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arXiv:2512.23874

Investigation of the benefits and disadvantages of using double-pair anti-Helmholtz coils in BEC-producing MOT setups and optimizing their design

Şenol Tarhan, Gabriel Goetten de Lima

physics.atom-phquant-phSubmitted Dec 29, 2025• Announced Dec 31, 2025• 0 citations
arXivHTMLPDF

Abstract

This work has investigated the Magneto-Optical Trap (MOT) system used to produce Bose-Einstein Condensate (BEC). A primary challenge addressed in this study concerns the geometric limitations of traditional single-pair anti-Helmholtz coil configurations, where the magnetic field peaks occur outside the accessible inter-coil region. To overcome this limitation, we have explored the use of double-pair anti-Helmholtz coil configurations that create well-shaped magnetic field potentials centered at the experimentally accessible $z=0$ location. This investigation encompasses the three sequential processes of atom cooling: cooling in a linear external magnetic field through Doppler cooling, cooling in a well-shaped magnetic field through trapping, and evaporative cooling of atoms to achieve sub-microkelvin temperatures. Through theoretical analysis and numerical simulation, we have determined optimal geometric parameters for the coil configuration and operational parameters including laser detuning, saturation intensity, and initial atom populations for ${}^{87}\text{Rb}$ BEC production. The results indicate that with the optimized configuration, the system can achieve final temperatures of approximately $T_f \sim 60\,\mathrm{nK}$ and produce condensate populations of $\sim 10^5$ atoms with a mean density of $n_0 = 4.9 \times 10^{15}\,\mathrm{m}^{-3}$, providing systematic design guidance for experimental BEC systems

Comments
5 figures (4 in the main text, 1 in Appendix C)

