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Physical Review A

Asymmetrical two-dimensional magnetic lattices for ultracold atoms

Ahmed Abdelrahman, Mikhail Vasiliev, Kamal Alameh, Peter Hannaford

Published Jul 19, 2010• 25 citations
Publisher

Abstract

A simple method for implementing an asymmetrical two-dimensional magnetic lattice is proposed. The asymmetrical two-dimensional magnetic lattice is created by periodically distributing nonzero magnetic minima across the surface of a magnetic thin film, where the magnetic patterns are formed by milling $n\ifmmode\times\else\texttimes\fi{}n$ square holes on the surface of the film. The method is proposed for trapping and confining quantum degenerate gases, such as Bose-Einstein condensates and ultracold Fermi gases, prepared in low-magnetic-field-seeking states. Analytical expressions and numerical simulation results of the magnetic local minima are shown where we analyze the effect of changing the magnetic lattice parameters, such as the separation of the holes, the hole size, and external bias magnetic fields, to maintain and locate the nonzero local minima at a suitable distance above the film surface to avoid the effect of Majorana spin flips and the Casimir-Polder potential.

DOI
10.1103/physreva.82.012320

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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 $n\times n$ 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 $z$-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.

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Scientific Reports•Aug 20, 2026•0 citations
A simple method for implementing an asymmetrical two-dimensional magnetic lattice is proposed. The asymmetrical two-dimensional magnetic lattice is created by periodically distributing nonzero magnetic minima across the surface of a magnetic thin film, where the magnetic patterns are formed by milling n\ifmmode×\else\texttimes\finn\ifmmode\times\else\texttimes\fi{}nn\ifmmode×\else\texttimes\fin square holes on the surface of the film. The method is proposed for trapping and confining quantum degenerate gases, such as Bose-Einstein condensates and ultracold Fermi gases, prepared in low-magnetic-field-seeking states. Analytical expressions and numerical simulation results of the magnetic local minima are shown where we analyze the effect of changing the magnetic lattice parameters, such as the separation of the holes, the hole size, and external bias magnetic fields, to maintain and locate the nonzero local minima at a suitable distance above the film surface to avoid the effect of Majorana spin flips and the Casimir-Polder potential.
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.
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.
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 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.
In this dissertation we explore the basic principles of the magnetic micro-confinement of the quantum degenerate gases where the approach of the so-called two-dimensional magnetic lattices has been theoretically and experimentally investigated. In this research a new generation of two-dimensional magnetic lattice has been proposed and considered as a developing phase for the previous approaches. Its advantage relies on introducing a simplified method to create single or multiple micro-traps of magnetic field local minima distributed, at a certain working distance, above the surface of a thin film of permanent magnetic material. The simplicity in creating the magnetic field local minima at the micro-scale manifests itself as a result of imprinting specific patterns through the thin film using suitable and available micro-fabrication techniques. In this approach, to create multiple micro-traps, patterned square holes of size αh X αh spaced by αs are periodically distributed across the x/y plane taking a two-dimensional grid configuration. These magnetic field local minima are recognized by their ability to trap and confine quantum single-particles and quantum degenerate gases at various levels of distribution in their phase spaces, such as ultracold atoms and virtual quantum particles. Based on the nature of the interaction between the external confining potential fields and the different types of quantum particles, this research is conducted through two separate but not different phases. We performed theoretical and/or experimental investigations, for both phases, at the vicinity of the magnetic micro-confinement and its suitability for trapping quantum particles. A special attention is paid to inspect the coherence in such systems defined in terms of providing an accessible coupling to the internal quantum states of the magnetically trapped particles. Such coherence is considered as one of the important ingredients for simulating condensed matter systems and processing quantum information.
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.