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Physics of Wave Processes and Radio Systems

Numerical simulations of the Ioffe-Pritchard trap for cold dressed atoms

KARL J. SAND, Sand Karl J

Published Mar 15, 2007• 1 citation
OpenAlex

Abstract

An Ioffe-Pritchard trap for cold dressed atoms is studied by numerical simulations. It is shown that the potential generated by static and alternating currents provides trapping of two sorts of cold dressed atoms. The studied topology is controlled with the frequency and static currents, and it is for study of the atom collision effects and the entanglement of the atoms after a collision.

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RF CONTROLLABLE IOFFE–PRITCHARD TRAP FOR COLD DRESSED ATOMS

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An Ioffe–Pritchard trap for cold dressed atoms is studied by analytical and numerical simulations. The effective potential in this trap is formed by the static magnetic and radio-frequency fields, and the minimums are formed around the current bars. The depth of the minimums and the overall topology of the effective potential are controlled electronically. The studied regime of the Ioffe–Pritchard trap is of interest for high-sensitivity cold atom interferometers.

Modern Physics Letters B•Jan 10, 2007•6 citations

RF Controllable Ioffe-Pritchard Trap

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An Ioffe-Pritchard trap for cold dressed atoms is studied by analytical and numerical simulations. The effective potential in this trap is formed by the static magnetic and radio-frequency fields, and the minimums are formed around the current bars. The depth of the minimums and the overall topology of the effective potential are controlled electronically. The studied regime of the Ioffe-Pritchard trap is of interest for high-sensitive cold atom interferometers.

arXiv:cond-mat/0602210•Feb 8, 2006•1 citation

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

KARL J. SAND

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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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. 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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.

•Jan 1, 2010•1 citation

Anisotropic two-dimensional RF-dressed potentials for ultracold atoms

A. Chakraborty, Satya Ram Mishra

In this work, the RF-dressed potentials generated using a static magnetic field of a quadrupole trap and various radio frequency (RF) fields have been theoretically investigated for trapping and manipulating of cold atoms in a two-dimensional (2D) geometry. In this scheme, the RF fields of some particular polarizations and phases are shown to give rise to some novel static and time-dependent anisotropic two-dimensional potentials that are useful to trap and manipulate the cold atoms in the 2D geometry. The generated time-dependent 2D potentials, rotating on a circular ring, can be used to control the rotation and the oscillation of the cold-atom cloud on the path of the circular ring. The ultracold atoms trapped in these potentials may be used to investigate interesting physics phenomena, such as tunnelling and superfluidity.

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Dynamics of atom trapping in an rf-dressed potential

A. Chakraborty, Satya Ram Mishra, Surjya Prakash Ram +2 more

The dynamics of atom trapping in a radio-frequency-dressed-state potential formed by static and radio frequency (rf) fields has been studied using the Direct Simulation Monte Carlo (DSMC) technique. Using the simulations, a case of formation of a toroidal trap for cold $^{87}Rb$ atoms is investigated for atoms trapped in a static quadrupole magnetic trap and exposed to an rf-field with temporally increasing amplitude and decreasing frequency. We first calculate the adiabatic rf-dressed potential for an atom interacting with these fields and then apply DSMC algorithm to simulate the motion of the atom in this time dependent adiabatic potential. In the simulations the Landau-Zener (LZ) transition probability is calculated to know if the atom is in the trappable or untrappable dressed state. The results show that, initially at lower rf-field strength, the rf-field ejects atoms from the trap and leads to evaporative cooling of the atom cloud. However at higher rf-field strength, the atoms make LZ transition to the trappable dressed state which results in a toroidal shape to the atom cloud. The results of numerical simulations show a qualitative agreement with the experimental observations.

•Jun 14, 2016•0 citations

Loading a dressed Zeeman trap with cold atoms

Yves Colombe, B. Mercier, Hélène Perrin +1 more

In this paper we report on our progress towards the realization of a quantum degenerate gas in two dimensions. Our goal is to transfer a BEC of 87Rb in a very anisotropic trap of oscillation frequencies $\omega_z \gg \omega_1, \omega_2$. Several schemes of such a trap exist. We focussed our attention to the proposal of Oliver Zobay and Barry Garraway published in 2001. The atoms firstly condensed in a Ioffe-Pritchard trap are transferred to an iso-B surface defined by a rf resonance. The upper Zeeman rf dressed states act as a trap at the iso-B surface surrounding the centre of the magnetic trap. The gravity pulls the atoms down in the bottom of the dressed trap and is responsible for pendulum oscillations of the trapped atomic cloud. This paper presents the characteristics of this trap loaded with very cold atoms.

Journal de Physique IV (Proceedings)•Oct 1, 2004•8 citations
An Ioffe-Pritchard trap for cold dressed atoms is studied by numerical simulations. It is shown that the potential generated by static and alternating currents provides trapping of two sorts of cold dressed atoms. The studied topology is controlled with the frequency and static currents, and it is for study of the atom collision effects and the entanglement of the atoms after a collision.
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.
In this work, the RF-dressed potentials generated using a static magnetic field of a quadrupole trap and various radio frequency (RF) fields have been theoretically investigated for trapping and manipulating of cold atoms in a two-dimensional (2D) geometry. In this scheme, the RF fields of some particular polarizations and phases are shown to give rise to some novel static and time-dependent anisotropic two-dimensional potentials that are useful to trap and manipulate the cold atoms in the 2D geometry. The generated time-dependent 2D potentials, rotating on a circular ring, can be used to control the rotation and the oscillation of the cold-atom cloud on the path of the circular ring. The ultracold atoms trapped in these potentials may be used to investigate interesting physics phenomena, such as tunnelling and superfluidity.
The dynamics of atom trapping in a radio-frequency-dressed-state potential formed by static and radio frequency (rf) fields has been studied using the Direct Simulation Monte Carlo (DSMC) technique. Using the simulations, a case of formation of a toroidal trap for cold 87Rb^{87}Rb87Rb atoms is investigated for atoms trapped in a static quadrupole magnetic trap and exposed to an rf-field with temporally increasing amplitude and decreasing frequency. We first calculate the adiabatic rf-dressed potential for an atom interacting with these fields and then apply DSMC algorithm to simulate the motion of the atom in this time dependent adiabatic potential. In the simulations the Landau-Zener (LZ) transition probability is calculated to know if the atom is in the trappable or untrappable dressed state. The results show that, initially at lower rf-field strength, the rf-field ejects atoms from the trap and leads to evaporative cooling of the atom cloud. However at higher rf-field strength, the atoms make LZ transition to the trappable dressed state which results in a toroidal shape to the atom cloud. The results of numerical simulations show a qualitative agreement with the experimental observations.
In this paper we report on our progress towards the realization of a quantum degenerate gas in two dimensions. Our goal is to transfer a BEC of 87Rb in a very anisotropic trap of oscillation frequencies ωz≫ω1,ω2\omega_z \gg \omega_1, \omega_2ωz​≫ω1​,ω2​. Several schemes of such a trap exist. We focussed our attention to the proposal of Oliver Zobay and Barry Garraway published in 2001. The atoms firstly condensed in a Ioffe-Pritchard trap are transferred to an iso-B surface defined by a rf resonance. The upper Zeeman rf dressed states act as a trap at the iso-B surface surrounding the centre of the magnetic trap. The gravity pulls the atoms down in the bottom of the dressed trap and is responsible for pendulum oscillations of the trapped atomic cloud. This paper presents the characteristics of this trap loaded with very cold atoms.