Geometric phases in astigmatic optical modes of arbitrary order

The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different order, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of non-astigmatic optical modes with orbital angular momentum states in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights in the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schr\"odinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.Comment: final versio

Rotationally induced vortices in optical cavity modes

We show that vortices appear in the modes of an astigmatic optical cavity when it is put into rotation about its optical axis. We study the properties of these vortices and discuss numerical results for a specific realization of such a set-up. Our method is exact up to first order in the time-dependent paraxial approximation and involves bosonic ladder operators in the spirit of the quantum-mechanical harmonic oscillator.Comment: 8 pages, 5 figures. Accepted for publication in a special issue (singular optics 2008) of Journal of Optics A: Pure and Applied Optic

Optomechanical quantum information processing with photons and phonons

We describe how strong resonant interactions in multimode optomechanical systems can be used to induce controlled nonlinear couplings between single photons and phonons. Combined with linear mapping schemes between photons and phonons, these techniques provide a universal building block for various classical and quantum information processing applications. Our approach is especially suited for nano-optomechanical devices, where strong optomechanical interactions on a single photon level are within experimental reach.Comment: 8 pages, 5 figure

Rotational stabilization and destabilization of an optical cavity

We investigate the effects of rotation about the axis of an astigmatic two-mirror cavity on its optical properties. This simple geometry is the first example of an optical system that can be destabilized and, more surprisingly, stabilized by rotation. As such, it has some similarity with both the Paul trap and the gyroscope. We illustrate the effects of rotational (de)stabilization of a cavity in terms of the spatial structure and orbital angular momentum of its modes.Comment: 5 pages, 3 figures. Accepted for publication in Physical Review

Need an L-band coronagraph with a small Inner Working Angle on a 10-m class telescope

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Continuous mode cooling and phonon routers for phononic quantum networks

We study the implementation of quantum state transfer protocols in phonon networks, where in analogy to optical networks, quantum information is transmitted through propagating phonons in extended mechanical resonator arrays or phonon waveguides. We describe how the problem of a non-vanishing thermal occupation of the phononic quantum channel can be overcome by implementing optomechanical multi- and continuous mode cooling schemes to create a 'cold' frequency window for transmitting quantum states. In addition, we discuss the implementation of phonon circulators and switchable phonon routers, which rely on strong coherent optomechanical interactions only, and do not require strong magnetic fields or specific materials. Both techniques can be applied and adapted to various physical implementations, where phonons coupled to spin or charge based qubits are used for on-chip networking applications.Comment: 33 pages, 8 figures. Final version, a few minor changes and updated reference

The Optimal Gravitational Lens Telescope

Given an observed gravitational lens mirage produced by a foreground deflector (cf. galaxy, quasar, cluster,...), it is possible via numerical lens inversion to retrieve the real source image, taking full advantage of the magnifying power of the cosmic lens. This has been achieved in the past for several remarkable gravitational lens systems. Instead, we propose here to invert an observed multiply imaged source directly at the telescope using an ad-hoc optical instrument which is described in the present paper. Compared to the previous method, this should allow one to detect fainter source features as well as to use such an optimal gravitational lens telescope to explore even fainter objects located behind and near the lens. Laboratory and numerical experiments illustrate this new approach