Assessing the Polarization of a Quantum Field from Stokes Fluctuation

We propose an operational degree of polarization in terms of the variance of the projected Stokes vector minimized over all the directions of the Poincar\'e sphere. We examine the properties of this degree and show that some problems associated with the standard definition are avoided. The new degree of polarization is experimentally determined using two examples: a bright squeezed state and a quadrature squeezed vacuum.Comment: 4 pages, 2 figures. Comments welcome

Entangled-State Lithography: Tailoring any Pattern with a Single State

We demonstrate a systematic approach to Heisenberg-limited lithographic image formation using four-mode reciprocal binominal states. By controlling the exposure pattern with a simple bank of birefringent plates, any pixel pattern on a $(N+1) \times (N+1)$ grid, occupying a square with the side half a wavelength long, can be generated from a $2 N$-photon state.Comment: 4 pages, 4 figure

Quantum degrees of polarization

We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since, despite being rooted in the Stokes operators, each of these measures only captures certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness.Comment: 9 pages, 3 figures. v2: Minor corrections and improvement

Two-photon imaging and quantum holography

It has been claimed that ``the use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever strength of the correlations between the two photons'' [A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001)]. While we believe that the cited statement is true, we show that the method proposed in that paper, with ``bucket detection'' of one of the photons, will give identical results for entangled states as for appropriately prepared classically correlated states.Comment: 4 pages, 2 figures, REVTe

Sub-wavelength lithography over extended areas

We demonstrate a systematic approach to sub-wavelength resolution lithographic image formation on films covering areas larger than a wavelength squared. For example, it is possible to make a lithographic pattern with a feature size resolution of $\lambda/[2(N+1)]$ by using a particular $2 M$-photon, multi-mode entangled state, where $N < M$, and banks of birefringent plates. By preparing a statistically mixed such a state one can form any pixel pattern on a $(N+1) 2^{M-N} \times (N+1) 2^{M-N}$ pixel grid occupying a square with a side of $L=2^{M-N-1}$ wavelengths. Hence, there is a trade-off between the exposed area, the minimum lithographic feature size resolution, and the number of photons used for the exposure. We also show that the proposed method will work even under non-ideal conditions, albeit with somewhat poorer performance.Comment: 8 pages, 8 figures, 1 table. Written in RevTe

Distance-based degrees of polarization for a quantum field

It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We use two different candidates of distance, namely the Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally different degrees of polarization. We apply these notions to relevant field states and we demonstrate that they avoid some of the problems arising with the classical definition.Comment: 8 pages, 1 eps figur

Maximally polarized states for quantum light fields

The degree of polarization of a quantum state can be defined as its Hilbert-Schmidt distance to the set of unpolarized states. We demonstrate that the states optimizing this degree for a fixed average number of photons $\bar{N}$ present a fairly symmetric, parabolic photon statistics, with a variance scaling as $\bar{N}^2$. Although no standard optical process yields such a statistics, we show that, to an excellent approximation, a highly squeezed vacuum can be considered as maximally polarized.Comment: 4 pages, 3 eps-color figure

Central-moment description of polarization for quantum states of light

We present a moment expansion method for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the Poincar\'{e} sphere, and provide a method of polarization tomography without resorting to full state tomography. We apply these ideas to the experimental first- and second-order polarization characterization of some two-photon quantum states. In addition, we show that there are classes of states whose polarization characteristics are dominated not by their first-order moments (i.e., the Stokes vector) but by higher-order polarization moments.Comment: 11 pages, 7 figures, 4 tables, In version 2, Figs. 2 and 4 are replaced, Sec. IV extended, Sec. VIII revised, a few references adde

Translocation of Crohn's disease Escherichia coli across M-cells: contrasting effects of soluble plant fibres and emulsifiers

Background Crohns disease is common in developed nations where the typical diet is low in fibre and high in processed food. Primary lesions overlie Peyers patches and colonic lymphoid follicles where bacterial invasion through M-cells occurs. We have assessed the effect of soluble non-starch polysaccharide (NSP) and food emulsifiers on translocation of Escherichia coli across M-cells. Methods To assess effects of soluble plant fibres and food emulsifiers on translocation of mucosa-associated E coli isolates from Crohns disease patients and from non-Crohns controls, we used M-cell monolayers, generated by co-culture of Caco2-cl1 and Raji B cells, and human Peyers patches mounted in Ussing chambers. Results E coli translocation increased across M-cells compared to parent Caco2-cl1 monocultures; 15.8-fold (IQR 6.2-32.0) for Crohns disease E coli (N=8) and 6.7-fold (IQR 3.7-21.0) for control isolates (N=5). Electronmicroscopy confirmed E coli within M-cells. Plantain and broccoli NSP markedly reduced E coli translocation across M-cells at 5 mg/ml (range 45.3-82.6% inhibition, pandlt;0.01); apple and leek NSP had no significant effect. Polysorbate-80, 0.01% vol/vol, increased E coli translocation through Caco2-cl1 monolayers 59-fold (pandlt;0.05) and, at higher concentrations, increased translocation across M-cells. Similarly, E coli translocation across human Peyers patches was reduced 45+/-7% by soluble plantain NSP (5 mg/ml) and increased 2-fold by polysorbate-80 (0.1% vol/vol). Conclusions Translocation of E coli across M-cells is reduced by soluble plant fibres, particularly plantain and broccoli, but increased by the emulsifier Polysorbate-80. These effects occur at relevant concentrations and may contribute to the impact of dietary factors on Crohns disease pathogenesis