43 research outputs found
Formal Solution of the Fourth Order Killing equations for Stationary Axisymmetric Vacuum Spacetimes
An analytic understanding of the geodesic structure around non-Kerr
spacetimes will result in a powerful tool that could make the mapping of
spacetime around massive quiescent compact objects possible. To this end, I
present an analytic closed form expression for the components of a the fourth
order Killing tensor for Stationary Axisymmetric Vacuum (SAV) Spacetimes. It is
as yet unclear what subset of SAV spacetimes admit this solution. The solution
is written in terms of an integral expression involving the metric functions
and two specific Greens functions. A second integral expression has to vanish
in order for the solution to be exact. In the event that the second integral
does not vanish it is likely that the best fourth order approximation to the
invariant has been found. This solution can be viewed as a generalized Carter
constant providing an explicit expression for the fourth invariant, in addition
to the energy, azimuthal angular momentum and rest mass, associated with
geodesic motion in SAV spacetimes, be it exact or approximate. I further
comment on the application of this result for the founding of a general
algorithm for mapping the spacetime around compact objects using gravitational
wave observatories.Comment: 5 Page
Optimal laser-control of double quantum dots
Coherent single-electron control in a realistic semiconductor double quantum
dot is studied theoretically. Using optimal-control theory we show that the
energy spectrum of a two-dimensional double quantum dot has a fully
controllable transition line. We find that optimized picosecond laser pulses
generate population transfer at significantly higher fidelities (>0.99) than
conventional sinusoidal pulses. Finally we design a robust and fast charge
switch driven by optimal pulses that are within reach of terahertz laser
technology.Comment: 5 pages, 4 figure
Optimal control of circuit quantum electrodynamics in one and two dimensions
Optimal control can be used to significantly improve multi-qubit gates in
quantum information processing hardware architectures based on superconducting
circuit quantum electrodynamics. We apply this approach not only to dispersive
gates of two qubits inside a cavity, but, more generally, to architectures
based on two-dimensional arrays of cavities and qubits. For high-fidelity gate
operations, simultaneous evolutions of controls and couplings in the two
coupling dimensions of cavity grids are shown to be significantly faster than
conventional sequential implementations. Even under experimentally realistic
conditions speedups by a factor of three can be gained. The methods immediately
scale to large grids and indirect gates between arbitrary pairs of qubits on
the grid. They are anticipated to be paradigmatic for 2D arrays and lattices of
controllable qubits.Comment: Published version
Analytic Controllability of Time-Dependent Quantum Control Systems
The question of controllability is investigated for a quantum control system
in which the Hamiltonian operator components carry explicit time dependence
which is not under the control of an external agent. We consider the general
situation in which the state moves in an infinite-dimensional Hilbert space, a
drift term is present, and the operators driving the state evolution may be
unbounded. However, considerations are restricted by the assumption that there
exists an analytic domain, dense in the state space, on which solutions of the
controlled Schrodinger equation may be expressed globally in exponential form.
