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International Symposium on High-capacity Optical Networks and Enabling Technologies

Adiabatic coherent quantum tunneling of ultracold atoms trapped in an asymmetrical two-dimensional magnetic lattices

Ahmed Abdelrahman, Kamal Alameh, P. Hannafordz

Published Dec 1, 2009• 0 citations
Publisher

Abstract

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.

DOI
10.1109/honet.2009.5423089

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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.
We propose a new method to create an asymmetric two-dimensional 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 two-dimensional 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.
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 new method to implement an asymmetrical two-dimensional magnetic lattice is proposed. The asymmetrical two-dimensional magnetic lattice can be created by periodically distributing magnetic minima across the surface of magnetic thin film where the periodicity can be achieved by milling n×nn\times nn×n square holes on the surface of the film. The quantum device is proposed for trapping and confining ultracold atoms and quantum degenerate gases prepared in the low magnetic field seeking-state at low temperature, such as the Bose-Einstein Condensate (BEC) and ultracold fermions. We present detailed analysis of the analytical expressions and the numerical simulation procedure used to calculate the external magnetic field. We also, describe the magnetic band gap structure exhibited by the asymmetric effect of the magnetic minima and show some of the possible application. We analyze the effect of changing the characteristic parameters of the magnetic lattice, such as the separating periodicity length and the hole size along with the applications of the external magnetic bias fields to maintain and allocate a suitable non-zero magnetic local minima at effective zzz-distance above the thin film surface. Suitable values are shown which keep the trapped ultracold atoms away from the thermal Majorana spin-flip and the surface Casimir-Polder effect.
An asymmetric multi-quantum state magnetic lattice is proposed to host excitons formed in a quantum degenerate gas of ultracold fermionic atoms to simulate Bose-Einstein condensation (BEC) of excitons. A Quasi-two dimensional degenerate gas of excitons can be collected in the in-plane asymmetric magnetic bands created at the surface of the proposed magnetic lattice, where the ultracold fermions simulate separately direct and indirect confined electronhole pairs (spin up fermions-spin down fermions) rising to the statistically degenerate Bose gas and eventually through controlled tunnelling to BEC of excitons. The confinement of the coupled magnetic quantum well (CMQWs) system may significantly improve the condition for long lived exciton BEC. The exciton BEC, formed in CMQWs can be regarded as a suitable host for the multi-qubits (multipartite) systems to be used in quantum information processors.
We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel ``macroscopic quantum self-trapping'' effect.
Confined indirect excitons in a two-dimensional magnetic lattice are promoted to simulate condensed matter systems. Excitonic particles are magnetically trapped so that a sufficient cooling mechanism can allow the trapped clouds of indirect excitons to experience the Bose-Einstein condensation phase transition. Thus, a long­ range spatial coherence can be resolved causing an inherited phase-locked across all of the coupled sites (single traps). Using an external magnetic bias field a mutual tunneling can adiabatically be exchanged between sites in which case the underline physics of Bose-Hubbard model can be explored such as Mott-insulator and Josephson Effect.