3,924 research outputs found
Angular momentum conservation in measurements on spin Bose-Einstein condensates
We discuss a thought experiment where two operators, Alice and Bob, perform
transverse spin measurements on a quantum system; this system is initially in a
double Fock spin state, which extends over a large distance in space so that
the two operators are far away from each other. Standard quantum mechanics
predicts that, when Alice makes a few measurements, a large transverse
component of the spin angular momentum may appear in Bob's laboratory. A
paradox then arises since local angular momentum conservation seems to be
violated. It has been suggested that this angular momentum may be provided by
the interaction with the measurement apparatuses. We show that this solution of
the paradox is not appropriate, so that another explanation must be sought. The
general question is the retroaction of a quantum system onto a measurement
apparatus. For instance, when the measured system is entangled with another
quantum system, can its reaction on a measurement apparatus be completely
changed? Is angular momentum conserved only on average over several
measurements, but not during one realization of the experiment?Comment: 11 pages, 3 figure
Quantum properties of a single beam splitter
When a single beam-splitter receives two beams of bosons described by Fock
states (Bose-Einstein condensates at very low temperatures), interesting
generalizations of the two-photon Hong-Ou-Mandel effect take place for larger
number of particles. The distributions of particles at two detectors behind the
beam splitter can be understood as resulting from the combination of two
effects, the spontaneous phase appearing during quantum measurement, and the
quantum angle. The latter introduces quantum "population oscillations", which
can be seen as a generalized Hong-Ou-Mandel effect, although they do not always
correspond to even-odd oscillations.Comment: 14 pages, 11 figure
Validity of the Hohenberg Theorem for a Generalized Bose-Einstein Condensation in Two Dimensions
Several authors have considered the possibility of a generalized
Bose-Einstein condensation (BEC) in which a band of low states is occupied so
that the total occupation number is macroscopic, even if the occupation number
of each state is not extensive. The Hohenberg theorem (HT) states that there is
no BEC into a single state in 2D; we consider its validity for the case of a
generalized condensation and find that, under certain conditions, the HT does
not forbid a BEC in 2D. We discuss whether this situation actually occurs in
any theoretical model system.Comment: 6 pages, Latex, JLTP class, accepted by Jour. Low Temp. Phys.,
Quantum Fluids and Solids Conference QFS200
Beyond spontaneously broken symmetry in Bose-Einstein condensates
Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot
treat phase off-diagonal effects, and thus not explain Bell inequality
violations. We describe another situation that is beyond a SSB treatment: an
experiment where particles from two (possibly macroscopic) condensate sources
are used for conjugate measurements of the relative phase and populations.
Off-diagonal phase effects are characterized by a "quantum angle" and observed
via "population oscillations", signaling quantum interference of
macroscopically distinct states (QIMDS).Comment: 10 pages 4 figure
Ursell Operators in Statistical Physics III: thermodynamic properties of degenerate gases
We study in more detail the properties of the generalized Beth Uhlenbeck
formula obtained in a preceding article. This formula leads to a simple
integral expression of the grand potential of the system, where the interaction
potential appears only through the matrix elements of the second order Ursell
operator . Our results remain valid for significant degree of degeneracy
of the gas, but not when Bose Einstein (or BCS) condensation is reached, or
even too close from this transition point. We apply them to the study of the
thermodynamic properties of degenerate quantum gases: equation of state,
magnetic susceptibility, effects of exchange between bound states and free
particles, etc. We compare our predictions to those obtained within other
approaches, especially the ``pseudo potential'' approximation, where the real
potential is replaced by a potential with zero range (Dirac delta function).
This comparison is conveniently made in terms of a temperature dependent
quantity, the ``Ursell length'', which we define in the text. This length plays
a role which is analogous to the scattering length for pseudopotentials, but it
is temperature dependent and may include more physical effects than just binary
collision effects; for instance at very low temperatures it may change sign or
increase almost exponentially, an effect which is reminiscent of a precursor of
the BCS pairing transition. As an illustration, numerical results for quantum
hard spheres are given.Comment: 26 pages, 4 figures, LaTeX (amssymb), slight changes to first versio
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Shot noise of interference between independent atomic systems
We study shot (counting) noise of the amplitude of interference between
independent atomic systems. In particular, for the two interfering systems the
variance of the fringe amplitude decreases as the inverse power of the number
of particles per system with the coefficient being a non-universal number. This
number depends on the details of the initial state of each system so that the
shot noise measurements can be used to distinguish between such states. We
explicitly evaluate this coefficient for the two cases of the interference
between bosons in number states and in broken symmetry states. We generalize
our analysis to the interference of multiple independent atomic systems. We
show that the variance of the interference contrast vanishes as the inverse
power of the number of the interfering systems. This result, implying high
signal to noise ratio in the interference experiments, holds both for bosons
and for fermions.Comment: 5 pages, 1 figure, final version, added a simple quantum-mechanical
argument why two independent condensates with fixed number of particles in
each must interfere in a generic experimental setu
Shear-flow transition: the basin boundary
The structure of the basin of attraction of a stable equilibrium point is
investigated for a dynamical system (W97) often used to model transition to
turbulence in shear flows. The basin boundary contains not only an equilibrium
point Xlb but also a periodic orbit P, and it is the latter that mediates the
transition. Orbits starting near Xlb relaminarize. We offer evidence that this
is due to the extreme narrowness of the region complementary to basin of
attraction in that part of phase space near Xlb. This leads to a proposal for
interpreting the 'edge of chaos' in terms of more familiar invariant sets.Comment: 11 pages; submitted for publication in Nonlinearit
Nonlocal appearance of a macroscopic angular momentum
We discuss a type of measurement in which a macroscopically large angular
momentum (spin) is "created" nonlocally by the measurement of just a few atoms
from a double Fock state. This procedure apparently leads to a blatant
nonconservation of a macroscopic variable - the local angular momentum. We
argue that while this gedankenexperiment provides a striking illustration of
several counter-intuitive features of quantum mechanics, it does not imply a
non-local violation of the conservation of angular momentum.Comment: 10 pages, 1 figur
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