Vitagliano, Giuseppe, Hyllus, Philipp, Egusquiza, Inigo L. et al. · arXiv (Cornell University) · 2011
We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.
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Giuseppe Vitagliano, Philipp Hyllus, I. L. Egusquiza et al. · Physical Review Letters · 2011
We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.
Cited by 104Open access
C. R. Hägen · arXiv (Cornell University) · 2014
The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin-orbit coupling term. It has yet to be extended successfully to the arbitrary spin S case primarily because of the unwieldiness of general spin Lorentz invariant wave equations. It is shown here using the formalism of totally symmetric multispinors that the Dirac oscillator can, however, be made to accommodate spin by incorporating it into the framework of Galilean relativity. This is done explicitly for spin zero and spin one as special cases of the arbitrary spin result. For the general case it is shown that the coefficient of the spin-orbit term has a 1/S behavior by techniques which are virtually identical to those employed in the derivation of the g-factor carried out over four decades ago.
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S. K. Lee · ArXiv.org · 2008
An ensemble of spins oriented along the $z$ direction exhibits nonzero fluctuation in the transverse ($x$- and $y$-) components of the spin angular momentum in accordance with the uncertainty principle. When the spins obey a spin temperature distribution, the mean square fluctuation in $S_{x}$ can be calculated by ensemble average of the expectation value of $S_{x}^{2}$ with respect to an equilibrium density matrix $ρ=e^{βS_{z}}/Z$. The fluctuation can also be calculated from the fluctuation-dissipation theorem as has been done in literature in the context of NMR spin noise. For spin 1/2 particles in the high temperature limit, appropriate for many NMR experiments, the two methods are known to produce the same, temperature-independent spin noise. We show that inclusion of the zero-point fluctuation term in the original Nyquist relation extends this correspondence to an arbitrary spin temperature for any spin $S$. This indicates that the uncertainty principle-limited spin projection noise can be viewed as a result of the zero-point fluctuation in the thermal bath coupled to the spins.
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Vitagliano, Giuseppe, Apellaniz, Iagoba, Egusquiza, Inigo L. et al. · arXiv (Cornell University) · 2013
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A method for mapping the spin-squeezing inequalities for spin-1/2 particles to entanglement conditions for spin-j particles is also presented. We apply our mapping to obtain a generalization of the original spin-squeezing inequality to higher spins. We show that, for large particle numbers, a spin-squeezing parameter for entanglement detection based on one of our inequalities is strictly stronger than the original spin-squeezing parameter defined in [A. Sorensen et al., Nature 409, 63 (2001)]. We present a coordinate system independent form of our inequalities that contains, besides the correlation and covariance tensors of the collective angular momentum operators, the nematic tensor appearing in the theory of spin nematics. Finally, we discuss how to measure the quantities appearing in our inequalities in experiments.
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Yongseok OH · New Physics Sae Mulli · 2011
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J. S. Dowker · Proceedings of the Physical Society · 1966
Explicit cross sections are derived to lowest order in e2 for the Coulomb scattering of a charged particle of arbitrary spin. The interaction employed is one derived from a consistent theory of interacting particles of any spin which was developed earlier. This theory is further discussed in the non-relativistic and classical limits and it is shown that it predicts a magnetic moment of e/2κ.
Cited by 7
T. L. Trueman · Physical Review Letters · 1966
It is shown how to generalize the recent suggestion of de Alfaro, Fubini, Rossetti, and Furlan to arbitrary spin in a simple way.Received 31 October 1966DOI:https://doi.org/10.1103/PhysRevLett.17.1198©1966 American Physical Society
Cited by 51
Jarmo Hietarinta · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1976
The infinitesimal generators of supersymmetry and translation form a solvable invariant subalgebra of the full graded Lie algebra. In O'Raifeartaigh's classification scheme this belongs to Case (iii). In general we may define the degree-$n$ supersymmetry generators by requiring their nth derived algebra to be equal to translations. In this paper we study degree-1 supersymmetries for which $[{S}_{i},{S}_{j}]=c{({\ensuremath{\alpha}}^{\ensuremath{\mu}}C)}_{\mathrm{ij}}{P}_{\ensuremath{\mu}}$, where a graded commutator is used. Supposing that ${S}_{i}$ belongs to some representation of the Lorentz group we study the conditions on ${\ensuremath{\alpha}}^{\ensuremath{\mu}}$ and $C$ which result from Jacobi identities and Hermitian conjugation. For the three-dimensional case the conditions are satisfied if ${({\ensuremath{\alpha}}^{k}C)}_{\mathrm{ij}}$ is chosen to be a Clebsch-Gordan coefficient. This allows $S$ to have any spin \ensuremath{\ne} 0 and also gives the correct spin-statistics connection (grading). In the four-dimensional case we show how the problem is related to that of finding Lagrangian densities ${L}_{k}=i\overline{\ensuremath{\psi}}{\ensuremath{\alpha}}^{\ensuremath{\mu}}{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\psi}$ and ${L}_{m}=\overline{\ensuremath{\psi}}\ensuremath{\psi}$, which are Hermitian scalars. There are an infinite number of possible representations to which ${S}_{i}$ can belong, including those of Bhabha type, for which the spin-statistics connection comes naturally from the representation. At the same time there can be supersymmetry generators of several different spins. The Volkov-Akulov nonlinear realization works in all cases and a supersymmetry-invariant Lagrangian can be constructed. Anticommutators seem to be important only in the sense that then we can have finite-dimensional linear realizations.
