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Register a new userDipolar Bose-Einstein condensates in a PT-symmetric double-well potential
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Added by
R\\\"udiger Fortanier
Publication date
2014
fields
Physics
and research's language is
English
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We investigate dipolar Bose-Einstein condensates in a complex external double-well potential that features a combined parity and time-reversal symmetry. On the basis of the Gross-Pitaevskii equation we study the effects of the long-ranged anisotropic dipole-dipole interaction on ground and excited states by the use of a time-dependent variational approach. We show that the property of a similar non-dipolar condensate to possess real energy eigenvalues in certain parameter ranges is preserved despite the inclusion of this nonlinear interaction. Furthermore, we present states that break the PT symmetry and investigate the stability of the distinct stationary solutions. In our dynamical simulations we reveal a complex stabilization mechanism for PT-symmetric, as well as for PT-broken states which are, in principle, unstable with respect to small perturbations.
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A Bose-Einstein condensate in a double-well potential features stationary solutions even for attractive contact interaction as long as the particle number and therefore the interaction strength do not exceed a certain limit. Introducing balanced gain and loss into such a system drastically changes the bifurcation scenario at which these states are created. Instead of two tangent bifurcations at which the symmetric and antisymmetric states emerge, one tangent bifurcation between two formerly independent branches arises [D. Haag et al., Phys. Rev. A 89, 023601 (2014)]. We study this transition in detail using a bicomplex formulation of the time-dependent variational principle and find that in fact there are three tangent bifurcations for very small gain-loss contributions which coalesce in a cusp bifurcation.
We investigate vortex excitations in dilute Bose-Einstein condensates in the presence of complex $mathcal{PT}$-symmetric potentials. These complex potentials are used to describe a balanced gain and loss of particles and allow for an easier calculation of stationary states in open systems than in a full dynamical calculation including the whole environment. We examine the conditions under which stationary vortex states can exist and consider transitions from vortex to non-vortex states. In addition, we study the influences of $mathcal{PT}$ symmetry on the dynamics of non-stationary vortex states placed at off-center positions.
We study the case of $mathcal{PT}$-symmetric perturbations of Hermitian Hamiltonians with degenerate eigenvalues using the example of a triple-well system. The degeneracy complicates the question, whether or not a stationary current through such a system can be established, i.e. whether or not the $mathcal{PT}$-symmetric states are stable. It is shown that this is only the case for perturbations that do not couple to any of the degenerate states. The physical explanation for the inhibition of stable currents is discussed. However, introducing an on-site interaction restores the capability to support stable currents.
The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external $mathcal{PT}$-symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the $mathcal{PT}$-symmetric as well as in the $mathcal{PT}$-broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the singular delta potential in the supersymmetry formalism is discussed, and the applicability of the formalism to the nonlinear Gross-Pitaevskii equation is analysed. In the latter case the formalism could be used to remove $mathcal{PT}$-broken states introducing an instability to the stationary $mathcal{PT}$-symmetric states.
The possibility of effectively inverting the sign of the dipole-dipole interaction, by fast rotation of the dipole polarization, is examined within a harmonically trapped dipolar Bose-Einstein condensate. Our analysis is based on the stationary states in the Thomas-Fermi limit, in the corotating frame, as well as direct numerical simulations in the Thomas-Fermi regime, explicitly accounting for the rotating polarization. The condensate is found to be inherently unstable due to the dynamical instability of collective modes. This ultimately prevents the realization of robust and long-lived rotationally tuned states. Our findings have major implications for experimentally accessing this regime.
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