31 research outputs found
Contradictory uncertainty relations
We show within a very simple framework that different measures of
fluctuations lead to uncertainty relations resulting in contradictory
conclusions. More specifically we focus on Tsallis and Renyi entropic
uncertainty relations and we get that the minimum uncertainty states of some
uncertainty relations are the maximum uncertainty states of closely related
uncertainty relations, and vice versa.Comment: 4 pages, 10 figure
Smooth quantum-classical transition in photon subtraction and addition processes
Recently Parigi et al. [Science 317, 1890 (2007)] implemented experimentally
the photon subtraction and addition processes from/to a light field in a
conditional way, when the required operations were produced successfully only
upon the positive outcome of a separate measurement. It was verified that for a
low intensity beam (quantum regime) the bosonic annihilation operator does
indeed describe a single photon subtraction, while the creation operator
describes a photon addition. Nonetheless, the exact formal expressions for
these operations do not always reduce to these simple identifications, and in
this connection here we deduce the general superoperators for multiple photons
subtraction and addition processes and analyze the statistics of the resulting
states for classical field states having an arbitrary intensity. We obtain
closed analytical expressions and verify that for classical fields with high
intensity (classical regime) the operators that describe photon subtraction and
addition processes deviate significantly from simply annihilation and creation
operators. Complementarily, we analyze in details such a smooth
quantum-classical transition as function of beam intensity for both processes.Comment: 7 pages, 5 figures. To appear in Phys. Rev.
Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion
A quantum damped-polariton model is constructed for an inhomogeneous
anisotropic linear dielectric with arbitrary dispersion in space and time. The
model Hamiltonian is completely diagonalized by determining the creation and
annihilation operators for the fundamental polariton modes as specific linear
combinations of the basic dynamical variables. Explicit expressions are derived
for the time-dependent operators describing the electromagnetic field, the
dielectric polarization and the noise term in the latter. It is shown how to
identify bath variables that generate the dissipative dynamics of the medium.Comment: 24 page
Alternative measures of uncertainty in quantum metrology: Contradictions and limits
We examine a family of intrinsic performance measures in terms of probability
distributions that generalize Hellinger distance and Fisher information. They
are applied to quantum metrology to assess the uncertainty in the detection of
minute changes of physical quantities. We show that different measures lead to
contradictory conclusions, including the possibility of arbitrarily small
uncertainty for fixed resources. These intrinsic performances are compared with
the averaged error in the corresponding estimation problem after single-shot
measurements.Comment: 4 pages, 4 figure
Balancing efficiencies by squeezing in realistic eight-port homodyne detection
We address measurements of covariant phase observables (CPOs) by means of
realistic eight-port homodyne detectors. We do not assume equal quantum
efficiencies for the four photodetectors and investigate the conditions under
which the measurement of a CPO may be achieved. We show that balancing the
efficiencies using an additional beam splitter allows us to achieve a CPO at
the price of reducing the overall effective efficiency, and prove that it is
never a smearing of the ideal CPO achievable with unit quantum efficiency. An
alternative strategy based on employing a squeezed vacuum as a parameter field
is also suggested, which allows one to increase the overall efficiency in
comparison to the passive case using only a moderate amount of squeezing. Both
methods are suitable for implementantion with current technology.Comment: 8 pages, 5 figures, revised versio
Phase Diffusion in Quantum Dissipative Systems
We study the dynamics of the quantum phase distribution associated with the
reduced density matrix of a system for a number of situations of practical
importance, as the system evolves under the influence of its environment,
interacting via a quantum nondemoliton type of coupling, such that there is
decoherence without dissipation, as well as when it interacts via a dissipative
interaction, resulting in decoherence as well as dissipation. The system is
taken to be either a two-level atom (or equivalently, a spin-1/2 system) or a
harmonic oscillator, and the environment is modeled as a bath of harmonic
oscillators, starting out in a squeezed thermal state. The impact of the
different environmental parameters on the dynamics of the quantum phase
distribution for the system starting out in various initial states, is
explicitly brought out. An interesting feature that emerges from our work is
that the relationship between squeezing and temperature effects depends on the
type of system-bath interaction. In the case of quantum nondemolition type of
interaction, squeezing and temperature work in tandem, producing a diffusive
effect on the phase distribution. In contrast, in case of a dissipative
interaction, the influence of temperature can be counteracted by squeezing,
which manifests as a resistence to randomization of phase. We make use of the
phase distributions to bring out a notion of complementarity in atomic systems.
We also study the dispersion of the phase using the phase distributions
conditioned on particular initial states of the system.Comment: Accepted for publication in Physical Review A; changes in section V;
20 pages, 12 figure
Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]
The quantization of phase is still an open problem. In the approach of
Susskind and Glogower so called cosine and sine operators play a fundamental
role. Their eigenstates in the Fock representation are related with the
Chebyshev polynomials of the second kind. Here we introduce more general cosine
and sine operators whose eigenfunctions in the Fock basis are related in a
similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1].
To each polynomial set defined in terms of a weight function there corresponds
a pair of cosine and sine operators. Depending on the symmetry of the weight
function we distinguish generalized or extended operators. Their eigenstates
are used to define cosine and sine representations and probability
distributions. We consider also the inverse arccosine and arcsine operators and
use their eigenstates to define cosine-phase and sine-phase distributions,
respectively. Specific, numerical and graphical results are given for the
classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure
Testing of quantum phase in matter wave optics
Various phase concepts may be treated as special cases of the maximum
likelihood estimation. For example the discrete Fourier estimation that
actually coincides with the operational phase of Noh, Fouge`res and Mandel is
obtained for continuous Gaussian signals with phase modulated mean.Since
signals in quantum theory are discrete, a prediction different from that given
by the Gaussian hypothesis should be obtained as the best fit assuming a
discrete Poissonian statistics of the signal. Although the Gaussian estimation
gives a satisfactory approximation for fitting the phase distribution of almost
any state the optimal phase estimation offers in certain cases a measurable
better performance. This has been demonstrated in neutron--optical experiment.Comment: 8 pages, 4 figure
Sampling the canonical phase from phase-space functions
We discuss the possibility of sampling exponential moments of the canonical
phase from the s-parametrized phase space functions. We show that the sampling
kernels exist and are well-behaved for any s>-1, whereas for s=-1 the kernels
diverge in the origin. In spite of that we show that the phase space moments
can be sampled with any predefined accuracy from the Q-function measured in the
double-homodyne scheme with perfect detectors. We discuss the effect of
imperfect detection and address sampling schemes using other measurable
phase-space functions. Finally, we discuss the problem of sampling the
canonical phase distribution itself.Comment: 10 pages, 7 figures, REVTe