We demonstrate theoretically that the shot noise produced by a tunnel barrier in a two-channel conductor violates a Bell inequality. The nonlocality is shown to originate from entangled electron-hole pairs created by tunneling events-without requiring electron-electron interactions. The degree of entanglement (concurrence) equals 2(T1T2)(1/2)(T1+T2)(-1), with T1,T2<<1 the transmission eigenvalues. A pair of edge channels in the quantum Hall effect is proposed as an experimental realization.

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We analyze the quantum-mechanical hmits to the plasmon-assisted entanglement tiansfei obseived by Altewischei, van Extei, and Woeidman [Natuie 418, 304 (2002)] The maximal violation 5 of Bell's mequahty at the photodetectors behmd two hneai media (such äs the peifoiated metal films in the expenment) can be descnbed by two laüo's T] , r 2 of polaiization-dependent tiansmission piobabilities A fully entangled incident state is tiansfened without degiadation foi τ\ = τ 2 , but a lelaüvely laige mismatch of TJ and r 2 can be toleiated with a small leduction of S We piedict that fully entangled Bell paus can be disülled out of pailially entangled ladiation if r, and r 2 satisfy a pau of inequahties The motivation foi thts woik came fiom the lecent lematkable demonstiation by Altewischei, van Extet, and Woeidman of the tiansfei of quantum-mechanical entanglement fiom photons to surface plasmons and back to photons [1] Since entanglement is a highly fiagile piopeity of a twophoton state, it came äs a suipuse that this piopeity could siuvive, with httle degiadation, the conveision to and fiom the macioscopic degiees of fieedom m a metal [2] We ptesent a quantitative descnption of the finding of Ref [1] that the entanglement is lost if it is measuied dm mg tiansfei, that is to say, if the medium thiough which the pan of polanzation-entangled photons is passed acts äs a "whichway" detectoi foi polanzation Oui analysis explams why a few peicent degiadation of entanglement could be leahzed wtthout lequnmg a highly symmetnc medium We piedict that the expenmental setup of Ref [1] could be used to "distill" [3,4] fully entangled Bell paus out of paitially entangled incident ladiation, and we identtfy the legion in paiametei space wheie this distillation is possibleWe assume that the medium is hneai, so that its elfect on the ladiation can be descnbed by a scatteung matnx The assumption of lineanty of the inteiaction of ladiation with suiface plasmons is cential to the hteiatuie on this topic [5-9] We will not make any specific assumptions on the mode and fiequency dependence of the scatteung matnx, but extiact the smallest numbei of mdependently measuiable palameteis needed to descnbe the expenment By concentiating on model-mdependent lesults we can isolate the fundamental quantum-mechanical limitations on the entanglement tiansfei, fiom the limitations specific to any paiüculai tiansfei mechamsmThe System consideied is shown schematically in Fig l Polanzation-entangled ladiation is scatteied by two objects and detected by a pan of detectoi s behmd the objects in the fai field The objects used m Ref [f] aie metal films peifoiated by a squaie anay of subwavelength holes The tiansmission amplitude t, rir i , oi object ;= 1,2 lelates the ttansmitted ladiation (with polanzation a=H,V) to the mcident ladiation (polanzation σ' = H, V) We assume a single-mode incident beam and a single-mode detectoi (smallei than the coheience aiea) so that we leqtme a sei of eight tiansmission amphtudes t (TiT i , out of the entne scatteung matnx (...

The equation of state of solid caesium (body-centred cubic (bcc) and face-centred cubic (fcc) structures) is examined theoretically by means of ab initio calculations. The Helmholtz free energies are calculated for pressures (P ) up to 5 GPa and temperatures (T ) in the range 0 300 K. The electronic contributions are calculated within density-functional theory (local density approximation (LDA) and generalized gradient approximation (GGA)), whereas vibrational contributions to energy and entropy are calculated within the quasi-harmonic approximation. The thermal expansion coefficients ( ) of bcc as well as fcc Cs are calculated as functions of P and T . Both phases are predicted to have (P , T ) regimes where is negative. For the fcc phase, goes negative for P above 3.5 GPa (and up to the end of the stability range of the fcc phase) for all T . The value = 3.0 ×10-4 K-1 found for Cs at ambient conditions agrees with experiments, and so does the Debye temperature, 39.5 K. The calculation shows that the bcc fcc transition occurs at P 2.2 GPa and low T , and at a higher pressure, 3 GPa, at room temperature. The fcc phase becomes unstable around 4.3 GPa, where a transverse phonon mode with q along (110) becomes soft. The calculations do not indicate that this transition is isostructural (fcc fcc), a result which is at variance with earlier theoretical and experimental work.

We calculate the effect of polanzation-dependent scattering by disorder on the degree of polanzation en tanglement of two beams of radiation Multimode detection conveits an miüally pure state mto a mixed state with respect to the polanzation degrees of freedom The degree of entanglement decays exponentially with the number of detected modes if the scattering mixes the polanzation directions and algebraically if it does not DOI 101103/PhysRevA 70 032325 PACS number(s) 03 67 Mn, 42 50 Dv, 03 65 Ud, 42 25 Dd