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

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 K39 atoms.

Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases

“…Then, cubic terms may be neglected in Eqs. (7), and approximation P|ψ 1 | 2 + P −1 |ψ 2 | 2 ≈ P −1/2 |ψ 2 | is used to simplify Eq. (7) to the following equations for stationary states (9):…”

“…The substitution of this in Eqs. (7) and the linearization with respect to ζ j and η j yields the dispersion equation for the perturbation:…”

Effective expression of the Lee-Huang-Yang energy functional for heteronuclear mixtures

“…stable states self-bound by interatomic attractive interactions. Such states resemble a liquid even if their density is several orders of magnitude lower than in ordinary liquids [14][15][16][17][18][19][20]. Similarly, LHY corrections also stabilize droplets with attractive dipolar forces [21,22].…”

Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates

“…In the course of the analysis, we take into account the effective renormalization of the strength of the LHY correction under the action of SOC, that was demonstrated in [51], in which, however, the formation of QDs in spin-orbitcoupled BEC was not addressed. In this connection, it relevant to mention that effects of another linear interaction between the two components in the spinor BEC, viz., the Rabi coupling, was considered in [52], including the effect of this interaction on the formation of the QDs under the action of the LHY terms.…”