Explicit constructions of unitary transformations between equivalent irreducible representations

Irreducible representations (irreps) of a finite group $G$ 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 $G$ is symmetric group $S(N)$.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 $\mu$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. $\textbf{139}$, 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 $n$-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 $n-$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 $S(n-1)$ induced by irreducible representations of the group $S(n-2)$. The second type is structurally connected with irreducible representations of the group $S(n-1)$.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 $g_{\mathrm{{S,AS}}}^{(2)}=72\pm5$ 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