arXiv subjects

E. Torrontegui

Publications and source records attributed to E. Torrontegui.

47 records · Page 3Linked to original sources

arXiv2011

Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity

A Schrödinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes 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 physics. 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.

quant-ph↗

arXiv2011

Fast transitionless expansions of cold atoms in optical Gaussian beam traps

We study fast expansions of cold atoms in a three-dimensional Gaussian-beam optical trap. Three different methods to avoid final motional excitation are compared: inverse engineering using Lewis-Riesenfeld invariants, which provides the best overall performance, a bang-bang approach, and a fast adiabatic approach. We analyze the excitation effect of anharmonic terms, radial-longitudinal coupling, and radial-frequency mismatch. In the inverse engineering approach these perturbations can be suppressed or mitigated by increasing the laser beam waist.

quant-ph↗

arXiv2011

Optimal trajectories for efficient atomic transport without final excitation

We design optimal harmonic-trap trajectories to transport cold atoms without final excitation, combining an inverse engineering techniqe based on Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are not really harmonic, we keep the relative displacement between the center of mass and the trap center bounded. Under this constraint, optimal protocols are found according to different physical criteria. The minimum time solution has a "bang-bang" form, and the minimum displacement solution is of "bang-off-bang" form. The optimal trajectories for minimizing the transient energy are also discussed.

quant-ph↗

arXiv2011

Fast transport of Bose-Einstein condensates

We propose an inverse method to accelerate without final excitation the adiabatic transport of a Bose Einstein condensate. The method, applicable to arbitrary potential traps, is based on a partial extension of the Lewis-Riesenfeld invariants, and provides transport protocols that satisfy exactly the no-excitation conditions without constraints or approximations. This inverse method is complemented by optimizing the trap trajectory with respect to different physical criteria and by studying the effect of noise.

quant-ph↗

arXiv2011

Quantum simulation of a triatomic chemical reaction with ultracold atoms on a waveguide

We study the scaling and coordinate transformation to physically simulate quantum three-body collinear chemical reactions of the type A+BC $\rightarrow$ AB+C by the motion of single ultracold atoms or a weakly interacting Bose-Einstein condensate on an $L$-shaped waveguide. As an example we show that the parameters to model the reaction F+HH $\to$ H+HF with lithium are at reach with current technology. This mapping provides also an inverse scattering tool to find an unknown potential, and a way to transfer the knowledge on molecular reaction dynamics to design beam splitters for cold atoms with control of the channel outcome and vibrational excitation.

quant-ph↗

arXiv2011

Lewis-Riesenfeld invariants and transitionless tracking algorithm

Different methods have been recently put forward and implemented experimentally to inverse engineer the time dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via non-adiabatic shortcuts. In the "transitionless tracking algorithm" proposed by Berry, shortcut Hamiltonians are designed so that the system follows exactly, in an arbitrarily short time, the approximate adiabatic path defined by a reference Hamiltonian. A different approach is based on designing first a Lewis-Riesenfeld invariant to carry the eigenstates of a Hamiltonian from specified initial to final configurations, again in an arbitrary time, and then constructing from the invariant the transient Hamiltonian connecting these boundary configurations. We show that the two approaches, apparently quite different in form and so far in results, are in fact strongly related and potentially equivalent, so that the inverse-engineering operations in one of them can be reinterpreted and understood in terms of the concepts and operations of the other one. We study as explicit examples the expansions of time-dependent harmonic traps and state preparation of two level systems.

quant-ph↗

arXiv2010

Explanation and observability of diffraction in time

Diffraction in time (DIT) is a fundamental phenomenon in quantum dynamics due to time-dependent obstacles and slits. It is formally analogous to diffraction of light, and is expected to play an increasing role to design coherent matter wave sources, as in the atom laser, to analyze time-of-flight information and emission from ultrafast pulsed excitations, and in applications of coherent matter waves in integrated atom-optical circuits. We demonstrate that DIT emerges robustly in quantum waves emitted by an exponentially decaying source and provide a simple explanation of the phenomenon, as an interference of two characteristic velocities. This allows for its controllability and optimization.

quant-ph↗

arXiv2010

Fast atomic transport without vibrational heating

We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven non-adiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies and accelerations involved are analyzed, as well as the relation to previous approaches (based on classical trajectories or "fast-forward" and "bang-bang" methods) which can be integrated in the invariant-based framework.

quant-ph↗

arXiv2010

Classical picture of post-exponential decay

Post-exponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the post-exponential regime, by means of an ensemble of classical particles emitted with constant probability per unit time and the same half-life as the quantum system. The energy distribution of the ensemble is chosen to be identical to the quantum distribution, and the classical point source is located at the scattering length of the corresponding quantum system. A 1D example is provided to illustrate the general argument.

quant-ph↗

arXiv2010

Cold atom dynamics in crossed laser beam waveguides

We study the dynamics of neutral cold atoms in an $L$-shaped crossed-beam optical waveguide formed by two perpendicular red-detuned lasers of different intensities and a blue-detuned laser at the corner. Complemented with a vibrational cooling process this setting works as a one-way device or "atom diode".

physics.atom-ph↗

arXiv2009

Enhanced observability of quantum post-exponential decay using distant detectors

We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability density at the transition time, and thus its observability, increases with the distance of the detector from the source, up to a critical distance beyond which exponential decay is no longer observed. Solvable models provide explicit expressions for the dependence of the transition on resonance and observational parameters, facilitating the choice of optimal conditions.

quant-ph↗