213 research outputs found
Invariant measures on multimode quantum Gaussian states
We derive the invariant measure on the manifold of multimode quantum Gaussian
states, induced by the Haar measure on the group of Gaussian unitary
transformations. To this end, by introducing a bipartition of the system in two
disjoint subsystems, we use a parameterization highlighting the role of
nonlocal degrees of freedom -- the symplectic eigenvalues -- which characterize
quantum entanglement across the given bipartition. A finite measure is then
obtained by imposing a physically motivated energy constraint. By averaging
over the local degrees of freedom we finally derive the invariant distribution
of the symplectic eigenvalues in some cases of particular interest for
applications in quantum optics and quantum information.Comment: 17 pages, comments are welcome. v2: presentation improved and typos
corrected. Close to the published versio
Zeno dynamics and constraints
We investigate some examples of quantum Zeno dynamics, when a system
undergoes very frequent (projective) measurements that ascertain whether it is
within a given spatial region. In agreement with previously obtained results,
the evolution is found to be unitary and the generator of the Zeno dynamics is
the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new
approach to this problem, this result is found to be valid in an arbitrary
-dimensional compact domain. We then propose some preliminary ideas
concerning the algebra of observables in the projected region and finally look
at the case of a projection onto a lower dimensional space: in such a situation
the Zeno ansatz turns out to be a procedure to impose constraints.Comment: 21 page
Classical Statistical Mechanics Approach to Multipartite Entanglement
We characterize the multipartite entanglement of a system of n qubits in
terms of the distribution function of the bipartite purity over balanced
bipartitions. We search for maximally multipartite entangled states, whose
average purity is minimal, and recast this optimization problem into a problem
of statistical mechanics, by introducing a cost function, a fictitious
temperature and a partition function. By investigating the high-temperature
expansion, we obtain the first three moments of the distribution. We find that
the problem exhibits frustration.Comment: 38 pages, 10 figures, published versio
Dephasing in matter-wave interferometry
We review different attempts to show the decoherence process in
double-slit-like experiments both for charged particles (electrons) and neutral
particles with permanent dipole moments. Interference is studied when electrons
or atomic systems are coupled to classical or quantum electromagnetic fields.
The interaction between the particles and time-dependent fields induces a
time-varying Aharonov phase. Averaging over the phase generates a suppression
of fringe visibility in the interference pattern. We show that, for suitable
experimental conditions, the loss of contrast for dipoles can be almost as
large as the corresponding one for coherent electrons and therefore, be
observed. We analyze different trajectories in order to show the dependence of
the decoherence factor with the velocity of the particles.Comment: 9 pages, 1 eps-figure. To appear in J. Phys. A: Math. Ge
Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics
We discuss an implementation of Quantum Zeno Dynamics in a Cavity Quantum
Electrodynamics experiment. By performing repeated unitary operations on atoms
coupled to the field, we restrict the field evolution in chosen subspaces of
the total Hilbert space. This procedure leads to promising methods for
tailoring non-classical states. We propose to realize `tweezers' picking a
coherent field at a point in phase space and moving it towards an arbitrary
final position without affecting other non-overlapping coherent components.
These effects could be observed with a state-of-the-art apparatus
Radon transform on the cylinder and tomography of a particle on the circle
The tomographic probability distribution on the phase space (cylinder)
related to a circle or an interval is introduced. The explicit relations of the
tomographic probability densities and the probability densities on the phase
space for the particle motion on a torus are obtained and the relation of the
suggested map to the Radon transform on the plane is elucidated. The
generalization to the case of a multidimensional torus is elaborated and the
geometrical meaning of the tomographic probability densities as marginal
distributions on the helix discussed.Comment: 9 pages, 3 figure
Non-Markovian Decay and Lasing Condition in an Optical Microcavity Coupled to a Structured Reservoir
The decay dynamics of the classical electromagnetic field in a leaky optical
resonator supporting a single mode coupled to a structured continuum of modes
(reservoir) is theoretically investigated, and the issue of threshold condition
for lasing in presence of an inverted medium is comprehensively addressed.
Specific analytical results are given for a single-mode microcavity resonantly
coupled to a coupled resonator optical waveguide (CROW), which supports a band
of continuous modes acting as decay channels. For weak coupling, the usual
exponential Weisskopf-Wigner (Markovian) decay of the field in the bare
resonator is found, and the threshold for lasing increases linearly with the
coupling strength. As the coupling between the microcavity and the structured
reservoir increases, the field decay in the passive cavity shows non
exponential features, and correspondingly the threshold for lasing ceases to
increase, reaching a maximum and then starting to decrease as the coupling
strength is further increased. A singular behavior for the "laser phase
transition", which is a clear signature of strong non-Markovian dynamics, is
found at critical values of the coupling between the microcavity and the
reservoir.Comment: to appear in Phys. Rev. A (December 2006 issue
Universal dynamical decoherence control of noisy single-and multi-qubit systems
In this article we develop, step by step, the framework for universal
dynamical control of two-level systems (TLS) or qubits experiencing amplitude-
or phase-noise (AN or PN) due to coupling to a thermal bath. A comprehensive
arsenal of modulation schemes is introduced and applied to either AN or PN,
resulting in completely analogous formulae for the decoherence rates, thus
underscoring the unified nature of this universal formalism. We then address
the extension of this formalism to multipartite decoherence control, where
symmetries are exploited to overcome decoherence.Comment: 28 pages, 4 figure
Quantum Zeno subspaces
The quantum Zeno effect is recast in terms of an adiabatic theorem when the
measurement is described as the dynamical coupling to another quantum system
that plays the role of apparatus. A few significant examples are proposed and
their practical relevance discussed. We also focus on decoherence-free
subspaces.Comment: 5 pages, 1 figure, to be published in Phys. Rev. Let
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