The issue of controllability then naturally focuses on the ability to steer the
quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert
space -- and thus on analytic controllability. A relatively straightforward
strategy allows the extension of Lie-algebraic conditions for strong analytic
controllability derived earlier for the simpler, time-independent system in
which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic
time dependence. Enlarging the state space by one dimension corresponding to
the time variable, we construct an augmented control system that can be treated
as time-independent. Methods developed by Kunita can then be implemented to
establish controllability conditions for the one-dimension-reduced system
defined by the original time-dependent Schrodinger control problem. The
applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page
Optimal Control of One-Qubit Gates
We consider the problem of carrying an initial Bloch vector to a final Bloch
vector in a specified amount of time under the action of three control fields
(a vector control field). We show that this control problem is solvable and
therefore it is possible to optimize the control. We choose the physically
motivated criteria of minimum energy spent in the control, minimum magnitude of
the rate of change of the control and a combination of both. We find exact
analytical solutions.Comment: 5 page
Control landscapes for two-level open quantum systems
A quantum control landscape is defined as the physical objective as a
function of the control variables. In this paper the control landscapes for
two-level open quantum systems, whose evolution is described by general
completely positive trace preserving maps (i.e., Kraus maps), are investigated
in details. The objective function, which is the expectation value of a target
system operator, is defined on the Stiefel manifold representing the space of
Kraus maps. Three practically important properties of the objective function
are found: (a) the absence of local maxima or minima (i.e., false traps); (b)
the existence of multi-dimensional sub-manifolds of optimal solutions
corresponding to the global maximum and minimum; and (c) the connectivity of
each level set. All of the critical values and their associated critical
sub-manifolds are explicitly found for any initial system state. Away from the
absolute extrema there are no local maxima or minima, and only saddles may
exist, whose number and the explicit structure of the corresponding critical
sub-manifolds are determined by the initial system state. There are no saddles
for pure initial states, one saddle for a completely mixed initial state, and
two saddles for other initial states. In general, the landscape analysis of
critical points and optimal manifolds is relevant to the problem of explaining
the relative ease of obtaining good optimal control outcomes in the laboratory,
even in the presence of the environment.Comment: Minor editing and some references adde
Thermodynamics of adiabatic feedback control
We study adaptive control of classical ergodic Hamiltonian systems, where the
controlling parameter varies slowly in time and is influenced by system's state
(feedback). An effective adiabatic description is obtained for slow variables
of the system. A general limit on the feedback induced negative entropy
production is uncovered. It relates the quickest negentropy production to
fluctuations of the control Hamiltonian. The method deals efficiently with the
entropy-information trade off.Comment: 6 pages, 1 figur
Dynamical Decoupling of Open Quantum Systems
We propose a novel dynamical method for beating decoherence and dissipation
in open quantum systems. We demonstrate the possibility of filtering out the
effects of unwanted (not necessarily known) system-environment interactions and
show that the noise-suppression procedure can be combined with the capability
of retaining control over the effective dynamical evolution of the open quantum
system. Implications for quantum information processing are discussed.Comment: 4 pages, no figures; Plain ReVTeX. Final version to appear in
Physical Review Letter
Explanation of the Gibbs paradox within the framework of quantum thermodynamics
The issue of the Gibbs paradox is that when considering mixing of two gases
within classical thermodynamics, the entropy of mixing appears to be a
discontinuous function of the difference between the gases: it is finite for
whatever small difference, but vanishes for identical gases. The resolution
offered in the literature, with help of quantum mixing entropy, was later shown
to be unsatisfactory precisely where it sought to resolve the paradox.
Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining
the paradox, since it does not deal explicitly with the difference between the
gases. The proper approach employs quantum thermodynamics, which deals with
finite quantum systems coupled to a large bath and a macroscopic work source.
Within quantum thermodynamics, entropy generally looses its dominant place and
the target of the paradox is naturally shifted to the decrease of the maximally
available work before and after mixing (mixing ergotropy). In contrast to
entropy this is an unambiguous quantity. For almost identical gases the mixing
ergotropy continuously goes to zero, thus resolving the paradox. In this
approach the concept of ``difference between the gases'' gets a clear
operational meaning related to the possibilities of controlling the involved
quantum states. Difficulties which prevent resolutions of the paradox in its
entropic formulation do not arise here. The mixing ergotropy has several
counter-intuitive features. It can increase when less precise operations are
allowed. In the quantum situation (in contrast to the classical one) the mixing
ergotropy can also increase when decreasing the degree of mixing between the
gases, or when decreasing their distinguishability. These points go against a
direct association of physical irreversibility with lack of information.Comment: Published version. New title. 17 pages Revte
Effect of internal friction on transformation twin dynamics in SrxBa1-xSnO3 perovskite
The dynamics of transformation twins in SrxBa1-xSnO3 (x=0.6,0.8) perovskite
has been studied by dynamical mechanical analysis in three-point bend geometry.
This material undergoes phase transitions from orthorhombic to tetragonal and
cubic structures on heating. The mechanical loss signatures of the
transformation twins include relaxation and frequency-independent peaks in the
orthorhombic and tetragonal phases, with no observed energy dissipation in the
cubic phase. The macroscopic shape, orientation and relative displacements of
twin walls have been calculated from bending and anisotropy energies. The
mechanical loss angle and distribution of relaxation time are discussed in term
of bending modes of domain walls.Comment: 20 pages, 4 figure