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arXiv:1810.11339 · Physical Review Letters

Dilute Fluid Governed by Quantum Fluctuations

Nils B. Jørgensen, Georg M. Bruun, J. Arlt

Published Oct 26, 2018• 71 citations
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Abstract

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.

DOI
10.1103/physrevlett.121.173403

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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.
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.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
We demonstrate how the beyond-mean-field Lee-Huang-Yang (LHY) corrections and its related physics can be naturally incorporated into the representation of an ultracold Bose gas using the truncated Wigner approach without invoking effective energy terms or local density approximation. By generating a Bogoliubov ground-state representation with appropriately tailored bare interaction strength g0g_0g0​ and condensate density n0n_0n0​, the expected initial energy and densities are obtained while retaining access to quantum effects beyond the reach of the extended Gross-Pitaevskii equation (EGPE) formulation. This approach enables the study of correlations, coherence decay, single realisations, and the onset of quantum fluctuation effects with growing interaction strength. Numerical demonstrations for a weakly interacting single-component Bose gas show that observables deviate significantly from both the plain GPE and the EGPE incorporating LHY corrections. In regimes of strong interaction, many of the interference effects predicted by the GPE and EGPE are suppressed, and the EGPE offers no improvement over the plain GPE compared to the full Wigner model. In the weakly interaction limit, the EGPE appears accurate but resolving its deviation from mean-field results requires extensive ensemble averaging.
We investigate the collective dynamics of two-component Bose-Einstein condensates in a double well potential. By taking into account the Lee-Huang-Yang (LHY) correction from quantum fluctuation, we find that the LHY term, though much smaller than the mean field interactions, can significantly change the coherent oscillating behaviors of the bosonic Josephson junction in the regime of g12≃−g11g22 . Besides the quantitative renormalization to the plasma frequencies of the Josephson oscillations, a series of unexpected nonzero fixed points beyond mean field emerges in the stationary state. More remarkably, unique macroscopic self-trapping states, which are usually absent in the mean field dynamics, can be sustained by the LHY nonlinearity. Our results reveal the nontrivial LHY effect on the Josephson dynamics, which can be tested in the current experiment. Published by the American Physical Society 2024
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.
We study liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under variable confinement introduced along one or two spatial dimensions. Although the atom-atom scattering has a three-dimensional character, discreteness of the available modes in the reduced dimension(s) strongly influences the zero-point energy, which for a weakly interacting three-dimensional system is given by the Lee-Huang-Yang term. Here, we generalize the result of Lee, Huang, and Yang and calculate the higher order corrections to the mean-field energy for a single component Bose-Einstein condensate under condition of a tight confinement in one or two spatial directions. We apply our results to the two-component mixture of bosonic species under conditions favorable for the creation of quantum liquid droplets, which constitute a perfect playground for studies of the beyond mean-field effects. Our findings allow one to analyze the properties of quantum droplets at the dimensional crossover and provide demanding conditions for accessing quasilow dimensions. They also pave a way for experimental exploration of this state of matter in reduced dimensions.