Beyond-Mean-Field Effects in Rabi-Coupled Two-Component Bose-Einstein Condensate

Abstract

We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently-coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi frequency, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang (LHY) scaling ∝ n 5/2 to an expansion in integer powers of density, where, in addition to a two-body BMF term ∝ n 2 , there emerges a repulsive three-body contribution ∝ n 3 . We work in a Rabi-coupled two-component 39 K condensate which is released in a waveguide. Its expansion dynamics is governed by the BMF energy allowing for its quantitative measurement. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of vanishing mean field.

Inducing spin-order with an impurity: phase diagram of the magnetic Bose polaron

“…In the latter expression k B is the Boltzmann constant, α ⊥ = /(mω ⊥ ) denotes the transversal confinement length scale and T refers to the temperature of the spinor Bose gas. In an experiment our results can be probed by coupling the spin components of the medium via a radiofrequency field [55]. The corresponding implementation involves an adiabatic ramp (within a time-interval τ ≫ ω −1 B ) of Ω R .…”

Polarized Rabi-Coupled and Spinor Boson Droplets

“…The internal states are coupled through a Rabi frequency ω R and detuning δ. Applying the rotating wave approximation to eliminate the explicit time dependence, the Hamiltonian of this Rabi-coupled binary mixture is given by [18]:…”

“…We calculate the BMF energy to analyse the possibility of droplet phase for various values of ω R and r. By applying a Bogoliubov transformation on the quadratic Hamiltonian (2), one can obtain the Bogoluibov modes of the Rabi-coupled binary mixture [18]:…”

“…Recently, the Bose mixtures with the Rabi-coupling between the hyperfine states of the particles attracted attention due to interesting many-body effects, such as effective tunable three-body interactions [8,[17][18][19]. The coupling between the two levels of the system makes the BMF energy depend on the Rabi frequency ω R [18] and provides an additional mechanism to tune the droplet density. Similar to a critical particle number, there is a critical Rabi frequency ω c above which the droplet is no longer self-trapped [8].…”

Hugenholtz -- Pines relations and the critical temperature of a Rabi coupled binary Bose system

“…For the mixtures made of atoms occupying different hyperfine states, it is possible experimentally to generate coherently coupled configurations via radio frequency transitions, giving rise to typical Rabi oscillations. Such experiments were performed with atoms evaporatively cooled in the |F = 2, m F = 2 and |F = 1, m F = −1 spin states of 87 Rb [2][3][4] and very recently, with 39 K atoms in |F = 1, m F = −1 and |F = 1, m F = 0 states [5].…”