J. A. Budagosky, D. V. Khomitsky, E. Ya. Sherman, and A. Castro, Phys. Rev. B 93, 035423 (2016).

We use quantum optimal control theory algorithms to design external electric fields that drive the coupled spin and orbital dynamics of an electron in a double quantum dot, subject to the spin-orbit coupling and Zeeman magnetic fields. We obtain time profiles of multifrequency electric field pulses which increase the rate of spin-flip transitions by several orders of magnitude in comparison with monochromatic fields, where the spin Rabi oscillations were predicted to be very slow. This precise (with fidelity higher than 1 × 10−4 ) and fast (at the time scale of the order of 0.1 ns, comparable with the Zeeman spin rotation and the interdot tunneling time) simultaneous control of the spin and position is achieved while keeping the electron in the four lowest tunneling and Zeeman-split levels through the duration of the pulse. The proposed algorithms suggest effective applications in spintronics and quantum information devices.

A. Castro, A. Rubio, and E. K. U. Gross, Eur. Phys. J. B 88, 191 (2015).

High harmonic generation (HHG) provides a flexible framework for the development of coherent light sources in the extreme-ultraviolet and soft X-ray regimes. However it suffers from low conversion efficiencies as the control of the HHG spectral and temporal characteristics requires manipulating electron trajectories on attosecond time scale. The phase matching mechanism has been employed to selectively enhance specific quantum paths leading to HHG. A few important fundamental questions remain open, among those how much of the enhancement can be achieved by the single-emitter and what is the role of
correlations (or the electronic structure) in the selectivity and control of HHG generation. Here we address those questions by examining computationally the possibility of optimizing the HHG spectrum of isolated hydrogen and helium atoms by shaping the slowly varying envelope of a 800 nm, 200-cycles long laser pulse. The spectra are computed with a fully quantum mechanical description, by explicitly computing the time-dependent dipole moment of the systems using a time-dependent density-functional approach (or the single-electron Schröodinger equation for the case of H), on top of a one-dimensional model. The sought optimization corresponds to the selective enhancement of single harmonics, which we find to be significant. This selectivity is entirely due to the single atom response, and not to any propagation or phase-matching effect. Moreover, we see that the electronic correlation plays a role in the determining the degree of optimization that can be obtained.

J. L. Alonso, A. Castro, J. Clemente-Gallardo, J. C. Cuch ́ı, P. Echenique, J. G. Esteve, and F. Falceto, Phys. Rev. E 91, 022137 (2015).

Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions and prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy, or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schrödinger’s idea cannot be used to construct an appropriate quantum equilibrium thermodynamics.