Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.

We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (n photons on average). We show that super-resolution and subHeisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolvesn times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/n.PACS numbers: 07.60. Ly, 95.75.kK, 42.50.St Different physical mechanisms contribute to phase measurement. Thus, measuring phase provides insight into a number of physical processes. Therefore, improved phase estimation benefits multiple areas of scientific research, such as quantum metrology, imaging, sensing, and information processing. Consequently, enormous efforts have been devoted to improve the resolution and sensitivity of interferometers. Sensitivity is a measure of the uncertainty in the phase estimation, while resolution is rate at which signal changes with changing phase.In what follows, we direct our attention to quantum interferometry. The benchmark that quantum interferometry is compared against is one with coherent light input and intensity difference measurement at the output of a Mach-Zehnder interferometer (MZI). In general, phase sensitivity of this benchmark is shot-noise limited, namely ∆ϕ = 1/ √n , wheren is the average number of photons. However, better sensitivity is possible if nonlinear interaction between photons in the MZI takes place [1]. In what follows, we only consider phase accumulation due to linear processes.In 1981, Caves pointed out that by using coherent light and squeezed vacuum one could beat the shot-noise limit ∆ϕ < 1/ √n (super-sensitivity) [2]. In the work of Boto et al., it was shown that by exploiting quantum states of light, such as N00N states, it is possible to beat the Rayleigh diffraction limit in imaging and lithography (super resolution) while also beating the shot-noise limit in phase estimation [3,4,5,6]. Finally, it was shown in Ref.[7] that input state entanglement is important in order to achieve super-sensitivity in a linear interferometer.non-classical light Experimental realization of these predictions have been hindered by the fact that entangled states of light, with large numbers of photons, are difficult to obtain. Therefore we turn our attention to the brightest (experimentally available) nonclassical light -two-mode squeezed vacuum (TMSV). A state of TMSV is a superposition of twin Fock states |ψn = ∞ n=0 p n (n) |n, n , where the probability of a twin Fock state |n, n = |n A |n B to be present de- pends on average number of photons in both modes of TMSV,n, in the following way p n (n) = (1 − tn)t n n with tn = 1/ (1 + 2/n) [8].Light entering a MZI in TMSV state exits a lossless interferometer in the state |ψ f =Û MZI |ψn , where the MZI is described by the unitary transformation U MZI (Fig. 1). This transformation, in terms of the field operators for the optical modesâ andb, isÛ MZI =ÛP ϕÛ = exp ϕ â †b −b †â /2 , wherê P ϕ =exp −...

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The Laguerre-Gauss modes are a class of fundamental and well-studied optical fields. These stable, shape-invariant photons - exhibiting circular-cylindrical symmetry - are familiar from laser optics, micro-mechanical manipulation, quantum optics, communication, and foundational studies in both classical optics and quantum physics. They are characterized, chiefly, by two modes numbers: the azimuthal index indicating the orbital angular momentum of the beam - which itself has spawned a burgeoning and vibrant sub-field - and the radial index, which up until recently, has largely been ignored. In this manuscript we develop a differential operator formalism for dealing with the radial modes in both the position and momentum representations, and - more importantly - give for the first time the meaning of this quantum number in terms of a well-defined physical parameter: the "intrinsic hyperbolic momentum charge".Comment: 12 pages, 4 figures, comments encourage

Photons with complex spatial mode structures open up possibilities for new fundamental high-dimensional quantum experiments and for novel quantum information tasks. Here we show for the first time entanglement of photons with complex vortex and singularity patterns called Ince-Gauss modes. In these modes, the position and number of singularities vary depending on the mode parameters. We verify 2-dimensional and 3-dimensional entanglement of Ince-Gauss modes. By measuring one photon and thereby defining its singularity pattern, we non-locally steer the singularity structure of its entangled partner, while the initial singularity structure of the photons is undefined. In addition we measure an Ince-Gauss specific quantum-correlation function with possible use in future quantum communication protocols.

We present a quantum mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically-symmetric stable light fields -the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the orbital angular momentum of these beams varies with their ellipticity and discover several compelling features, including: non-monotonic behavior, stable beams with real continuous (non-integer) orbital angular momenta, and orthogonal modes with the same orbital angular momenta. We explore, and explain in detail, the reasons for this behavior. These features may have application to quantum key distribution, atom trapping, and quantum informatics in general -as the ellipticity opens up a new way of navigating the photonic Hilbert space.

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