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arXiv:1710.10092 · Scientific Reports

Hybrid setup for stable magnetic fields enabling robust quantum control

Frederick Hakelberg, Philip Kiefer, Matthias Wittemer, Tobias Schaetz, Ulrich Warring

Published Mar 7, 2018• 7 citations
arXivHTMLPDF

Abstract

Abstract Well controlled and highly stable magnetic fields are desired for a wide range of applications in physical research, including quantum metrology, sensing, information processing, and simulation. Here we introduce a low-cost hybrid assembly of rare-earth magnets and magnetic field coils to generate a field strength of $$\simeq $$ ≃ 10.9 mT with a calculated spatial variation of less than 10−6 within a diameter of spherical volume of 150 μm. We characterise its tuneability and stability performance using a single Mg+ atom confined in a radio-frequency surface-electrode trap under ultra-high vacuum conditions. The strength of the field can be tuned with a relative precision of ≤2 × 10−5 and we find a passive temporal stability of our setup of better than 1.0 × 10−4 over the course of one hour. Slow drifts on time scales of a few minutes are actively stabilised by adjusting electric currents in the magnetic field coils. In this way, we observe coherence times of electronic superposition states of greater than six seconds using a first-order field insensitive (clock) transition. In a first application, we demonstrate sensing of magnetic fields with amplitudes of ≥0.2 μT oscillating at $$\simeq $$ ≃ 2π × 60 MHz. Our approach can be implemented in compact and robust applications with strict power and load requirements.

DOI
10.1038/s41598-018-22671-5

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Abstract Well controlled and highly stable magnetic fields are desired for a wide range of applications in physical research, including quantum metrology, sensing, information processing, and simulation. Here we introduce a low-cost hybrid assembly of rare-earth magnets and magnetic field coils to generate a field strength of ≃\simeq ≃ ≃ 10.9 mT with a calculated spatial variation of less than 10−6 within a diameter of spherical volume of 150 μm. We characterise its tuneability and stability performance using a single Mg+ atom confined in a radio-frequency surface-electrode trap under ultra-high vacuum conditions. The strength of the field can be tuned with a relative precision of ≤2 × 10−5 and we find a passive temporal stability of our setup of better than 1.0 × 10−4 over the course of one hour. Slow drifts on time scales of a few minutes are actively stabilised by adjusting electric currents in the magnetic field coils. In this way, we observe coherence times of electronic superposition states of greater than six seconds using a first-order field insensitive (clock) transition. In a first application, we demonstrate sensing of magnetic fields with amplitudes of ≥0.2 μT oscillating at ≃\simeq ≃ ≃ 2π × 60 MHz. Our approach can be implemented in compact and robust applications with strict power and load requirements.
Cold atom experiments usually need a controllable and low-noise bias magnetic field to provide a quantization axis. Most labs need home-made stabilization of the field according to the actual setup, as commercially available power supply cannot directly satisfy their requirements. Here, by measuring the field fluctuations and active feedback modulating current supply of the applied magnetic field, we successfully demonstrate a field of 10.58 G with a stability to the level of 2.8 × 10−7 in a duration of 5 min. The root mean square noise is reduced to 0.05 mG, compared to the noise of 1.3 mG without stabilization. The coherence time of the magnetic-field sensitive transition between the rubidium ground states F=1,mF=−1 and 1,0, as measured by Rabi oscillation, is extended to 19.2 ms from the unstabilized value of 1.3 ms. This result is long enough for most experiments on quantum simulation and precision measurement. As our system has no passive magnetic shielding and additional compensation coils, it is highly simple and compact to provide the stable magnetic field and would be adapted to various applications with cold atoms.
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Magnetic field fluctuations are a dominant source of dephasing in Zeeman-encoded trapped-ion qubits, limiting coherence time and the fidelity of quantum operations, particularly in modular quantum networks where phase stability must be maintained across spatially separated nodes. In this work, we design and characterize an active magnetic field stabilization system based on real-time feedback using a high-resolution magnetometer, a digitally controlled Red Pitaya platform, and a coil actuator with a measured gain of ∼ −5.37 G/V. Spectral measurements of the laboratory environment reveal dominant 60 Hz magnetic noise with amplitudes on the order of 400 µG and significant harmonic content. The system operates at a sampling rate of ∼ 605 Hz with an actuator bandwidth of ∼ 85 Hz, enabling targeted suppression of these low-frequency components. Given a Zeeman sensitivity of ∼ 2.8 MHz/G, such fluctuations correspond to kilohertz-scale frequency noise, which rapidly dephases qubit superpositions. Suppression of these fluctuations is therefore expected to reduce phase noise and extend coherence times, with first-order estimates suggesting improvement from the submillisecond regime into the few-millisecond regime for Zeeman-sensitive qubits. These results demonstrate that active magnetic-field stabilization is a practical approach to reducing environmental dephasing and improving the performance of trapped-ion quantum network experiments.
Cold atoms form the backbone of many quantum technology applications, including quantum computation, sensing, and networking. These experiments require a robust cold atom source, precise control of beam parameters, and large optical access. We demonstrate a compact cesium magneto-optical trap (MOT) directly loaded from background vapor, with a footprint of 34 × 56 cm2. The quadrupole and compensation coils are mounted on additively manufactured components, eliminating the need for water cooling and minimizing eddy currents, which enables fast magnetic field switching with a measured settling time of 240 μs. Finite element analysis confirms the mechanical robustness and thermal stability of the coil mounts. The MOT achieves 5 × 106 atoms at a density of 109 cm-3, with a temperature of 76 ± 2 μK, demonstrating a reliable and compact platform suitable for quantum technology experiments.
This thesis describes an ion trap magnetometer, in which experimental hardware and theory for trapped ion magnetometry has been developed and demonstrated. Quantum magnetometry has been a fast expanding field in recent years due to the plethora of military, medical and security applications. The current quantum magnetometer literature has shown great improvements on the standard magnetometer success metrics such as sensitivity, spacial resolution, frequency tuneability, noise shielding and vector field resolution. Ion trap magnetometry could potentially boast several advantages over some of the better established methods such as, nano-meter spatial resolution, broadband tuneability over radio-frequency (RF) and microwave frequencies, and magnetic field noise shielding and sensitivity improvements through dynamic decoupling methods; all in room temperature environments. The experimental setup discussed uses a micro-fabricated Paul trap for ion confinement due to the scalability of this technology. The method for sensing that was demonstrated utilises long-wavelength radiation dressed states to extend the coherence time of a single 171Yb+ ion beyond the bare states and to allow for a high level of frequency tuneability. The coherence times measured were T2 = 0:645 s for RF field sensing at 15.616 MHz and T2 = 1.153 s for microwave field sensing at 12.658466 GHz. Sensitivities of SB = 125.857 ± 26.155 pT/ vHz for RF magnetic fields and SB = 102.054 ± 11.046 pT/ vHz for microwave magnetic fields were achieved experimentally. A novel micro-fabricated Paul trap for trapping multiple ion clusters was developed to improve sensitivity values by increasing the total number of trapped ions. The design confines ions over a two-dimensional surface spanning 0.65 x 1.00 mm which would also allow for magnetic field gradient measurements. Efforts have been made to miniaturise certain experimental hardware to further the development of portable trapped ion experiments. For this, a miniaturised RF resonator that could be used for radial confinement of ions within Paul traps has been developed. At the current stage of development it is capable of applying a peak RF voltage of 114.9 V with a Q value of 70 at a resonant frequency of O/2p = 12.65 MHz.
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.