50 research outputs found
Quadratic-exponential coherent feedback control of linear quantum stochastic systems
This paper considers a risk-sensitive optimal control problem for a
field-mediated interconnection of a quantum plant with a coherent
(measurement-free) quantum controller. The plant and the controller are
multimode open quantum harmonic oscillators governed by linear quantum
stochastic differential equations, which are coupled to each other and driven
by multichannel quantum Wiener processes modelling the external bosonic fields.
The control objective is to internally stabilize the closed-loop system and
minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential
functional which penalizes the plant variables and the controller output. We
obtain first-order necessary conditions of optimality for this problem by
computing the partial Frechet derivatives of the cost functional with respect
to the energy and coupling matrices of the controller in frequency domain and
state space. An infinitesimal equivalence between the risk-sensitive and
weighted coherent quantum LQG control problems is also established. In addition
to variational methods, we employ spectral factorizations and infinite cascades
of auxiliary classical systems. Their truncations are applicable to numerical
optimization algorithms (such as the gradient descent) for coherent quantum
risk-sensitive feedback synthesis.Comment: 29 pages, 3 figure
Levitation and control of particles with internal degrees of freedom
Levitodynamics is a fast growing field that studies the levitation and manipulation of micro- and nanoobjects, fuelled by both fundamental physics questions and technological applications. Due to the isolated nature of trapped particles, levitated systems are highly decoupled from the environment, and offer experimental possibilities that are absent in clamped nanomechanical oscillators. In particular, a central question in quantum physics is how the transition between the classical and quantum world materializes, and levitated objects represent a promising avenue to study this intermediate regime.
In the last years, most levitation experiments have been restricted to optically trapped silica nanoparticles in vacuum, controlling the particle's position with intensity modulated laser beams. However, the use of optical traps severely constrains the experiments that can be performed, because few particle materials can withstand the optical absorption and resulting heating in vacuum. This completely prevents the use of objects with internal degrees of freedom, which---coupled to mechanical variables---offer a clear path towards the study of quantum phenomena at the macroscale.
In this thesis, we address these issues by considering other types of trap and feedback schemes, achieving excellent control on the dynamics of optically active nanoparticles. With stochastic calculus, simulations and experiments, we study the dynamics of trapped particles in different regimes, considering also a hybrid quadrupole-optical trapping scheme. Then, using a Paul trap of our own design, we demonstrate the trapping, interrogation and feedback cooling of a nanodiamond hosting a single NV center in vacuum, a clear candidate to perform quantum physics experiments at the single spin level. Finally, we discuss and implement an optimal controller to cool the center of mass motion of an optically levitated nanoparticle. The feedback is realized by exerting a Coulomb force on a charged particle with a pair of electrodes, and thus requires no optics.La levitodinà mica és un camp de la fÃsica en rà pida expansió que estudia la levitació i manipulació de micro- i nano-objectes, empesa per la possibilitat de solucionar trencaclosques de fÃsica fonamental i de desenvolupar noves aplicacions tecnològiques. Grà cies al gran aïllament de les partÃcules en levitació, l’evolució dels sistemes levitodinà mics està molt desacoplada del seu entorn. Per consegüent, permeten fer experiments que no serien possibles en nanooscil·ladors mecà nics sobre substrat. En particular, una qüestió central en fÃsica consisteix en entendre com es produeix la transició entre els mons clà ssic i quà ntic;
els objectes en levitació permeten estudiar aquest règim intermedi de manera innovadora.
En els últims anys, la majoria d’experiments de levitodinà mica s’han limitat a atrapar òpticament partÃcules de sÃlice en el buit, tot controlant la posició de la partÃcula amb feixos là ser modulats. Tot i aixÃ, l’ús de trampes òptiques suposa un obstacle a l’hora d’exportar
aquests experiments a règims més diversos perquè, a baixes pressions, pocs materials són capaços de suportar les altes temperatures resultants de l’absorció de llum là ser. Això impedeix l’ús d’objectes amb graus de llibertat interns, que –acoplats a variables mecà niques–
suposen un full de ruta clar per estudiar fenòmens quà ntics a escala macroscòpica
En aquesta tesi, adrecem aquestes qüestions tot considerant altres tipus de trampa i tècniques de feedback, i assolim un control excel·lent de la dinà mica de nanopartÃcules òpticament actives en levitació.
Mitjançant cà lcul estocà stic, simulacions i experiments, estudiem la dinà mica de les partÃcules en règims diversos, à dhuc considerant un esquema hÃbrid de trampa de Paul-òptica. A continuació, utilitzant una trampa de Paul, demostrem experimentalment l’atrapament, interrogació i feedback-cooling en el buit d’un nanodiamant que conté un únic NV− center, un clar candidat per a la realització d’experiments de fÃsica quà ntica amb un únic spin. Finalment, estudiem i implementem un controlador òptim per a refredar el centre de massa d’una partÃcula
òpticament levitada. El feedback es realitza exercint una força de Coulomb sobre una partÃcula carregada positivament mitjançant un parell d’elèctrodes, i per tant no requereix elements òptic