Three wires ring magnetic guide based on Archimedean spirals
Authors: Ling Yun-Long , Wang Chuan , Zhang Hai-Chao ,   Key Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China,   University of Chinese Academy of Sciences, Beijing 100049, China
Published: December 2020

<sec>We propose a scheme to create a ring magnetic guide based on Archimedean spirals. This scheme is significant to obtaining large circle area for atom interference and the realization of guided atom-interferometer gyroscopes. Then the scheme can be used to realize an inertial sensing system which is independent of the GPS system.</sec><sec>The wires structure with <inline-formula><tex-math id="M2">\begin{document}$ {\text{π}}/3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M2.png"/></alternatives></inline-formula> rotational symmetry is composed of three wires. Each wire is centrosymmetric and consists of a pair of Archimedean spirals connected by two arcs. Consequently, the leading wire ends of the layout can be arranged separately in the different place of the layout plane. If the leading wire ends are put together somewhere, the closed ring guide cannot form and a gap appears in the guide due to the concentrated distribution of the leading wire ends. Since the leading wire ends distribute in the different location with <inline-formula><tex-math id="M3">\begin{document}$ {\text{π}}/3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M3.png"/></alternatives></inline-formula> rotational symmetry in our scheme, when direct currents are applied, the closed ring trap can be generated ingeniously.</sec><sec>We calculate and analyze the magnetic field distribution generated by our structure after loading currents in the cylindrical coordinates system. To get higher sensitivity compared to GPS and make the ring trap locate in a proper height above the chip surface, we set the initial radius of Archimedean spirals <inline-formula><tex-math id="M4">\begin{document}$ a=5\ {\rm{mm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M4.png"/></alternatives></inline-formula> and the distance between neighboring spirals <inline-formula><tex-math id="M5">\begin{document}$ d=0.1\ {\rm{mm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M5.png"/></alternatives></inline-formula>. When three wires carry direct currents in an opposite current-phase-difference between the adjacent wires, a closed ring magnetic guide indeed appears but with six zero magnetic field points along the guide center. Because of the variation of the current density along <i>r</i> direction in Archimedean spirals, the magnetic field of the guide center is not zero at most angle. However, the variation cannot avoid the existence of zero points and the distribution of the zero points is determined by the rotational symmetry of the wires structure.</sec><sec>Since atoms near the zero points of the magnetic field would be lost from the trap, the zero points must be removed from the center of the ring guide. Based on the time-orbiting-potential principle (TOP), we add an ac current modulation on the direct currents above to eliminate the influence of the zero points of the guide center. We give the ac current expressions and discuss the effects of currents parameters on the ring guide. The current phase reflects how the currents change in three wires. The modulation depth determines the effect of the modulation: if the modulation depth is too high, the trap may disappear; if the modulation depth is too low, the effect is minimal. The modulation frequency reflects the change rate of the modulation magnetic field.</sec><sec>To ensure the smoothness of the guide along angular direction and adiabatic following of the magnetic field, we set the modulation depth <inline-formula><tex-math id="M6">\begin{document}$ I_j/I_i=0.1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M6.png"/></alternatives></inline-formula>, the current-phase <inline-formula><tex-math id="M7">\begin{document}$ \phi=2{\text{π}}/3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M7.png"/></alternatives></inline-formula> and the modulation frequency <inline-formula><tex-math id="M8">\begin{document}$ \omega_b=2{\text{π}}\times10\ {\rm{kHz}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M8.png"/></alternatives></inline-formula>. The numerical calculation results indicate that ac current modulation can change the magnetic field intensity of the guide center and smooth the variance of the magnetic field intensity of the guide along angular direction. We take the cross section of the guide with <inline-formula><tex-math id="M9">\begin{document}$ \theta={\text{π}}/2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M9.png"/></alternatives></inline-formula>, for example. The minimum of the instantaneous magnetic field rotates and our structure has formed a TOP trap in both the <i>r</i> and <i>z</i> directions. In angular direction, the magnetic field intensity of the guide center changes near <inline-formula><tex-math id="M10">\begin{document}$ 0.25\ {\rm{mT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M10.png"/></alternatives></inline-formula>. The difference between the maximum and the minimum is <inline-formula><tex-math id="M11">\begin{document}$ \Delta\,B\approx0.007\ {\rm{mT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M11.png"/></alternatives></inline-formula> which is small enough compared to applying direct current only.</sec><sec>Therefore, based on the Archimedean spirals and ac current modulation, we obtain an enclosed and smooth ring magnetic guide without zero magnetic fields along the guide center for neutral atoms. The location of the guide center also changes along the angle direction. The amplitudes of variation along <i>r</i> and <i>z</i> directions are <inline-formula><tex-math id="M12">\begin{document}$ \Delta r=0.015\ {\rm{mm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M12.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M13">\begin{document}$ \Delta z=0.005\ {\rm{mm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M13.png"/></alternatives></inline-formula>, which are <inline-formula><tex-math id="M14">\begin{document}$ \Delta r/l\approx0.3\,\%$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M14.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M15">\begin{document}$ \Delta z/l\approx0.1\,\%$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M15.png"/></alternatives></inline-formula> compared with <inline-formula><tex-math id="M16">\begin{document}$ l\approx2{\text{π}} a/6\approx5.236\ {\rm{mm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200284_M16.png"/></alternatives></inline-formula>.</sec><sec>Compared to other schemes, our structure can be etched on an atom chip and is easily to apply modulation currents, which is simple and stable to form a ring magnetic guide. This scheme can be used to realize a compact, low power and stable inertial sensor based on atom-chip gyroscope device.</sec>