Degree of entanglement as a physically ill-posed problem: The case of entanglement with vacuum

We analyze an example of a photon in superposition of different modes, and ask what is the degree of their entanglement with vacuum. The problem turns out to be ill-posed since we do not know which representation of the algebra of canonical commutation relations (CCR) to choose for field quantization. Once we make a choice, we can solve the question of entanglement unambiguously. So the difficulty is not with mathematics, but with physics of the problem. In order to make the discussion explicit we analyze from this perspective a popular argument based on a photon leaving a beam splitter and interacting with two two-level atoms. We first solve the problem algebraically in Heisenberg picture, without any assumption about the form of representation of CCR. Then we take the $\infty$-representation and show in two ways that in two-mode states the modes are maximally entangled with vacuum, but single-mode states are not entangled. Next we repeat the analysis in terms of the representation of CCR taken from Berezin's book and show that two-mode states do not involve the mode-vacuum entanglement. Finally, we switch to a family of reducible representations of CCR recently investigated in the context of field quantization, and show that the entanglement with vacuum is present even for single-mode states. Still, the degree of entanglement is here difficult to estimate, mainly because there are $N+2$ subsystems, with $N$ unspecified and large.Comment: This paper is basically a reply to quant-ph/0507189 by S. J. van Enk and to the remarks we got from L. Vaidman after our preliminary quant-ph/0507151. Version accepted in Phys. Rev.

π+−π−\pi^+ - \pi^- Asymmetry and the Neutron Skin in Heavy Nuclei

In heavy nuclei the spatial distribution of protons and neutrons is different. At CERN SPS energies production of $\pi^+$ and $\pi^-$ differs for $pp$, $pn$, $np$ and $nn$ scattering. These two facts lead to an impact parameter dependence of the $\pi^+$ to $\pi^-$ ratio in $^{208}Pb + ^{208}Pb$ collisions. A recent experiment at CERN seems to confirm qualitatively these predictions. It may open a possibility for determination of neutron density distribution in nuclei.Comment: 6 pages and 2 figures, a talk by A.Szczurek at the international conference MESON2004, June 4-8, Cracow, Polan

Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses

We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using non-coupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.Comment: Journal version (except for small editorial modifications), 4+12 pages, 7 figure

The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model

We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including among others bicritical, tricritical, critical-end and isolated critical points.Comment: 12 pages, 7 figures; final version, pdf-ReVTeX; corrected typos in reference; submitted to Journal of Physics: Condensed Matte

Valence electronic structure of Mn in undoped and doped lanthanum manganites from relative K x-ray intensity studies

Relative $K$ x-ray intensities of $Mn$ in $Mn$, $MnO_{2}$, $LaMnO_{3}$ and $La_{0.7}B_{0.3}MnO_{3}$ ($B$ = $Ca$, $Sr$, and $Ce$) systems have been measured following excitation by 59.54 keV $\gamma$-rays from a 200 mCi $^{241}$Am point-source. The measured results for the compounds deviate significantly from the results of pure $Mn$. Comparison of the experimental data with the multiconfiguration Dirac-Fock (MCDF) effective atomic model calculations indicates reasonable agreement with the predictions of ionic model for the doped {manganites except} that the electron doped $La_{0.7}Ce_{0.3}MnO_{3}$ and hole doped $La_{0.7}Ca_{0.3}MnO_{3}$ compounds show some small deviations. The results of $MnO_{2}$ and $LaMnO_{3}$ deviate considerably from the predictions of the ionic model. Our measured $K\beta/K\alpha$ ratio of $Mn$ in $La_{0.7}Ca_{0.3}MnO_{3}$ cannot be explained as a linear superposition of $K\beta/K\alpha$ ratios of $Mn$ for the end members which is in contrast to the recent proposal by Tyson et al. from their $Mn$ $K\beta$ spectra.Comment: 14 pages, 4 figures. to appear in NIM-B.Please send an e-mail for figure

Evidence for Spinodal Decomposition in Nuclear Multifragmentation

Multifragmentation of a ``fused system'' was observed for central collisions between 32 MeV/nucleon 129Xe and natSn. Most of the resulting charged products were well identified thanks to the high performances of the INDRA 4pi array. Experimental higher-order charge correlations for fragments show a weak but non ambiguous enhancement of events with nearly equal-sized fragments. Supported by dynamical calculations in which spinodal decomposition is simulated, this observed enhancement is interpreted as a ``fossil'' signal of spinodal instabilities in finite nuclear systems.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Letter

The ALPS project release 1.3: open source software for strongly correlated systems

We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the new release include a DMRG program for interacting models, support for translation symmetries in the diagonalization programs, the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps. The software is available from our web server at http://alps.comp-phys.org/