Precision measurements can be brought to their ultimate limit by harnessing the principles of quantum mechanics. In optics, multiphoton entangled states, known as NOON states, can be used to obtain high-precision phase measurements, becoming more and more advantageous as the number of photons grows. We generated "high-NOON" states (N = 5) by multiphoton interference of quantum down-converted light with a classical coherent state in an approach that is inherently scalable. Super-resolving phase measurements with up to five entangled photons were produced with a visibility higher than that obtainable using classical light only.

The characterization and conditional preparation of multiphoton quantum states require the use of photonnumber resolving detectors. We study the use of detectors based on multiple avalanche photodiode pixels in this context. We develop a general model that provides the positive operator value measures for these detectors. The model incorporates the effect of cross talk between pixels which is unique to these devices. We validate the model by measuring coherent-state photon-number distributions and reconstructing them with high precision. Finally, we evaluate the suitability of such detectors for quantum state tomography and entanglement-based quantum state preparation, highlighting the effects of dark counts and cross talk between pixels.

We have performed experimental quantum state tomography of NOON states with up to four photons. The measured states are generated by mixing a classical coherent state with spontaneous parametric down-conversion. We show that this method produces states which exhibit a high fidelity with ideal NOON states. The fidelity is limited by the overlap of the two-photon down-conversion state with any two photons originating from the coherent state, for which we introduce and measure a figure of merit. A second limitation on the fidelity set by the total setup transmission is discussed. We also apply the same tomography procedure for characterizing correlated photon hole states.

We demonstrate a scheme to spectrally manipulate a collinear, continuous stream of time and energy entangled photons to generate beamlike, bandwidth-limited fluxes of polarization-entangled photons with nearly degenerate wavelengths. Utilizing an ultrashort-pulse shaper to control the spectral phase and polarization of the photon pairs, we tailor the shape of the Hong-Ou-Mandel interference pattern, demonstrating the rules that govern the dependence of this interference pattern on the spectral phases of the photons. We then use the pulse shaper to generate all four polarization Bell states. The singlet state generated by this scheme forms a very robust decoherence-free subspace, extremely suitable for long-distance fiber-optics-based quantum communication. DOI: 10.1103/PhysRevA.75.043804 PACS number͑s͒: 42.50.Dv, 03.67.Mn, 42.65.Lm, 42.65.Re Parametrically generated polarization-entangled photons are a primary resource in the fields of quantum communication and quantum information ͓1͔, motivating an ongoing search for better means for the generation and control of high fluxes of such photons ͓2-4͔. In particular, the generation of the singlet Bell state has raised a considerable interest due to the fact that it forms a decoherence-free subspace ͑DFS͒, which is inherently immune to collective decoherence ͓5,6͔. The upper limit for the flux of entangled photon pairs is typically set by the spatial divergence of the down-converted photons, or by the repetition rate of the pump pulses, in the case of pulsed down-conversion. In both cases, the achievable flux is many orders of magnitude lower than the physical upper limit, which is set by the down-converted bandwidth ͓7,8͔. Although collinear and continuous downconversion enables efficient generation and collection of photon pairs, resulting in ultrahigh ͑bandwidth-limited͒ fluxes as high as 10 12 s −1 ͓8͔, such a single-mode configuration does not readily enable polarization entanglement.Pulse-shaping techniques were recently introduced as a means to control the spectral properties of broadband downconverted photons ͓9͔. In this work we use a phase and polarization pulse shaper ͓10͔ to control both the phase and the polarization of each of the spectral modes of copropagating entangled photons. Our precise control of the phase and polarization in the frequency domain is demonstrated by tailoring the shape of the Hong-Ou-Mandel interference pattern ͓11͔. Exploiting the fact that the photon pairs are hyperentangled, i.e., entangled in more than one degree of freedom ͓12͔, we treat the frequency domain as a two-dimensional subspace and thus use the pulse shaper as a Bell-state synthesizer, generating all four polarization Bell states in a collinear, beamlike fashion, which enables bandwidth-limited fluxes, and is suitable for fiber-optic-based quantum communication. The fact that in this scheme the photons of each pair share the same single spatial mode and are nearly degenerate makes it a very robust and practical DFS. Specifically, if the photons travel through th...

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Postmortem analysis of the resulting fracture surfaces of ductile and brittle materials on the microm-mm and the nm scales, respectively, reveals self-affine cracks with anomalous scaling exponent zeta approximately = 0.8 in 3 dimensions and zeta approximately = 0.65 in 2 dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2 dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.