3,324 research outputs found
Soft-Pulse Dynamical Decoupling with Markovian Decoherence
We consider the effect of broadband decoherence on the performance of
refocusing sequences, having in mind applications of dynamical decoupling in
concatenation with quantum error correcting codes as the first stage of
coherence protection. Specifically, we construct cumulant expansions of
effective decoherence operators for a qubit driven by a pulse of a generic
symmetric shape, and for several sequences of - and -pulses. While,
in general, the performance of soft pulses in decoupling sequences in the
presence of Markovian decoherence is worse than that of the ideal
-pulses, it can be substantially improved by shaping.Comment: New version contains minor content clarification
Universal Leakage Elimination
``Leakage'' errors are particularly serious errors which couple states within
a code subspace to states outside of that subspace thus destroying the error
protection benefit afforded by an encoded state. We generalize an earlier
method for producing leakage elimination decoupling operations and examine the
effects of the leakage eliminating operations on decoherence-free or noiseless
subsystems which encode one logical, or protected qubit into three or four
qubits. We find that by eliminating the large class of leakage errors, under
some circumstances, we can create the conditions for a decoherence free
evolution. In other cases we identify a combination decoherence-free and
quantum error correcting code which could eliminate errors in solid-state
qubits with anisotropic exchange interaction Hamiltonians and enable universal
quantum computing with only these interactions.Comment: 14 pages, no figures, new version has references updated/fixe
Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
Lipkin model of arbitrary particle-number N is studied in terms of exact
differential-operator representation of spin-operators from which we obtain the
low-lying energy spectrum with the instanton method of quantum tunneling. Our
new observation is that the well known quantum phase transition can also occur
in the finite-N model only if N is an odd-number. We furthermore demonstrate a
new type of quantum phase transition characterized by level-crossing which is
induced by the geometric phase interference and is marvelously periodic with
respect to the coupling parameter. Finally the conventional quantum phase
transition is understood intuitively from the tunneling formulation in the
thermodynamic limit.Comment: 4 figure
Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems
The use of d-state systems, or qudits, in quantum information processing is
discussed. Three-state and higher dimensional quantum systems are known to have
very different properties from two-state systems, i.e., qubits. In particular
there exist qudit states which are not equivalent under local unitary
transformations unless a selection rule is violated. This observation is shown
to be an important factor in the theory of decoherence-free, or noiseless,
subsystems. Experimentally observable consequences and methods for
distinguishing these states are also provided, including the explicit
construction of new decoherence-free or noiseless subsystems from qutrits.
Implications for simulating quantum systems with quantum systems are also
discussed.Comment: 13 pages, 1 figures, Version 2: Typos corrected, references fixed and
new ones added, also includes referees suggested changes and a new exampl
Bistable light detectors with nonlinear waveguide arrays
Bistability induced by nonlinear Kerr effect in arrays of coupled waveguides
is studied and shown to be a means to conceive light detectors that switch
under excitation by a weak signal. The detector is obtained by coupling two
single 1D waveguide to an array of coupled waveguides with adjusted indices and
coupling. The process is understood by analytical description in the
conservative and continuous case and illustrated by numerical simulations of
the model with attenuation.Comment: Phys. Rev. Lett., v.94, (2005, to be published
Third-order superintegrable systems separable in parabolic coordinates
In this paper, we investigate superintegrable systems which separate in
parabolic coordinates and admit a third-order integral of motion. We give the
corresponding determining equations and show that all such systems are
multi-separable and so admit two second-order integrals. The third-order
integral is their Lie or Poisson commutator. We discuss how this situation is
different from the Cartesian and polar cases where new potentials were
discovered which are not multi-separable and which are expressed in terms of
Painlev\'e transcendents or elliptic functions
Driven Macroscopic Quantum Tunneling of Ultracold Atoms in Engineered Optical Lattices
Coherent macroscopic tunneling of a Bose-Einstein condensate between two
parts of an optical lattice separated by an energy barrier is theoretically
investigated. We show that by a pulsewise change of the barrier height, it is
possible to switch between tunneling regime and a self-trapped state of the
condensate. This property of the system is explained by effectively reducing
the dynamics to the nonlinear problem of a particle moving in a double square
well potential. The analysis is made for both attractive and repulsive
interatomic forces, and it highlights the experimental relevance of our
findings
Characterizing Planetary Orbits and the Trajectories of Light
Exact analytic expressions for planetary orbits and light trajectories in the
Schwarzschild geometry are presented. A new parameter space is used to
characterize all possible planetary orbits. Different regions in this parameter
space can be associated with different characteristics of the orbits. The
boundaries for these regions are clearly defined. Observational data can be
directly associated with points in the regions. A possible extension of these
considerations with an additional parameter for the case of Kerr geometry is
briefly discussed.Comment: 49 pages total with 11 tables and 10 figure
Local Identities Involving Jacobi Elliptic Functions
We derive a number of local identities of arbitrary rank involving Jacobi
elliptic functions and use them to obtain several new results. First, we
present an alternative, simpler derivation of the cyclic identities discovered
by us recently, along with an extension to several new cyclic identities of
arbitrary rank. Second, we obtain a generalization to cyclic identities in
which successive terms have a multiplicative phase factor exp(2i\pi/s), where s
is any integer. Third, we systematize the local identities by deriving four
local ``master identities'' analogous to the master identities for the cyclic
sums discussed by us previously. Fourth, we point out that many of the local
identities can be thought of as exact discretizations of standard nonlinear
differential equations satisfied by the Jacobian elliptic functions. Finally,
we obtain explicit answers for a number of definite integrals and simpler forms
for several indefinite integrals involving Jacobi elliptic functions.Comment: 47 page
Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds
In this paper we obtain a description of the Hermitian operators acting on
the Hilbert space \C^n, description which gives a complete solution to the
over parameterization problem. More precisely we provide an explicit
parameterization of arbitrary -dimensional operators, operators that may be
considered either as Hamiltonians, or density matrices for finite-level quantum
systems. It is shown that the spectral multiplicities are encoded in a flag
unitary matrix obtained as an ordered product of special unitary matrices, each
one generated by a complex -dimensional unit vector, . As a
byproduct, an alternative and simple parameterization of Stiefel and Grassmann
manifolds is obtained.Comment: 21 page
- …