37,251 research outputs found
Explicit constructions of unitary transformations between equivalent irreducible representations
Irreducible representations (irreps) of a finite group are equivalent if
there exists a similarity transformation between them. In this paper, we
describe an explicit algorithm for constructing this transformation between a
pair of equivalent irreps, assuming we are given an algorithm to compute the
matrix elements of these irreps. Along the way, we derive a generalization of
the classical orthogonality relations for matrix elements of irreps of finite
groups. We give an explicit form of such unitary matrices for the important
case of conjugated Young-Yamanouchi representations, when our group is
symmetric group .Comment: 14 page
Microchannel plate cross-talk mitigation for spatial autocorrelation measurements
Microchannel plates (MCP) are the basis for many spatially-resolved
single-particle detectors such as ICCD or I-sCMOS cameras employing image
intensifiers (II), MCPs with delay-line anodes for the detection of cold gas
particles or Cherenkov radiation detectors. However, the spatial
characterization provided by an MCP is severely limited by cross-talk between
its microchannels, rendering MCP and II ill-suited for autocorrelation
measurements. Here we present a cross-talk subtraction method experimentally
exemplified for an I-sCMOS based measurement of pseudo-thermal light
second-order intensity autocorrelation function at the single- photon level.
The method merely requires a dark counts measurement for calibration. A
reference cross- correlation measurement certifies the cross-talk subtraction.
While remaining universal for MCP applications, the presented cross-talk
subtraction in particular simplifies quantum optical setups. With the
possibility of autocorrelation measurement the signal needs no longer to be
divided into two camera regions for a cross- correlation measurement, reducing
the experimental setup complexity and increasing at least twofold the
simultaneously employable camera sensor region
Bright sink-type localized states in exciton-polariton condensates
The family of one-dimensional localized solutions to dissipative nonlinear
equations includes a variety of objects such as sources, sinks, shocks (kinks),
and pulses. These states are in general accompanied by nontrivial density
currents, which are not necessarily related to the movement of the object
itself. We investigate the existence and physical properties of sink-type
solutions in nonresonantly pumped exciton-polariton condensates modeled by an
open-dissipative Gross-Pitaevskii equation. While sinks possess density
profiles similar to bright solitons, they are qualitatively different objects
as they exist in the case of repulsive interactions and represent a
heteroclinic solution. We show that sinks can be created in realistic systems
with appropriately designed pumping profiles. We also conclude that in
two-dimensional configurations, due to the proliferation of vortices, sinks do
not appear.Comment: 8 pages, 7 figure
Einstein-Podolsky-Rosen paradox in a hybrid bipartite system
Entanglement of light and matter is an essential resource for effective
quantum engineering. In particular, collective states of atomic ensembles are
robust against decoherence while preserving the possibility of strong
interaction with quantum states of light. While previous approaches to
continous-variable quantum interfaces relied on quadratures of light, here we
present an approach based on spatial structure of light-atom entanglement. We
create and characterize a 12-dimensional entangled state exhibiting quantum
correlations between a photon and an atomic ensemble in position and momentum
bases. This state allows us to demonstrate the original Einstein-Podolsky-Rosen
(EPR) paradox with two different entities, with an unprecedented delay time of
6 s between generation of entanglement and detection of the atomic state.Comment: 4 pages, 3 figures, 1 table, supplement available at
https://doi.org/10.1364/OPTICA.4.00027
Calculation of the molecular integrals with the range-separated correlation factor
Explicitly correlated quantum chemical calculations require calculations of
five types of molecular integrals beyond the standard electron repulsion
integrals. We present a novel scheme, which utilises general ideas of the
McMurchie-Davidson technique, to compute these integrals when the so-called
\range-separated" correlation factor is used. This correlation factor combines
the well-known short range behaviour, resulting from the electronic cusp
condition, with the exact long-range asymptotics found for the helium atom [M.
