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arXiv:2011.02745 · Physical Review Letters

Observation of a Lee-Huang-Yang Fluid

Thomas G. Skov, Magnus G. Skou, Nils B. Jørgensen, J. Arlt

Published Jun 11, 2021• 77 citations
arXivHTMLPDF

Abstract

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 Jrgensen et al. [Phys. Rev. Lett. 121, 173403 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.173403] 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 nonlinearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.

DOI
10.1103/physrevlett.126.230404

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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 Jrgensen et al. [Phys. Rev. Lett. 121, 173403 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.173403] 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 nonlinearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.
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Understanding the effects of interactions in complex quantum systems beyond the mean-field paradigm constitutes a fundamental problem in physics. We show how the atom numbers and interactions in a Bose-Bose mixture can be tuned to cancel mean-field interactions completely. The resulting system is entirely governed by quantum fluctuations-specifically the Lee-Huang-Yang correlations. We derive an effective one-component Gross-Pitaevskii equation for this system, which is shown to be very accurate by comparison with a full two-component description. This allows us to show how the Lee-Huang-Yang correlation energy can be accurately measured using two powerful probes of atomic gases: collective excitations and radio-frequency spectroscopy. Importantly, the behavior of the system is robust against deviations from the atom number and interaction criteria for canceling the mean-field interactions. This shows that it is feasible to realize a setting where quantum fluctuations are not masked by mean-field forces, allowing investigations of the Lee-Huang-Yang correction at unprecedented precision.
The nucleation and dynamics of vortices in the quasi-two-dimensional rotating dipolar Bose-Einstein condensate are explored by taking into account the Lee-Huang-Yang (LHY) correction to the mean-field (MF) theory. Assuming approximate cancellation of the MF interactions, we focus on the formation of a pure LHY superfluid. The effect of rotational frequency ΩΩΩ is investigated numerically by determining the corresponding number of stable vortices in the superfluid, together with the respective energy per particle EEE and chemical potential μμμ. The LHY superfluid provides a deep minimum of EEE and μμμ, indicating that it is a remarkably robust state of quantum matter. By fixing the LHY interaction strength, an exact single-vortex critical frequency is found, along with the respective chemical potential. A notable feature, observed when creating the LHY superfluid with fewer than five vortices, which is understood as being due to the superfluid's nonlinearity and trapping aspect ratio, is the large frequency ranges admitting the production of two and four vortices, as compared to the small frequency ranges to obtain one and three vortices.
Motivated by recent experimental advances in bubble traps which confine atoms on a thin shell, we investigate the stabilization of droplet states of a Bose-Bose mixture on a spherical surface due to quantum fluctuations. We analytically calculate the energy of a weakly interacting Bose-Bose mixture on a spherical surface with attractive interspecies and repulsive intraspecies interactions using the Bogoliubov approximation. Our findings show that the energy per particle has a minimum at a finite density in the presence of the Lee-Huang-Yang (LHY) term, which indicates the presence of liquidlike droplet state stabilized by quantum fluctuations. We also numerically solve the extended Gross-Pitaevskii equation, incorporating both bubble traps and an additional repulsive LHY correction derived from the Bogoliubov spectrum of a three-dimensional homogeneous mixture. Our calculations show that, due to the size limitations of the sphere, droplet states can only exist within specific parameter ranges. We also verify the transition between droplet states and uniform condensates in spherical confinement potentials, as well as the coexistence of the two. Our results pave the way for future exploration of quantum droplets in curved geometries with nontrivial real-space topologies.
The interplay of quantum fluctuation through the Lee-Huang-Yang (LHY) correction and spin-orbit coupling can modify the stability of the ultradilute Bose-Bose mixtures and result in rich nonlinear physics. Here, under the action of spin-orbit coupling, LHY correction, and rotation, the ground state and vortex excitation of spin-orbit coupled Bose-Einstein condensates (BECs) with LHY correction trapped in a rotating potential are studied. Stable isotropic and anisotropic ground states with zero momentum (in the zero-momentum phase) and nonzero momentum (in the plane wave phase) are obtained. It is shown that anisotropic ground states are persistent near the phase boundary. Particularly, unpolarized and polarized vortex states are predicted. The phase transition condition, the effective mass and quadrupole surface mode describing the anisotropic (deformation) of the condensates, and the critical rotation frequency for vortex excitation are provided analytically. Owing to the action of spin-orbit coupling, the effective mass of the condensates is spatially dependent and asymmetric in two phases, resulting in distinct quadrupole modes, deformations, and vortex excitations in the two phases, especially when the LHY correction is present. The LHY correction promotes the system in the zero-momentum phase with unpolarized vortex states, while the spin-orbit coupling promotes the emergence of a plane wave phase with polarized vortex states. The phase transition and vortex excitation can be well manipulated by spin-orbit coupling, Raman coupling, LHY correction, and external potential.
The discovery of ultracold dilute liquids has significantly elevated our interest in various phenomena which go under the name of beyond-mean-field (BMF) physics. In these lecture notes we give an elementary introduction to the quantum stabilization and liquefaction of a collapsing weakly interacting Bose-Bose mixture. A detailed derivation of the leading BMF correction, also known as the Lee-Huang-Yang (LHY) term, in this system is presented in a manner suitable for further generalizations and extensions. Although the LHY term is a nonanalytic function of the density nnn, under certain conditions the leading BMF correction becomes analytic and can be expanded in integer powers of nnn, effectively introducing three-body and higher-order interactions. We discuss why and how well the Bogoliubov approach can predict these few-body observables.