We describe an analytical design method of shielding-coupled uniform magnetic coils for miniature quantum devices. The theoretical and simulation results point out that the 99% range along the symmetrical axis and the 50% range along the radius of the proposed m = 3 coils are uniform, and more important is that both the uniformity and the uniform region for these kinds of coils can be systematically improved only by adding more loops at specific places obtained from our analytical formula. A relevant experiment demonstrates the feasibility of this method and realizes the m = 3 coils with the inhomogeneity below 2.6 × 10−3 along nearly the whole symmetrical axis. In addition, a practical technology to remove the influence of the shielding’s nonideal gaps and openings is proposed and realized. All of these results are crucial for the miniaturization and high performance of quantum devices.
We describe an analytical design method of shielding-coupled uniform magnetic coils for miniature quantum devices. The theoretical and simulation results point out that the 99% range along the symmetrical axis and the 50% range along the radius of the proposed m = 3 coils are uniform, and more important is that both the uniformity and the uniform region for these kinds of coils can be systematically improved only by adding more loops at specific places obtained from our analytical formula. A relevant experiment demonstrates the feasibility of this method and realizes the m = 3 coils with the inhomogeneity below 2.6 × 10−3 along nearly the whole symmetrical axis. In addition, a practical technology to remove the influence of the shielding’s nonideal gaps and openings is proposed and realized. All of these results are crucial for the miniaturization and high performance of quantum devices.
The accurate control of magnetic fields is a cornerstone of multiple emerging quantum technologies. These technologies often require passive high permeability magnetic shielding and internal active field-generating coils to create their own bespoke magnetic field landscape. However, magnetic fields generated by coils are distorted by high permeability shielding, preventing the accurate and efficient generation of the desired field environment. Here, we design a cylindrical four-layer magnetic shield with an interior hybrid active-passive coil system that is explicitly optimised to include the electromagnetic coupling between the active and passive components. We use a combination of analytical methods and numerical simulations to determine the shield parameters - geometry, thickness, and access hole positions - to maximise the passive shielding efficiency and minimise the shield-induced Johnson noise and weight. Then, we apply an analytical formulation of the magnetic field, which accounts for the interaction with the magnetic shield, to design nine orthogonal hybrid active-passive field-generating coils inside the shield. The coils will be manufactured on thin low-via flex-PCBs near the shield's interior surface and generate three uniform fields and six gradient fields that deviate by less than 0.4% and 2%, respectively, over an internal cylindrical region extending over half the diameter and length of the innermost shield layer. These hybrid active-passive coils can accurately remove deviations in the background field or generate various complex magnetic field landscapes. Consequently, the hybrid shield provides an ideal platform for miniaturising and commercialising quantum technologies that require precisely-controlled magnetic fields within a low-noise environment.
The miniaturization of quantum sensors is a popular trend for the development of quantum technology. One of the key components of these sensors is a coil which is used for spin modulation and manipulation. The bi-planar coils have the advantage of producing three-dimensional magnetic fields with only two planes of current confinement, whereas the traditional Helmholtz coils require three-dimensional current distribution. Thus, the bi-planar coils are compatible with the current micro-fabrication process and are quite suitable for the compact design of the chip-scale atomic devices that require stable or modulated magnetic fields. This paper presents a design of a miniature bi-planar coil. Both the magnetic fields produced by the coils and their inhomogeneities were designed theoretically. The magnetic field gradient is a crucial parameter for the coils, especially for generating magnetic fields in very small areas. We used a NMR (Nuclear Magnetic Resonance) method based on the relaxation of 131Xe nuclear spins to measure the magnetic field gradient in situ. This is the first time that the field inhomogeneities of the field of such small bi-planar coils have been measured. Our results indicate that the designed gradient caused error is 0.08 for the By and the Bx coils, and the measured gradient caused error using the nuclear spin relaxation method is 0.09±0.02, suggesting that our method is suitable for measuring gradients. Due to the poor sensitivity of our magnetometer under a large Bz bias field, we could not measure the Bz magnetic field gradient. Our method also helps to improve the gradients of the miniature bi-planar coil design, which is critical for chip-scale atomic devices.
Abstract Quantum sensors based on cold atoms are being developed which produce measurements of unprecedented accuracy. Due to shifts in atomic energy levels, quantum sensors often have stringent requirements on their internal magnetic field environment. Typically, background magnetic fields are attenuated using high permeability magnetic shielding, with the cancelling of residual and introduction of quantisation fields implemented with coils inside the shield. The high permeability shield, however, distorts all magnetic fields, including those generated inside the sensor. Here, we demonstrate a solution by designing multiple coils overlaid on a 3D-printed former to generate three uniform and three constant linear gradient magnetic fields inside the capped cylindrical magnetic shield of a cold atom interferometer. The fields are characterised in-situ and match their desired forms to high accuracy. For example, the uniform transverse field, Bx, deviates by less than 0.2% over more than 40% of the length of the shield. We also map the field directly using the cold atoms and investigate the potential of the coil system to reduce bias from the quadratic Zeeman effect. This coil design technology enables targeted field compensation over large spatial volumes and has the potential to reduce systematic shifts and noise in numerous cold atom systems.
Recently, there is a growing interest in non-uniform coupled SQUID devices in the science community. Similar to how antenna array technology has moved from uniform arrays to non-uniform, sparsely populated arrays, the traditional uniform SQUID arrays evolves to an unconventional structure making these mesoscopic quantum devices (for RF reception) a feasible concept. The focus of this work covers theoretical and numerical computations which exploits well-designed coupling schemes to modeling the dynamics of the device where the behavior of the non-periodic voltage response related to the external flux exhibits an anti-peak which is present only around the zero applied magnetic field. It is know that many nonlinear dynamical systems are highly sensitive to small external perturbations, especially when they are near the onset of a bifurcation. Exploring parameter variations, such as; inductive coupling between neighboring elements, unconventional grating and fabrication parameters may lead to a significant performance enhancement. There are theoretical indications that variations in coupling could provide very high dynamic range. Application of these devices with the ability to detect and amplify will result in a new generation of electrically small antennas.
To avoid the broadening of Zeeman resonances of the vector atomic magnetometer working in an unshielded environment, the rapid and accurate magnetic compensation is necessary. A three dimensional mini spherical compensating system is presented, which can be used together with a chip-scale atomic magnetometer to realize an ultra-high precision field measurement. Based on the field gradient method, parameters are optimized to obtain a uniformity of 10-3over the region of one half radius with a good tolerance on dimensional variations. A prototype applied in the single laser beam scheme has been built and the experimental results demonstrate the validity of the design.
The homogeneity of the microwave magnetic field is essential in controlling a large volume of ensemble spins, for example, in the case of sensitive magnetometry with nitrogen-vacancy (NV) centers in diamond. This is particularly important for pulsed measurement, where the fidelity of control pulses plays a crucial role in its sensitivity. So far, several magnetic field-forming systems have been proposed, but no detailed comparison has been made. Here, we numerically study the homogeneity of five different systems, including a planar antenna, a dielectric resonator, a cylindrical inductor, a barrel-shaped coil, and a nested barrel-shaped coil. The results of the simulation allowed us to optimize the design parameters of the barrel-shaped field-forming system, which led to significantly improved magnetic field uniformity. To measure this effect, we experimentally compared the homogeneity of a field-forming system having a barrel shape with that of a planar field-forming system by measuring Rabi oscillations of an ensemble of NV centers with them. Significant improvements in inhomogeneity were confirmed in the barrel-shaped coil.