2,806 research outputs found
Motion planning in quantum control via intersection of eigenvalues
International audienceIn this paper we consider the problem of inducing a transition in a controlled quantum mechanical system whose spectrum loses simplicity for some values of the control. We study the situation in which the Hamiltonian of the system is real, and we are in presence of two controls. In this case, eigenvalue crossings are generically conical. Adiabatic approximation is used to decouple a finite dimensional sub-system from the original one (usually infinite dimensional). The main advantage of this method is that as a byproduct of the controllability result it permits to get an explicit expression of the controls. Moreover it may be used in the case in which the dependence of the Hamiltonian from the controls is non-linear, for which at the moment, no other method works. In this paper we study the basic block of this controllability method, that is a two by two system whose spectrum presents a conical intersection. We show how to control exactly this system with a control strategy that can be slowed down. The possibility of slowing down the control law is essential to obtain an adiabatic decoupling from the rest of the system with an arbitrary precision
Controllability and observability of grid graphs via reduction and symmetries
In this paper we investigate the controllability and observability properties
of a family of linear dynamical systems, whose structure is induced by the
Laplacian of a grid graph. This analysis is motivated by several applications
in network control and estimation, quantum computation and discretization of
partial differential equations. Specifically, we characterize the structure of
the grid eigenvectors by means of suitable decompositions of the graph. For
each eigenvalue, based on its multiplicity and on suitable symmetries of the
corresponding eigenvectors, we provide necessary and sufficient conditions to
characterize all and only the nodes from which the induced dynamical system is
controllable (observable). We discuss the proposed criteria and show, through
suitable examples, how such criteria reduce the complexity of the
controllability (respectively observability) analysis of the grid
Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates
We study the dynamical stability of the macroscopic quantum oscillations
characterizing a system of three coupled Bose-Einstein condensates arranged
into an open-chain geometry. The boson interaction, the hopping amplitude and
the central-well relative depth are regarded as adjustable parameters. After
deriving the stability diagrams of the system, we identify three mechanisms to
realize the transition from an unstable to stable behavior and analyze specific
configurations that, by suitably tuning the model parameters, give rise to
macroscopic effects which are expected to be accessible to experimental
observation. Also, we pinpoint a system regime that realizes a
Josephson-junction-like effect. In this regime the system configuration do not
depend on the model interaction parameters, and the population oscillation
amplitude is related to the condensate-phase difference. This fact makes
possible estimating the latter quantity, since the measure of the oscillating
amplitudes is experimentally accessible.Comment: 25 pages, 12 figure
Adiabatic control of the Schr\"odinger equation via conical intersections of the eigenvalues
In this paper we present a constructive method to control the bilinear
Schr\"odinger equation via two controls. The method is based on adiabatic
techniques and works if the spectrum of the Hamiltonian admits eigenvalue
intersections, and if the latter are conical (as it happens generically). We
provide sharp estimates of the relation between the error and the
controllability time
Thermodynamics of relativistic quantum fields confined in cavities
We investigate the quantum thermodynamical properties of localised
relativistic quantum fields, and how they can be used as quantum thermal
machines. We study the efficiency and power of energy transfer between the
classical gravitational degrees of freedom, such as the energy input due to the
motion of boundaries or an impinging gravitational wave, and the excitations of
a confined quantum field. We find that the efficiency of energy transfer
depends dramatically on the input initial state of the system. Furthermore, we
investigate the ability of the system to extract energy from a gravitational
wave and store it in a battery. This process is inefficient in optical cavities
but is significantly enhanced when employing trapped Bose Einstein condensates.
We also employ standard fluctuation results to obtain the work probability
distribution, which allows us to understand how the efficiency is related to
the dissipation of work. Finally, we apply our techniques to a setup where an
impinging gravitational wave excites the phononic modes of a Bose Einstein
condensate. We find that, in this case, the percentage of energy transferred to
the phonons approaches unity after a suitable amount of time. These results
give a quantitative insight into the thermodynamic behaviour of relativistic
quantum fields confined in cavities.Comment: 35 pages, 3 figures. Manuscript substantially updated. I. Fuentes
also published as I. Fuentes-Guridi and I. Fuentes-Schulle
Adiabatic passage and ensemble control of quantum systems
This paper considers population transfer between eigenstates of a finite
quantum ladder controlled by a classical electric field. Using an appropriate
change of variables, we show that this setting can be set in the framework of
adiabatic passage, which is known to facilitate ensemble control of quantum
systems. Building on this insight, we present a mathematical proof of
robustness for a control protocol -- chirped pulse -- practiced by
experimentalists to drive an ensemble of quantum systems from the ground state
to the most excited state. We then propose new adiabatic control protocols
using a single chirped and amplitude shaped pulse, to robustly perform any
permutation of eigenstate populations, on an ensemble of systems with badly
known coupling strengths. Such adiabatic control protocols are illustrated by
simulations achieving all 24 permutations for a 4-level ladder
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues
We study the inverse eigenvalue problem for finding doubly stochastic
matrices with specified eigenvalues. By making use of a combination of
Dykstra's algorithm and an alternating projection process onto a non-convex
set, we derive hybrid algorithms for finding doubly stochastic matrices and
symmetric doubly stochastic matrices with prescribed eigenvalues. Furthermore,
we prove that the proposed algorithms converge and linear convergence is also
proved. Numerical examples are presented to demonstrate the efficiency of our
method.Comment: 16 page
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