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arXiv:1109.4977 · New Journal of Physics

A dielectric superfluid of polar molecules

Ryan Wilson, Seth T. Rittenhouse, John L. Bohn

Published Apr 17, 2012• 11 citations
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Abstract

We show that, under achievable experimental conditions, a Bose–Einstein condensate of polar molecules can exhibit dielectric character. In particular, we derive a set of self-consistent mean-field equations that couple the condensate density to its electric dipole field, leading to the emergence of polarization modes that are coupled to the rich quasi-particle spectrum of the condensate. While the usual roton instability is suppressed in this system, the coupling can give rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function.

DOI
10.1088/1367-2630/14/4/043018

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We show that, under achievable experimental conditions, a Bose–Einstein condensate of polar molecules can exhibit dielectric character. In particular, we derive a set of self-consistent mean-field equations that couple the condensate density to its electric dipole field, leading to the emergence of polarization modes that are coupled to the rich quasi-particle spectrum of the condensate. While the usual roton instability is suppressed in this system, the coupling can give rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function.
We consider an oblate Bose-Einstein condensate of heteronuclear polar molecules in a weak applied electric field. This system supports a rich quasiparticle spectrum that plays a critical role in determining its bulk dielectric properties. In particular, in sufficiently weak fields the system undergoes a polarization wave rotonization, leading to the development of textured electronic structure and a dielectric instability that is characteristic of the onset of a negative static dielectric function.
We investigate the properties of the ground state and low-lying excitations of an oblate Bose-Einstein condensate composed of rigid rotor molecules in the presence of an external polarizing electric field. We build in a quantum model of molecular polarizability by including the full manifold of rotational states. The interplay between spatial and microscopic degrees of freedom via feedback between the molecular polarizability and inter-molecular dipole-dipole interactions leads to a rich quasi-particle spectrum. Under large applied fields, we reproduce the well-understood density-wave rotonization that appears in a fully polarized dipolar BEC, but under smaller applied fields, we predict the emergence of a spin wave instability and possible new stable ground state phases.
Abstract We consider a BEC of rigid rotor molecules confined to quasi-2D through harmonic trapping. The molecules are subjected to an external electric field which polarizes the gas, and the molecules interact via dipole–dipole interactions. We present a description of the ground state and low-energy excitations of the system including an analysis of the mean-field energy, polarization, and stability. Under large electric fields the gas becomes fully polarized and we reproduce a well known density-wave instability which arises in polar BECs. Under smaller applied electric fields the gas develops an in-plane polarization leading to the emergence of a new global instability as the molecules ‘tilt’. The character of these instabilities is clarified by means of momentum-space density–density structure factors. A peak at zero momentum in the spin–spin structure factor for the in-plane component of the polarization indicates that the tilt instability is a global phonon-like instability.
Today, sixteen years after the realization of the first Bose-Einstein condensate (BEC), the field of ultracold many-body physics is booming. In particular, much excitement has been generated by the prospect of creating a degenerate quantum gas of dipolar atoms or molecules. Already, some experimental groups have succeeded in Bose-condensing atomic 52Cr and 164Dy, while other groups have made significant progress towards achieving degeneracy of heteronuclear molecules, such as fermionic 40K87Rb and bosonic 87Rb133Cs, where the strength of the dipolar interaction promises to be much greater than that of the already rich 52Cr condensate. Just as the creation of BEC launched a whole new field of research, dipolar BECs are likely to do the same. However, such systems present a theoretical challenge due to the long-range, anisotropic nature of the dipolar interaction. In this thesis, I present a theoretical investigation of ultracold Bose gases with dipolar interactions.\nThe first part of this thesis is dedicated to the field theoretical treatment of a quantum Bose fluid with dipolar interactions in the ultracold, dilute regime, where the system is well-described by a classical condensate field with quasiparticle excitations. The set of nonlinear integrodifferential equations that describe these objects are derived and novel methods for solving them are presented that, in general, require intricate numerical treatment. Of particular importance is the emergence of a roton mode, reminiscent of that in superfluid 4He. In the second part of this thesis, I show how the roton plays a critical role in the ground state structure and dynamics of a dipolar BEC. Full numerical simulations show that the roton can, for example, be seen in the radial density profile of a quantized vortex state or in the angular collapse and explosion of a dipolar BEC. Additionally, I show the crucial role that this roton plays in determining the transition to superfluidity in these systems. Thus, a set of novel phenomena in ultracold dipolar Bose gases is explained by the presence of the roton, and experimental signatures of these phenomena are made clear.
We present an analytic Bogoliubov description of a Bose-Einstein condensate of polar molecules trapped in a quasi-two-dimensional geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and static structure factors. This method can be applied to any homogeneous, two-component system with linear coupling and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. The nature of these instabilities is clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave responses in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $\mathrm{\ensuremath{\Lambda}}$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$\mathrm{\ensuremath{\Sigma}}$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field.