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arXiv:cond-mat/0512371 · Journal of Physics B Atomic Molecular and Optical Physics

Permanent magnetic lattices for ultracold atoms and quantum degenerate gases

Saeed Ghanbari, Tien D. Kieu, Andrei I. Sidorov, Peter Hannaford

Published Jan 18, 2006• 74 citations
arXivHTMLPDF

Abstract

We propose the use of periodic arrays of permanent magnetic films for producing magnetic lattices of microtraps for confining, manipulating and controlling small clouds of ultracold atoms and quantum degenerate gases. Using analytical expressions and numerical calculations we show that periodic arrays of magnetic films can produce one-dimensional (1D) and two-dimensional (2D) magnetic lattices with non-zero potential minima, allowing ultracold atoms to be trapped without losses due to spin flips. In particular, we show that two crossed layers of periodic arrays of parallel rectangular magnets plus bias fields, or a single layer of periodic arrays of square-shaped magnets with three different thicknesses plus bias fields, can produce 2D magnetic lattices of microtraps having non-zero potential minima and controllable trap depth. For arrays with micron-scale periodicity, the magnetic microtraps can have very large trap depths ($\sim$0.5 mK for the realistic parameters chosen for the 2D lattice) and very tight confinement.

DOI
10.1088/0953-4075/39/4/009

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•Jan 1, 2006•0 citations
We propose the use of periodic arrays of permanent magnetic films for producing magnetic lattices of microtraps for confining, manipulating and controlling small clouds of ultracold atoms and quantum degenerate gases. Using analytical expressions and numerical calculations we show that periodic arrays of magnetic films can produce one-dimensional (1D) and two-dimensional (2D) magnetic lattices with non-zero potential minima, allowing ultracold atoms to be trapped without losses due to spin flips. In particular, we show that two crossed layers of periodic arrays of parallel rectangular magnets plus bias fields, or a single layer of periodic arrays of square-shaped magnets with three different thicknesses plus bias fields, can produce 2D magnetic lattices of microtraps having non-zero potential minima and controllable trap depth. For arrays with micron-scale periodicity, the magnetic microtraps can have very large trap depths (∼\sim∼0.5 mK for the realistic parameters chosen for the 2D lattice) and very tight confinement.
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 an infinite magnetic lattice for the relevant physical quantities and compare them with our numerical results. 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.
We propose a new permanent magnetic lattice for creating periodic arrays of Ioffe-Pritchard permanent magnetic microtraps for holding and controlling ultracold atoms and Bose-Einstein condensates (BECs). Lattice can be designed on thin layer of magnetic films such as Tb6Tb_6Tb6​Gd10Gd_10Gd1​0Fe80Fe_{80}Fe80​Co4Co_4Co4​. In details, we investigate single layer and two crossed layers of sawtooth magnetic patterns with thicknesses of 50 and 500nm respectively with a periodicity of 1μμμm. Trap depth and frequencies can be changed via an applied bias field to handle tunneling rates between lattice sites. We present analytical expressions and using numerical calculations show that this lattice has non-zero potential minima to avoid majorana spin flips. One advantage of this lattice over previous ones is that it is easier to manufacture.
We investigate the conditions under which a proposed square magnetic lattice, produced by a periodic array of square holes patterned on a magnetic film plus bias fields, can lead to magnetic microtraps with non-zero potential minima suitable for trapping periodic arrays of ultracold atoms and quantum degenerate gases.We find that the magnetic field pattern created by the array of square holes plus bias fields exhibits a complex dependence on distance z from the magnetic film, due largely to competing contributions from kz and √ 2 kz decay terms (where k = 2π /a and a is the lattice period) and interference between the magnetic field pattern of the square-hole structure and the bias fields.We find that in order to avoid zero potential minima and hence losses due to Majorana spin flips, bias fields of unequal magnitude need to be applied along both the x and y (in-plane) directions plus a bias field within a specific range along the z (perpendicular) direction.We also find that for a finite-size (n s × n s ) lattice, a z-bias field B 1z ≈ -6 √ 2M 0 (t/a)n -1 s (where M 0 and t are the film magnetization and thickness) is needed to compensate for the effect of the missing magnetic structure which would otherwise reduce the magnetic potential minima to zero.
Abstract We introduce 3D permanent magnetic lattices for ultracold atoms which can be created by arbitrary number of 2D arrays of square permanent magnetic slabs plus a bias magnetic field. Instead of the square magnets, we can also use magnetic films with square holes. We find analytical expressions for the location of the nonzero magnetic field minima and physical quantities such as trap depths, absolute value of the magnetic field and curvatures as well as trap frequencies at each minimum. We show that most of them, including the trap depths, modulation depths, and trap frequencies can be controlled by the bias field. Accessible trap depths and trap frequencies in the permanent magnetic lattices are much higher compared to the optical lattices. Between the magnetic layers, the trap frequencies are higher compared to above the top layer (under the bottom layer). In principle, our method can be generalized to other 2D permanent magnetic lattices and we show how to transform a 2D lattice of a given geometry into 3D by using multiple layers of magnets.
We propose and analyze a trilayer permanent magnetic lattice formed by two patterned magnetic films, each containing a two-dimensional array of square holes, generating three distinct two-dimensional arrays of three-dimensional microtraps with nonzero minima, thereby suppressing Majorana spin-flip losses. Analytical expressions for key trapping parameters are derived and show good agreement with numerical calculations. A bias magnetic field enables tunable control of trap frequencies, depths, and modulation amplitudes. We find that the interlayer region supports higher trap frequencies than the outer layers, and that the confinement properties depend sensitively on the separation distance between the films. The trilayer architecture enables vertical confinement engineering, allowing precise three-dimensional positioning of traps and independent control of trap curvatures in the central and outer regions, including the formation of an interlayer potential with enhanced confinement. Owing to its stability, low decoherence, and experimental feasibility, the proposed lattice provides a promising platform for the manipulation of ultracold atoms and potential applications in quantum information processing.
We propose a new class of permanent magnetic lattices on an atom chip for producing 1D and 2D periodic arrays of Ioffe-Pritchard magnetic micro-traps with variable barrier height for trapping and manipulating ultracold atoms and Bose-Einstein condensates. The barrier height of the microtraps may be varied by changing a bias magnetic field. In one of the con gurations, we show how we can go from a 1D array of 2D microtraps to a 2D array of 3D microtraps by changing the angle between two crossed arrays of parallel rectangular magnets. Furthermore, by changing the angle between the crossed arrays of magnets, the barrier heights can be varied. This suggests the possibility of performing a type of 'mechanical' BEC to Mott insulator quantum phase transition in a permanent magnetic lattice.