Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Trilayer permanent magnetic lattice for ultracold atoms formed by two square-hole magnetic layers

Saeed Ghanbari, Parvin Karimi

Published Aug 20, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-026-65077-4

Related papers

Permanent magnetic lattices for ultracold atoms and quantum degenerate gases

Saeed Ghanbari, Tien D. Kieu, Andrei I. Sidorov +1 more

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

A two-dimensional permanent magnetic lattice for ultracold atoms

Amir Mohammadi, Saeed Ghanbari, Aref Pariz

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 $Tb_6$$Gd_10$$Fe_{80}$$Co_4$. In details, we investigate single layer and two crossed layers of sawtooth magnetic patterns with thicknesses of 50 and 500nm respectively with a periodicity of 1$μ$m. 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.

arXiv:1101.6068•Physica Scripta•Jun 5, 2013•5 citations

3D permanent magnetic lattices for ultracold atoms

Saeed Ghanbari

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.

Physica Scripta•Sep 15, 2023•1 citation

Analysis of a simple square magnetic lattice for ultracold atoms

Saeed Ghanbari, Ahmed Abdalrahman, Andrei I. Sidorov +1 more

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.

Journal of Physics B Atomic Molecular and Optical Physics•May 13, 2014•11 citations

Asymmetric Two-dimensional Magnetic Lattices for Ultracold Atoms Trapping and Confinement

Ahmed Abdelrahman, P. Hannaford M. Vasiliev, Kamal Alameh

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.

arXiv:0910.5032•Oct 27, 2009•1 citation

Lattice of microtraps for ultracold atoms based on patterned magnetic films

R. Gerritsma, S. Whitlock, T. Fernholz +5 more

We have realized a two-dimensional permanent magnetic lattice of Ioffe-Pritchard microtraps for ultracold atoms. The lattice is formed by a single $300\text{\ensuremath{-}}\mathrm{nm}$ magnetized layer of FePt, patterned using optical lithography. Our magnetic lattice consists of more than 15 000 tightly confining microtraps with a density of $1250\phantom{\rule{0.3em}{0ex}}\text{traps}∕{\mathrm{mm}}^{2}$. Simple analytical approximations for the magnetic fields produced by the lattice are used to derive relevant trap parameters. We load ultracold atoms into at least 30 lattice sites at a distance of approximately $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ from the film surface. The present result is an important first step toward quantum information processing with neutral atoms in magnetic lattice potentials.

arXiv:0706.1170•Physical Review A•Sep 19, 2007•56 citations
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 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 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.
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 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.
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 have realized a two-dimensional permanent magnetic lattice of Ioffe-Pritchard microtraps for ultracold atoms. The lattice is formed by a single $300\text{\ensuremath{-}}\mathrm{nm}$ magnetized layer of FePt, patterned using optical lithography. Our magnetic lattice consists of more than 15 000 tightly confining microtraps with a density of 1250traps∕mm21250\phantom{\rule{0.3em}{0ex}}\text{traps}∕{\mathrm{mm}}^{2}1250traps∕mm2. Simple analytical approximations for the magnetic fields produced by the lattice are used to derive relevant trap parameters. We load ultracold atoms into at least 30 lattice sites at a distance of approximately $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ from the film surface. The present result is an important first step toward quantum information processing with neutral atoms in magnetic lattice potentials.