• Thesis and Dissertation Defenses

April 8, 2026 4:00 PM
PAIS 2540

Presenter:

Andrew Forbes

Title: A Quantum Phase Space Description of Local Noise in Atomic Ensembles (and applications to metrology)

Time: Wednesday, April 8th, 4:00PM Mountain Time

 Place: PAIS 2540

 Abstract: 

Ensembles of cold atoms have shown promise as platforms for quantum sensors. Many proposed protocols can, in principle, exceed the sensitivity allowed by classical mechanics by generating nonclassical states of these systems. However, these nonclassical states are often highly entangled and are typically fragile to the deleterious effects of noise. In this dissertation I will demonstrate that local noise sources, which are present in almost all many-spin systems, can be tractably modeled when assuming permutation symmetry of the system. By taking advantage of this assumption, we show that many common local noise sources can be mapped to a simple diffusion and drift equation acting on a Wigner function in bosonic quantum phase space. Thus, we define a generalized Holstein-Primakoff approximation from noisy ensembles of spin-1/2 particles to a bosonic mode. 

Extending this further, we study a very broad class of sensing protocols, limited only to measurement schemes with a countable number of outcomes. We demonstrate that even optimal measurements (those for which the Fisher information equals the quantum Fisher information) can lose significant Fisher information when the measurement contains one or more outcomes with vanishing probability. This vanishing probability leads to a discontinuity in the Fisher information as a function of some unitary transformation on the measurement basis. We explain the connection between loss of Fisher information and discontinuities through the convexity of the Fisher information, and provide a framework for implementing robust measurement schemes.

Finally, we develop a new spin Wigner function, which we call the solid spin Wigner function. This is an extension of the SU(2) Wigner function to describe the dynamics of local symmetric noise, which has a larger Hilbert space than a single spin irrep. We develop this new Wigner function by noting that the collective state space used to describe symmetric local noise resembles the weight space of the symmetric subspace of an ensemble of SU(3) particles. Further, since SU(2) is a subgroup of SU(3), it is possible to embed the SU(2) group structure of the collective state space within this larger group. By making special simplifications to the Wigner function which arise from the physical properties of symmetric local noise, we arrive at a Wigner function which takes 3 real parameters, which can be interpreted as a polar, azimuthal, and radial component. This gives rise to a Bloch “ball” rather than a Bloch sphere on which the Wigner function is visualized.