Adiabatically induced coherent Josephson oscillations of ultracold atoms in an asymmetric two-dimensional magnetic lattice

Abstract

Abstract:We propose a new method to create an asymmetric twodimensional magnetic lattice which exhibits magnetic band gap structure similar to semiconductor devices. The quantum device is assumed to host bound states of collective excitations formed in a magnetically trapped quantum degenerate gas of ultracold atoms such as a Bose-Einstein condensate (BEC) or a degenerate Fermi gas. A theoretical framework is established to describe possible realization of the exciton-Mott to discharging Josephson states oscillations in which the adiabatically controlled oscillations induce ac and dc Josephson atomic currents where this effect can be used to transfer n Josephson qubits across the asymmetric twodimensional magnetic lattice. We consider second-quantized Hamiltonians to describe the Mott insulator state and the coherence of multiple tunneling between adjacent magnetic lattice sites where we derive the self consistent non-linear Schrödinger equation with a proper field operator to describe the exciton Mott quantum phase transition via the induced Josephson atomic current across the n magnetic bands.

Solitons in nonlinear lattices

“…Usually, the periodic potential is created as an optical lattice, OL, which is induced by the interference of coherent laser beams illuminating the condensate, as proposed by Jaksch et al (1998) and demonstrated by Greiner et al (2002). More recently, it was demonstrated by Ghanbari, Kieu, Sidorov, and Hannaford (2006), and by Abdelrahman, Hannaford, and Alameh (2009) that 2D and 1D periodic potentials may also be induced by magnetic lattices, created by a plate made of a permanent magnet with a lattice of holes drilled in it, or more sophisticated variants of this setting.…”

Design and characterization of a field-switchable nanomagnetic atom mirror

“…This in turn will inform experiments in which we will attempt to achieve our ultimate goal of trapping a single atom in the potential well created by a DW. Nanowire arrays with geometries similar to that which we have investigated in this paper could ultimately be used to create two dimensional arrays of magnetic traps, which have been shown to be useful tools for studying phenomena such as Josephson oscillations [41] and Mott insulator transitions [42] in atomic ensembles. The inset figure shows the differential of the data in the region of the "on" to "q-off" transition for the negative field sweep.…”

3D permanent magnetic lattices for ultracold atoms

“…Periodic arrays of magnetic microtraps created by arrays of current-carrying wires [11,12] and permanent magnetic slabs [13][14][15][16][17][18][19][20] have been introduced for trapping and manipulating ultracold atoms. They have been used in fundamental researches on ultracold atoms including quantum degenerate gases and BECs [21].…”

“…Moreover, 2D lattices of magnetic microtraps produced by crossed arrays of current-carrying wires have been proposed [26,27]. So far, several configurations of permanent magnetic lattices have been proposed [13][14][15][16][17][18][19][20]. In reference [13], arrays of permanent magnetic waveguides and the first 2D permanent magnetic lattice consisting of arrays of either rectangular or square slabs has been proposed.…”