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arXiv:0908.4336 · Physical Review A

Rayleigh-Taylor instability in binary condensates

Sandeep Gautam, D. Angom

Published May 17, 2010• 67 citations
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Abstract

We propose a well-controlled experimental scheme to initiate and examine the Rayleigh-Taylor instability in two-species Bose-Einstein condensates. We identify the $^{85}\mathrm{Rb}$-$^{87}\mathrm{Rb}$ mixture as an excellent candidate to observe experimentally. The instability is initiated by tuning the $^{85}\mathrm{Rb}$-$^{85}\mathrm{Rb}$ interaction through a magnetic Feshbach resonance. We show that the observable signature of the instability is the damping of the radial oscillations. We also propose a semianalytic scheme to determine the stationary state of binary condensates with the Thomas-Fermi approximation for axisymmetric traps.

DOI
10.1103/physreva.81.053616

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We propose a well-controlled experimental scheme to initiate and examine the Rayleigh-Taylor instability in two-species Bose-Einstein condensates. We identify the 85Rb^{85}\mathrm{Rb}85Rb-87Rb^{87}\mathrm{Rb}87Rb mixture as an excellent candidate to observe experimentally. The instability is initiated by tuning the 85Rb^{85}\mathrm{Rb}85Rb-85Rb^{85}\mathrm{Rb}85Rb interaction through a magnetic Feshbach resonance. We show that the observable signature of the instability is the damping of the radial oscillations. We also propose a semianalytic scheme to determine the stationary state of binary condensates with the Thomas-Fermi approximation for axisymmetric traps.
We examine the generation and subsequent evolution of Rayleigh Taylor instability in anisotropic binary Bose-Einstein condensates. Considering a pancake-shaped geometry, to initiate the instability we tune the intraspecies interaction and analytically study the normal modes of the interface in elliptic cylindrical coordinates. The normal modes are then Mathieu functions and undergoes bifurcation at particular values of anisotropy and ratio of number of atoms. We find that the analytical estimates of the bifurcation parameters are in good agreement with the numerical results.
We show how a two dimensional Bose-Einstein Condensate trapped in a nonequilibrium state can be driven into the Rayleigh-Taylor instability if an outward in-plane force is exerted on it. If the condensate is inside a semiconductor, the above force could arise from an inhomogeneous strain applied on the host semiconductor crystal. On the other hand, for a BEC of alkali atoms, the force could be exerted by an inhomogeneous magnetic field turned on after the BEC has been released from its magnetic trap. During its expansion, the condensate will break into droplets each a separate BEC. Therefore, one can create BEC droplets out of a single large BEC and study the coherence properties of the droplets with respect to each other. The discussion on the linear onset of the Rayleigh-Taylor instability in a BEC is generalized to three dimensions.
We investigate three kinds of instabilities in binary immiscible homogeneous Bose-Einstein condensate, considering rubidium isotopes 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb confined in two-dimensional circular box. Rayleigh-Taylor and Kelvin-Helmholtz (KH) instability types are studied under strong perturbations. Without external perturbation, instabilities are also probed by immiscible-to-miscible quenching transition, under two different initial configurations. Our numerical simulations show that all such instability dynamics are dominated by large vortex production and sound-wave (phonon) propagation. For long-term propagation, vortex dynamics become dominant over sound waves in the KH instability, while sound-wave excitations predominate in the other cases. For all the dynamical simulations, the emergence of possible scaling laws are investigated for the compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number kkk. The corresponding results are compared with the classical Kolmogorov scalings, ${k}^{\ensuremath{-}5/3}$ and ${k}^{\ensuremath{-}3}$, for turbulence, which are observed in the kinetic energy spectra at some specific time intervals.
We control the interspecies interaction in a two-species atomic quantum mixture by tuning the magnetic field at a Feshbach resonance. The mixture is composed by fermionic 40K^{40}\mathrm{K}40K and bosonic 87Rb^{87}\mathrm{Rb}87Rb. We observe effects of the large attractive and repulsive interaction energy across the resonance, such as collapse or a reduced spatial overlap of the mixture, and we accurately locate the resonance position and width. Understanding and controlling instabilities in this mixture opens the way to a variety of applications, including formation of heteronuclear molecular quantum gases.
We describe our experimental setup for creating stable Bose-Einstein condensates (BECs) of (85)Rb with tunable interparticle interactions. We use sympathetic cooling with (87)Rb in two stages, initially in a tight Ioffe-Pritchard magnetic trap and subsequently in a weak, large-volume, crossed optical dipole trap, using the 155 G Feshbach resonance to manipulate the elastic and inelastic scattering properties of the (85)Rb atoms. Typical (85)Rb condensates contain 4 x 10(4) atoms with a scattering length of a=+200a(0). Many aspects of the design presented here could be adapted to other dual-species BEC machines, including those involving degenerate Fermi-Bose mixtures. Our minimalist apparatus is well suited to experiments on dual-species and spinor Rb condensates, and has several simplifications over the (85)Rb BEC machine at JILA, which we discuss at the end of this article.
We report on the production of a 41 K- 87 Rb dual-species Bose–Einstein condensate with tunable interspecies interaction and we study the mixture in the attractive regime; i.e., for negative values of the interspecies scattering length a 12 . The binary condensate is prepared in the ground state and confined in a pure optical trap. We exploit Feshbach resonances for tuning the value of a 12 . After compensating the gravitational sag between the two species with a magnetic field gradient, we drive the mixture into the attractive regime. We let the system evolve both in free space and in an optical waveguide. In both geometries, for strong attractive interactions, we observe the formation of self-bound states, recognizable as quantum droplets. Our findings prove that robust, long-lived droplet states can be realized in attractive two-species mixtures, despite the two atomic components possibly experiencing different potentials.