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Acta Physica Sinica

Three wire toroidal magnetic guide based on the vertical leads and ac current modulation

Cheng Jun, Jingfang Zhang, Xu Xin-Ping, Xiaojun Jiang, Xiaolin Li, Haichao Zhang, Wang Yu-zhu

Published Jan 1, 2016• 3 citations
Publisher

Abstract

A new scheme to create a closed toroidal magnetic waveguide for deBroglie wave on a single layer atom chip is proposed and there is no zero magnetic field along the guide center. The guide is a two-dimensional magnetic trap for trapping weak-field seeking states of atoms with a magnetic dipole moment. The designed wire structure on the atom chip consists of three concentric and isometric ring wires, and six vertical current leads of the three ring wires. By using the through silicon via technology, the current leads can be made perpendicular to the atom chip surface instead of being generally arranged side by side on the chip surface. Compared with the general wiring way, the vertical lead way has two advantages. One is that each ring wire gap caused by the current leads is substantially smaller than the distance between the ring wires, which permits the generation of a closed toroidal magnetic guide near the atom chip surface when dc currents are supplied to the three ring wires. The other is that the distance between two leads of each ring wire is considerably reduced, resulting in the fact that the magnetic perturbation of the leads to the whole toroidal magnetic guide is negligible. We numerically calculate the magnetic field distribution generated by our wire layout when dc currents are applied, and it is shown that a closed and tight toroidal magnetic guide is formed near the atom chip surface. However, there are zero magnetic fields existing along the center of the toroidal guide, which leads to Majorana spin flips from trapped magnetic substate to an un-trapped magnetic sub-state. According to the time-orbiting-potential principle, we propose an ac current modulation method, which is simple and stable, to reduce the atom losses and suppress the atomic decoherence in the toroidal magnetic guide. We deduce the ac current expressions for the case of three isometric infinite straight wires and apply the ac modulation current expressions directly to our three ring wire structure. The numerical calculation results show that the closed toroidal guide does no longer have zero magnetic fields near the magnetic field minimum, and that the magnetic field fluctuation of the guide is smaller. Based on the vertical leads and ac current modulation, the closed toroidal wave guide with no zero magnetic field along the guide center can be generated near the atom chip surface. This scheme has important scientific significance and engineering value for developing the cold atomic chip gyroscope.

DOI
10.7498/aps.65.060302

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On the Design and Simulation of Electromagnetic Traps and Guides for Ultra-Cold Matter

