Physics & Astronomy ETDs


Leigh Norris

Publication Date



Large atomic ensembles interacting with light are one of the most promising platforms for quantum information processing. In the past decade, novel applications for these systems have emerged in quantum communication, quantum computing, and metrology. Essential to all of these applications is the controllability of the atomic ensemble, which is facilitated by a strong coupling between the atoms and light. Non-classical spin squeezed states are a crucial step in attaining greater ensemble control. The degree of entanglement present in these states, furthermore, serves as a benchmark for the strength of the atom-light interaction. Outside the broader context of quantum information processing with atomic ensembles, spin squeezed states have applications in metrology, where their quantum correlations can be harnessed to improve the precision of magnetometers and atomic clocks. This dissertation focuses upon the production of spin squeezed states in large ensembles of cold trapped alkali atoms interacting with optical fields. While most treatments of spin squeezing consider only the case in which the ensemble is composed of two level systems or qubits, we utilize the entire ground manifold of an alkali atom with hyperfine spin f greater or equal to 1/2, a qudit. Spin squeezing requires non-classical correlations between the constituent atomic spins, which are generated through the atoms' collective coupling to the light. Either through measurement or multiple interactions with the atoms, the light mediates an entangling interaction that produces quantum correlations. Because the spin squeezing treated in this dissertation ultimately originates from the coupling between the light and atoms, conventional approaches of improving this squeezing have focused on increasing the optical density of the ensemble. The greater number of internal degrees of freedom and the controllability of the spin-f ground hyperfine manifold enable novel methods of enhancing squeezing. In particular, we find that state preparation using control of the internal hyperfine spin increases the entangling power of squeezing protocols when f>1/2. Post-processing of the ensemble using additional internal spin control converts this entanglement into metrologically useful spin squeezing. By employing a variation of the Holstein-Primakoff approximation, in which the collective spin observables of the atomic ensemble are treated as quadratures of a bosonic mode, we model entanglement generation, spin squeezing and the effects of internal spin control. The Holstein-Primakoff formalism also enables us to take into account the decoherence of the ensemble due to optical pumping. While most works ignore or treat optical pumping phenomenologically, we employ a master equation derived from first principles. Our analysis shows that state preparation and the hyperfine spin size have a substantial impact upon both the generation of spin squeezing and the decoherence of the ensemble. Through a numerical search, we determine state preparations that enhance squeezing protocols while remaining robust to optical pumping. Finally, most work on spin squeezing in atomic ensembles has treated the light as a plane wave that couples identically to all atoms. In the final part of this dissertation, we go beyond the customary plane wave approximation on the light and employ focused paraxial beams, which are more efficiently mode matched to the radiation pattern of the atomic ensemble. The mathematical formalism and the internal spin control techniques that we applied in the plane wave case are generalized to accommodate the non-homogeneous paraxial probe. We find the optimal geometries of the atomic ensemble and the probe for mode matching and generation of spin squeezing.

Degree Name


Level of Degree


Department Name

Physics & Astronomy

First Committee Member (Chair)

Jessen, Poul

Second Committee Member

Miyake, Akimasa

Third Committee Member

Becerra, Elohim

Project Sponsors

National Science Foundation




Quantum Information

Document Type