TRANSLATIONAL ENTANGLEMENT AND TELEPORTATION OF MATTER WAVEPACKETS BY COLLISIONS AND HALF-COLLISIONS

2005 ◽  
Vol 19 (26) ◽  
pp. 3897-3921
Author(s):  
L. FISCH ◽  
A. TAL ◽  
G. KURIZKI
Keyword(s):  
Phase Space ◽  
Initial Phase ◽  
Sufficient Accuracy ◽  
Matter Wave ◽  
Entangled State ◽  
Different Types ◽  
Epr Pair ◽  
Cold Molecule ◽  
Epr State ◽  
Conceptual Difficulties

To date, the translationally-entangled state originally proposed by Einstein, Podolsky and Rosen (EPR) in 1935 has not been experimentally realized for massive particles. Opatrný and Kurizki [Phys. Rev. Lett.86, 3180 (2000)] have suggested the creation of a position- and momentum-correlated, i.e., translationally-entangled, pair of particles approximating the EPR state by dissociation of cold diatomic molecules, and further manipulation of the EPR pair effecting matter-wave teleportation. Here we aim at setting the principles of and quantifying translational entanglement by collisions and half-collisions. In collisions, the resonance width s and the initial phase-space distributions are shown to determine the degree of post-collisional momentum entanglement. Half-collisions (dissociation) are shown to yield different types of approximate EPR states. We analyse a feasible realization of translational EPR entanglement and teleportation via cold-molecule Raman dissociation and subsequent collisions, resolving both practical and conceptual difficulties it has faced so far: How to avoid entanglement loss due to the wavepacket spreading of the dissociation fragments? How to measure both position and momentum correlations of the dissociation fragments with sufficient accuracy to verify their EPR correlations? How to reliably perform two-particle (Bell) position and momentum measurements on one of the fragments and the wavepacket to be teleported?

TRANSLATIONAL ENTANGLEMENT BY COLLISIONS AND HALF-COLLISIONS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1648-1660
Author(s):  
LIOR FISCH ◽  
ASSAF TAL ◽  
GERSHON KURIZKI
Keyword(s):  
Phase Space ◽  
Initial Phase ◽  
Resonance Width ◽  
Different Types ◽  
Cold Molecule ◽  
Conceptual Difficulties

Here we aim at setting the principles of and quantifying translational entanglement by collisions and half-collisions. In collisions, the resonance width s and the initial phase-space distributions are shown to determine the degree of post-collisional momentum entanglement. Half-collisions (dissociation) are shown to yield different types of approximate EPR states. We analyse a feasible realization of translational EPR entanglement and teleportation via cold-molecule Raman dissociation and subsequent collisions, resolving both practical and conceptual difficulties it has faced so far.

A model to determine the initial phase space of a clinical electron beam from measured beam data

2000 ◽  
Vol 46 (2) ◽  
pp. 269-286 ◽  
Author(s):  
J J Janssen ◽  
E W Korevaar ◽  
L J van Battum ◽  
P R M Storchi ◽  
H Huizenga
Keyword(s):  
Electron Beam ◽  
Phase Space ◽  
Initial Phase

scholarly journals Entanglement-enhanced matter-wave interferometry in a high-finesse cavity

2021 ◽  
Author(s):  
James Thompson ◽  
Graham Greve ◽  
Chengyi Luo ◽  
Baochen Wu
Keyword(s):  
Cavity Qed ◽  
Degrees Of Freedom ◽  
Inertial Sensors ◽  
Mean Field ◽  
New Physics ◽  
Matter Wave ◽  
Quantum Limit ◽  
Entangled State ◽  
Standard Quantum ◽  
Standard Quantum Limit

