11,835 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
The Geometry of the Cholesteric Phase
We propose a construction of a cholesteric pitch axis for an arbitrary
nematic director field as an eigenvalue problem. Our definition leads to a
Frenet-Serret description of an orthonormal triad determined by this axis, the
director, and the mutually perpendicular direction. With this tool we are able
to compare defect structures in cholesterics, biaxial nematics, and smectics.
Though they all have similar ground state manifolds, the defect structures are
different and cannot be, in general, translated from one phase to the other.Comment: 5 pages, the full catastroph
Hybrid Bloch-Anderson localization of light
We investigate the interplay of Bloch oscillations and Anderson localization
in optics. Gradual washing out of Bloch oscillations and the formation of
nearly stationary averaged intensity distributions, which are symmetric for
narrow and strongly asymmetric for broad input excitations, are observed
experimentally in laser-written waveguide arrays. At large disorder levels
Bloch oscillations are completely destroyed and both narrow and wide
excitations lead to symmetric stationary averaged intensity distributions with
exponentially decaying tails.Comment: 3 pages, 6 figures, to appear in Optics Letter
Two-Photon Spiral Imaging with Correlated Orbital Angular Momentum States
The concept of correlated two-photon spiral imaging is introduced. We begin
by analyzing the joint orbital angular momentum (OAM) spectrum of correlated
photon pairs. The mutual information carried by the photon pairs is evaluated,
and it is shown that when an object is placed in one of the beam paths the
value of the mutual information is strongly dependent on object shape and is
closely related to the degree of rotational symmetry present. After analyzing
the effect of the object on the OAM correlations, the method of correlated
spiral imaging is described. We first present a version using parametric
downconversion, in which entangled pairs of photons with opposite OAM values
are produced, placing an object in the path of one beam. We then present a
classical (correlated, but non-entangled) version. The relative problems and
benefits of the classical versus entangled configurations are discussed. The
prospect is raised of carrying out compressive imaging via twophoton OAM
detection to reconstruct sparse objects with few measurements
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