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Solid State Communications

The macroscopic quantum phase of ultracold degenerate gases in the asymmetrical two-dimensional magnetic lattice

Ahmed Abdelrahman, Mikhail Vasiliev, Kamal Alameh

Published Apr 14, 2011• 0 citations
Publisher
DOI
10.1016/j.ssc.2011.03.010

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We investigate the existence of the macroscopicmacroscopicmacroscopic quantumquantumquantum phasephasephase in trapped ultracold quantum degenerate gases, such as Bose-Einstein condensate, in an asymmetrical two-dimensional magnetic lattice. We show the key to adiabatically control the tunneling in the new two-dimensional magnetic lattice by means of external magnetic bias fields. The macroscopic quantum phase signature is identified as a Rabi-like oscillation when solving the system of coupled time-dependent differential equations, described here by the Boson Josephson Junctions (BJJs). In solving the system of the BJJs we used an order parameter that includes both time-dependent variational parameters which are the fractional population at each lattice site and the phase difference. The BJJs solution presents a clear evidence for the macroscopic quantum coherence.
A simple method for implementing an asymmetrical two-dimensional magnetic lattice is proposed. The asymmetrical two-dimensional magnetic lattice is created by periodically distributing nonzero magnetic minima across the surface of a magnetic thin film, where the magnetic patterns are formed by milling $n\ifmmode\times\else\texttimes\fi{}n$ square holes on the surface of the film. The method is proposed for trapping and confining quantum degenerate gases, such as Bose-Einstein condensates and ultracold Fermi gases, prepared in low-magnetic-field-seeking states. Analytical expressions and numerical simulation results of the magnetic local minima are shown where we analyze the effect of changing the magnetic lattice parameters, such as the separation of the holes, the hole size, and external bias magnetic fields, to maintain and locate the nonzero local minima at a suitable distance above the film surface to avoid the effect of Majorana spin flips and the Casimir-Polder potential.
We propose a new method to realize a two-dimensional magnetic lattice, having two different configurations of asymmetric magnetic lattice, which exhibits magnetic band gap structure, and a symmetric magnetic lattice. We also describe the tunneling mechanisms of magnetically trapped ultracold atoms, prepared in a degenerate quantum gas such as Bose-Einstein Condensate (BEC). A coherent quantum tunneling of ultracold atoms between the sites of the asymmetrical magnetic lattice can be realized which induces the adiabatically controlled dc Josephson current. At critical phase transitions, namely at certain values of site phase difference and population fraction, a plasma oscillation can be observed in which it forms a discharging Josephson state to be used as coherently coupled n quantum bits.