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arXiv:1208.2147 · Physical Review A

Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

Andrej Junginger, Jörg Main, Günter Wunner, Thomas Bartsch

Published Aug 27, 2012• 12 citations
arXivHTMLPDF

Abstract

We investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the ``activated complex'' that mediates the collapse of the condensate. For a certain value of the $s$-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetry-breaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading-order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows the bifurcation to be smoothly passed.

DOI
10.1103/physreva.86.023632

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We investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the ``activated complex'' that mediates the collapse of the condensate. For a certain value of the sss-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetry-breaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading-order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows the bifurcation to be smoothly passed.
We investigate thermally excited, dipolar Bose-Einstein condensates (BECs). Quasiparticle excitations of the atomic cloud cause density fluctuations which can induce the collapse of the condensate if the interparticle interaction is attractive. Within a variational approach, we identify the collectively excited stationary states of the gas which form transition states on the way to the BEC's collapse. We analyze transition states with different mmm-fold rotational symmetry and identify the one which mediates the collapse. The latter's symmetry depends on the trap aspect ratio of the external trapping potential, which determines the shape of the BEC. Moreover, we present the collapse dynamics of the BEC and calculate the corresponding decay rate using transition-state theory. We observe that the thermally induced collapse mechanism is important near the critical scattering length, where the lifetime of the condensate can be significantly reduced. Our results are valid for an arbitrary strength of the dipole-dipole interaction. Specific applications are discussed for the elements 52{}^{52}52Cr, 164{}^{164}164Dy, and 168{}^{168}168Er with which dipolar BECs have been experimentally realized.
We present a general method for obtaining the exact static solutions and collective excitation frequencies of a trapped Bose-Einstein condensate (BEC) with dipolar atomic interactions in the Thomas-Fermi regime. The method incorporates analytic expressions for the dipolar potential of an arbitrary polynomial density profile, thereby reducing the problem of handling nonlocal dipolar interactions to the solution of algebraic equations. We comprehensively map out the static solutions and excitation modes, including non-cylindrically-symmetric traps, and also the case of negative scattering length where dipolar interactions stabilize an otherwise unstable condensate. The dynamical stability of the excitation modes gives insight into the onset of collapse of a dipolar BEC. We find that global collapse is consistently mediated by an anisotropic quadrupolar collective mode, although there are two trapping regimes in which the BEC is stable against quadrupole fluctuations even as the ratio of the dipolar to sss-wave interactions becomes infinite. Motivated by the possibility of a fragmented condensate in a dipolar Bose gas due to the partially attractive interactions, we pay special attention to the scissors modes, which can provide a signature of superfluidity, and identify a long-range restoring force which is peculiar to dipolar systems. As part of the supporting material for this paper we provide the computer program used to make the calculations, including a graphical user interface.
We experimentally investigate how the collapse dynamics of a Cr-52 Bose-Einstein condensate depends on the external harmonic trap geometry. When the collapse is initiated by reducing the s-wave scattering length below its critical value, a complex dynamics is observed, involving a d-wave symmetric explosion. We find good agreement between our experiments and simulations of the Gross-Pitaevskii equation including 3-body losses. In order to probe the phase-coherence of collapsed condensates we induce the collapse in several condensates simultaneously and let them interfere.
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 Thomas-Fermi 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 nonadiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyze the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.
It has been shown that quantum fluctuations in dipolar Bose–Einstein condensates (BECs) lead to a stabilisation against collapse, thereby providing access to a range of states with different symmetries. In this paper, we discuss variational approaches to approximately determine the phase diagrams for dipolar BECs that are trapped along the dipolar orientation and otherwise infinite in the perpendicular direction (thermodynamic limit). The two-dimensional symmetry breaking occurs in the plane perpendicular to the polarisation axis. We show in detail how to derive approximate expressions that are valid in a region where modulations to an otherwise unmodulated perfect superfluid emerge gradually with a small modulation amplitude and compare the results to rigorous numerics.
The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time-dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.