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D. B. Saakyan · Theoretical and Mathematical Physics · 1987
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K R James · Journal of Physics A Mathematical and General · 1968
A form of the Dirac equations for arbitrary spin, with minimal electromagnetic coupling, is considered in the non-relativistic limit to first order in e. An approximate expansion of the Hamiltonian in powers of 1/m is obtained. The electric quadrupole moment, spin-orbit coupling and Darwin term are evaluated, and for spin 1 are found to differ from those obtained on Proca theory. A higher approximation is calculated for static magnetic and electric fields.
Cited by 0
A. G. Nikitin · Ukrainian Journal of Physics · 2013
Superintegrable quantum mechanical systems with spin are presented. These systems admit a generalized Laplace–Runge–Lenz vector and possess the dynamical symmetry with respect to group SO(4) for bound states. Our discussion is restricted mainly to 2d and 3d systems, but a special class of arbitrary dimension systems is presented as well.
Cited by 9Open access
Xiaoyu Li, Xiang-Kun Dong, Hao-Jie Jing · Nuclear Physics A · 2023
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Giuseppe Vitagliano, Iagoba Apellaniz, I. L. Egusquiza et al. · Physical Review A · 2014
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A method for mapping the spin-squeezing inequalities for spin-$\frac{1}{2}$ particles to entanglement conditions for spin-$j$ particles is also presented. We apply our mapping to obtain a generalization of the original spin-squeezing inequality to higher spins. We show that, for large particle numbers, a spin-squeezing parameter for entanglement detection based on one of our inequalities is strictly stronger than the original spin-squeezing parameter defined in S\o{}rensen et al. [Nature (London) 409, 63 (2001)]. We present a coordinate system independent form of our inequalities that contains, besides the correlation and covariance tensors of the collective angular momentum operators, the nematic tensor appearing in the theory of spin nematics. Finally, we discuss how to measure the quantities appearing in our inequalities in experiments.
Cited by 70Open access
Z. Hu, Qixian Li, Xuanchen Zhang et al. · Physical review. A/Physical review, A · 2023
Spin squeezing is vitally important in quantum metrology and quantum information science. The noise reduction resulting from spin squeezing can surpass the standard quantum limit and even reach the Heisenberg limit (HL) in some special circumstances. However, systems that can reach the HL are very limited. Here, we study the spin squeezing in atomic systems with a generic form of the quadratic collective-spin interaction, which can be described by the Lipkin-Meshkov-Glick model. We find that the squeezing properties are determined by the initial states and the anisotropic parameters. Moreover, we propose a pulse rotation scheme to transform the model into a two-axis twisting model with Heisenberg-limited spin squeezing. Our study paves the way for reaching HL in a broad variety of systems.
Cited by 9
Sergey M. Sikach · ArXiv.org · 2002
We consider the spin calculations in arbitrary and diagonal spin bases
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Z. Hu, Qixian Li, Xuanchen Zhang et al. · arXiv (Cornell University) · 2023
Spin squeezing is vitally important in quantum metrology and quantum information science. The noise reduction resulting from spin squeezing can surpass the standard quantum limit and even reach the Heisenberg Limit (HL) in some special circumstances. However, systems that can reach the HL are very limited. Here we study the spin squeezing in atomic systems with a generic form of quadratic collective-spin interaction, which can be described by the Lipkin-Meshkov-Glick(LMG) model. We find that the squeezing properties are determined by the initial states and the anisotropic parameters. Moreover, we propose a pulse rotation scheme to transform the model into two-axis twisting model with Heisenberg-limited spin squeezing. Our study paves the way for reaching HL in a broad variety of systems.
Cited by 0Open access
Tin-Lun Ho, Sungkit Yip · Physical Review Letters · 1999
Motivated by the recent success of optical trapping of alkali Bose condensate, we have studied the superfluid state of optically trapped alkali fermions, which can have Cooper pairs with total spin $J\ensuremath{\ge}2$. In this paper, we shall discuss the general structure of these large spin Cooper pairs and their close relation with singlet Cooper pairs with nonzero orbital angular momentum. We also present the exact solution for the $J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ pairing which shows a surprising change of ground state as the spin $f$ of the constituent fermion increases.
Cited by 96Open access
Ho, Tin-Lun, Yip, Sungkit · arXiv (Cornell University) · 1998
Motivated by the recent success of optical trapping of alkali Bose condensate, we have studied the superfluid state of optically trapped alkali fermions, which can have Cooper pairs with total spin $J\geq 2$. In this paper, we shall discuss the general structure of these large spin Cooper pairs and their close relation with singlet Cooper pairs with non-zero orbital angular momentum. We also present the exact solution for the J=2 pairing which shows a surprising change of ground state as the spin $f$ of the constituent fermion increases.
Cited by 0Open access
Dmitry Chicherin, S. É. Derkachov, D. Karakhanyan et al. · Nuclear Physics B · 2011
Cited by 19Open access