From Polymers to Bosons: Can AMO Physics Benefit from Polymer Field Theory?

Feynman’s work on path integral descriptions of helium-4 revealed a deep connection between the statistical mechanics of Bose superfluids and classical ensembles of reacting ring polymers. This analogy is the basis for the predominant finite-temperature quantum simulation technique, path integral Monte Carlo (PIMC). While PIMC is implemented using a basis of particle coordinates, equivalent field-theoretic representations of the quantum many-body problem utilize linear combinations of occupation number states known as coherent states (CS). We recently found that methods for simulating CS-inspired field theories of classical reacting polymers work equally well on quantum field theories of cold atoms. Moreover, quantum field-theoretic simulations offer similar advantages over coordinate-based methods as in the classical context, including linear scaling with system size and direct access to free energies.

We have applied this new field-theoretic simulation method to investigate the thermal phase behavior of a model of cold alkali atoms subject to Rashba spin-orbit coupling, a current topic in AMO physics and an exciting venue for creating mesostructured quantum states such as spin stripes. Our work has revealed that spin stripes in 2D melt into a new quantum “spin microemulsion” phase that resembles bicontinuous microemulsions observed in classical block copolymer and surfactant systems. The defect-mediated nature of the phase transition resembles that predicted by Toner and Nelson for the 2D nematic to isotropic phase transition of classical liquid crystals and verified in monolayers of cylinder-forming block copolymers by Kramer.