651 research outputs found
Remarks on the Extended Characteristic Uncertainty Relations
Three remarks concerning the form and the range of validity of the
state-extended characteristic uncertainty relations (URs) are presented. A more
general definition of the uncertainty matrix for pure and mixed states is
suggested. Some new URs are provided.Comment: LaTex, 4 pages, no figure
Comment on "On the uncertainty relations and squeezed states for the quantum mechanics on a circle"
It is shown by examples that the position uncertainty on a circle, proposed
recently by Kowalski and Rembieli\'nski [J. Phys. A 35 (2002) 1405] is not
consistent with the state localization. We argue that the relevant
uncertainties and uncertainty relations (UR's) on a circle are that based on
the Gram-Robertson matrix. Several of these generalized UR's are displayed and
related criterions for squeezed states are discussed.Comment: 5 pages, LaTex2e, 3 figures.ep
Photon recoil momentum in a Bose-Einstein condensate of a dilute gas
We develop a "minimal" microscopic model to describe a
two-pulse-Ramsay-interferometer-based scheme of measurement of the photon
recoil momentum in a Bose-Einstein condensate of a dilute gas [Campbell et al.,
Phys. Rev. Lett. 94, 170403 (2005)]. We exploit the truncated coupled
Maxwell-Schroedinger equations to elaborate the problem. Our approach provides
a theoretical tool to reproduce essential features of the experimental results.
Additionally, we enable to calculate the quantum-mechanical mean value of the
recoil momentum and its statistical distribution that provides a detailed
information about the recoil event.Comment: 6 pages, 4 figure
Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions
The Barut-Girardello coherent states (BG CS) representation is extended to
the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson
realizations. The sp(N,R) BG CS take the form of multimode ordinary
Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n
canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode
Hilbert space and the relation between the canonical CS and the u(p,q) BG-type
CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and
their discrete superpositions contain many states studied in quantum optics
(even and odd N-mode CS, pair CS) and provide an approach to quadrature
squeezing, alternative to that of intelligent states. New subsets of weakly and
strongly nonclassical states are pointed out and their statistical properties
(first- and second-order squeezing, photon number distributions) are discussed.
For specific values of the angle parameters and small amplitude of the
canonical CS components these states approaches multimode Fock states with one,
two or three bosons/photons. It is shown that eigenstates of a squared
non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of
the quadratures of A.Comment: 29 pages, LaTex, 5 figures. Improvements in text, corrections in some
formulas. To appear in J. Phys. A, v. 3
Stretching an heteropolymer
We study the influence of some quenched disorder in the sequence of monomers
on the entropic elasticity of long polymeric chains. Starting from the
Kratky-Porod model, we show numerically that some randomness in the favoured
angles between successive segments induces a change in the elongation versus
force characteristics, and this change can be well described by a simple
renormalisation of the elastic constant. The effective coupling constant is
computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur
Uncertainty Relations in Deformation Quantization
Robertson and Hadamard-Robertson theorems on non-negative definite hermitian
forms are generalized to an arbitrary ordered field. These results are then
applied to the case of formal power series fields, and the
Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations
in deformation quantization are found. Some conditions under which the
uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte
Light scattering from ultracold atoms in optical lattices as an optical probe of quantum statistics
We study off-resonant collective light scattering from ultracold atoms
trapped in an optical lattice. Scattering from different atomic quantum states
creates different quantum states of the scattered light, which can be
distinguished by measurements of the spatial intensity distribution, quadrature
variances, photon statistics, or spectral measurements. In particular,
angle-resolved intensity measurements reflect global statistics of atoms (total
number of radiating atoms) as well as local statistical quantities (single-site
statistics even without an optical access to a single site) and pair
correlations between different sites. As a striking example we consider
scattering from transversally illuminated atoms into an optical cavity mode.
For the Mott insulator state, similar to classical diffraction, the number of
photons scattered into a cavity is zero due to destructive interference, while
for the superfluid state it is nonzero and proportional to the number of atoms.
Moreover, we demonstrate that light scattering into a standing-wave cavity has
a nontrivial angle dependence, including the appearance of narrow features at
angles, where classical diffraction predicts zero. The measurement procedure
corresponds to the quantum non-demolition (QND) measurement of various atomic
variables by observing light.Comment: 15 pages, 5 figure
Disordered, stretched, and semiflexible biopolymers in two dimensions
We study the effects of intrinsic sequence-dependent curvature for a two
dimensional semiflexible biopolymer with short-range correlation in intrinsic
curvatures. We show exactly that when not subjected to any external force, such
a system is equivalent to a system with a well-defined intrinsic curvature and
a proper renormalized persistence length. We find the exact expression for the
distribution function of the equivalent system. However, we show that such an
equivalent system does not always exist for the polymer subjected to an
external force. We find that under an external force, the effect of
sequence-disorder depends upon the averaging order, the degree of disorder, and
the experimental conditions, such as the boundary conditions. Furthermore, a
short to moderate length biopolymer may be much softer or has a smaller
apparent persistent length than what would be expected from the "equivalent
system". Moreover, under a strong stretching force and for a long biopolymer,
the sequence-disorder is immaterial for elasticity. Finally, the effect of
sequence-disorder may depend upon the quantity considered
Photon Recoil in Light Scattering by a Bose-Einstein Condensate of a Dilute Gas
Abstract: Photon recoil upon light scattering by a Bose–Einstein condensate (BEC) of a dilute atomic gas is analyzed theoretically accounting for a weak interatomic interaction. Our approach is based on the Gross–Pitaevskii equation for the condensate, which is coupled to the Maxwell equation for the field. The dispersion relations of recoil energy and momentum are calculated, and the effect of weak nonideality of the condensate on the photon recoil is ubraveled. A good agreement between the theory and experiment [7] on the measurement of the photon recoil momentum in a dispersive medium is demonstrated
Robertson Intelligent States
Diagonalization of uncertainty matrix and minimization of Robertson
inequality for n observables are considered. It is proved that for even n this
relation is minimized in states which are eigenstates of n/2 independent
complex linear combinations of the observables. In case of canonical
observables this eigenvalue condition is also necessary. Such minimizing states
are called Robertson intelligent states (RIS).
The group related coherent states (CS) with maximal symmetry (for semisimple
Lie groups) are particular case of RIS for the quadratures of Weyl generators.
Explicit constructions of RIS are considered for operators of su(1,1), su(2),
h_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong
squeezing of group generators. Multimode squared amplitude squeezed states are
naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices
for quadratures of q-deformed boson operators a_{q,j} (q > 0) and of any k
power of a_j = a_{1,j} are positive definite and can be diagonalized by
symplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.DvComment: 23 pages, LaTex. Minor changes in text and references. Accepted in J.
Phys.
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