Abstract Entanglement is a fundamental resource that allows quantum sensors to surpass the standard quantum limit set by the quantum collapse of independent atoms. Collective cavity-QED systems have succeeded in generating large amounts of directly observed entanglement involving the internal degrees of freedom of laser-cooled atomic ensembles. Here we demonstrate cavity-QED entanglement of external degrees of freedom to realize a matter-wave interferometer of 700 atoms in which each individual atom falls freely under gravity and simultaneously traverses two paths through space while also entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed metrological gain 3.4^{+1.1}_{-0.9} dB and 2.5^{+0.6}_{-0.6} dB below the standard quantum limit respectively. An entangled state is for the first time successfully injected into a Mach-Zehnder light-pulse interferometer with 1.7^{+0.5}_{-0.5} dB of directly observed metrological enhancement. These results open a new path for combining particle delocalization and entanglement for inertial sensors, searches for new physics, particles, and fields, future advanced gravitational wave detectors, and accessing beyond mean-field quantum many-body physics.

“Single Value” Soil Properties: A Study of the Significance of Certain Soil Constants. V. On the Changes Produced in a Soil by Oven Drying (With One Text-figure.)

1930 ◽  
Vol 20 (4) ◽  
pp. 541-548 ◽  
Author(s):  
J. R. H. Coutts
Keyword(s):  
Soil Properties ◽  
Soil Water ◽  
Soil Property ◽  
Sufficient Accuracy ◽  
Smooth Curves ◽  
Oven Drying ◽  
Satisfactory Degree ◽  
Different Types ◽  
Text Figure ◽  
Soil Colloids

1. It is shown that results for the loss in weight of a soil on oven heating can be obtained to a very satisfactory degree of accuracy when a Hearson electrically controlled oven is used.2. Results obtained by heating soils to temperatures ranging from 5° to 250° give smooth curves connecting loss in weight with rise in temperature; from which it is concluded that there is no sudden alteration in the structure of a soil when it is heated to 100°, and that the airdry moisture of a soil, as determined with sufficient accuracy by the usual methods, is a convenient empirical factor, but not a representation of any fundamental soil property.3. An examination is made of the factors contributing to the observed total loss in weight when the soil is heated, and an explanation offered of the contributions made by the different types of soil water and by the soil colloids. It is found that the conclusions drawn from this discussion confirm views developed earlier with regard to the behaviour of the water in the soil, and the absence of any sharp dividing line between the different classes into which the soil water is usually divided.

scholarly journals Chaotic ray propagation in corrugated layers

2005 ◽  
Vol 12 (6) ◽  
pp. 1003-1009 ◽  
Author(s):  
M. Bottiglieri ◽  
S. De Martino ◽  
M. Falanga ◽  
C. Godano
Keyword(s):  
Phase Space ◽  
Power Law ◽  
Chaotic Behaviour ◽  
Kam Theorem ◽  
Different Types ◽  
Corrugated Wall

Abstract. The aim of this paper is to study the effects of a corrugated wall on the behaviour of propagating rays. Different types of corrugation are considered, using different distributions of the corrugation heights: white Gaussian, power law, self-affine perturbation. In phase space, a prevalent chaotic behaviour of rays, and the presence of a lot of caustics, are observed. These results entail that the KAM theorem is not fulfilled.

WEAK DISSIPATION IN A HAMILTONIAN MAP

1994 ◽  
Vol 04 (04) ◽  
pp. 921-932 ◽  
Author(s):  
RAÚL J. MONDRAGÓN C. ◽  
PETER H. RICHTER
Keyword(s):  
Phase Space ◽  
Hamiltonian System ◽  
Periodic Orbits ◽  
Adiabatic Invariance ◽  
Bifurcation Tree ◽  
Bouncing Ball ◽  
Different Types ◽  
Weak Dissipation ◽  
Hamiltonian Map

The dynamics of a bouncing ball reflected off a harmonic spring is investigated, with weak dissipation of three different types. The phase space is found to be organized into a system of tubes that wind around the branches of the bifurcation tree of periodic orbits of the Hamiltonian system. Instead of attraction towards special periodic orbits we observe a kind of piecewise adiabatic invariance of the tubes, with jumps occurring when the branches penetrate each other.

