39 research outputs found
Optimal Control of Superconducting N-level quantum systems
We consider a current-biased dc SQUID in the presence of an applied
time-dependent bias current or magnetic flux. The phase dynamics of such a
Josephson device is equivalent to that of a quantum particle trapped in a D
anharmonic potential, subject to external time-dependent control fields, {\it
i.e.} a driven multilevel quantum system. The problem of finding the required
time-dependent control field that will steer the system from a given initial
state to a desired final state at a specified final time is formulated in the
framework of optimal control theory. Using the spectral filter technique, we
show that the selected optimal field which induces a coherent population
transfer between quantum states is represented by a carrier signal having a
constant frequency but which is time-varied both in amplitude and phase. The
sensitivity of the optimal solution to parameter perturbations is also
addressed
Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments
This work studies the feasibility of optimal control of high-fidelity quantum
gates in a model of interacting two-level particles. One particle (the qubit)
serves as the quantum information processor, whose evolution is controlled by a
time-dependent external field. The other particles are not directly controlled
and serve as an effective environment, coupling to which is the source of
decoherence. The control objective is to generate target one-qubit gates in the
presence of strong environmentally-induced decoherence and under physically
motivated restrictions on the control field. It is found that interactions
among the environmental particles have a negligible effect on the gate fidelity
and require no additional adjustment of the control field. Another interesting
result is that optimally controlled quantum gates are remarkably robust to
random variations in qubit-environment and inter-environment coupling
strengths. These findings demonstrate the utility of optimal control for
management of quantum-information systems in a very precise and specific
manner, especially when the dynamics complexity is exacerbated by inherently
uncertain environmental coupling.Comment: tMOP LaTeX, 9 pages, 3 figures; Special issue of the Journal of
Modern Optics: 37th Winter Colloquium on the Physics of Quantum Electronics,
2-6 January 200
Optimal switching of a nanomagnet assisted by microwaves
We develop an efficient and general method for optimizing the microwave field
that achieves magnetization switching with a smaller static field. This method
is based on optimal control and renders an exact solution for the 3D microwave
field that triggers the switching of a nanomagnet with a given anisotropy and
in an oblique static field. Applying this technique to the particular case of
uniaxial anisotropy, we show that the optimal microwave field, that achieves
switching with minimal absorbed energy, is modulated both in frequency and in
magnitude. Its role is to drive the magnetization from the metastable
equilibrium position towards the saddle point and then damping induces the
relaxation to the stable equilibrium position. For the pumping to be efficient,
the microwave field frequency must match at the early stage of the switching
process the proper precession frequency of the magnetization, which depends on
the magnitude and direction of the static field. We investigate the effect of
the static field (in amplitude and direction) and of damping on the
characteristics of the microwave field. We have computed the switching curves
in the presence of the optimal microwave field. The results are in qualitative
agreement with micro-SQUID experiments on isolated nanoclusters. The strong
dependence of the microwave field and that of the switching curve on the
damping parameter may be useful in probing damping in various nanoclusters.Comment: 9 pages, 8 figure
Optimal generation of Fock states in a weakly nonlinear oscillator
We apply optimal control theory to determine the shortest time in which an
energy eigenstate of a weakly anharmonic oscillator can be created under the
practical constraint of linear driving. We show that the optimal pulses are
beatings of mostly the transition frequencies for the transitions up to the
desired state and the next leakage level. The time of a shortest possible pulse
for a given nonlinearity scale with the nonlinearity parameter delta as a power
law of alpha with alpha=-0.73 +/-0.029. This is a qualitative improvement
relative to the value alpha=1 suggested by a simple Landau-Zener argument.Comment: 10 pages, 6 figure
Universality of Level Spacing Distributions in Classical Chaos
We suggest that random matrix theory applied to a classical action matrix can
be used in classical physics to distinguish chaotic from non-chaotic behavior.
We consider the 2-D stadium billiard system as well as the 2-D anharmonic and
harmonic oscillator. By unfolding of the spectrum of such matrix we compute the
level spacing distribution, the spectral auto-correlation and spectral
rigidity. We observe Poissonian behavior in the integrable case and Wignerian
behavior in the chaotic case. We present numerical evidence that the action
matrix of the stadium billiard displays GOE behavior and give an explanation
for it. The findings present evidence for universality of level fluctuations -
known from quantum chaos - also to hold in classical physics
Closed Path Integrals and Renormalisation in Quantum Mechanics
We suggest a closed form expression for the path integral of quantum
transition amplitudes. We introduce a quantum action with renormalized
parameters. We present numerical results for the potential. The
renormalized action is relevant for quantum chaos and quantum instantons.Comment: Revised text, 1 figure added; Text (LaTeX file), 1 Figure (ps file
Hamiltonian lattice QCD at finite chemical potential
At sufficiently high temperature and density, quantum chromodynamics (QCD) is
expected to undergo a phase transition from the confined phase to the
quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo
method works well for QCD at finite temperature, however, it breaks down at
finite chemical potential. We develop a Hamiltonian approach to lattice QCD at
finite chemical potential and solve it in the case of free quarks and in the
strong coupling limit. At zero temperature, we calculate the vacuum energy,
chiral condensate, quark number density and its susceptibility, as well as mass
of the pseudoscalar, vector mesons and nucleon. We find that the chiral phase
transition is of first order, and the critical chemical potential is (dynamical quark mass at ). This is consistent with
(where is the nucleon mass at ).Comment: Final version appeared in Phys. Rev.
Essential spectra of difference operators on \sZ^n-periodic graphs
Let (\cX, \rho) be a discrete metric space. We suppose that the group
\sZ^n acts freely on and that the number of orbits of with respect to
this action is finite. Then we call a \sZ^n-periodic discrete metric
space. We examine the Fredholm property and essential spectra of band-dominated
operators on where is a \sZ^n-periodic discrete metric space.
Our approach is based on the theory of band-dominated operators on \sZ^n and
their limit operators.
In case is the set of vertices of a combinatorial graph, the graph
structure defines a Schr\"{o}dinger operator on in a natural way. We
illustrate our approach by determining the essential spectra of Schr\"{o}dinger
operators with slowly oscillating potential both on zig-zag and on hexagonal
graphs, the latter being related to nano-structures
Crossed Andreev reflection at ferromagnetic domain walls
We investigate several factors controlling the physics of hybrid structures
involving ferromagnetic domain walls (DWs) and superconducting (S) metals. We
discuss the role of non collinear magnetizations in S/DW junctions in a spin
Nambu Keldysh formalism. We discuss transport in S/DW/N and
S/DW/S junctions in the presence of inelastic scattering in the domain wall. In
this case transport properties are similar for the S/DW/S and S/DW/N junctions
and are controlled by sequential tunneling of spatially separated Cooper pairs
across the domain wall. In the absence of inelastic scattering we find that a
Josephson current circulates only if the size of the ferromagnetic region is
smaller than the elastic mean free path meaning that the Josephson effect
associated to crossed Andreev reflection cannot be observed under usual
experimental conditions. Nevertheless a finite dc current can circulate across
the S/DW/S junction due to crossed Andreev reflection associated to sequential
tunneling.Comment: 18 pages, 8 figures, references added at the end of the introductio