Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions

We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed.Comment: 4 pages, one figure, revised versio

Resonance-like piezoelectric electron-phonon interaction in layered structures

We show that mismatch of the piezoelectric parameters between layers of multiple-quantum well structures leads to modification of the electron-phonon interaction. In particular, short-wavelength phonons propagating perpendicular to the layers with wavevector close to $2\pi n/d$, where $d$ is the period of the structure, induce a strong smoothly-varying component of the piezo-potential. As a result, they interact efficiently with 2D electrons. It is shown, that this property leads to emission of collimated quasi-monochromatic beams of high-frequency acoustic phonons from hot electrons in multiple-quantum well structures. We argue that this effect is responsible for the recently reported monochromatic transverse phonon emission from optically excited GaAs/AlAs superlattices, and provide additional experimental evidences of this.Comment: 6 pages, 7 figure

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Electron-phonon interaction via Pekar mechanism in nanostructures

We consider an electron-acoustic phonon coupling mechanism associated with the dependence of crystal dielectric permittivity on the strain (the so-called Pekar mechanism) in nanostructures characterized by strong confining electric fields. The efficiency of Pekar coupling is a function of both the absolute value and the spatial distribution of the electric field. It is demonstrated that this mechanism exhibits a phonon wavevector dependence similar to that of piezoelectricity and must be taken into account for electron transport calculations in an extended field distribution. In particular, we analyze the role of Pekar coupling in energy relaxation in silicon inversion layers. Comparison with the recent experimental results is provided to illustrate its potential significance

Phonon spectroscopy with chirped shear and compressive acoustic pulses

Picosecond duration compressive and shear phonon wave packets injected into (311) GaAs slabs transform after propagation through ∼1  mm into chirped acoustic pulses with a frequency increasing in time due to phonon dispersion. By probing the temporal optical response to coherent phonons in a near surface layer of the GaAs slab, we show that phonon chirping opens a transformational route for high-sensitivity terahertz and subterahertz phonon spectroscopy. Temporal gating of the chirped phonon pulse allows the selection of a narrow band phonon spectrum with a central frequency up to 0.4 THz for longitudinal and 0.2 THz for transverse phonons