Structure formation during the collapse of a dipolar atomic Bose-Einstein condensate

Abstract

We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the ThomasFermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the non-adiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyse the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.PACS numbers: 03.75. Kk, 75.80.+q Wavepacket collapse is a phenomenon seen in diverse physical systems whose common feature is that they obey non-linear wave equations [1], e.g., in nonlinear optics [2], plasmas [3] and trapped atomic Bose-Einstein condensates (BECs) [4,5,6,7,8,9]. In the latter case, collapse occurs when the atomic interactions are sufficiently attractive. For the usual case of isotropic s-wave interactions experiments have demonstrated both global [5] and local collapse [7] depending upon, respectively, whether the imaginary healing length is of similar size or much smaller than the BEC [10]. During global collapse the monopole mode becomes dynamically unstable and the BEC evolves towards a point singularity, with the threshold for collapse generally exhibiting a weak dependence on trap geometry [11,12]. Local collapse occurs when a phonon mode is dynamically unstable such that the collapse length scale is considerably smaller than the BEC.Recently, the Stuttgart group demonstrated collapse in a BEC with dipole-dipole interactions, where the atomic dipoles were polarized in a common direction by an external field [8,9]. The long-range nature of dipolar interactions means that the Gross-Pitaevskii wave equation that governs the BEC is not only non-linear but also non-local [13,14,15,16]. On top of being long-range, dipolar interactions are also anisotropic, being attractive in certain directions and repulsive in others. This anisotropy has manifested itself experimentally in the stability of the ground state, which is strongly dependent on the trap geometry [8], and in the anisotropic collapse of the condensate [9]. Some uncertainty exists over the mechanism of collapse in these systems. In the latter experiment, striking images indicate that the condensate underwent global collapse, which is likely to have occurred through a quadrupole mode [16,17,18]. In the former experiment, however, recent theoretical results suggest that local collapse played a dominant role [19].A unique feature of trapped dipolar BECs in comparison to s-wave BECs is that they are predicted to exhibit minima in their excitation spec...

Stability and collapse of fermions in a binary dipolar boson-fermion164Dy-161Dy mixture

“…Because of the peculiar features, there has been enhanced interest in the study of dynamic as well as static properties of dipolar BECs. Among the novel features of a dipolar BEC, one can mention the peculiar stability phase diagrams [6], red-blood-cell-like biconcave density distribution due to radial and angular rotonlike excitations [11], anisotropic D-wave collapse [12], formation of anisotropic soliton, vortex soliton [13] and vortex lattice [14], anisotropic shock and sound waves [15], entanglement [16], localization in disordered potential [17], and anisotropic Landau critical * adhikari@ift.unesp.br velocity [18] among others. Stable checkerboard, star, and stripe configurations in dipolar BECs have been identified in a two-dimensional (2D) optical lattice as stable Mott insulator [19] as well as superfluid soliton [20] states.…”

“…After the pioneering experiments on BEC of alkali-metal atoms, degenerate spin-polarized gases of fermionic 6 Li [22], 40 K [23], and 87 Sr [24] atoms were observed. Later, superfluid states of paired 6 Li [25] and 40 K [26] atoms have also been studied.…”

“…Later, superfluid states of paired 6 Li [25] and 40 K [26] atoms have also been studied. More recently, a degenerate dipolar gas of fermionic 161 Dy atoms with large magnetic moment has been created and studied [27].…”

Vortices and vortex lattices in quantum ferrofluids

“…Outside of this regime the condensate becomes prone to collapse [115,116]. Under the Thomas-Fermi approximation the time-independent GPE (13) reduces to,…”

Mixing, demixing, and structure formation in a binary dipolar Bose-Einstein condensate

“…More recently, the BEC of 164 Dy [6,7] and 168 Er [8] atoms with larger dipole moments became available for experimental studies, and polar molecules with much larger (electric) dipole moments are being considered [9] for BEC experiments. Among the novel features of a BEC with anisotropic dipolar interaction, one can mention the peculiar shape and stability properties of a stationary state [10], a red-blood-cell-like biconcave shape in density due to radial and angular roton-like excitations [11]; anisotropic d-wave collapse [12]; the formation of an anisotropic soliton, vortex soliton [13], and vortex lattice [14]; anisotropic sound and shock wave propagation [15]; and anisotropic Landau critical velocity [16] among others. Distinct stable checkerboard, stripe, and star configurations in dipolar BECs have been identified in a two-dimensional (2D) optical lattice as a stable Mott insulator [17] as well as superfluid soliton [18] states.…”