Classification and Optimization of SU(3) Spin-Nematic Squeezing

Christopher D. Hamley, Corey Gerving, Thai M. Hoang +2 more

Chris Hamley, Corey Gerving, Thai M. Hoang +3 more

Christopher D. Hamley

The primary study of this thesis is spin-nematic squeezing in a spin-1 condensate. \nThe measurement of spin-nematic squeezing builds on the success of previous experiments of spin-mixing together with advances in low noise atom counting. \nThe major contributions of this thesis are linking theoretical models to experimental results and the development of the intuition and tools to address the squeezed subspaces. \nUnderstanding how spin-nematic squeezing is generated and how to measure it has required a review of several theoretical models of spin-mixing as well as extending these existing models. This extension reveals that the squeezing is between quadratures of a spin moment and a nematic (quadrapole) moment in abstract subspaces of the SU(3) symmetry group of the spin-1 system. \nThe identification of the subspaces within the SU(3) symmetry allowed the development of techniques using RF and microwave oscillating magnetic fields to manipulate the phase space in order to measure the spin-nematic squeezing. Spin-mixing from a classically meta-stable state, the phase space manipulation, and low noise atom counting form the core of the experiment to measure spin-nematic squeezing. Spin-nematic squeezing is also compared to its quantum optics analogue, two-mode squeezing generated by four-wave mixing. \n \nThe other experimental study in this thesis is performing spin-dependent photo-association spectroscopy. Spin-mixing is known to depend on the difference of the strengths of the scattering channels of the atoms. Optical Feshbach resonances have been shown to be able to alter these scattering lengths but with prohibitive losses of atoms near the resonance. The possibility of using multiple nearby resonances from different scattering channels has been proposed to overcome this limitation. However there was no spectroscopy in the literature which analyzes for the different scattering channels of atoms for the same initial states. Through analysis of the initial atomic states, this thesis studies how the spin state of the atoms affects what photo-association resonances are available to the colliding atoms based on their scattering channel and how this affects the optical Feshbach resonances. From this analysis a prediction is made for the extent of alteration of spin-mixing achievable as well as the impact on the atom loss rate.

Anders Søndberg Sørensen, Klaus Mølmer

M. Reboiro, Osvaldo Civitarese, Lorena Rebón

Emi Yukawa, Masahito Ueda, Kae Nemoto

In spin-1 collective atomic systems, the spin and nematic-tensor operators constitute the su(3) Lie algebra, whose su(2) subalgebras are shown to give two distinct classes of squeezing which are unitarily equivalent to spin squeezing and spin-nematic squeezing. We explicitly construct a unitary operator that generates an arbitrary squeezed spin-nematic state from an arbitrary spin-1 condensate state. In particular, we demonstrate that squeezed spin states can be generated from a polar state and that squeezed spin-nematic states can be generated from a fully spin-polarized state.