6,670 research outputs found
Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces
We propose an interferometric method for statistically discriminating between
nonorthogonal states in high dimensional Hilbert spaces for use in quantum
information processing. The method is illustrated for the case of photon
orbital angular momentum (OAM) states. These states belong to pairs of bases
that are mutually unbiased on a sequence of two-dimensional subspaces of the
full Hilbert space, but the vectors within the same basis are not necessarily
orthogonal to each other. Over multiple trials, this method allows
distinguishing OAM eigenstates from superpositions of multiple such
eigenstates. Variations of the same method are then shown to be capable of
preparing and detecting arbitrary linear combinations of states in Hilbert
space. One further variation allows the construction of chains of states
obeying recurrence relations on the Hilbert space itself, opening a new range
of possibilities for more abstract information-coding algorithms to be carried
out experimentally in a simple manner. Among other applications, we show that
this approach provides a simplified means of switching between pairs of
high-dimensional mutually unbiased OAM bases
Quantum simulation of topologically protected states using directionally unbiased linear-optical multiports
It is shown that quantum walks on one-dimensional arrays of special
linear-optical units allow the simulation of discrete-time Hamiltonian systems
with distinct topological phases. In particular, a slightly modified version of
the Su-Schrieffer-Heeger (SSH) system can be simulated, which exhibits states
of nonzero winding number and has topologically protected boundary states. In
the large-system limit this approach uses quadratically fewer resources to
carry out quantum simulations than previous linear-optical approaches and can
be readily generalized to higher-dimensional systems. The basic optical units
that implement this simulation consist of combinations of optical multiports
that allow photons to reverse direction
Quantum simulation of discrete-time Hamiltonians using directionally unbiased linear optical multiports
Recently, a generalization of the standard optical multiport was proposed [Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow photons to reverse direction and exit backwards from the input port, providing a realistic linear optical scattering vertex for quantum walks on arbitrary graph structures. Here, it is shown that arrays of these multiports allow the simulation of a range of discrete-time Hamiltonian systems. Examples are described, including a case where both spatial and internal degrees of freedom are simulated. Because input ports also double as output ports, there is substantial savings of resources compared to feed-forward networks carrying out the same functions. The simulation is implemented in a scalable manner using only linear optics, and can be generalized to higher dimensional systems in a straightforward fashion, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.This research was supported by the National Science Foundation EFRI-ACQUIRE Grant No. ECCS-1640968, NSF Grant No. ECCS-1309209, and by the Northrop Grumman NG Next. (ECCS-1640968 - National Science Foundation EFRI-ACQUIRE Grant; ECCS-1309209 - NSF Grant; Northrop Grumman NG Next
Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I
We analyze the issue of anomaly-free representations of the constraint
algebra in Loop Quantum Gravity (LQG) in the context of a
diffeomorphism-invariant gauge theory in three spacetime dimensions. We
construct a Hamiltonian constraint operator whose commutator matches with a
quantization of the classical Poisson bracket involving structure functions.
Our quantization scheme is based on a geometric interpretation of the
Hamiltonian constraint as a generator of phase space-dependent diffeomorphisms.
The resulting Hamiltonian constraint at finite triangulation has a conceptual
similarity with the "mu-bar"-scheme in loop quantum cosmology and highly
intricate action on the spin-network states of the theory. We construct a
subspace of non-normalizable states (distributions) on which the continuum
Hamiltonian constraint is defined which leads to an anomaly-free representation
of the Poisson bracket of two Hamiltonian constraints in loop quantized
framework.Comment: 60 pages, 6 figure
Strong Upper Limits on Sterile Neutrino Warm Dark Matter
Sterile neutrinos are attractive dark matter candidates. Their parameter
space of mass and mixing angle has not yet been fully tested despite intensive
efforts that exploit their gravitational clustering properties and radiative
decays. We use the limits on gamma-ray line emission from the Galactic Center
region obtained with the SPI spectrometer on the INTEGRAL satellite to set new
constraints, which improve on the earlier bounds on mixing by more than two
orders of magnitude, and thus strongly restrict a wide and interesting range of
models.Comment: 4 pages, 2 figures; minor revisions, accepted for publication in
Physical Review Letter
A Two-Dimensional MagnetoHydrodynamics Scheme for General Unstructured Grids
We report a new finite-difference scheme for two-dimensional
magnetohydrodynamics (MHD) simulations, with and without rotation, in
unstructured grids with quadrilateral cells. The new scheme is implemented
within the code VULCAN/2D, which already includes radiation-hydrodynamics in
various approximations and can be used with arbitrarily moving meshes (ALE).
The MHD scheme, which consists of cell-centered magnetic field variables,
preserves the nodal finite difference representation of div(\bB) by
construction, and therefore any initially divergence-free field remains
divergence-free through the simulation. In this paper, we describe the new
scheme in detail and present comparisons of VULCAN/2D results with those of the
code ZEUS/2D for several one-dimensional and two-dimensional test problems. The
code now enables two-dimensional simulations of the collapse and explosion of
the rotating, magnetic cores of massive stars. Moreover, it can be used to
simulate the very wide variety of astrophysical problems for which multi-D
radiation-magnetohydrodynamics (RMHD) is relevant.Comment: 22 pages, including 11 figures; Accepted to the Astrophysical
Journal. Higher resolution figures available at
http://zenith.as.arizona.edu/~burrows/mhd-code
Second wind of the Dulong-Petit Law at a quantum critical point
Renewed interest in 3He physics has been stimulated by experimental
observation of non-Fermi-liquid behavior of dense 3He films at low
temperatures. Abnormal behavior of the specific heat C(T) of two-dimensional
liquid 3He is demonstrated in the occurrence of a T-independent term in C(T).
To uncover the origin of this phenomenon, we have considered the group velocity
of transverse zero sound propagating in a strongly correlated Fermi liquid. For
the first time, it is shown that if two-dimensional liquid 3He is located in
the vicinity of the quantum critical point associated with a divergent
quasiparticle effective mass, the group velocity depends strongly on
temperature and vanishes as T is lowered toward zero. The predicted vigorous
dependence of the group velocity can be detected in experimental measurements
on liquid 3He films. We have demonstrated that the contribution to the specific
heat coming from the boson part of the free energy due to the transverse
zero-sound mode follows the Dulong-Petit Law. In the case of two-dimensional
liquid 3He, the specific heat becomes independent of temperature at some
characteristic temperature of a few mK.Comment: 5 pages, 1 figur
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