218 research outputs found
Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback
The stabilization of steady states is studied in a modified Lang-Kobayashi
model of a semiconductor laser. We show that multiple time-delayed feedback,
realized by a Fabry-Perot resonator coupled to the laser, provides a valuable
tool for the suppression of unwanted intensity pulsations, and leads to stable
continuous-wave operation. The domains of control are calulated in dependence
on the feedback strength, delay time (cavity round trip time), memory parameter
(mirror reflectivity), latency time, feedback phase, and bandpass filtering,
Due to the optical feedback, multistable behavior can also occur in the form of
delay-induced intensity pulsations or other modes for certain choices of the
control parameters. Control may then still be achieved by slowly ramping the
injection current during turn-on.Comment: 12 pages, 17 figure
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
A random laser as a dynamical network
The mode dynamics of a random laser is investigated in experiment and theory. The laser consists of a ZnCdO/ZnO multiple quantum well with air-holes that provide the necessary feedback. Time-resolved measurements reveal multi-mode spectra with individually developing features but no variation from shot to shot. These findings are qualitatively reproduced with a model that exploits the specifics of a dilute system of weak scatterers and can be interpreted in terms of a lasing network. Introducing the phase-sensitive node coherence reveals new aspects of the self-organization of the laser field. Lasing is carried by connected links between a subset of scatterers, the fields on which are oscillating coherently in phase. In addition, perturbing feedback with possibly unfitting phases from frustrated other scatterers is suppressed by destructive superposition. We believe that our findings are representative at least for weakly scattering random lasers. A generalization to random laser with dense and strong scatterers seems to be possible when using a more complex scattering theory for this case.Peer Reviewe
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
Husimi Transform of an Operator Product
It is shown that the series derived by Mizrahi, giving the Husimi transform
(or covariant symbol) of an operator product, is absolutely convergent for a
large class of operators. In particular, the generalized Liouville equation,
describing the time evolution of the Husimi function, is absolutely convergent
for a large class of Hamiltonians. By contrast, the series derived by
Groenewold, giving the Weyl transform of an operator product, is often only
asymptotic, or even undefined. The result is used to derive an alternative way
of expressing expectation values in terms of the Husimi function. The advantage
of this formula is that it applies in many of the cases where the anti-Husimi
transform (or contravariant symbol) is so highly singular that it fails to
exist as a tempered distribution.Comment: AMS-Latex, 13 page
Unifying the theory of Integration within normal-, Weyl- and antinormal-ordering of operators and the s--ordered operator expansion formula of density operators
By introducing the s-parameterized generalized Wigner operator into
phase-space quantum mechanics we invent the technique of integration within
s-ordered product of operators (which considers normal ordered, antinormally
ordered and Weyl ordered product of operators as its special cases). The
s-ordered operator expansion formula of density operators is derived, and the
s-parameterized quantization scheme is thus completely established.Comment: 7 page
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
Analytic representations based on SU(1,1) coherent states and their applications
We consider two analytic representations of the SU(1,1) Lie group: the
representation in the unit disk based on the SU(1,1) Perelomov coherent states
and the Barut-Girardello representation based on the eigenstates of the SU(1,1)
lowering generator. We show that these representations are related through a
Laplace transform. A ``weak'' resolution of the identity in terms of the
Perelomov SU(1,1) coherent states is presented which is valid even when the
Bargmann index is smaller than one half. Various applications of these
results in the context of the two-photon realization of SU(1,1) in quantum
optics are also discussed.Comment: LaTeX, 15 pages, no figures, to appear in J. Phys. A. More
information on http://www.technion.ac.il/~brif/science.htm
On the squeezed states for n observables
Three basic properties (eigenstate, orbit and intelligence) of the canonical
squeezed states (SS) are extended to the case of arbitrary n observables. The
SS for n observables X_i can be constructed as eigenstates of their linear
complex combinations or as states which minimize the Robertson uncertainty
relation. When X_i close a Lie algebra L the generalized SS could also be
introduced as orbit of Aut(L^C). It is shown that for the nilpotent algebra h_N
the three generalizations are equivalent. For the simple su(1,1) the family of
eigenstates of uK_- + vK_+ (K_\pm being lowering and raising operators) is a
family of ideal K_1-K_2 SS, but it cannot be represented as an Aut(su^C(1,1))
orbit although the SU(1,1) group related coherent states (CS) with symmetry are
contained in it.
Eigenstates |z,u,v,w;k> of general combination uK_- + vK_+ + wK_3 of the
three generators K_j of SU(1,1) in the representations with Bargman index k =
1/2,1, ..., and k = 1/4,3/4 are constructed and discussed in greater detail.
These are ideal SS for K_{1,2,3}. In the case of the one mode realization of
su(1,1) the nonclassical properties (sub-Poissonian statistics, quadrature
squeezing) of the generalized even CS |z,u,v;+> are demonstrated. The states
|z,u,v,w;k=1/4,3/4> can exhibit strong both linear and quadratic squeezing.Comment: 25 pages, LaTex, 4 .pic and .ps figures. Improvements in text,
discussion on generation scheme added. To appear in Phys. Script
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
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