# Equation of state and self-bound droplet in Rabi-coupled Bose mixtures

## TL;DR

This paper investigates how quantum fluctuations influence the equation of state and stability of Rabi-coupled two-component Bose gases, revealing conditions for self-bound droplets and proposing an experimental observation with potassium atoms.

## Contribution

It provides an analytical treatment of quantum fluctuations in Rabi-coupled Bose mixtures, demonstrating the formation of self-bound droplets and identifying an instability at high Rabi frequencies.

## Key findings

- Quantum fluctuations regularize the equation of state.
- Self-bound droplets can form in attractive Bose mixtures.
- Droplet stability is affected by Rabi frequency.

## Abstract

Laser induced transitions between internal states of atoms have been playing a fundamental role to manipulate atomic clouds for many decades. In absence of interactions each atom behaves independently and their coherent quantum dynamics is described by the Rabi model. Since the experimental observation of Bose condensation in dilute gases, static and dynamical properties of multicomponent quantum gases have been extensively investigated. Moreover, at very low temperatures quantum fluctuations crucially affect the equation of state of many-body systems. Here we study the effects of quantum fluctuations on a Rabi-coupled two-component Bose gas of interacting alkali atoms. The divergent zero-point energy of gapless and gapped elementary excitations of the uniform system is properly regularized obtaining a meaningful analytical expression for the beyond-mean-field equation of state. In the case of attractive inter-particle interaction we show that the quantum pressure arising from Gaussian fluctuations can prevent the collapse of the mixture with the creation of a self-bound droplet. We characterize the droplet phase and discover an energetic instability above a critical Rabi frequency provoking the evaporation of the droplet. Finally, we suggest an experiment to observe such quantum droplets using Rabi-coupled internal states of $^{39}$K atoms.