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The objective of this thesis is the design and simulation of new electromagnetic traps and guides for ultra-cold matter. The traps and guides are intended for future experiments with small amounts of alkali atoms to study the quantum-mechanical effects of condensation and coupling between trapped drops of cold matter.\n\nThe main results are with the development and simulation of new wire traps and guides based on the dressing effect realised in strong DC magnetic and RF fields of certain frequencies. Some designs are proposed using only trapping by the DC magnetic field.\n\nThe principal methodology used in the thesis is to first develop the necessary theory and design formulas to make an initial design, followed by analytical and numerical simulation of the effective trapping potential. 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•Jan 1, 2010•1 citation
A new scheme to create a closed toroidal magnetic waveguide for deBroglie wave on a single layer atom chip is proposed and there is no zero magnetic field along the guide center. The guide is a two-dimensional magnetic trap for trapping weak-field seeking states of atoms with a magnetic dipole moment. The designed wire structure on the atom chip consists of three concentric and isometric ring wires, and six vertical current leads of the three ring wires. By using the through silicon via technology, the current leads can be made perpendicular to the atom chip surface instead of being generally arranged side by side on the chip surface. Compared with the general wiring way, the vertical lead way has two advantages. One is that each ring wire gap caused by the current leads is substantially smaller than the distance between the ring wires, which permits the generation of a closed toroidal magnetic guide near the atom chip surface when dc currents are supplied to the three ring wires. The other is that the distance between two leads of each ring wire is considerably reduced, resulting in the fact that the magnetic perturbation of the leads to the whole toroidal magnetic guide is negligible. We numerically calculate the magnetic field distribution generated by our wire layout when dc currents are applied, and it is shown that a closed and tight toroidal magnetic guide is formed near the atom chip surface. However, there are zero magnetic fields existing along the center of the toroidal guide, which leads to Majorana spin flips from trapped magnetic substate to an un-trapped magnetic sub-state. According to the time-orbiting-potential principle, we propose an ac current modulation method, which is simple and stable, to reduce the atom losses and suppress the atomic decoherence in the toroidal magnetic guide. We deduce the ac current expressions for the case of three isometric infinite straight wires and apply the ac modulation current expressions directly to our three ring wire structure. The numerical calculation results show that the closed toroidal guide does no longer have zero magnetic fields near the magnetic field minimum, and that the magnetic field fluctuation of the guide is smaller. Based on the vertical leads and ac current modulation, the closed toroidal wave guide with no zero magnetic field along the guide center can be generated near the atom chip surface. This scheme has important scientific significance and engineering value for developing the cold atomic chip gyroscope.
We describe a method to create a circular magnetic waveguide for deBroglie waves on a microchip. The guide is a two-dimensional magnetic minimum for trapping weak-field seeking states of atoms or molecules with a magnetic dipole moment. It is created completely by electric currents in wires that are lithographically patterned on a multi-level chip. We describe the geometry and time-dependent currents of the wires and show that it is possible to wrap the waveguide in a complete circle with minimal perturbations due to the leads or wire crossings. This maximal area geometry is suited for rotation sensing with atom interferometry via the Sagnac effect using either cold thermal atoms and molecules or Bose-condensed systems.
We propose a robust scheme that creates a toroidal magnetic potential on a single-layer atom chip. The wire layout consists of two interleaved Archimedean spirals, which avoids the trapping perturbation caused by the input and output ports. By using a rotation bias field, the minimum of the time-averaged orbiting potential is lifted from zero, and then a relatively smooth and harmonic ring trap is formed. The location of the waveguide is immune to the magnetic variations, as it is only determined by the wire layout. The ring waveguide offers an ideal solution to developing a compact and portable atomic gyroscope.
We present a scheme for generating a ring magnetic waveguide on a single-layer atom chip. The wire layout consists of two interleaved Archimedean spirals of the same size. The waveguide avoids the trapping perturbation caused by the input and output ports, resulting in an enclosed guiding loop for neutral atoms in weak-field seeking states. Such a configuration can create a tight and deep trap potential with a small current. Taking the |F = 2, m F = 2〉 state of 87 Rb as an example, the trap frequency and depth are estimated to be 18 kHz and 335 μK, respectively, with a dc current of 2 A.
We describe the design and function of a circular magnetic waveguide produced from wires on a microchip for atom interferometry using de Broglie waves. The guide is a two-dimensional magnetic minimum for trapping weak-field seeking states of atoms or molecules with a magnetic dipole moment. The design consists of seven circular wires sharing a common radius. We describe the design, the time-dependent currents of the wires and show that it is possible to form a circular waveguide with adjustable height and gradient while minimizing perturbation resulting from leads or wire crossings. This maximal area geometry is suited for rotation sensing with atom interferometry via the Sagnac effect using either cold atoms, molecules and Bose-condensed systems.
We present atom chip traps and guides created by a combination of two current-carrying wires and a bias field pointing perpendicular to the chip surface. These elements can be arranged in any orientation on the chip surface. We study loading schemes for the traps and present a detailed study of the guiding of thermal atomic clouds in an omnidirectional matter waveguide along a $25\text{\ensuremath{-}}\mathrm{mm}$-long curved path at various atom-surface distances $(35--450\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})$. An extension of the scheme for the guiding of Bose-Einstein condensates is outlined. Such a concept enables utilizing the full two-dimensional surface of the chip.
