140 research outputs found
Properties of Squeezed-State Excitations
The photon distribution function of a discrete series of excitations of
squeezed coherent states is given explicitly in terms of Hermite polynomials of
two variables. The Wigner and the coherent-state quasiprobabilities are also
presented in closed form through the Hermite polynomials and their limiting
cases. Expectation values of photon numbers and their dispersion are
calculated. Some three-dimensional plots of photon distributions for different
squeezing parameters demonstrating oscillatory behaviour are given.Comment: Latex,35 pages,submitted to Quant.Semiclassical Op
Wigner function evolution in self-Kerr Medium derived by Entangled state representation
By introducing the thermo entangled state representation, we convert the
calculation of Wigner function (WF) of density operator to an overlap between
"two pure" states in a two-mode enlarged Fock space. Furthermore, we derive a
new WF evolution formula of any initial state in self-Kerr Medium with photon
loss and find that the photon number distribution for any initial state is
independent of the coupling factor with Kerr Medium, where the number state is
not affected by the Kerr nonlinearity and evolves into a density operator of
binomial distribution.Comment: 9 pages, 1 figur
Radon transform and pattern functions in quantum tomography
The two-dimensional Radon transform of the Wigner quasiprobability is
introduced in canonical form and the functions playing a role in its inversion
are discussed. The transformation properties of this Radon transform with
respect to displacement and squeezing of states are studied and it is shown
that the last is equivalent to a symplectic transformation of the variables of
the Radon transform with the contragredient matrix to the transformation of the
variables in the Wigner quasiprobability. The reconstruction of the density
operator from the Radon transform and the direct reconstruction of its
Fock-state matrix elements and of its normally ordered moments are discussed.
It is found that for finite-order moments the integration over the angle can be
reduced to a finite sum over a discrete set of angles. The reconstruction of
the Fock-state matrix elements from the normally ordered moments leads to a new
representation of the pattern functions by convergent series over even or odd
Hermite polynomials which is appropriate for practical calculations. The
structure of the pattern functions as first derivatives of the products of
normalizable and nonnormalizable eigenfunctions to the number operator is
considered from the point of view of this new representation.Comment: To appear on Journal of Modern Optics.Submitted t
Generalized thermo vacuum state derived by the partial trace method
By virtue of the technique of integration within an ordered product (IWOP) of
operators we present a new approach for deriving generalized thermo vacuum
state which is simpler in form that the result by using the Umezawa-Takahashi
approach, in this way the thermo field dynamics can be developed. Applications
of the new state are discussed.Comment: 5 pages, no figure, revtex
Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final
published versio
Retrodictively Optimal Localisations in Phase Space
In a previous paper it was shown that the distribution of measured values for
a retrodictively optimal simultaneous measurement of position and momentum is
always given by the initial state Husimi function. This result is now
generalised to retrodictively optimal simultaneous measurements of an arbitrary
pair of rotated quadratures x_theta1 and x_theta2. It is shown, that given any
such measurement, it is possible to find another such measurement,
informationally equivalent to the first, for which the axes defined by the two
quadratures are perpendicular. It is further shown that the distribution of
measured values for such a meaurement belongs to the class of generalised
Husimi functions most recently discussed by Wuensche and Buzek. The class
consists of the subset of Wodkiewicz's operational probability distributions
for which the filter reference state is a squeezed vaccuum state.Comment: 11 pages, 2 figures. AMS Latex. Replaced with published versio
Continuous photodetection model: quantum jump engineering and hints for experimental verification
We examine some aspects of the continuous photodetection model for
photocounting processes in cavities. First, we work out a microscopic model
that describes the field-detector interaction and deduce a general expression
for the Quantum Jump Superoperator (QJS), that shapes the detector's
post-action on the field upon a detection. We show that in particular cases our
model recovers the QJSs previously proposed ad hoc in the literature and point
out that by adjusting the detector parameters one can engineer QJSs. Then we
set up schemes for experimental verification of the model. By taking into
account the ubiquitous non-idealities, we show that by measuring the lower
photocounts moments and the mean waiting time one can check which QJS better
describes the photocounting phenomenon.Comment: 12 pages, 7 figures. Contribution to the conference Quantum Optics
III, Pucon - Chile, November 27-30, 200
Monge Distance between Quantum States
We define a metric in the space of quantum states taking the Monge distance
between corresponding Husimi distributions (Q--functions). This quantity
fulfills the axioms of a metric and satisfies the following semiclassical
property: the distance between two coherent states is equal to the Euclidean
distance between corresponding points in the classical phase space. We compute
analytically distances between certain states (coherent, squeezed, Fock and
thermal) and discuss a scheme for numerical computation of Monge distance for
two arbitrary quantum states.Comment: 9 pages in LaTex - RevTex + 2 figures in ps. submitted to Phys. Rev.
Generalized Husimi Functions: Analyticity and Information Content
The analytic properties of a class of generalized Husimi functions are
discussed, with particular reference to the problem of state reconstruction.
The class consists of the subset of Wodkiewicz's operational probability
distributions for which the filter reference state is a squeezed vacuum state.
The fact that the function is analytic means that perfectly precise knowledge
of its values over any small region of phase space provides enough information
to reconstruct the density matrix. If, however, one only has imprecise
knowledge of its values, then the amplification of statistical errors which
occurs when one attempts to carry out the continuation seriously limits the
amount of information which can be extracted. To take account of this fact a
distinction is made between explicate, or experimentally accessible
information, and information which is only present in implicate, experimentally
inaccessible form. It is shown that an explicate description of various aspects
of the system can be found localised on various 2 real dimensional surfaces in
complexified phase space. In particular, the continuation of the function to
the purely imaginary part of complexified phase space provides an explicate
description of the Wigner function.Comment: 16 pages, 2 figures, AMS-latex. Replaced with published versio
Sampling functions for multimode homodyne tomography with a single local oscillator
We derive various sampling functions for multimode homodyne tomography with a
single local oscillator. These functions allow us to sample multimode
s-parametrized quasidistributions, density matrix elements in Fock basis, and
s-ordered moments of arbitrary order directly from the measured quadrature
statistics. The inevitable experimental losses can be compensated by proper
modification of the sampling functions. Results of Monte Carlo simulations for
squeezed three-mode state are reported and the feasibility of reconstruction of
the three-mode Q-function and s-ordered moments from 10^7 sampled data is
demonstrated.Comment: 12 pages, 8 figures, REVTeX, submitted Phys. Rev.
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