40 research outputs found
On a generalization of the binomial distribution and its Poisson-like limit
We examine a generalization of the binomial distribution associated with a
strictly increasing sequence of numbers and we prove its Poisson-like limit.
Such generalizations might be found in quantum optics with imperfect detection.
We discuss under which conditions this distribution can have a probabilistic
interpretation.Comment: 17 pages, 6 figure
Quadrature-dependent Bogoliubov transformations and multiphoton squeezed states
We introduce a linear, canonical transformation of the fundamental
single--mode field operators and that generalizes the linear
Bogoliubov transformation familiar in the construction of the harmonic
oscillator squeezed states. This generalization is obtained by adding to the
linear transformation a nonlinear function of any of the fundamental quadrature
operators and , making the original Bogoliubov transformation
quadrature--dependent. Remarkably, the conditions of canonicity do not impose
any constraint on the form of the nonlinear function, and lead to a set of
nontrivial algebraic relations between the --number coefficients of the
transformation. We examine in detail the structure and the properties of the
new quantum states defined as eigenvectors of the transformed annihilation
operator . These eigenvectors define a class of multiphoton squeezed states.
The structure of the uncertainty products and of the quasiprobability
distributions in phase space shows that besides coherence properties, these
states exhibit a squeezing and a deformation (cooling) of the phase--space
trajectories, both of which strongly depend on the form of the nonlinear
function. The presence of the extra nonlinear term in the phase of the wave
functions has also relevant consequences on photon statistics and correlation
properties. The non quadratic structure of the associated Hamiltonians suggests
that these states be generated in connection with multiphoton processes in
media with higher nonlinearities.Comment: 16 pages, 15 figure
Schroedinger cat-like states by conditional measurements on a beam-splitter
A scheme for generating Schr\"{o}dinger cat-like states of a single-mode
optical field by means of conditional measurement is proposed. Feeding into a
beam splitter a squeezed vacuum and counting the photons in one of the output
channels, the conditional states in the other output channel exhibit a number
of properties that are very similar to those of superpositions of two coherent
states with opposite phases. We present analytical and numerical results for
the photon-number and quadrature-component distributions of the conditional
states and their Wigner and Husimi functions. Further, we discuss the effect of
realistic photocounting on the states.Comment: 6 figures(divided in subfigures) using a4.st
A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements
A generic model of measurement device which is able to directly measure
commonly used quantum-state characteristics such as fidelity, overlap, purity
and Hilbert-Schmidt distance for two general uncorrelated mixed states is
proposed. In addition, for two correlated mixed states, the measurement
realizes an entanglement witness for Werner's separability criterion. To
determine these observables, the estimation only one parameter - the visibility
of interference, is needed. The implementations in cavity QED, trapped ion and
electromagnetically induced transparency experiments are discussed.Comment: 6 pages, 3 figure
Generation of two-mode nonclassical states and a quantum phase gate operation in trapped ion cavity QED
We propose a scheme to generate nonclassical states of a quantum system,
which is composed of the one-dimensional trapped ion motion and a single cavity
field mode. We show that two-mode SU(2) Schr\"odinger-cat states, entangled
coherent states, two-mode squeezed vacuum states and their superposition can be
generated. If the vibration mode and the cavity mode are used to represent
separately a qubit, a quantum phase gate can be implemented.Comment: to appear in PR
Motional effects of single trapped atomic/ionic qubit
We investigate theoretical decoherence effects of the motional degrees of
freedom of a single trapped atomic/ionic electronically coded qubit. For single
bit rotations from a resonant running wave laser field excitation, we found the
achievable fidelity to be determined by a single parameter characterized by the
motional states. Our quantitative results provide a useful realistic view for
current experimental efforts in quantum information and computing.Comment: 3 fig
Generation of arbitrary two dimensional motional state of a trapped ion
We present a scheme to generate an arbitrary two-dimensional quantum state of
motion of a trapped ion. This proposal is based on a sequence of laser pulses,
which are tuned appropriately to control transitions on the sidebands of two
modes of vibration. Not more than laser pulses are needed to
generate a pure state with upper phonon number and in the and
direction respectively.Comment: to appear in PR