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arXiv:1208.2198 · Physical Review A

Roton immiscibility in a two-component dipolar Bose gas

Ryan Wilson, Christopher Ticknor, John L. Bohn, Eddy Timmermans

Published Sep 7, 2012• 83 citations
arXivHTMLPDF

Abstract

We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two-dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a rotonlike IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single-component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled nonlocal Gross-Pitaevskii equations.

DOI
10.1103/physreva.86.033606

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We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two-dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a rotonlike IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single-component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled nonlocal Gross-Pitaevskii equations.
We investigate the effects of dipole-dipole (DD) interactions on immiscibility-miscibility transitions (IMT's) in two-component Bose-Einstein condensates (BEC's) trapped in the harmonic-oscillator (HO) potential, with the components linearly coupled by a resonant electromagnetic field (accordingly, the components represent two different spin states of the same atom). The problem is studied by means of direct numerical simulations. Different mutual orientations of the dipolar moments in the two components are considered. It is shown that, in the binary BEC formed by dipoles with the same orientation and equal magnitudes, the IMT cannot be induced by the DD interaction alone, being possible only in the presence of the linear coupling between the components, while the miscibility threshold is affected by the DD interactions. However, in the binary condensate with the two dipolar components polarized in opposite directions, the IMT can be induced without any linear coupling. Further, we demonstrate that those miscible and immiscible localized states, formed in the presence of the DD interactions, which are unstable evolve into robust breathers, which tend to keep the original miscibility or immiscibility, respectively. An exception is the case of a very strong DD attraction, when narrow stationary modes are destroyed by the instability. The binary BEC composed of copolarized dipoles with different magnitudes are briefly considered as well.
This work concerns a theoretical study of a two-component ultra-cold bosonic gas of polarised magnetic dipolar atoms. The atoms interact by short-ranged contact interactions and long-ranged dipole-dipole interactions. The two components can correspond to two different spin-states of a single atomic species or two different atomic species, as realised in recent experiments. Here, we develop a general theory for the ground states and excitations of a two-component dipolar Bose-Einstein condensate. The ground states are described by dipolar Gross-Pitaevskii equations and Bogoliubov-de Gennes equations describe the excitations. We apply these theories to systems in 3D harmonic traps and a uniform planar potential. Specialised numerical methods are developed to provide accurate solutions of these equations, and to deal with the singular dipole-dipole interaction kernel. These methods involve spectral representations based on plane waves and Bessel functions. We also discuss the methods we used for obtaining ground state solutions of the nonlinear Gross-Pitaevskii energy functional. Dipole-dipole interactions can favour spatial structure, as demonstrated in the recent observation of supersolid states of matter in a single-component dipolar gas. In the two-component system these interactions can also favour a ground state with a periodic order in the pseudo-spin density. A two-component system can be either miscible (components overlap) or immiscible (components are separated). Our focus here is in the spin-stripe state, which occurs in a flattened trap geometry and involves an immiscible stripe pattern along one of the weakly trapped or untrapped directions. We examine the dynamical stability conditions of the uniform miscible state in planar confinement, and produce an associated stability phase diagram. We identify the various instabilities and analytical criteria for estimating these. We focus on the occurrence of, and conditions that favour, density-roton or spin-roton excitations, anticipating that the softening of these excitations will lead to structured ground states. To characterize these excitations we introduce density and spin dynamical structure factors, which can be measured in experiments using Bragg spectroscopy. Building on the stability phase diagram we compute ground states where the immiscible state is unstable to spin-rotons, finding triangular and stripe immiscible states with a length scale set by the confinement and interactions. We find that the transition to the stripe state is continuous and coincides with the spin-roton softening in the uniform miscible state. We study the excitations of the spin stripe state which exhibits three gapless excitation branches arising from the spontaneous broken symmetries. We identify a balanced parameter regime, where the excitations exhibit a nonsymmorphic symmetry (a symmetry is nonsymmorphic when it is a combination of point-group operations with nonprimitive lattice translations, i.e. not an integer multiple of lattice constants), which is revealed in the density and spin dynamical structure factors. We also consider the dynamics of the system following a quench from the uniform to immiscible stripe states. In the early time dynamics, a spin-stripe state is formed in a such way that the stripe order only extends over small domains. In subsequent dynamics, these domain sizes grow as the system phase-orders towards its equilibrium state. We identify the relevant topological defects such as disclinations, dislocations and grain boundaries. Using ensembles of large scale simulations we show that dynamical scaling holds for the growth of order.
Combining two Bose-Einstein condensates (BECs) may result in a miscible or immiscible mixture, or even a violent implosion. We theoretically demonstrate that dipolar two-component BECs produce far richer physics than their nondipolar counterparts. Intriguingly, when both components have equivalent dipoles, the transition to immiscibility is largely unaffected by dipolar physics, yet the dipoles maximally affect stability. Conversely, antiparallel dipoles strongly affect miscibility but have little effect on stability. By performing three-dimensional calculations of the ground states and their excitations, we find strong dependencies on the confinement geometry. We explore and elucidate the various phononic and rotonic phase transitions, as well as symmetry-preserving crossovers.
We develop a theory for a two-component miscible dipolar condensate in a planar trap. Using numerical solutions and a variational theory we solve for the excitation spectrum and identify regimes where density- and spin-roton excitations are favored. We characterize the various instabilities that can emerge in this system over a wide parameter regime and present results for the stability phase diagram. Importantly this allows us to identify the parameter regimes where a novel roton-immiscibility transition can occur, driven by the softening of the spin-roton excitation.
We perform a full three-dimensional study on miscible-immiscible conditions for coupled dipolar and non-dipolar Bose–Einstein condensates (BEC), confined in anisotropic traps. In view of recent experimental studies, our focus was the atomic erbium–dysprosium ( 168 Er– 164 Dy) and dysprosium–dysprosium ( 164 Dy– 162 Dy) mixtures. The miscibility is quantified by the overlap of the two-component densities, using an appropriate defined parameter. By verifying that stable regimes for pure-dipolar coupled BECs are only possible in pancake-type traps, we obtain some non-trivial local minimum biconcave-shaped states with density oscillations in both components. For non-dipolar systems with repulsive interactions, we show that immiscible stable configurations are also possible in cigar-type geometries. The main role of the trap aspect ratio and inter-species contact interaction for the miscibility is verified for different configurations, from non-dipolar to pure dipolar systems.
We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate that is perturbed by a weak lattice potential along its axis. Our numerical simulations demonstrate that systems exhibiting a roton-maxon structure destabilize readily when the lattice wavelength equals either half the roton wavelength or a low roton subharmonic. We apply perturbation theory to the Gross-Pitaevskii and Bogoliubov--de Gennes equations to illustrate the mechanisms behind the instability threshold. The features of our stability diagram may be used as a direct measurement of the roton wavelength for quasi-one-dimensional geometries.