Theory of ultrafast exciton dynamics in the Quantum Hall system

Abstract

We discuss a theory of the ultrafast non-linear optical response of excitons in the Quantum Hall system. Our theory focusses on the role of the low energy collective electronic excitations of the cold, strongly correlated, two-dimensional electron gas (2DEG) present in the ground state. It takes into account ground state electron correlations and Pauli exchange and interaction effects between the photoexcited excitons and the collective excitations. Our formulation addresses both the initial coherent regime, where the dynamics is determined by exciton and 2DEG polarizations, and the subsequent incoherent regime, dominated by population dynamics.We describe non-Markovian memory, dephasing, and correlation effects and a non-linear exciton hybridization due to the non-instantaneous interactions. We identify the signature of the coherent inter-Landau level magnetoplasmon (MP) in the temporal profile of the three-pulse time-integrated four-wave-mixing signal in the initial coherent regime.Comment: 36 pages, 6 figures, to appear in Chemical Physics; There are some differences between this version and the version published in Chemical Physic

Correlation effects in the ultrafast dynamics of the Quantum Hall system close to v = 1

“…X is the dipole interband transition operator [7,9]. We consider right-circularly polarized optical pulses (σ + ), which excite only spin-↓ electrons, and consider filling factors close to 1 ν ∼ , where the ground state is predominantly populated by spin-↑ LL0 electrons.…”

“…Two different such excitations play a role here: the interband excitons, created by the LLn electron-LLm hole exciton operator † nm X q [9], and the LLn electron-LLm 2DEG hole MPs, created by the collective density operators ˆe nmσ ρ q (single mode approximation) [3,9]. Similar to the MP states [3], in the doped system the LLn exciton states † | | n n X X G Ò = Ò are strongly correlated, created by the exciton operator † † 0n n n X X = acting on the correlated ground state |GÒ.…”

“…We use the standard two-band Hamiltonian H that describes discrete LLs coupled by the Coulomb interactions [7,9,17]. The coupling of the optical field is characterized by the Rabi energy ( )…”

Magnetization relaxation and collective spin excitations in correlated double-exchange ferromagnets

“…47,48 In Ref. [49], a similar method was used to calculate the density matrix that describes the coherent ultrafast nonlinear optical dynamics of the Quantum Hall system. Refs.…”

“…Our approach, used before in the context of the Hubbard Hamiltonian, 47,48 is in the same spirit as the projection and factorization scheme of Ref. [49], used to calculate the ultrafast nonlinear optical response of systems with a strongly correlated ground state, and the correlation expansion of Ref. [50].…”