397 research outputs found

### Experimentally testable geometric phase of sequences of Everett's relative quantum states

Everett's concept of relative state is used to introduce a geometric phase
that depends nontrivially on entanglement in a pure quantum state. We show that
this phase can be measured in multiparticle interferometry. A
correlation-dependent generalization of the relative state geometric phase to
mixed quantum states is outlined.Comment: Minor changes, journal reference adde

### Geometry of an adiabatic passage at a level crossing

We discuss adiabatic quantum phenomena at a level crossing. Given a path in
the parameter space which passes through a degeneracy point, we find a
criterion which determines whether the adiabaticity condition can be satisfied.
For paths that can be traversed adiabatically we also derive a differential
equation which specifies the time dependence of the system parameters, for
which transitions between distinct energy levels can be neglected. We also
generalize the well-known geometric connections to the case of adiabatic paths
containing arbitrarily many level-crossing points and degenerate levels.Comment: 7 pages, 6 figures, RevTeX4, changes requested by Phys. Rev.

### Transport study of Berry's phase, the resistivity rule, and quantum Hall effect in graphite

Transport measurements indicate strong oscillations in the Hall-,$R_{xy}$,
and the diagonal-, $R_{xx}$, resistances and exhibit Hall plateaus at the
lowest temperatures, in three-dimensional Highly Oriented Pyrolytic Graphite
(HOPG). At the same time, a comparative Shubnikov-de Haas-oscillations-based
Berry's phase analysis indicates that graphite is unlike the GaAs/AlGaAs 2D
electron system, the 3D n-GaAs epilayer, semiconducting $Hg_{0.8}Cd_{0.2}Te$,
and some other systems. Finally, we observe the transport data to follow
$B\times dR_{xy}/dB \approx - \Delta R_{xx}$. This feature is consistent with
the observed relative phases of the oscillatory $R_{xx}$ and $R_{xy}$.Comment: 5 pages, 4 figure

### Geometric phase for an accelerated two-level atom and the Unruh effect

We study, in the framework of open quantum systems, the geometric phase
acquired by a uniformly accelerated two-level atom undergoing nonunitary
evolution due to its coupling to a bath of fluctuating vacuum electromagnetic
fields in the multipolar scheme. We find that the phase variation due to the
acceleration can be in principle observed via atomic interferometry between the
accelerated atom and the inertial one, thus providing an evidence of the Unruh
effect.Comment: 12 pages, no figure

### Fractional topological phase for entangled qudits

We investigate the topological structure of entangled qudits under unitary
local operations. Different sectors are identified in the evolution, and their
geometrical and topological aspects are analyzed. The geometric phase is
explicitly calculated in terms of the concurrence. As a main result, we predict
a fractional topological phase for cyclic evolutions in the multiply connected
space of maximally entangled states.Comment: REVTex, 4 page

### On Geometric Phase from Pure Projections

The geometric phase is usually treated as a quantity modulo 2\pi, a
convention carried over from early work on the subject. The results of a series
of optical interference experiments involving polarization of light, done by
the present author (reviewed in R.Bhandari, Phys. Rep. 281 (1997) p.1) question
the usefulness of such a definition of the geometric phase in that it throws
away useful and measurable information about the system, for example strengths
of singularities giving rise to the geometric phase. Such singularities have
been directly demonstrated by phase-shift measurement in interference
experiments. In this paper, two recent polarization experiments (Hariharan
et.al., J.Mod.Opt. 44 (1997)p.707 and Berry and Klein, J.Mod.Opt. 43
(1996)p.165) are analysed and compared with previous experiments and
potentially detectible singularities in these experiments pointed out.Comment: Latex, 15 pages, 6 figures; ([email protected]

### Pancharatnam and Berry Phases in Three-Level Photonic Systems

A theoretical analysis of Pancharatnam and Berry phases is made for biphoton
three-level systems, which are produced via frequency degenerate co-linear
spontaneous parametric down conversion (SPDC). The general theory of
Pancharatnam phases is discussed with a special emphasis on geodesic 'curves'in
Hilbert space. Explicit expressions for Pancharatnam, dynamical and geometrical
phases are derived for the transformations produced by linear phase-converters.
The problem of gauge invariance is treated along all the article

### Geometric Phase, Bundle Classification, and Group Representation

The line bundles which arise in the holonomy interpretations of the geometric
phase display curious similarities to those encountered in the statement of the
Borel-Weil-Bott theorem of the representation theory. The remarkable relation
of the geometric phase to the classification of complex line bundles provides
the necessary tools for establishing the relevance of the Borel-Weil-Bott
theorem to Berry's adiabatic phase. This enables one to define a set of
topological charges for arbitrary compact connected semisimple dynamical Lie
groups. In this paper, the problem of the determination of the parameter space
of the Hamiltonian is also addressed. A simple topological argument is
presented to indicate the relation between the Riemannian structure on the
parameter space and Berry's connection. The results about the fibre bundles and
group theory are used to introduce a procedure to reduce the problem of the
non-adiabatic (geometric) phase to Berry's adiabatic phase for cranked
Hamiltonians. Finally, the possible relevance of the topological charges of the
geometric phase to those of the non-abelian monopoles is pointed out.Comment: 30 pages (LaTeX); UT-CR-12-9

### Fidelity and coherence measures from interference

By utilizing single particle interferometry, the fidelity or coherence of a pair of quantum states is identified with their capacity for interference. We consider processes acting on the internal degree of freedom (e.g., spin or polarization) of the interfering particle, preparing it in states ρA or ρB in the respective path of the interferometer. The maximal visibility depends on the choice of interferometer, as well as the locality or nonlocality of the preparations, but otherwise depends only on the states ρA and ρB and not the individual preparation processes themselves. This allows us to define interferometric measures which probe locality and correlation properties of spatially or temporally separated processes, and can be used to differentiate between processes that cannot be distinguished by direct process tomography using only the internal state of the particle

### Composite Geometric Phase for Multipartite Entangled States

When an entangled state evolves under local unitaries, the entanglement in
the state remains fixed. Here we show the dynamical phase acquired by an
entangled state in such a scenario can always be understood as the sum of the
dynamical phases of its subsystems. In contrast, the equivalent statement for
the geometric phase is not generally true unless the state is separable. For an
entangled state an additional term is present, the mutual geometric phase, that
measures the change the additional correlations present in the entangled state
make to the geometry of the state space. For $N$ qubit states we find this
change can be explained solely by classical correlations for states with a
Schmidt decomposition and solely by quantum correlations for W states.Comment: 4 pages, 1 figure, improved presentation, results and conclusions
unchanged from v1. Accepted for publication in PR

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