Lesiuk, B. Jeziorski, and R. Moszynski, J. Chem. Phys. , 134102
(2013)]. Almost all steps of the presented procedure are formulated
recursively, so that an efficient implementation and control of the precision
are possible. Additionally, the present formulation is very flexible and
general, and it allows for use of an arbitrary correlation factor in the
electronic structure calculations with minor or no changes
Simplified formalism of the algebra of partially transposed permutation operators with applications
Hereunder we continue the study of the representation theory of the algebra
of permutation operators acting on the -fold tensor product space, partially
transposed on the last subsystem. We develop the concept of partially reduced
irreducible representations, which allows to simplify significantly previously
proved theorems and what is the most important derive new results for
irreducible representations of the mentioned algebra. In our analysis we are
able to reduce complexity of the central expressions by getting rid of sums
over all permutations from symmetric group obtaining equations which are much
more handy in practical applications. We also find relatively simple matrix
representations for the generators of underlying algebra. Obtained
simplifications and developments are applied to derive characteristic of the
deterministic port-based teleportation scheme written purely in terms of
irreducible representations of the studied algebra. We solve an eigenproblem
for generators of algebra which is the first step towards to hybrid port-based
teleportation scheme and gives us new proofs of asymptotic behaviour of
teleportation fidelity. We also show connection between density operator
characterising port-based teleportation and particular matrix composed of
irreducible representation of the symmetric group which encodes properties of
the investigated algebra.Comment: 32 page
Structure and properties of the algebra of partially transposed permutation operators
We consider the structure of algebra of operators, acting in fold tensor
product space, which are partially transposed on the last term. Using purely
algebraical methods we show that this algebra is semi-simple and then,
considering its regular representation, we derive basic properties of the
algebra. In particular, we describe all irreducible representations of the
algebra of partially transposed operators and derive expressions for matrix
elements of the representations. It appears that there are two types of
irreducible representations of the algebra. The first one is strictly connected
with the representations of the group induced by irreducible
representations of the group . The second type is structurally
connected with irreducible representations of the group .Comment: 34 pages, 1 tabl
Quantum optics of spin waves through ac Stark modulation
We bring the set of linear quantum operations, important for many fundamental
studies in photonic systems, to the material domain of collective excitations
known as spin waves. Using the ac Stark effect we realize quantum operations on
single excitations and demonstrate a spin-wave analogue of Hong-Ou-Mandel
effect, realized via a beamsplitter implemented in the spin wave domain. Our
scheme equips atomic-ensemble-based quantum repeaters with quantum information
processing capability and can be readily brought to other physical systems,
such as doped crystals or room-temperature atomic ensembles.Comment: 6 pages + 12 pages supplemental, 5 figures + 13 supplementary figure
Wavevector multiplexed quantum memory via spatially-resolved single-photon detection
Parallelized quantum information processing requires tailored quantum
memories to simultaneously handle multiple photons. The spatial degree of
freedom is a promising candidate to facilitate such photonic multiplexing.
Using a single-photon resolving camera we demonstrate a wavevector multiplexed
quantum memory based on a cold atomic ensemble. Observation of nonclassical
correlations between Raman scattered photons is confirmed by an average value
of the second-order correlation function in
665 separated modes simultaneously. The proposed protocol utilizing the
multimode memory along with the camera will facilitate generation of
multi-photon states, which are a necessity in quantum-enhanced sensing
technologies and as an input to photonic quantum circuits.Comment: 11 pages, 6 figures + 3 pages, 3 figures supplemen
Spatially-resolved control of fictitious magnetic fields in a cold atomic ensemble
Effective and unrestricted engineering of atom-photon interactions requires
precise spatially-resolved control of light beams. The significant potential of
such manipulations lies in a set of disciplines ranging from solid state to
atomic physics. Here we use a Zeeman-like ac-Stark shift of a shaped laser beam
to perform rotations of spins with spatial resolution in a large ensemble of
cold rubidium atoms. We show that inhomogeneities of light intensity are the
main source of dephasing and thus decoherence, yet with proper beam shaping
this deleterious effect is strongly mitigated allowing rotations of 15 rad
within one spin-precession lifetime. Finally, as a particular example of a
complex manipulation enabled by our scheme, we demonstrate a range of
collapse-and-revival behaviours of a free-induction decay signal by imprinting
comb-like patterns on the atomic ensemble.Comment: 4 pages, 4 figure
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