The objective of this thesis is the design and simulation of new electromagnetic traps and guides for ultra-cold matter. The traps and guides are intended for future experiments with small amounts of alkali atoms to study the quantum-mechanical effects of condensation and coupling between trapped drops of cold matter.\n\nThe main results are with the development and simulation of new wire traps and guides based on the dressing effect realised in strong DC magnetic and RF fields of certain frequencies. Some designs are proposed using only trapping by the DC magnetic field.\n\nThe principal methodology used in the thesis is to first develop the necessary theory and design formulas to make an initial design, followed by analytical and numerical simulation of the effective trapping potential. This may be followed by optimization of the geometry and the DC driving currents to enhance the trapping performance of the structure.\n\nA wire carrying both DC and RF currents is surrounded by a cylindrical minimum potential manifold and can be used as a guide for cold atoms. Bias rings are necessary around the wire to avoid a potential minimum of zero and to move the resulting circular potential minimum up and down along the wire. The minimum potential surfaces around two crossed or two parallel wires touch each other for certain critical values of the DC currents in the two wires. The DC currents must be in opposite directions in two parallel wires. Equations are derived in Chapter 2 for the distance to the circular minimum potential manifold for a single wire, for two crossed wires and for two parallel wires. It is then explained how prospective cold atom transfer between two crossed wires can be achieved by changing the magnitudes of the RF currents in the bias rings around the wires. Electrically controlled atom transfer between two parallel wires does not seem to be practical.\n\nA four-wire cell trap made from two crossing pairs of parallel wires has been designed and optimized using a simple Matlab script. It can be used to trap both strong- and weak-field-seeking atoms and may possibly be used to study collision and entanglement between the two types of atoms. With only DC excitation the trap becomes a trap for weak-field-seeking atoms. It then unfortunately has a potential minimum of zero at its centre. A similar 3 x 3 wire dual-well trap has also been designed and optimized in Matlab. It is prospective for the study of entanglement of BEC matter placed in the two wells. A quite low potential barrier in the direction normal to the wireplanes when the two wells are merged could however entail that the trap is inadequate for this purpose or that additional bias fields are necessary.\n\nSeveral multi-wire cell-grids that may find use as part of a quantum register are also described. The cell-grids can be stacked in threedimensions and can trap both strong- and weak-field-seeking atoms. The optimization, also here performed in Matlab, showed weaknesses due to a lack of complexity. A different and better optimization technique is most likely necessary to improve the optimization further.\n\nScaling to micrometre and nanometre size is demonstrated in Chapter 3. When scaling to micrometre size thermally induced spin-flip transitions should be considered. Scaling to nanometre size demands that both thermally induced spin-flips and the effect of the Casimir-Polder force must be taken into account. The effect of the Casimir-Polder force is minimized by the use of carbon nanotubes as conductors. The minimum feasible trapping distance is expected to be no less than 100 nm from the surface of a carbon nanotube.\n\nA four micro-wire cell and a 3 x 3 micro-wire structure, both adapted for future realization on a micro-machined substrate, are given as examples of micrometre size structures. Several nanometre size structures are also demonstrated. It is shown that prospective atom transfer between two crossed nanotubes can be done essentially in the same way as for two crossed wires.\n\nA four-nanotube cell and several nanotube cell-grids are also exemplified. The depth of the trapping potential is found to be proportional to the RF frequency. If the RF frequency is increased then the DC current level must also increase to maintain the same DC current to angular frequency ratio. The depth of the trap is accordingly also proportional to the DC current level in the conductors. The depth of the trap is thus ultimately limited by the maximum conductor current.\n\nA quadrupolar trap similar to the well known Ioffe-Pritchard trap is studied in Chapter 4 with combined DC and RF current excitation of the bias rings. A non-uniform potential minimum is found around the local maximum at the centre of the trap, but this does not prevent the trap from being used to trap weak-field-seeking atoms. The potential maximum at the centre of the quadrupolar trap is more than sufficient for trapping strongfield- seeking atoms. The quadrupolar trap can therefore be used to trap both strong- and weak-field-seeking atoms if the DC bar currents are large enough. Simulations also indicate that the bias rings can be placed relatively closely together to compress clouds of cold atoms into successively smaller traps. As the gap distances become very small the B-field becomes very strong between the bias rings and there is a risk of dielectric breakdown.\n\nA metallic cylinder atom guide consisting of a cylinder with a small hole and an external wire is described analytically in Chapter 5 and simulation results from Amperes are compared favourably with the results of calculations in Matlab. It is found that there can only be a B-field zero at the centre of the hole in the cylinder when there is a second field zero further inside the cylinder. The barrier between the two field zeros typically increases in width with increasing cylinder radius and in height with decreasing cylinder radius for a given cylinder current (DC). The smallest cylinder had the highest barrier between the field zeros, but also required the highest DC current in the external wire. Bias rings around the guide must be centred on the hole in the cylinder and the DC ring currents and the spacing between the bias rings must be scaled by the same factor as the ring radius to maintain the same shape and height of the trapping potential along the centre of the hole. The cylinder guide looks promising as a hermetic guide for cold matter. Bias rings are required both to pump atoms along the guide and to remove the zero in the B-field inside the hole.