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arXiv:1711.06478 · Physical Review A

Enhanced quantum spin fluctuations in a binary Bose-Einstein condensate

R. N. Bisset, P. G. Kevrekidis, Christopher Ticknor

Published Feb 1, 2018• 13 citations
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Abstract

For quantum fluids, the role of quantum fluctuations may be significant in several regimes such as when the dimensionality is low, the density is high, the interactions are strong, or for low particle numbers. In this paper, we propose a fundamentally different regime for enhanced quantum fluctuations without being restricted by any of the above conditions. Instead, our scheme relies on the engineering of an effective attractive interaction in a dilute, two-component Bose-Einstein condensate (BEC) consisting of thousands of atoms. In such a regime, the quantum spin fluctuations are significantly enhanced (atom bunching with respect to the noninteracting limit) since they act to reduce the interaction energy, a remarkable property given that spin fluctuations are normally suppressed (antibunching) at zero temperature. In contrast to the case of true attractive interactions, our approach is not vulnerable to BEC collapse. We numerically demonstrate that these quantum fluctuations are experimentally accessible by either spin or single-component Bragg spectroscopy, offering a useful platform on which to test beyond-mean-field theories. We also develop a variational model and use it to analytically predict the shift of the immiscibility critical point, finding good agreement with our numerics.

DOI
10.1103/physreva.97.023602

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For quantum fluids, the role of quantum fluctuations may be significant in several regimes such as when the dimensionality is low, the density is high, the interactions are strong, or for low particle numbers. In this paper, we propose a fundamentally different regime for enhanced quantum fluctuations without being restricted by any of the above conditions. Instead, our scheme relies on the engineering of an effective attractive interaction in a dilute, two-component Bose-Einstein condensate (BEC) consisting of thousands of atoms. In such a regime, the quantum spin fluctuations are significantly enhanced (atom bunching with respect to the noninteracting limit) since they act to reduce the interaction energy, a remarkable property given that spin fluctuations are normally suppressed (antibunching) at zero temperature. In contrast to the case of true attractive interactions, our approach is not vulnerable to BEC collapse. We numerically demonstrate that these quantum fluctuations are experimentally accessible by either spin or single-component Bragg spectroscopy, offering a useful platform on which to test beyond-mean-field theories. We also develop a variational model and use it to analytically predict the shift of the immiscibility critical point, finding good agreement with our numerics.
A dilute gas Bose-Einstein condensate (BEC) near a Feshbach resonance offers a system that can be tuned from the well-understood regime of weak interactions to the complex regime of strong interactions. Strong interactions play a central role in the phenomena of superfluidity in liquid He, and theoretical treatments for this regime have existed since the 1950’s. However, these theories have not been experimentally tested as superfluid He offers no similar mechanism with which to tune the interactions. In dilute gas condensates near a Feshbach resonance, where interactions can be tuned, strong interactions have proven difficult to study due to the condensate’s metastable nature with respect to the formation of weakly bound molecules. In this thesis, I introduce an experimental system and novel probes of the gas that have been specifically designed to study strongly interacting BECs. I present Bragg spectroscopy measurements that have accessed this regime, as well as proof-of-principle experiments using photon-counting for Bragg spectroscopy at low-momentum. Finally, I show preliminary data using contact spectroscopy, which is a method that could lead to the first measurements of the predicted interaction energies for a dilute Bose gas of atoms in the strongly interacting regime.
We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a U(1)\mathrm{U}(1)U(1) order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.
We study the thermodynamic properties of binary Bose mixtures by developing a beyond mean-field Popov theory which properly includes the effects of quantum and thermal fluctuations in both the density and spin channels. Results for key thermodynamic quantities, such as the isothermal compressibility and the magnetic susceptibility, are derived from a perturbative calculation of the grand-canonical potential. We find that thermal fluctuations can play a crucial role on the miscibility condition of a binary mixture, favoring phase separation at finite temperature even if the mixture is soluble at zero temperature, as already anticipated in a previous work [M. Ota et al., Phys. Rev. Lett. 123, 075301 (2019)]. We further investigate the miscibility condition for binary mixtures in the presence of asymmetry in the intraspecies interactions, as well as in the masses of the two components. Furthermore, we discuss the superfluid behavior of the mixture and the temperature dependence of the Andreev-Bashkin effect.
This thesis investigates the response of coherently coupled spin-mixture Bose-Einstein condensates across a broad range of nonlinear regimes, extending from the deep-Rabi regime to the strongly nonlinear regime. On the theoretical side, collision processes induced and enhanced by strong coherent coupling are analyzed within a perturbative framework. Interaction channels arising from both mean-field and beyond-mean-field processes are identified, providing a microscopic description of the mechanisms through which few-body interactions contribute to the energy of the many-body system. On the experimental side, precise control over the interaction landscape is achieved in a 39-K spin mixture through improved stabilization of the magnetic field near 57 G, the operating point of the system. A feedforward compensation circuit is implemented to suppress magnetic-field noise, and Ramsey spectroscopy measurements demonstrate a twelvefold reduction in field fluctuations, corresponding to a residual root-mean-square noise level of a few tens of μG. This enhanced stability enables controlled measurements of the density-dependent equation of state of the coherently driven two-component condensate. As the density is increased, the system exhibits distinct interaction regimes. At low densities, the equation of state is dominated by repulsive two-body interactions. At intermediate densities, three-body contributions emerge and become increasingly relevant. At higher densities, the interaction energy shows an unusual saturation-like behavior. This behaviour reflects the nontrivial interplay between coherent coupling and interactions.
We investigate the effects of quantum fluctuations (QFs) and finite-range interatomic interactions on the ground state and wall tension of a Bose-Einstein condensate (BEC) at zero temperature by means of modified Gross-Pitaevskii equations. The QFs are shown to stiffen the condensate near the hard wall, narrowing the density profile and raising the wall tension above its mean-field value by an amount proportional to square-root of the gas parameter. Finite-range corrections always reduces the wall tension relative to the QFs correction value regardless of the effective range. We find the ordering γ0<γII<γIγ_0 < γ_{\rm II} < γ_{\rm I}γ0​<γII​<γI​ in the dilute regime and identify a crossover condition under which the two beyond-mean-field contributions mutually cancel. These results provide an experimentally accessible way for probing beyond-LHY physics through precision measurements of the wall tension in ultracold Bose gases.
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.