We investigated the spatial distribution of quantum fluctuations in a squeezed vacuum field, generated via polarization self-rotation (PSR) interaction of an ensemble of Rb atoms and a strong near-resonant linearly polarized laser field. We found that the noise suppression is greatly effected by the transverse profile of a spatial mask, placed in both the squeezed field and the local oscillator, as well as its position along the focused beam near the focal point. These observations indicate the spatial multi-mode structure of the squeezed vacuum field. We have developed a theoretical model that describes the generation of higher-order Laguerre-Gauss modes as a result of PSR light-atom interaction. The prediction of this model are in a good qualitative agreement with the experimental measurements.

We present a general, Gaussian spatial mode propagation formalism for describing the generation of higher order multi-spatial-mode beams generated during nonlinear interactions. Furthermore, to implement the theory, we simulate optical angular momentum transfer interactions, and show how one can optimize the interaction to reduce the undesired modes. Past theoretical treatments of this problem have often been phenomenological, at best. Here we present an exact solution for the single-pass no-cavity regime, in which the the nonlinear interaction is not overly strong. We apply our theory to two experiments, with very good agreement, and give examples of several more configurations, easily tested in the laboratory.

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We study a squeezed vacuum field generated in hot Rb vapor via the polarization self-rotation effect. Our previous experiments showed that the amount of observed squeezing may be limited by the contamination of the squeezed vacuum output with higher-order spatial modes, also generated inside the cell. Here, we demonstrate that the squeezing can be improved by making the light interact several times with a less dense atomic ensemble. With optimization of some parameters we can achieve up to −2.6 dB of squeezing in the multi-pass case, which is 0.6 dB improvement compared to the single-pass experimental configuration. Our results show that other than the optical depth of the medium, the spatial mode structure and cell configuration also affect the squeezing level.

Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various spatial modes. We demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field. Using numerical simulations, we also show that with single-mode squeezed-vacuum state input, the prediction of our theory is in qualitative agreement with our experimental data. We also give several additional examples of how the theory works, for various quantum input states, which may be easily tested in the lab; including two single-mode squeezed vacuums, single-and two-photon inputs, where we show the diffraction process produces two-mode squeezed vacuum, number-path entanglement and a Hong-Ou-Mandel-like effect-analogous to a beam splitter.