scholarly journals -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS

2017 ◽  
Vol 18 (3) ◽  
pp. 531-559 ◽  
Author(s):  
Julio Delgado ◽  
Michael Ruzhansky
Keyword(s):  
Phase Space ◽  
Vector Fields ◽  
Differential Operators ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
Pseudo Differential Operators ◽  
Different Types ◽  
Unitary Dual ◽  
Laplacian Operators ◽  
Noncommutative Analogue

Given a compact Lie group$G$, in this paper we establish$L^{p}$-bounds for pseudo-differential operators in$L^{p}(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space$G\times \widehat{G}$, where$\widehat{G}$is the unitary dual of$G$. We obtain two different types of$L^{p}$bounds: first for finite regularity symbols and second for smooth symbols. The conditions for smooth symbols are formulated using$\mathscr{S}_{\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF}}^{m}(G)$classes which are a suitable extension of the well-known$(\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF})$ones on the Euclidean space. The results herein extend classical$L^{p}$bounds established by C. Fefferman on$\mathbb{R}^{n}$. While Fefferman’s results have immediate consequences on general manifolds for$\unicode[STIX]{x1D70C}>\max \{\unicode[STIX]{x1D6FF},1-\unicode[STIX]{x1D6FF}\}$, our results do not require the condition$\unicode[STIX]{x1D70C}>1-\unicode[STIX]{x1D6FF}$. Moreover, one of our results also does not require$\unicode[STIX]{x1D70C}>\unicode[STIX]{x1D6FF}$. Examples are given for the case of$\text{SU}(2)\cong \mathbb{S}^{3}$and vector fields/sub-Laplacian operators when operators in the classes$\mathscr{S}_{0,0}^{m}$and$\mathscr{S}_{\frac{1}{2},0}^{m}$naturally appear, and where conditions$\unicode[STIX]{x1D70C}>\unicode[STIX]{x1D6FF}$and$\unicode[STIX]{x1D70C}>1-\unicode[STIX]{x1D6FF}$fail, respectively.

Generation of four-photon polarization entangled states with cross-Kerr nonlinearity

2015 ◽  
Vol 13 (05) ◽  
pp. 1550024 ◽  
Author(s):  
Meiyu Wang ◽  
Fengli Yan
Keyword(s):  
Kerr Nonlinearity ◽  
Entangled States ◽  
Entangled State ◽  
Kerr Medium ◽  
Coherent Light ◽  
Photon Polarization ◽  
Beam Splitters ◽  
Ghz States ◽  
Different Types ◽  
Quantum Optical

We show how to prepare three different types of four-photon polarization entangled states among four modes. The scheme only use cross-Kerr medium, polarization beam splitters and X homodyne measurements on coherent light fields, which can be efficiently implemented in quantum optical laboratories. GHZ states and symmetric Dick states can be generated in deterministic way based on the scheme. With the possible availability of suitable strong Kerr nonlinearity, another type of entangled state called genuine four-photon entangled state can be realized as well.

scholarly journals Einstein-Podolsky-Rosen correlation seen from moving observers

2003 ◽  
Vol 3 (3) ◽  
pp. 224-228
Author(s):  
H. Terashima ◽  
M. Ueda
Keyword(s):  
Quantum Theory ◽  
Quantum Communication ◽  
Relativistic Quantum ◽  
Entangled State ◽  
Local Correlation ◽  
Relativistic Quantum Theory ◽  
Gedanken Experiment ◽  
Einstein Podolsky Rosen ◽  
Non Local ◽  
Epr Pair

Within the framework of relativistic quantum theory, we consider the Einstein-Podolsky-Rosen (EPR) gedanken-experiment in which measurements of the spin are performed by moving observers. We find that the perfect anti-correlation in the same direction between the EPR pair no longer holds in the observers' frame. This does not imply a breakdown of the non-local correlation. We explicitly show that the observers must measure the spin in appropriately chosen different directions in order to observe the perfect anti-correlation. This fact should be taken into account in utilizing the entangled state in quantum communication by moving observers.

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