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arXiv:1406.3453 · Physical Review Letters

Number Fluctuations of a Dipolar Condensate: Anisotropy and Slow Approach to the Thermodynamic Regime

D. Baillie, R. N. Bisset, Christopher Ticknor, P. B. Blakie

Published Dec 24, 2014• 11 citations
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Abstract

We present a theory for the number fluctuations of a quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate measured with finite resolution cells. We show that when the dipoles are tilted to have a component parallel to the plane of the trap, the number fluctuations become anisotropic, i.e., depend on the in-plane orientation of the measurement cell. We develop analytic results for the quantum and thermal fluctuations applicable to the cell sizes accessible in experiments. We show that as cell size is increased the thermodynamic fluctuation result is approached much more slowly than in condensates with short range interactions, so experiments would not require high numerical aperture imaging to observe the predicted effect.

DOI
10.1103/physrevlett.113.265301

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We present a theory for the number fluctuations of a quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate measured with finite resolution cells. We show that when the dipoles are tilted to have a component parallel to the plane of the trap, the number fluctuations become anisotropic, i.e., depend on the in-plane orientation of the measurement cell. We develop analytic results for the quantum and thermal fluctuations applicable to the cell sizes accessible in experiments. We show that as cell size is increased the thermodynamic fluctuation result is approached much more slowly than in condensates with short range interactions, so experiments would not require high numerical aperture imaging to observe the predicted effect.
We develop theory for fluctuations in atom number and spin within finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a model of measurements that can be performed in current experiments using finite resolution in situ imaging. We develop analytic results for quantum and thermodynamic limits of the fluctuations and apply our theory to the four equilibrium phases of a spin-1 condensate. We then validate these limits and examine the behavior over a wide parameter regime using numerical calculations specialized to the case of a spinor condensate confined to be quasi-two-dimensional.
We consider the fluctuations in atom number that occur within finite-sized measurement cells in a trapped Bose-Einstein condensate. These approximate the fluctuation measurements made in current experiments with finite-resolution in situ imaging. A numerical scheme is developed to calculate these fluctuations using the quasiparticle modes of a cylindrically symmetric three-dimensionally trapped condensate with either contact or dipole-dipole interactions. We use this scheme to study the properties of a pancake-shaped condensate using cylindrical cells. The extension of the theory to washer-shaped cells with azimuthal weighting is made and used to discriminate between the low-energy roton modes in a dipolar condensate according to their projection of angular momentum. Our results are based on the Bogoliubov approach valid for zero and small finite temperatures.
Two-dimensional (2D) dipolar atomic gases present unique opportunities for exploring novel quantum phases due to their anisotropic and long-range interactions. However, the behavior of strongly dipolar Bose gases in 2D remains unclear, especially when dipoles are tilted. Here, we demonstrate the creation and characterization of strongly dipolar 2D condensates in a quasi-2D harmonic trap with tunable dipole orientation. By investigating scale invariance properties through breathing collective mode measurements, we observe significant breaking of scale invariance when dipoles are tilted in-plane indicating the dominance of the nonlocal dipole-dipole interactions (DDIs) in this regime. Interestingly, the breaking of the scale invariant dynamics is accompanied by an increase in quantum fluctuations, as shown by comparison with mean-field and beyond mean-field theoretical studies. Our experiments also reveal that at critical tilt angles around 70°, stripe-type density modulations emerge, suggesting the presence of a roton spectrum in 2D, while the system still shows hydrodynamic nature with the phase-locking breathing behavior. This observation elucidates the many-body effect induced by DDIs in 2D, thus marking a crucial step toward realizing 2D supersolids and other exotic quantum phases.
The work of this thesis concerns the properties of a Bose gas of polarised dipoles that have long-range and anisotropic interactions. Our work is divided into two parts. First, the stability of a dipolar Bose gas at finite temperature (both above and below the critical Bose-Einstein condensation (BEC) temperature Tc). Second, the fluctuations of a dipolar BEC at zero and small finite temperature (T ≪ Tc) in a regime where rotonic excitations emerge. \n \nPart I: Stability of a Trapped Finite Temperature Dipolar Bose Gas: Above Tc we implement a semiclassical Hartree-Fock theory and characterise the dependence of the stability boundary on temperature, trap geometry and the strength of the dipole-dipole interaction and contact interaction. We find that stability is greatly enhanced above Tc and that trap geometry continues to play a key role. Furthermore, we find that for oblate traps a novel double instability feature emerges. \nTo extend our stability analysis to the low temperature regime, T < Tc, we develop a beyond semiclassical Hartree theory. We use this to characterise the stability boundary as a function of geometry. Interestingly, we find large beyond semiclassical effects above Tc for prolate trapping geometries. We characterise thermal effects on biconcave condensate states. \n \nPart II: Rotons and Fluctuations in a Trapped Dipolar Condensate: To study density fluctuations we implement a numerical scheme to solve the Gross-Pitaevskii equation and the Bogoliubov de Gennes equations. We find that the phonon and roton gases spatially separate and we characterise the role of the anomalous density on the density fluctuations of the thermally activated rotons. We develop a numerical scheme that calculates number fluctuations within cells of various shapes and sizes, and find a strong peak in the fluctuations when the cell size is around half the roton wavelength, which should be detectable by current experiments. By tailoring the cell shape we predict that experiments should be able to detect the effects of individual roton modes. \nFor the study of zero temperature fluctuations we deploy the Gross-Pitaevskii and Bogoliubov de Gennes equations to calculate the dynamic and static structure factors for a highly oblate BEC. We find a clear signature of the roton gas dispersion relation within the structure factors. This signature should be detectible in current experiments using Bragg spectroscopy.
We consider a trapped quasi-two-dimensional dipolar Bose-Einstein condensate with a polarization tilted into the plane of motion. We show that by tilting the polarization axis, the coherence properties are anisotropic. Such a system will have density fluctuations, the amplitude of which depends on their trap location. Additionally, interference contrast will also be anisotropic despite an isotropic density profile. The anisotropy is related to a rotonlike mode that becomes unstable and supports local collapse along the polarization axis.
We study the rotational properties of a dipolar Bose-Einstein condensate confined in a quasi-two-dimensional anisotropic trap for an arbitrary orientation of the dipoles with respect to their plane of motion. Within the mean-field approximation, we find that the lowest-energy state of the system depends strongly on the relative strength between the dipolar and the contact interactions, as well as on the size and the orientation of the dipoles and the size and the orientation of the deformation of the trapping potential.