A class of permanent magnetic lattices for ultracold atoms

Abstract

Abstract. We report on a class of configurations of permanent magnets on an atom chip for producing 1D and 2D periodic arrays of magnetic microtraps with non-zero potential minima and variable barrier height for trapping and manipulating ultracold atoms and quantum degenerate gases. We present analytical expressions for the relevant physical quantities and compare them with our numerical results and with some previous numerical calculations. In one of the configurations of permanent magnets, we show how it is possible by changing the angle between the crossed periodic arrays of magnets to go from a 1D array of 2D microtraps to a 2D array of 3D microtraps and thus to continuously vary the barrier heights between the microtraps. This suggests the possibility of performing a type of 'mechanical' BEC to Mott insulator quantum phase transition in a magnetic lattice. We also discuss a configuration of magnets which could realize a two-qubit quantum gate in a magnetic lattice.

A two-dimensional permanent magnetic lattice for ultracold atoms

“…For the calculating of c 1 , narrow slabs can be shifted by small steps of a/4n along y axis to make initial array. The component of the magnetic field for these shifted narrow slabs, for example in y-direction must be consistent with Eq.18, so we have B ∆,y = c 1 B 0y n/2−1 j=0 sin k(y ± (2j + 1)∆)e −kz (19) = B 0y sin (ky)e −kz where c 1 is determined…”

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

“…These minima are localized in confining volumes representing the magnetic potential wells that contain a certain number of quantized energy levels occupied by the ultracold atoms. In our design, we assumed that the width of the holes α h and the separation of the holes α s are equal, α h = α s ≡ α, to simplify the mathematical derivations and analyses which are similar to those reported in [4,7].…”

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

“…These minima are localized in small volumes representing the potential wells that contain certain number of quantized energy levels for the cold atoms to occupy. In our design, we assumed that the size of the holes α h and the holes separation α s are both equal, α h = α s ≡ α, to simplify the mathematical derivation where we adopted an analysis approach similar to that reported in [4], [8]. The spatial magnetic field components B x , B y and B z can be written analytically as a combination of a field decaying away from the surface of the trap in the zdirection and a periodically distributed magnetic field in the x − y plane produced only by the magnetic induction, B o , at the surface of the permanently magnetized thin film, where…”

“…Both the density plot and contour plot representation types are shown for both simulation results of a 10 × 10 magnetic lattice at the initial magnetic state, formed by B ref only, and with the external application of B x−bias and B y−bias , respectively. The analytical expressions that describe the non-zero local minima, periodically positioned in the x − y plan, take into account the strength of the effective field and α [8]. These expression are derived and simplified to the following set of equations…”