# Theory of strongly paired fermions with arbitrary short-range interactions

## TL;DR

This paper develops an effective field theory for strongly interacting fermions with short-range attractions, incorporating Gaussian pair fluctuations to predict equations of state and non-universal energy dependence, validated against quantum Monte Carlo results.

## Contribution

It extends existing theories by including non-trivial phase shift effects and Gaussian fluctuations, providing a more accurate description of strongly paired fermion systems.

## Key findings

- Good agreement with quantum Monte Carlo simulations on effective-range dependence.
- The theory predicts non-universal ground-state energy variations.
- Proposes experimental probing via dark-state optical control of Feshbach resonances.

## Abstract

We develop an effective field theory to describe the superfluid pairing in strongly interacting fermions with arbitrary short-range attractions, by extending Kaplan's idea of coupling fermions to a fictitious boson state in Nucl. Phys. B \textbf{494}, 471 (1997). This boson field is assigned with unconventional kinetic term to recover the exact scattering phase shift obtained either from scattering data or model calculations. The theory works even if the explicit form of the interaction potential has not been constructed from scattering data. The contact boson-fermion coupling allows us to go beyond mean-field to include Gaussian pair fluctuations, yielding reliable predictions on equations of state. As an application, we use our theory to address the non-univerisal ground-state energy of strongly paired fermions, due to the non-trivial momentum dependence of the phase shift characterized, for example, by effective range. We find a good agreement between our predictions and recent quantum Monte Carlo simulations on the effective-range dependence in both three and two spatial dimensions. We propose that in cold-atom experiments, the non-universal dependence in thermodynamics can be probed using dark-state optical control of Feshbach resonances.