Jonas Soderholm

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 binomial states. By controlling the exposure pattern with a simple bank of birefringent plates, any pixel pattern on a (N+1) x (N+1) grid, occupying a square with the side half a wavelength long, can be generated from a 2N-photon state.

Complementarity and the uncertainty relations

We formulate a general complementarity relation starting from any Hermitian operator with discrete nondegenerate eigenvalues. We then elucidate the relationship between quantum complementarity and the Heisenberg-Robertson uncertainty relation. We show that they are intimately connected. Finally we exemplify the general theory with some specific suggested experiments.

Experimental verification of differences between classical and quantum polarization properties

We have carried out polarization measurements on a two-photon quantum state generated by spontaneous parametric down conversion. Our measurements show that the state is unpolarized in the classical theory, but they also show that the state is not invariant under geometric rotation. Therefore, it is not unpolarized in the quantum theory. This is another example of a rather simple experiment that clearly shows the effects of quantum interference. It also confirms the theoretical investigation by Klyshko [Phys. Lett. A 163 (1992) 349]. The experiment is explained theoretically and a systematic treatment of polarization in quantum theory is outlined.

Quantum polarization properties of two-mode energy eigenstates

We show that any pure, two-mode, N-photon state with N odd or equal to two can be transformed into an orthogonal state using only linear optics. According to a recently suggested definition of polarization degree, this implies that all such states are fully polarized. This is also found to be true for any pure, two-mode, energy eigenstate belonging to a two-dimensional SU(2) orbit. Complete two- and three-photon bases whose basis states are related by only phase shifts or geometrical rotations are also derived.

Experimental demonstration of the relative phase operator

We have experimentally demonstrated a realization of the two-mode relative phase operator introduced by Luis and Sanchez-Soto (Luis A and Sanchez-Soto L L 1993 Phys. Rev. A 48 4702). The relative phase distribution function was measured for a weakly excited relative phase eigenstate and weakly excited two-mode coherent states. The experiment is also (using the eigenstates) a demonstration of Heisenberg-limited interferometry.

Assessing the polarization of a quantum field from stokes fluctuations.

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.

Comprehensive experimental test of quantum erasure

Abstract:In an interferometer, path information and interference visibility are incompatible quantities. Complete determination of the path will exclude any possibility of interference, rendering zero visibility. However, it is, under certain conditions, possible to trade the path information for improved (conditioned) visibility. This procedure is called quantum erasure. We have performed such experiments with polarization-entangled photon pairs. Using a partial polarizer, we could vary the degree of entanglement between the object and the probe. We could also vary the interferometer splitting ratio and thereby vary the a priori path predictability. This allowed us to test quantum erasure under a number of different experimental conditions. All experiments were in good agreement with theory.

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 [6]. Our derivation makes use of some basic group theory, is straightforward, and offers some new insights.

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, where each of the photons carries (partial) information of the initial state, was used to perform such a measurement.

Applications of entangled-state interference

Interference phenomena lead to a wealth of applications in many areas of physics. Entangled quantum states allow one to surpass the classical measurement sensitivity or resolution in polarimetry, interferometry, and imaging. In this paper we shall review, in some depth, polarization properties of quantized two-mode electromagnetic fields and show how interference and quantum entanglement lead to new phenomena. We shall also briefly discuss subwavelength quantum lithography.