# Slow interaction quench in BCS superconductors: emergence of pre-formed pairs

## TL;DR

This paper studies how slow changes in interaction strength affect BCS superconductors, revealing regimes where pairs survive without coherence, oscillations occur, or thermal distributions emerge, enabling control of superconducting properties.

## Contribution

It introduces a detailed analysis of non-equilibrium dynamics in BCS superconductors during slow interaction ramps, highlighting the emergence of pre-formed pairs and regimes of coherence loss and retention.

## Key findings

- Short ramps destroy phase coherence but preserve pairing.
- Intermediate ramps sustain superconductivity with oscillations.
- Long ramps maintain near-thermal pair distributions.

## Abstract

We investigate the non-equilibrium behavior of BCS superconductors subjected to slow ramps of their internal interaction strength. We identify three dynamical regimes as a function of ramp duration. For short ramp times, these systems become non-superconducting; however, fermions with opposite momenta remain paired albeit with reduced amplitudes, and the associated pair amplitude distribution is non-thermal. In this first regime, the disappearance of superconductivity is due to the loss of phase coherence between pairs. By contrast, for intermediate ramp times, superconductivity survives but the magnitude of the order parameter is reduced and presents long-lived oscillations. Finally, for long ramp times, phase coherence is almost fully retained during the slow interaction quench, and the steady-state is characterized by a thermal-like pair amplitude distribution. Using this approach, one can therefore dynamically tune the coherence between pairs in order to control the magnitude of the superconducting order parameter and even engineer a non-equilibrium state made of pre-formed pairs.