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

Joshua Rayne

Published Jul 11, 2019• 0 citations
OpenAlex

Abstract

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. \nAs 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. \nThe 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. \nThe 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. \nGiven 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}\\). \nThese 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.

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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. \nAs 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. \nThe 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. \nThe 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. \nGiven 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\(^{-1}\). \nThese 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.
The spatial character of the noise on a light field affects its usefulness for imaging. Multi-spatial-mode (MSM) squeezed light has noise below the quantum noise limit in multiple spatial modes, and can be used for super resolution imaging. The generation of such light has long been an experimental goal within the field of quantum optics. \n \nThis work introduces the theory behind the generation of squeezed light, and its measurement using a homodyne detector. A four-wave mixing process in a rubidium 85 vapour is used to experimentally generate squeezed light. The properties of this squeezed light are investigated, through the use of homodyne detection with a bichromatic LO. \n \nThis thesis further investigates how the squeezed quadrature changes from amplitude to phase over a range of 40 MHz. The MSM nature of a squeezed light field is directly investigated. The field is shown to contain at least 75 squeezed spatial modes in the frequency domain, each squeezed at a level of up to -2.5 dB. This thesis develops techniques to measure the spatial character of noise on a light field in the time domain. These are promising techniques for the analysis of the MSM nature of a squeezed light in the time domain.
Noise suppression across multiple spatial modes of a light field would serve to improve the field's imaging capabilities and allow it to act as a more effective carrier \nof quantum information. This thesis describes a scheme that utilises a nonlinear process (four wave mixing (4WM)) in Rubidium 85 in order to generate a single beam of \nlight that demonstrates sub quantum noise limit (QNL) quadrature fluctuations of up to -4dB across a multitude of spatial modes simultaneously. \n \nIncluded is a description of sub-QNL (squeezed) light, followed by a breakdown of how this 4WM arrangement generates the desired quantum noise suppression. Analysis \nhas been performed that displays explicitly how the phase matching arrangement that maximises the noise suppression differs from that which optimises the efficiency of the process. This consideration is crucial to understanding why the setup achieves the levels of squeezing observed despite the presence of a strong absorption feature. \n \nFinally, the multi-spatial-mode nature of the generated squeezing is observed directly via homodyne detection using local oscillators with a range of transverse profiles. These profiles select the mode of the signal to be analysed and as such the ability to detect squeezing using a range of them demonstrates its presence across all of these modes simultaneously.
Entangled multi-spatial-mode fields have interesting applications in quantum information, such as parallel quantum information protocols, quantum computing, and quantum imaging. We study the use of a nondegenerate four-wave mixing process in rubidium vapor at 795 nm to demonstrate generation of quantum-entangled images. Owing to the lack of an optical resonator cavity, the four-wave mixing scheme generates inherently multi-spatialmode output fields. We have verified the presence of entanglement between the multi-mode beams by analyzing the amplitude difference and the phase sum noise using a dual homodyne detection scheme, measuring more than 4 dB of squeezing in both cases. This paper will discuss the quantum properties of amplifiers based on four-wave-mixing, along with the multi mode properties of such devices.
Entangled multi-spatial-mode fields have interesting applications in quantum information, such as parallel quantum information protocols, quantum computing, and quantum imaging. We study the use of a nondegenerate four-wave mixing process in rubidium vapor at 795 nm to demonstrate generation of quantum-entangled images. Owing to the lack of an optical resonator cavity, the four-wave mixing scheme generates inherently multi-spatialmode output fields. We have verified the presence of entanglement between the multi-mode beams by analyzing the amplitude difference and the phase sum noise using a dual homodyne detection scheme, measuring more than 4 dB of squeezing in both cases. This paper will discuss the quantum properties of amplifiers based on four-wave-mixing, along with the multi mode properties of such devices.
Multi-photon nonlinear processes in atoms have served as important tools for quantum metrology, quantum communications, and quantum sensing. In this thesis, we experimentally address the interplay of various multi-photon Raman processes in hot Rb vapor, with the four-wave mixing (FWM) process being a central theme. FWM is the nonlinear response of a medium to a strong optical pump field inelastically scattering off atomic resonances and resulting in the generation of additional photons in different modes. FWM is a detrimental, but inherent part of electromagnetically induced transparency (EIT) and Raman based quantum memories. However, we were able to weaken the four-photon resonance by utilizing two-photon absorption to remove the additional photons without interfering with the signal beam. We also demonstrate the ability to tailor FWM to generate new photons in a controlled fashion for mode conversion. With this, we showed the conversion of 795 nm light to 420 nm light. While FWM is a source of noise in quantum memories, it can also be used for the generation squeezed twin-beams. Such beams have relative intensity noise reduced below the classical shot noise limit and share mode dependence based on the phase-matching conditions. Using this, we demonstrated that twin-beams can be generated with largely different spatial structure (optical angular momentum) and still share strong correlations, so long as the phase-matching conditions are satisfied. We then constructed and demonstrated the operation of a polarization-based quantum interferometer using squeezed twin-beams and showed that our beams were entangled under the inseparability condition. Using this interferometer, we were also able to achieve squeezing at low detection frequencies, which is necessary for things like quantum imaging and gravitational wave detection. We also demonstrated that squeezed twin-beams can be utilized to enhance the sensitivity of two-photon absorption spectroscopy. This research has touched on many different subjects related to quantum information science and improved upon some of the tools needed for the implementation of such technologies.