15 January 2010 New ICFO PhD Graduate

Dr. Noelia González

Thesis Committee

Dr. Noelia González obtained her PhD with a thesis on measurements of the spatial shape of photons. Dr. Noelia González graduated in Physics from the Universitat Autònoma de Barcelona in 2004. She joined ICFO in 2005 to work in the field of Quantum Optics.

Dr. González\'s thesis, \'Measurement of the Spatial Shape of Photons\', was supervised by ICFO Prof. Juan P. Torres.


Quantum systems entanglement in continuous variables has recently been receiving increasing attention from the scientific community. The transverse spatial shape of photons (i.e. transverse position and momentum degree of freedom) is one such continuous variable system which, due to its ease of control is prone to be used for testing some of the new physical predictions that continuous variable quantum systems can offer, such as the improvement of the security of quantum key distribution cryptography and the efficiency enhancement of quantum communication protocols. Following this line of thought, the main goal of this thesis has been the characterization and measurement of the spatial shape of photons. Another outstanding problem in Quantum Optics Information Technology (QOIT) is the coherent and reversible storage of photon states in matter, i.e. the necessity of a quantum memory. Theoretical and experimental results on this topic have been shown.

Below we summarize the more important contributions of this thesis: Demonstration of the non-validity of the OAM transformation rule lħ > -lħ for highly focused light beams: We have shown from a theoretical and experimental point of view that the OAM transformation rule lħ > -lħ is not valid for highly focused light beams, since Dove prisms inherently introduce astigmatism and, therefore, further OAM changes. We have analyzed how light beams with a well-defined value of the OAM per photon, after traversing the Dove prism, are transformed into a superposition of states with well-defined OAM. The violation of the rule lħ > -lħ turns out to be more important for highly focused light beams. We have provided a quantitative study of the properties of the Dove prism, and we have verified experimentally the validity of the theoretical results in a series of experiments with a commercially available Dove prism.

Presentation of a new method to measure the amplitude and phase of Laguerre-Gaussian like beams: A method to measure the amplitude and phase of Laguerre-Gaussian like beams has been presented from a theoretical and experimental point of view. This method is based on a small variation of the spiral phase interferometry technique, which allows avoiding some technical problems that can be found in the reconstruction of finite sized beams and beams with phase singularities. A few examples of the use of our technique for the characterization of complex beams have been presented.

Description of the transverse spatial shape of bipartite entangled photons generated in Spontaneous Parametric Down Conversion (SPDC) using the Wigner function formulism: We have shown some theoretical and experimental results regarding the spatial Wigner function of entangled paired photons generated in SPDC. Specifically, we have studied the remote preparation of one of the photons of the pair, when the photon is in a Gaussian beam and in a superposition of two modes. Also, we have analyzed and measured the case of the Wigner function of only one of the two photons of the pair, which shows that one photon of the pair is in a statistical mixture of modes. Finally, an experiment to completely measure the spatial state of the two photons was proposed, and analytical expressions for the results one would expect in this case were given.

Investigation of the storage of spatial light polarization grating into the Zeeman ground states of cold cesium atoms: We have investigated theoretically and experimentally the dynamics of light grating stored in an electromagnetically induced transparent (EIT) medium associated with a degenerate two-level system. The dependence of the stored light grating with the intensities of the incident and reading beams has been investigated. Bragg diffraction into the stored grating has been employed to probe the dynamics under different conditions showing reasonable results in agreement with the theoretical model developed. Moreover, we have also observed the coherent evolution of the stored grating in the presence of an applied magnetic field, which allows collapses and revivals of the stored grating that are associated with the Larmor precession of the induced grating around the applied magnetic field.

We believe that the results of this thesis are an important step towards exploring the quantum capabilities of the transverse spatial shape of photons and may encourage further development of this line of research. Moreover, the investigation on the dynamics of light grating stored in an EIT medium is of considerable importance for a better understanding of coherent memory for multidimensional state spaces. Thus, a further and more detailed investigation of the topics presented here should be of special interest to the scientific community.