Unpolarized light in quantum optics

We present a new derivation of the unpolarized quantum states of light, whose general form was first derived by Prakash and Chandra [Phys. Rev. A 4, 796 (1971)]. Our derivation makes use of some basic group theory, is straightforward, and offers some new insights.Comment: 3 pages, REVTeX, presented at ICQO'200

Quantum limits on phase-shift detection using multimode interferometers

Fundamental phase-shift detection properties of optical multimode interferometers are analyzed. Limits on perfectly distinguishable phase shifts are derived for general quantum states of a given average energy. In contrast to earlier work, the limits are found to be independent of the number of interfering modes. However, the reported bounds are consistent with the Heisenberg limit. A short discussion on the concept of well-defined relative phase is also included.Comment: 6 pages, 3 figures, REVTeX, uses epsf.st

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

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

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

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

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

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

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state was used to perform such measurements. Each of the photons carries (partial) information of the initial state thus leaving a room for measurements of two complementary observables on every member in an ensemble.Comment: 4 pages, 4 figures, REVTeX, submitted to PR