
InsubriaSPACE  Thesis PhD Repository >
Insubria Thesis Repository >
01  Tesi di dottorato >
Utilizza questo identificativo per citare o creare un link a questo documento:
http://hdl.handle.net/10277/117

Autori:  Rebuzzini, Laura Francesca 
Tutor interno:  ARTUSO, ROBERTO 
Titolo:  Theoretical aspects of Quantum Accelerator Modes. 
Abstract:  This thesis is devoted to the study of some theoretical aspects of the problem of Quantum Accelerator Modes (QAMs), which has received considerable interest in recent years both by experimentalists and theorists in the fields of Quantum Chaos, Quantum Optics and coldultracold atomic physics.
QAMs, recently observed in cold atom optics, are formed by exposing cold alkali atoms to periodic kicks in the direction of the gravitational field. The kicks are generated by a pulsed standing wave of light. A QAM is characterized by a momentum transfer, which increases linearly with the number of pulses, to a substantial fraction of the atoms. QAMs arise for values of the pulse period close to a integer multiple of half of a characteristic time TB (the Talbot time), typical of the kind of atoms used.
A detailed theoretical explanation of this quantum effect is presented. The system can be modelled by a variant of the wellknown quantum Kicked Rotator, in which the effects of a static force, produced by the earth gravitational field, are taken into account. A pseudoclassical theory has been formulated, in which the role of Planck constant is played by the detuning of the kicking period from the resonant value: in the asymptotic limit for a vanishing detuning, QAMs are described by the stable periodic orbit of a “formally” classical map on the 2torus. An analysis of parametric dependence of the map is performed perturbatively; the parameter regions where the motion is stable and periodic exhibit Arnol’d tongueslike structures. The ordering of Arnol’d tongues and hence the classification of experimentally observed accelerator modes is provided by a numbertheoretic construction known as the Farey Tree.
Quantum decay of the modes from classical stable islands immersed in a chaotic sea is analysed and its relations to the famous WannierStark problem are investigated. Theoretical estimates for the lifetimes of the metastable states as a function of the effective Planck constant are obtained.
QAM dynamics in a BoseEinstein condensate is then considered. Modifications on transport phenomena, imposed by nonlinearities of GrossPitaevskii type, which describe the atomic interactions in a meanfield approach, are examined by computerassisted analysis.
Finally, the problem of QAMs in the vicinity of a generic quantum resonance, namely for kicking period sufficiently close to any rational multiple of the Talbot time, is studied.
The theoretical framework is nontrivially generalized in terms of spinor dynamics: an ansatz of the BornOppenheimer type allows to decouple the dynamics of spinor and orbital degrees of freedom and a description of the orbital motion by means of “formally” classical equations is achieved. New rich families of experimental observable QAMs are predicted. 
MIUR :  FIS/01 FISICA SPERIMENTALE 
Data:  2008 
Lingua:  en 
Corso di dottorato:  Fisica 
Ciclo di dottorato:  21 
Università di conseguimento titolo:  Università degli Studi dell'Insubria 
Citazione:  Rebuzzini, L.F.Theoretical aspects of Quantum Accelerator Modes. (Doctoral Thesis, Università degli Studi dell'Insubria, 2008). 

Full text:
File 
Descrizione 
Dimensioni  Formato  Consultabilità 
Phd thesis Rebuzzini completa.pdf  testo completo tesi  81,68 MB  Adobe PDF  non consultabile
Visualizza/apri


Tutti i documenti archiviati in InsubriaSPACE sono protetti da copyright. Tutti i diritti riservati.