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This work has investigated the Magneto-Optical Trap (MOT) system used to produce Bose-Einstein Condensate (BEC). A primary challenge addressed in this study concerns the geometric limitations of traditional single-pair anti-Helmholtz coil configurations, where the magnetic field peaks occur outside the accessible inter-coil region. To overcome this limitation, we have explored the use of double-pair anti-Helmholtz coil configurations that create well-shaped magnetic field potentials centered at the experimentally accessible z=0z=0z=0 location. This investigation encompasses the three sequential processes of atom cooling: cooling in a linear external magnetic field through Doppler cooling, cooling in a well-shaped magnetic field through trapping, and evaporative cooling of atoms to achieve sub-microkelvin temperatures. Through theoretical analysis and numerical simulation, we have determined optimal geometric parameters for the coil configuration and operational parameters including laser detuning, saturation intensity, and initial atom populations for 87Rb{}^{87}\text{Rb}87Rb BEC production. The results indicate that with the optimized configuration, the system can achieve final temperatures of approximately Tf∼60 nKT_f \sim 60\,\mathrm{nK}Tf​∼60nK and produce condensate populations of ∼105\sim 10^5∼105 atoms with a mean density of n0=4.9×1015 m−3n_0 = 4.9 \times 10^{15}\,\mathrm{m}^{-3}n0​=4.9×1015m−3, providing systematic design guidance for experimental BEC systems
We demonstrate a new magneto-optical trap (MOT) configuration using a simple pair of crossed wires rotated at 45 deg and an appropriate bias field to generate a MOT of >10^8 atoms. The same pair of wires, with slightly adjusted control parameters, is then used to magnetically trap the atoms and cool them via forced evaporative cooling into a Bose-Einstein condensate (BEC) with >10^4 atoms. We present the theoretical framework for generating a quadrupole field using a pair of crossed wires with arbitrary rotation angle, along with the atom chip design and fabrication. Finally, we describe the experimental protocols required for BEC production using only a single crossed-wire atom chip.
In this paper, we have developed a combined magnetic field system to explore an alternative technical route for the generation of Bose–Einstein condensates containing numerous atoms on an atom chip. The system is characterized by the fact that the quadrupole magnetic field required by the magneto-optic trap is generated by U-shaped current-carrying wires combined with bias magnetic fields, whereas the quadrupole magnetic field adopted for the magnetic trap is generated by anti-Helmholtz coils. By fine-tuning the bias magnetic fields, the collection of atoms in the mirror MOT and the loading of the quadrupole magnetic trap can be optimized. The initial number of [Formula: see text]Rb atoms in the magnetic trap is approximately [Formula: see text], and the lifetime of the atoms is over 30 s. This scheme can facilitate the chip-surface design and is suitable for the precise manipulation of Bose–Einstein condensates near the chip surface.
A rapid atomic beam of rubidium (87Rb) is produced by two-dimensional magneto-optical trap (2D MOT), and then trapped by three-dimensional magneto-optical trap (3D MOT) with high vacuum for further cooling. After a process of optical molasses cooling, atoms are reloaded into a magnetic trap, where radio frequency (RF) evaporation cooling is implemented. The precooled atoms in the magnetic trap are then transferred into a far detuning optical dipole trap, where Bose-Einstein condensate (BEC) appears by further evaporation cooling. The 3D MOT is loaded to its maximum within 25 s and then BEC is prepared in 16 s. Due to the linear intensity of magnetic trap, the frequency can be scanned fast in the RF evaporation cooling process. In our experiment, the frequency scans from 39 MHz to 15 MHz in 6 s and then scans to 2 MHz in 5 s. The number of atoms in 3D MOT is about 11010, and there are 5105 atoms in the BEC after a succession of cooling processes. To optimize the performances of 2D MOT, a special light path is constructed. And prisms with high reflectivity are used to reduce the imbalance between opposite propagating cooling +beams. Furthermore, quarter-wave plates are used to keep the polarization state of the cooling beam when reflected by prisms or mirrors. The atoms are cooled to a temperature about 15 K in the magnetic trap by RF evaporation. In such a low temperature, the loss of magnetic trap (Majorana loss) will prevent the atoms from reaching a high density, and the atoms cannot be cooled further. To reduce the loss rate of the magnetic trap, the far blue detuning light (532 nm, 18 W) is added to plug the zero point of the magnetic trap. In the optically plugged magnetic trap, atoms with high density are cooled down enough, which gives a good start for the loading of optical dipole trap.
The Bose-Einstein condensate (BEC) is created in a magnetic trap in the Quadrupole-Ioffe configuration (QUIC). This kind of trap combines an anti-Helmholtz quadrupole field with an offset field produced by a single coil perpendicular to the quadrupole field axis to suppress Majorana transitions. In the quadrupole trap evaporative cooling is performed by using radio frequency, reaching the phase transition to a BEC in the QUIC trap. By using Time of Flight (TOF) technique, the expansion velocity is measured with and which lead to temperature of and It is roughly around the recoil temperature.
This thesis describes the design, construction and optimisation of a new apparatus to produce Bose-Einstein condensates (BECs) of 87Rb atoms. The main aim in building this system was to include a high resolution imaging system capable of resolving single atoms. Optical access for the imaging system was created by including a stage of atom transport in which the atoms are magnetically transferred ~50 cm from a magneto-optical trap (MOT), where they are initially collected, to a glass science cell where experiments are carried out and imaging takes place. Two magnetic transport schemes have been demonstrated, based on approaches first used in other laboratories. First, a scheme in which the atoms are transferred in a moving pair of magnetic trapping coils. Second, a hybrid scheme where the atoms are translated part of the distance in the moving coils, and the rest of the way by switching the current in a chain of fixed coils. This second scheme was designed to allow optical access for a high numerical aperture microscope objective to be placed immediately next to the science cell for high resolution imaging.The atoms were first collected in a large pyramid MOT which can be loaded with 3 × 10^9 atoms in a time of 20 s. Around half of these atoms – those in the |F = 1, mF = −1> magnetic substate – were then magnetically trapped prior to transport. The typical fraction of the trapped atoms transferred to the science cell was ~30% and ~18% for the moving coils and hybrid schemes respectively.Evaporative cooling was carried out on the atom cloud following transport with the moving coils and loading into a time-orbiting potential trap. The optimised cooling sequence lasted for 28 s and consistently produced a pure condensate with 5 × 10^5 atoms. A BEC has also been produced by evaporative cooling following hybrid transport. The next experimental steps will be to optimise the hybrid transfer approach further and install the high resolution imaging system.The system is well-placed to continue an ongoing series of experiments in which ultracold atoms are trapped in RF-dressed potentials. These potentials will be used to study low-dimensional quantum gases as well as in experiments where small atom number BECs are rapidly rotated to enter the fractional quantum Hall regime.
ENGLISH ABSTRACT: A Magneto Optical Trap (MOT) is a configuration formed by three orthogonal pairs of counterpropagating circularly polarized laser beams and a magnetic field gradient. A MOT is used to cool, capture and trap large numbers of atoms in vacuum at very low temperature in K range. In this thesis the development of an experimental setup for realising a MOT of 87Rb atoms is presented. The atomic structure of Rb and the theoretical background of laser cooling and magneto optical trapping was reviewed. The influence of rubidium background pressure in the vacuum system, the laser beam size and the power and frequency on the number of the trapped atoms were studied in literature. The trapping and repumping lasers were characterised experimentally. Six circularly polarised trapping beams with equal power were formed and properly aligned to intersect at the center of the trapping cell. Two optical setups were designed and exploited to investigate and optimise the trapping beam polarisation. The repumping laser beam was successfully aligned and colinearly combined into all the trapping beams. Three different experimental setups for saturated absorption spectroscopy were developed. Saturated absorption spectra showing the hyperfine structure of both 85Rb and 87Rb isotopes were measured and are discussed. Using two saturated absorption spectroscopy setups, the frequencies of both lasers were successfully locked to the trapping and repumping transitions of 87Rb respectively. A rectangular trapping cell was designed and attached to the vacuum system. A pressure of about 10­¯7 mbar was achieved. The magnetic field coils were characterised and affixed on both sides of the cell in an anti-Helmholtz configuration. Setups for imaging and quantification of the 87Rb atoms in the MOT were designed. Finally, the procedures for demonstrating a MOT are presented. In conclusion, the current status of the project is reported, with recommendations for the future work.