Multi-mode squeezing of light via four-wave mixing in a hot rubidium vapour

Light is used across a broad range of applications from imaging to communications. These fields have advanced sufficiently that measurements are now limited by the fundamental behaviour of light, such as fluctuations inherent to its quantum nature. This is dictated by quantum mechanics, most noticeably Heisenberg's uncertainty principle, having been adapted to describe light and form quantum optics. As it is bound by the uncertainty principle, measuring an observable of light can be made more accurate by adding uncertainty to conjugate observables. This improved accuracy is then gauged against the quantum noise limit (QNL) of the measured observable. Such measurements are then squeezed where the noise of the measurement is below this QNL. In this thesis, we examine the squeezing of light via four wave mixing (4WM) in a rubidium 85 (Rb85) atomic vapour. This includes the generation and detection of squeezed light in its temporal and spatial degrees of freedom. We consider various methods of detection, such as homodyne detection to measure field quadratures, then intensity difference after a waveguide to observe preservation of local correlations, and finally local intensity difference squeezing with a CCD camera. The three experiments each present different results. The broadband squeezing of light yielded variable squeezing across a bandwidth of 60MHz, displaying the multi-temporal mode nature of the process. Photodetection measurements and intensity difference of entangled light after being passed through a waveguide displayed local correlations between a range of corresponding regions within the beam profile, with squeezing of \(\sim\)-1dB. CCD photodetection and intensity difference of this light showed squeezing of approximately -0.75dB in a single set of spatial Fourier frequencies encircling the central spatial frequency, 0mm\(^{-1}\), also referred to as DC, corresponding to 8 distinct squeezed spatial modes within the beams. The use of a waveguide in transmitting local multi-spatial mode (MSM) correlations presents interesting possibilities in guiding said correlations for use in quantum communications and encryption protocols, with a vastly improved bit rate, if not also transmission of quantum images. This supplements the use of a CCD camera in measuring local MSM correlations in these beams which, in yielding positive results, can be utilized as a means of improved imaging beyond the QNL. Given this exhaustive computational investigation, the results have conclusively shown MSM squeezing in signal beams generated from 4WM in a Rb85 vapour. Using the results from Chapter 6, this squeezing is distributed across 8 distinct spatial modes, with vertical spatial frequencies of ±4.96mm\(^{-1}\), ±2.48mm\(^{-1}\) and 0mm\(^{-1}\) and horizontal frequencies ±0.60mm\(^{-1}\), ±0.30mm\(^{-1}\) and 0mm\(^{-1}\). These frequencies correspond to real space vertical sizes of 0.20mm and 0.40mm and horizontal sizes of 1.66mm and 3.33mm. These can be seen to be MSM squeezed regions, given that the size of the beams in the results were larger than this. The average height of the probe was 0.70mm, while the conjugate was 0.66mm while the average lengths were 6.17mm and 5.95mm. As these size exceed the length scales derived from the spatial frequencies, these frequencies thus show MSM squeezing