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Register a new userEffect of Anharmonicity on the WKB Energy Splitting in a Double Well Potential
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We investigate the effect of anharmonicity on the WKB approximation in a double well potential. By incorporating the anharmonic perturbation into the WKB energy splitting formula we show that the WKB approximation can be greatly improved in the region over which the tunneling is appreciable. We also observe that the usual WKB results can be obtained from our formalism as a limiting case in which the two potential minima are far apart.
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We derive a general WKB energy splitting formula in a double-well potential by incorporating both phase loss and anharmonicity effect in the usual WKB approximation. A bare application of the phase loss approach to the usual WKB method gives better results only for large separation between two potential minima. In the range of substantial tunneling, however, the phase loss approach with anharmonicity effect considered leads to a great improvement on the accuracy of the WKB approximation.
By using a usual instanton method we obtain the energy splitting due to quantum tunneling through the triple well barrier. It is shown that the term related to the midpoint of the energy splitting in propagator is quite different from that of double well case, in that it is proportional to the algebraic average of the frequencies of the left and central wells.
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.
We experimentally study the spin dynamics of mesoscopic ensembles of ultracold magnetic spin-3 atoms located in two separated wells of an optical dipole trap. We use a radio-frequency sweep to selectively flip the spin of the atoms in one of the wells, which produces two separated spin domains of opposite polarization. We observe that these engineered spin domains are metastable with respect to the long-range magnetic dipolar interactions between the two ensembles. The absence of inter-cloud dipolar spin-exchange processes reveals a classical behavior, in contrast to previous results with atoms loaded in an optical lattice. When we merge the two subsystems, we observe spin-exchange dynamics due to contact interactions which enable the first determination of the s-wave scattering length of 52Cr atoms in the S=0 molecular channel a_0=13.5^{+11}_{-10.5}a_B (where a_B is the Bohr radius).
The anharmonicity of the potential well confining the position of the magnetic vortex core is measured dynamically with a Magnetic Resonance Force Microscope (MRFM). The stray field of the MRFM tip is used to displace the core position away from the well minimum. Anharmonicity is then inferred from the relative frequency shift induced on the eigen-frequency of the vortex core translational mode. Traces of these shifts are recorded while scanning the tip above an isolated nanodot, patterned out of a single crystal FeV film. An analytical framework is proposed to analyze the data. It results in a quantitative measurement of the anharmonic coefficient found to be positive and 50% of the parabolic contribution. This calibrates the tunability of the gyrotropic mode by external magnetic fields. In our sample, we observe a variation of the eigen-frequency as high as +10% for a displacement of the vortex core to about one third of the nanodot radius.
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