^{1,a)}and A. S. Sanz

^{2}

### Abstract

Magnetic trapping is a cornerstone of modern ultracold physics and its applications, including quantum information processing, quantum metrology, quantum optics, and high-resolution spectroscopy. Here, a comprehensive analysis and discussion of the basic physics behind the most commonly used magnetic traps used in Bose-Einstein condensation is presented. This analysis includes the quadrupole trap, the time-averaged orbiting potential trap, and the Ioffe-Pritchard trap. The trapping conditions and efficiency of these devices can be determined from simple derivations based on classical electromagnetism, even though they operate on quantum objects.

The authors would like to thank two anonymous referees for their valuable remarks. Partial support from the IFRAF (France) and the Ministerio de Economía y Competitividad (Spain) under Project Nos. FIS2010-22082 and FIS2011-29596-C02-01 is acknowledged. A. S. Sanz would also like to thank the Ministerio de Economía y Competitividad for a “Ramón y Cajal” Research Grant and the University College London for its kind hospitality during the elaboration of this work.

I. INTRODUCTION

II. ZEEMAN EFFECT AND EARNSHAW'S THEOREM

III. TYPES OF MAGNETIC TRAPS

A. Quadrupole trap

B. TOP trap

C. Ioffe-Pritchard trap

IV. EFFICIENCY COMPARISONS

V. CONCLUDING REMARKS

### Key Topics

- Magnetic fields
- 35.0
- Quadrupoles
- 16.0
- Atom trapping
- 12.0
- Zeeman effect
- 8.0
- Field theory
- 7.0

##### H05H1/02

## Figures

Zeeman splitting of the molecular energy levels (in temperature units) as a function of the magnetic field intensity. High-field and low-field seeker states are denoted, respectively, by solid lines (red) and dashed lines (blue); gray dotted lines illustrate the appearance of Zeeman splitting in higher energy levels. These results have been obtained using realistic values in the simulation: ^{24} (rotational constant), (spin-rotation interaction), and (spin-spin coupling).

Zeeman splitting of the molecular energy levels (in temperature units) as a function of the magnetic field intensity. High-field and low-field seeker states are denoted, respectively, by solid lines (red) and dashed lines (blue); gray dotted lines illustrate the appearance of Zeeman splitting in higher energy levels. These results have been obtained using realistic values in the simulation: ^{24} (rotational constant), (spin-rotation interaction), and (spin-spin coupling).

Magnetic field configurations for a quadrupole trap (a) and an Ioffe-Pritchard trap (b). The arrows indicate the directions of the currents flowing around the coils (tori) and through the straight wires [gray bars along the z-direction in (b)].

Magnetic field configurations for a quadrupole trap (a) and an Ioffe-Pritchard trap (b). The arrows indicate the directions of the currents flowing around the coils (tori) and through the straight wires [gray bars along the z-direction in (b)].

Arrow map of the magnetic field of Eq. (16) , generated by the four parallel wires of Fig. 2(b) . The lengths of the arrows indicate the intensity of field, while the direction of each current is indicated by a dot (outward) or a cross (inward). The length of each arrow is proportional to the field intensity at the point where it is placed. The field in the neighborhood of the origin (0, 0) is described to a good approximation by Eq. (18) , obtained from the assumption .

Arrow map of the magnetic field of Eq. (16) , generated by the four parallel wires of Fig. 2(b) . The lengths of the arrows indicate the intensity of field, while the direction of each current is indicated by a dot (outward) or a cross (inward). The length of each arrow is proportional to the field intensity at the point where it is placed. The field in the neighborhood of the origin (0, 0) is described to a good approximation by Eq. (18) , obtained from the assumption .

Magnitude of the magnetic field described by Eq. (21) . This is the field generated by the four parallel wires of an Ioffe-Pritchard trap [see Fig. 2(b) ] along the y = 0 line for three different values of the homogeneous field: (lower dotted line), (middle dashed line), and (upper solid line). The parameters considered are typical values: and d = 0.01 m. The horizontal line in each case indicates the limit where the magnetic field is 10 mT above the corresponding minimum.

Magnitude of the magnetic field described by Eq. (21) . This is the field generated by the four parallel wires of an Ioffe-Pritchard trap [see Fig. 2(b) ] along the y = 0 line for three different values of the homogeneous field: (lower dotted line), (middle dashed line), and (upper solid line). The parameters considered are typical values: and d = 0.01 m. The horizontal line in each case indicates the limit where the magnetic field is 10 mT above the corresponding minimum.

(a) Magnitude of the magnetic field along the x-direction (for y = z = 0) for a quadrupole trap (dotted line), a TOP trap (dashed line), and an Ioffe-Pritchard trap (solid line). (b) Same as in (a) but along the z-direction (for x = y = 0). (c) Effective particle density associated with these traps as a function of the temperature (the same convention of line types as in (a)and (b) has been followed). This density has been obtained as the inverse of the trap effective volume obtained from Eq. (29) . The numerical parameters for the three panels are: Quadrupole trap: a = 0.01 m, b = 0.0125 m, and ; TOP trap: a = 0.01 m, b = 0.0125 m, , and ; Ioffe-Pritchard trap: a = 0.01 m, b = 0.0125 m, d = 0.01 m, , and .

(a) Magnitude of the magnetic field along the x-direction (for y = z = 0) for a quadrupole trap (dotted line), a TOP trap (dashed line), and an Ioffe-Pritchard trap (solid line). (b) Same as in (a) but along the z-direction (for x = y = 0). (c) Effective particle density associated with these traps as a function of the temperature (the same convention of line types as in (a)and (b) has been followed). This density has been obtained as the inverse of the trap effective volume obtained from Eq. (29) . The numerical parameters for the three panels are: Quadrupole trap: a = 0.01 m, b = 0.0125 m, and ; TOP trap: a = 0.01 m, b = 0.0125 m, , and ; Ioffe-Pritchard trap: a = 0.01 m, b = 0.0125 m, d = 0.01 m, , and .

Article metrics loading...

Full text loading...

Commenting has been disabled for this content