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Journal of Low Temperature Physics

Analytic Expressions for a 2D Permanent Magnetic Lattice with a 3D Bias Magnetic Field for Ultracold Atoms

Parvin Karimi, Saeed Ghanbari

Published May 17, 2018• 4 citations
Publisher
DOI
10.1007/s10909-018-1958-4

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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.

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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.

arXiv:cond-mat/0512371•Journal of Physics B Atomic Molecular and Optical Physics•Jan 18, 2006•74 citations
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 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.