Christian Gabriel

A generator for unique quantum random numbers based on vacuum states

Researchers demonstrate random-number generation by exploiting the intrinsic randomness of vacuum states. The approach may lead to reliable and high-speed quantum random-number generators for applications ranging from gambling to cryptography.

Classical and quantum properties of cylindrically polarized states of light

We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electromagnetic field, calculate their total angular momentum and highlight the subtleties of their structure. Furthermore, a hybrid spatio-polarization description for such modes is introduced and developed. In particular, two independent Poincaré spheres have been introduced to represent simultaneously the polarization and spatial degree of freedom of CPMs. Possible mode-to-mode transformations accomplishable with the help of Bconventional polarization and spatial phase retarders are shown within this representation. Moreover, the importance of these CPMs in the quantum optics domain due to their classical features is highlighted.

Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes.

C. Gabriel1,2,∗, A. Aiello1,2, W. Zhong1,2, T. G. Euser1, N.Y. Joly2,1, P. Banzer1,2, M. Förtsch1,2, D. Elser1,2, U. L. Andersen1,2,3, Ch. Marquardt1,2, P. St.J. Russell1,2 and G. Leuchs1,2 1 Max Planck Institute for the Science of Light, Guenther-Scharowsky-Str. 1, D-91058 Erlangen, Germany 2 Institute for Optics, Information and Photonics, University Erlangen-Nuremberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany 3 Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark ∗ Christian.Gabriel@mpl.mpg.de

Quantum polarization tomography of bright squeezed light

We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized bright states, the Wigner function can be approximated by an inverse three-dimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, thus finding excellent agreement.

Geometric Spin Hall Effect of Light at polarizing interfaces

The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector.We introduce the concept of a tilted polarizing interface and provide a scheme for its experimental implementation. A light beam passing through such an interface undergoes a shift resembling the original geometric SHEL in a tilted reference frame. This displacement is generated at the polarizer and its occurrence does not depend on the properties of the detection system. We give explicit results for this novel type of geometric SHEL and show that at grazing incidence this effect amounts to a displacement of multiple wavelengths, a shift larger than the one introduced by Goos–Hänchen and Imbert–Fedorov effects.

Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes

AbstractQuadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, −1.2 dB ± 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.

Single-mode squeezing in arbitrary spatial modes

As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light.

A high-speed secure quantum random number generator based on vacuum states

A high-speed continuous-variable quantum random bit generator with an expected effective bit generation rate of up to 10 GBit/s is presented. The obtained bit sequences are truly random and unique, i.e. they cannot be known by an adversary.

Cluster state generation with quadrature squeezed cylindrically polarized modes

We present schemes which exploit the hybrid-entanglement in quadrature squeezed cylindrically polarized modes to generate cluster states. Such states are essential for one-way quantum computing.

Optical properties of a tilted polarizer and geometric Spin Hall Effect of Light

The well-known Goos-Hänchen and Imbert-Fedorov effects, the latter one also known as Spin Hall Effect of Light (SHEL), describe a polarization-dependent displacement of a light beam transmitted across a dielectric interface. Recently a similar shift, the so-called geometric SHEL, has been discovered [1]. It does not depend on the properties of an interface but only on the geometry of the system and amounts to a displacement of up to several wavelengths. This work discusses a tilted polarizing interface in connection to this shift.