We present the experimental quantum tomography of 7- and 8-dimensional quantum systems based on projective measurements in the mutually unbiased basis (MUB-QT). One of the advantages of MUB-QT is that it requires projections from a minimal number of bases to be performed. In our scheme, the higher dimensional quantum systems are encoded using the propagation modes of single photons, and we take advantage of the capabilities of amplitude- and phase-modulation of programmable spatial light modulators to implement the MUB-QT.

Abstract:The study of how to generate high-dimensional quantum states (qudits) is justified by the advantages that they can bring for the field of quantum information. However, to have some real practical potential for quantum communication, these states must be also of simple manipulation. Spatial qudits states, which are generated by engineering the transverse momentum of the parametric down-converted photons, have been until now considered of hard manipulation. Nevertheless, we show in this work a simple technique for modifying these states. This technique is based on the use of programmable diffractive optical devices, that can act as spatial light modulators, to define the Hilbert space of these photons instead of pre-fabricated multi-slits. by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000). 12. J. S. Bell, "On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447-452 (1966). 13. A. Aspect, "Bells inequality test: more ideal than ever," Nature 398, 189-190 (1999

We investigate the practicality of the method proposed by Maciel et al. [Phys. Rev. A. 80, 032325(2009)] for detecting the entanglement of two spatial qutrits (3-dimensional quantum systems), which are encoded in the discrete transverse momentum of single photons transmitted through a multi-slit aperture. The method is based on the acquisition of partial information of the quantum state through projective measurements, and a data processing analysis done with semi-definite programs. This analysis relies on generating gradually an optimal entanglement witness operator, and numerical investigations have shown that it allows for the entanglement detection of unknown states with a cost much lower than full state tomography.Comment: 8 pages, 6 figure

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We present an intuitive and versatile method that can dynamically generate 2D and 3D tailored light patterns. The light structures are generated by dynamically implementing discrete and continuous split lens configurations onto a spatial light modulator. These configurations can be dynamically modified by tuning a reduced number of control parameters with simple physical interpretation. We demonstrate the versatility of the method by experimentally implementing a wide number of structured beams, including optical lattices, a light cone, and vortex beams carrying orbital angular momentum. Compared with other optical illuminators, the advantages of our method are its simple interpretation and control for creating the light structures, and that it is based on a robust, dynamic and easy-to-build optical set-up. The proposed method may be useful in a large number of applications, such as optical trapping, super-resolution imaging or illuminating arrays of photonic switching devices.

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We present a universal design and proof-of-concept of a tunable linear retarder of uniform wavelength response in a broad spectral range. It consists of two half-wave retarders (HWR) between two quarter-wave retarders (QWRs), where the uniform retardance can be tuned continuously by simply rotating one of the HWRs. A proof-of-concept of this design is built by using commercially available Fresnel rhomb retarders that provide retardation with almost wavelength uniformity in the visible and near infrared from 450 to 1550 nm. The design is universal, since other achromatic QWRs and HWRs could also be employed. The system is experimentally demonstrated to control the state of polarization of a supercontinuum laser.

Multiple internal reflection effects on the optical modulation of a commercial reflective parallel-aligned liquid-crystal on silicon (PAL-LCoS) spatial light modulator (SLM) are analyzed. The display is illuminated with different wavelengths and different angles of incidence. Non-negligible Fabry-Perot (FP) effect is observed due to the sandwiched LC layer structure. A simplified physical model that quantitatively accounts for the observed phenomena is proposed. It is shown how the expected pure phase modulation response is substantially modified in the following aspects: 1) a coupled amplitude modulation, 2) a non-linear behavior of the phase modulation, 3) some amount of unmodulated light, and 4) a reduction of the effective phase modulation as the angle of incidence increases. Finally, it is shown that multiple reflections can be useful since the effect of a displayed diffraction grating is doubled on a beam that is reflected twice through the LC layer, thus rendering gratings with doubled phase modulation depth.