J. G. Muga

Physical realization of -symmetric potential scattering in a planar slab waveguide

A physical realization of scattering by -symmetric potentials is provided: we show that the Maxwell equations, for an electromagnetic wave travelling along a planar slab waveguide filled with gain and absorbing media in contiguous regions, can be approximated in a parameter range by a Schrodinger equation with a -symmetric scattering potential.

Shortcut to Adiabatic Passage in Two- and Three-Level Atoms

We propose a method to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. It supplements or substitutes the standard laser beam setups with auxiliary pulses that steer the system along the adiabatic path. Compared to other strategies, such as composite pulses or the original adiabatic techniques, it provides a fast and robust approach to population control.

Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity

A method is proposed to cool down atoms in a harmonic trap without phase-space compression as in a perfectly slow adiabatic expansion, i.e., keeping the same populations of instantaneous levels in the initial and final traps, but in a much shorter time. This may require that the harmonic trap become transiently an expulsive parabolic potential. The cooling times achieved are shorter than those obtained using optimal-control bang-bang methods and real frequencies.

Optimally robust shortcuts to population inversion in two-level quantum systems

We examine the stability versus different types of perturbations of recently proposed shortcuts to adiabaticity to speed up the population inversion of a two-level quantum system. We find the optimally robust processes by using invariant-based engineering of the Hamiltonian. Amplitude noise and systematic errors require different optimal protocols.

Multiple schrodinger pictures and dynamics in shortcuts to adiabaticity

A Schrödinger equation may be unitarily transformed into dynamical equations in different interaction pictures which describe a common physical process, i.e., the same underlying interactions and dynamics. In contrast to this standard scenario, other relations are also possible, such as a common interaction-picture dynamical equation corresponding to several Schrödinger equations that represent different physical processes. This may enable us to design alternative and feasible experimental routes for operations that are a priori difficult or impossible to perform. The power of this concept is exemplified by engineering Hamiltonians that improve the performance or make realizable several shortcuts to adiabaticity.

Frictionless dynamics of Bose–Einstein condensates under fast trap variations

A method is proposed to design the time dependence of the trap frequency and achieve in a short time an adiabatic-like (frictionless) evolution of Bose-Einstein condensates governed by the Gross-Pitaevskii equation. Different cases depending on the effective dimension of the trap and the interaction regimes are considered. 2D traps are particularly suitable as the method can be applied without the need to impose any additional time-dependent change in the strength of the interatomic interaction or a Thomas-Fermi regime as it occurs for 1D and 3D traps.

Engineering of fast population transfer in three-level systems

The laser control of internal state preparation and dynamics is of importance in atomic and molecular physics for applications such as metrology, interferometry, quantum information processing and driving of chemical reactions [1–5]. In twoor three-level systems, resonant pulses, rapid adiabatic passage (RAP), stimulated Raman adiabatic passage (STIRAP), and their variants have been widely used to perform population transfers [2–4]. Generally, resonant pulses may be fast, but are highly sensitive to the deviations of pulse areas and exact resonances, whereas the adiabatic passage techniques are robust versus variations in experimental parameters but slow. To combine the advantages of resonant pulses and adiabatic techniques and achieve fast and high-fidelity quantum state control, some alternative approaches, like composite pulses [6–8] and optimal control theory [9–11], have been proposed. Several recent works on “shortcuts to adiabaticity” have been also devoted to internal state population transfer and control [12–19]. The shortcut techniques include counter-diabatic control protocols [12] or, equivalently, transitionless quantum driving [13–15], “fast-forward” scaling [20], and inverse engineering based on Lewis-Riesenfeld invariants [21, 22]. These methods are in fact strongly related, and even potentially equivalent [16, 23]. However, they provide in general different shortcuts [16, 19].

Arrival time in quantum mechanics

A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a spatial point.

Transitionless quantum drivings for the harmonic oscillator

Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.

Free-motion time-of-arrival operator and probability distribution

We reappraise and clarify the contradictory statements found in the literature concerning the time-of-arrival operator introduced by Aharonov and Bohm in Phys. Rev. 122, 1649 (1961). We use Naimarks dilation theorem to reproduce the generalized decomposition of unity (or positive-operator-valued measures) from any self-adjoint extension of the operator, emphasizing a natural one, which arises from the analogy with the momentum operator on the half-line. General time operators are set within a unifying perspective. It is shown that they are not in general related to the time of arrival, even though they may have the same form.