Carlo Presilla

On Schrödinger Equations with Concentrated Nonlinearities

Abstract Schrodinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to separate the relevant degrees of freedom by noting that in the regions where the nonlinearities are effective all states are suppressed but the metastable ones (resonances). In this way the description of the nonlinear regions is reduced to ordinary differential equations weakly coupled to standard Schrodinger equations valid in the linear regions. The idea is illustrated through the study of a prototype equation recently proposed for resonant tunneling of electrons through a double barrier heterostructure and for which nonlinear oscillations have been numerically predicted.

Measurement Quantum Mechanics and Experiments on Quantum Zeno Effect

Abstract Measurement quantum mechanics, the theory of a quantum system which undergoes a measurement process, is introduced by a loop of mathematical equivalencies connecting previously proposed approaches. The unique phenomenological parameter of the theory is linked to the physical properties of an informational environment acting as a measurement apparatus which allows for an objective role of the observer. Comparison with a recently reported experiment suggests how to investigate novel interesting regimes for the quantum Zeno effect.

NONLINEAR FEEDBACK OSCILLATIONS IN RESONANT TUNNELING THROUGH DOUBLE BARRIERS

We analyze the dynamical evolution of the resonant tunneling of an ensemble of electrons through a double barrier in the presence of the self-consistent potential created by the charge accumulation in the well. The intrinsic nonlinearity of the transmission process is shown to lead to oscillations of the stored charge and of the transmitted and reflected fluxes. The dependence on the electrostatic feedback induced by the self-consistent potential and on the energy width of the incident distribution is discussed.

Transport properties in resonant tunneling heterostructures

An adiabatic approximation in terms of instantaneous resonances to study the steady‐state and time‐dependent transport properties of interacting electrons in biased resonant tunneling heterostructures is used. This approach leads, in a natural way, to a transport model of large applicability consisting of reservoirs coupled to regions where the system is described by a nonlinear Schrodinger equation. From the mathematical point of view, this work is nonrigorous but may offer some fresh and interesting problems involving semiclassical approximation, adiabatic theory, nonlinear Schrodinger equations, and dynamical systems.

Interaction Induced Localization in a Gas of Pyramidal Molecules

We propose a model to describe a gas of pyramidal molecules interacting via dipole-dipole interactions. The interaction modifies the tunneling properties between the classical equilibrium configurations of the single molecule and, for sufficiently high pressure, the molecules become localized in these classical configurations. We explain quantitatively, without free parameters, the shift to zero frequency of the inversion line observed upon increase of the pressure in a gas of ammonia or deuterated ammonia. For sufficiently high pressures, our model suggests the existence of a super-selection rule for states of different chirality in substituted derivatives.

Uncertainty-principle noise in vacuum-tunneling transducers

The fundamental sources of noise in a vacuum-tunneling probe used as an electromechanical transducer to monitor the location of a test mass are examined using a first-quantization formalism. We show that a tunneling transducer enforces the Heisenberg uncertainty principle for the position and momentum of a test mass monitored by the transducer through the presence of two sources of noise: the shot noise of the tunneling current and the momentum fluctuations transferred by the tunneling electrons to the test mass. We analyze a number of cases including symmetric and asymmetric rectangular potential barriers and a barrier in which there is a constant electric field. Practical configurations for reaching the quantum limit in measurements of the position of macroscopic bodies with such a class of transducers are studied.

Cooling Dynamics of Ultracold Two-Species Fermi-Bose Mixtures

We compare strategies for evaporative and sympathetic cooling of two-species Fermi-Bose mixtures in single-color and two-color optical dipole traps. We show that in the latter case a large heat capacity of the bosonic species can be maintained during the entire cooling process. This could allow one to efficiently achieve a deep Fermi degeneracy regime having at the same time a significant thermal fraction for the Bose gas, crucial for a precise thermometry of the mixture. Two possible signatures of a superfluid phase transition for the Fermi species are discussed.

Stationary solutions of the Gross-Pitaevskii equation with linear counterpart

Abstract We study the stationary solutions of the Gross–Pitaevskii equation that reduce, in the limit of vanishing non-linearity, to the eigenfunctions of the associated Schrodinger equation. By providing analytical and numerical support, we conjecture an existence condition for these solutions in terms of the ratio between their proper frequency (chemical potential) and the corresponding linear eigenvalue. We also give approximate expressions for the stationary solutions which become exact in the opposite limit of strong non-linearity. For one-dimensional systems these solutions have the form of a chain of dark or bright solitons depending on the sign of the non-linearity. We demonstrate that in the case of negative non-linearity (attractive interaction) the norm of the solutions is always bounded for dimensions greater than one.

Quantum Zeno effect with the Feynman-Mensky path-integral approach

Abstract A model for the quantum Zeno effect based upon an effective Schrodinger equation originated by the path-integral approach is developed and applied to a two-level system simultaneously stimulated by a resonant perturbation. It is shown that inhibition of stimulated transitions between the two levels appears as a consequence of the influence of the meter whenever measurements of energy, either continuous or pulsed, are performed at quantum level of sensitivity. The generality of this approach allows one to qualitatively understand the inhibition of spontaneous transitions as the decay of unstable particles, originally presented as a paradox of the quantum measurement theory.

Reaching fermi degeneracy in two-species optical dipole traps.

We propose the use of a combined optical dipole trap to achieve Fermi degeneracy by sympathetic cooling with a different bosonic species. Two far-detuned pairs of laser beams focused on the atomic clouds are used to confine the two atomic species with different trapping strengths. We show that a deep Fermi degeneracy regime can be potentially achieved earlier than Bose-Einstein condensation, as discussed in the favorable situation of a 6Li-23Na mixture. This opens up the possibility of experimentally investigating a mixture of superfluid Fermi and normal Bose gases.