16,17,18,19,20].…”