Analytical approach to semiconductor Bloch equations

Abstract

Although semiconductor Bloch equations have been widely used for decades to address ultrafast optical phenomena in semiconductors, they have a few important drawbacks: (i) Coulomb terms between free electron-hole pairs require Hartree-Fock treatment which, in its usual form, preserves excitonic poles but loses biexcitonic resonances. (ii) Solving the resulting coupled differential equations imposes heavy numerics which completely hide the physics. This can be completely avoided if, instead of free electron-hole pairs, we use correlated pairs, i.e., excitons. Their interactions are easy to handle through the recently constructed composite-exciton manybody theory, which allows us to analytically obtain the time evolution of the polarization induced by a laser pulse. This polarization comes from Coulomb interactions between virtual excitons, but also from Coulomb-free fermion exchanges, which are dominant at large detuning.

Polarons and dressed molecules near narrow Feshbach resonances

“…The energy E M of a dressed molecule with momentum p is given in the 1PHA by the pole of the kernel K of the integral equation [17][18][19]:…”

“…The polaron equation yields the correct result in the limit |k F a| ≪ 1, where the attractive/repulsive polaron energies become simply E ∓ = 2πa/m r . The dressed molecule equation instead becomes exact in the deep BEC regime, where it reduces to E M = E b − ǫ F + 2πa AD /m 3 with a AD the atom-dimer scattering length [17][18][19]32].…”

“…We wish to investigate the low-energy excitation spectrum of a single impurity ↓ immersed in a large Fermi gas of particles ↑. In presence of a broad resonance, the physical scenario is by now well understood [14][15][16][17][18][19][20][21][22][23]. On the BCS side, the impurity experiences a weak attractive interaction with the Fermi sea, yielding a thinly dressed quasiparticle, the attractive polaron.…”

Decay of Polarons and Molecules in a Strongly Polarized Fermi Gas

“…The interaction between the ↓ and ↑ particles is short-ranged and described by the scattering length a, whereas the interactions between identical fermions can be ignored. Various approaches locate the polaron-molecule transition at the critical coupling 1/k F a c ∼ 0.9 for m ↑ = m ↓ [4,[6][7][8]. In the strong coupling regime 1/k F a > 1/k F a c , a polaron with energy ω P (we take = 1) is unstable and will decay into a molecule with energy ω M by removing a particle from the FS.…”

Finite Temperature Formalism for Composite Quantum Particles

“…It has proved very powerful to solve longstanding problems related to nonlinear optical susceptibilities [7] or semiconductor Bloch equations [8]. It also allowed us to predict a number of nonlinear optical effects.…”