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Register a new userEffective expression of the Lee-Huang-Yang energy functional for heteronuclear mixtures
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We consider a homogeneous heteronuclear Bose mixture with contact interactions at the mean-field collapse, i.e. with interspecies attraction equal to the mean geometrical intraspecies repulsion. We show that the Lee-Huang-Yang (LHY) energy functional is accurately approximated by an expression that has the same functional form as in the homonuclear case. The approximated energy functional is characterized by two exponents, which can be treated as fitting parameters. We demonstrate that the values of these parameters which preserve the invariance under permutation of the two atomic species are exactly those of the homonuclear case. Deviations from the exact expression of LHY energy functional are discussed quantitatively and a specific application is described.
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We observe monopole oscillations in a mixture of Bose-Einstein condensates, where the usually dominant mean-field interactions are canceled. In this case, the system is governed by the next-order Lee-Huang-Yang (LHY) correction to the ground state energy, which describes the effect of quantum fluctuations. Experimentally such a LHY fluid is realized by controlling the atom numbers and interaction strengths in a $^{39}$K spin mixture confined in a spherical trap potential. We measure the monopole oscillation frequency as a function of the LHY interaction strength as proposed recently by J{o}rgensen et al. [Phys. Rev. Lett. 121, 173403 (2018)] and find excellent agreement with simulations of the complete experiment including the excitation procedure and inelastic losses. This confirms that the system and its collective behavior are initially dominated by LHY interactions. Moreover, the monopole oscillation frequency is found to be stable against variations of the involved scattering lengths in a broad region around the ideal values, confirming the stabilizing effect of the LHY interaction. These results pave the way for using the non-linearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.
We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory we derive a zero-temperature modified Gross-Pitaevskii equation with beyond-mean-field corrections due to quantum depletion and anomalous density. This result is obtained from the stationary equation of the Bose-Einstein order parameter coupled to the Bogoliubov-de Gennes equations of the out-of-condensate field operator. We show that, in the presence of a generic external trapping potential, the key steps to get the modified Gross-Pitaevskii equation are the semiclassical approximation for the Bogoliubov-de Gennes equations, a slowly-varying order parameter, and a small quantum depletion. In the uniform case, from the modified Gross-Pitaevskii equation we get the familiar equation of state with Lee-Huang-Yang correction.
Quantum collapse in three and two dimensions (3D and 2D) is induced by attractive potential ~ -1/r^2. It was demonstrated that the mean-field (MF) cubic self-repulsion in the 3D bosonic gas suppresses the collapse and creates the missing ground state (GS). However, the cubic nonlinearity is not strong enough to suppress the 2D collapse. We demonstrate that the Lee-Hung-Yang (LHY) quartic term, induced by quantum fluctuations around the MF state, is sufficient for the stabilization of the 2D gas against the collapse. By means of numerical solution of the Gross-Pitaevskii equation including the LHY term, as well as with the help of analytical methods, such as expansions of the wave function at small and large distances from the center and the Thomas-Fermi approximation, we construct stable GS, with a singular density, ~ 1/r^{4/3}, but convergent integral norm. Counter-intuitively, the stable GS exists even if the external potential is repulsive, with the strength falling below a certain critical value. An explanation to this finding is given. Along with the GS, singular vortex states are produced too, and their stability boundary is found analytically. Unstable vortices spontaneously transform into the stable GS, expelling the vorticity to periphery.
The beyond-mean-field Lee-Huang-Yang (LHY) correction is ubiquitous in dilute ultracold quantum gases. However, its effects are often elusive due to the typically much larger influence of the mean-field energy. In this work, we study an ultracold mixture of $^{23}$Na and $^{87}$Rb with tunable attractive interspecies interactions. The LHY effects manifest in the formation of self-bound quantum liquid droplets and the expansion dynamics of the gas-phase sample. A liquid-to-gas phase diagram is obtained by measuring the critical atom numbers below which the self-bound behavior disappears. In stark contrast to trapped gas-phase condensates, the gas-phase mixture formed following the liquid-to-gas phase transition shows an anomalous expansion featuring a larger release energy for increasing mean-field attractions.
Lee-Huang-Yang (LHY) fluids are an exotic quantum matter emerged in a Bose-Bose mixture where the mean-field interactions, interspecies attraction $(g_{12})$ and intraspecies repulsive $(g_{11}, g_{22})$, are tuned to cancel completely when $g_{12}=-sqrt{g_{11}g_{22}}$ and atom number $N_2=sqrt{g_{11}/g_{22}}N_1$, and as such the fluids are purely dominated by beyond mean-field (quantum many-body) effect -- quantum fluctuations.Three-dimensional LHY fluids were proposed in 2018 and demonstrated by the same group from Denmark in recent ultracold atoms experiments [T. G. Skov,et al., Phys. Rev. Lett. 126, 230404], while their low-dimensional counterparts remain mysterious even in theory. Herein, we derive the Gross-Pitaevskii equation of one-dimensional LHY quantum fluids in two-component Bose-Einstein condensates, and reveal the formation, properties, and dynamics of matter-wave structures therein. An exact solution is found for fundamental LHY fluids. Considering a harmonic trap, approximate analytical results are obtained based on variational approximation, and higher-order nonlinear localized modes with nonzero nodes $Bbbk=1$ and $2$ are constructed numerically. Stability regions of all the LHY nonlinear localized modes are identified by linear-stability analysis and direct perturbed numerical simulations. Movements and oscillations of single localized mode, and collisions between two modes, under the influence of different incident momenta are also studied in dynamical evolutions. The predicted results are available to quantum-gas experiments, providing a new insight into LHY physics in low-dimensional settings.
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