Electron Optics in Phase Space

Vladimir Chernyak, Shaul Mukamel

A time-dependent functional approach is developed for calculating the dynamical optical response and ground-state properties of nonrelativistic fermion systems. The functional (effective action) uses the particle-hole components of the reduced single-electron density matrix as variables and is constructed using the natural orbitals as a reference. It is defined on pairs of trajectories that constitute a Liouville space path in the phase space of the classical analog of the quantum system. A perturbative ``semiclassical'' calculation of the effective Liouville-space action is used to incorporate correlation effects in the linear optical response.

D. C. Glattli

Sujit Sarkar

We study the effect of the long-range random potential on optical conductivity in a one-dimensional interacting electron system with extended-Fermi surface. We apply Abelian bosonization to show that in one part of the momentum space the system has a metallic behavior with a gap in the spin sector, while in the other region of momentum space it behaves like a gapless Luttinger liquid (paramagnetic metallic phase). Consequently we consider the scattering of electrons with the long-range random potential (forward scattering disorder) in that region of momentum space, where the system is in gapless Luttinger liquid phase. The real part of the optical conductivity has no Drude peak for small frequency $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}0),$ but the Drude weight is nonzero and it has the doping dependence, while the imaginary part of the optical conductivity shows the usual $1/\ensuremath{\omega}$ behavior, like in the clean system, and it has no doping dependence. We explain the doping dependence with the help of one-dimensional exact density of states.

S. Olivares

Alatz Alvarez-Ahedo, Miriam Lazo, Tian-Niu Xu +3 more

Light-electron interactions generate synthetic momentum-space dynamics that can be used to engineer free electron quantum states. Here we develop coherent control protocols in which the optical phase acts as the controllable hopping phase of a Floquet-Bloch momentum lattice. Pontryagin optimization designs phase-only waveforms that prepare selected momentum populations and coherent few-sideband superpositions with programmable relative phases. In a complementary Bragg regime protocol, dynamical phase matching selectively couples neighboring sidebands and enables deterministic sequential state synthesis. Full wave-packet simulations based on the minimal-coupling Hamiltonian identify the tolerance window set by phase noise, detuning, and finite momentum spread. The two protocols expose a speed-selectivity tradeoff between ultrafast multilevel interference control and slower resonant engineering, establishing programmable free electron sidebands as a platform for ultrafast quantum state synthesis.

Wolfgang P. Schleich