Reduction of characteristic RL time for fast, efficient magnetic levitation Yuqing Li, Guosheng Feng, Xiaofeng Wang, Jizhou Wu, Jie Ma, Liantuan Xiao, and Suotang Jia
Citation: AIP Advances 7, 095016 (2017); doi: 10.1063/1.4989504 View online: http://dx.doi.org/10.1063/1.4989504 View Table of Contents: http://aip.scitation.org/toc/adv/7/9 Published by the American Institute of Physics
AIP ADVANCES 7, 095016 (2017)
Reduction of characteristic RL time for fast, efficient magnetic levitation Yuqing Li,1,2 Guosheng Feng,1 Xiaofeng Wang,1 Jizhou Wu,1,2 Jie Ma,1,2,a Liantuan Xiao,1,2 and Suotang Jia1,2 1 State
Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, College of Physics and Electronics Engineering, Shanxi University, Taiyuan 030006, P. R. China 2 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, P. R. China (Received 9 June 2017; accepted 11 September 2017; published online 19 September 2017)
We demonstrate the reduction of characteristic time in resistor-inductor (RL) circuit for fast, efficient magnetic levitation according to Kirchhoff’s circuit laws. The loading time is reduced by a factor of ∼4 when a high-power resistor is added in series with the coils. By using the controllable output voltage of power supply and voltage of feedback circuit, the loading time is further reduced by ∼ 3 times. The overshoot loading in advance of the scheduled magnetic field gradient is equivalent to continuously adding a resistor without heating. The magnetic field gradient with the reduced loading time is used to form the upward magnetic force against to the gravity of the cooled Cs atoms, and we obtain an effectively levitated loading of the Cs atoms to a crossed optical dipole trap. © 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4989504] The Anti-Helmholtz coils refers to the geometrical arrangement of two identical, parallel, circular, coaxial, reversely current-carrying coils whose midplane separation is equal to their mean radius. Anti-Helmholtz coils are similar to Helmholtz coils1,2 except for the current with an opposite direction in the coils. Anti-Helmholtz coils are commonly used to produce magnetic field gradients needed for many fundamental and applied sciences.3–7 Magnetic field gradients have been widely used to form effective magnetic trapping potentials for confining and capturing many kinds of microscopic particles, such as magnetic traps widely used in laser cooling and trapping of neutral atoms.8–11 For the microscopic particles with intrinsic magnetic moments, magnetic field gradients in the vertical direction are of particular interest for the magnetically levitated effect12–15 due to its wide applications on both the compensation for the gravities of these microscopic particles and the researches for out-of-equilibrium physics in the underdamped regime and nonlinear dynamics. Most Anti-Helmholtz coils are usually constructed out of copper wire or refrigeration tubing wound into cylinders. Well-developed feedback techniques enable the magnetic field gradient to be controlled with a high precision by regulating the current in the coils. For a large magnetic field gradient, the water cooling has been designed to dissipate the electric power produced by the large current in the geometrically symmetric coils.16,17 Nevertheless, the inductor of the coils leads to a delay of the loading time for the current in the coils. The delay of loading time has many drawbacks to both effectively trapping more microscopic particles and quickly levitating against to the gravities. A bipolar current amplification circuit had been employed to obtain a fast switching of magnetic field in a magneto-optic trap.18 In this paper, we present an another efficient method to reduce the loading time of the current in Anti-Helmholtz coils by the combination of adding a high-power resistor with three times as large as the effective resistor of the coils and using an ingeniously designed overshoot loading of magnetic field gradient prior to arriving its scheduled value according to Kirchhoff’s circuit laws. The variation of magnetic field gradient with time in its loading process is measured at three a
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different stages towards to reducing the loading time. The efficiency of magnetically levitated loading of the ultracold Cs atoms into a crossed optical dipole trap (ODT) can be enhanced by reducing the loading time of the current in Anti-Helmholtz coils. A pair of coils in the Anti-Helmholtz configuration is used for the magnetically levitated loading of the ultracold Cs atoms, which are prepared by three-dimensional degenerated Raman sideband cooling,19 into a crossed ODT,20 as shown in Fig. 1. The coils consist of many copper tubes with the outside diameter of 4 mm, and each of the coils has a total of 35 turns. The mean diameter of the coils and their distance are D = 150 mm and d = 80 mm, which is a result of a compromise between the standard Anti-Helmholtz configuration and the geometric construction of the vacuum chamber in the experiment. The resistor of coils is measured to be Rcoil = 0.1 Ω. The water cooling, which allows a high current to flow in the coils for a long time, is applied to the coils by the water flowing in the copper tubes with the inner diameter of 1.5 mm. Thus we can obtain a maximum gradient of 61 G/cm at a current of 60 A. Two field-effect transistors (FETs) in parallel and a high-precision Hall sensor are used to form a feedback circuit for the precision magnetic field gradient. The power supply is set on the controllable voltage output mode and provides the power of the whole circuit. The variation of magnetic field gradient in the center of atomic collection with time is measured by using an additional Hall detector. The control for magnetic field gradient is implemented by accurately manipulating the current in the circuit. The loading time of magnetic field gradient is determined by the characteristic time of the typical resistor-inductor (RL) circuit. A feedback circuit is realized by altering the resistance of FETs in series with the coils for the controllable current with the constant-voltage output of power supply. When the magnetic field gradient is switched on, the PID feedback circuit immediately provides a voltage more than the threshold for the complete conduction of conducting channel in the FETs. At the initial loading stage of the current, the resistance of FETs is reduced to zero as a result of the feedback circuit and so has little effect on the loading time. Figure 2 shows the variation of magnetic field gradient with the loading time, where the characteristic loading time determined by the coils is given as τ = 14.3 ms by fitting the experimental result using Eq. (2). The scheduled magnetic field gradient of ∂B ∂z = 31.3 G/cm is used for the magnetically levitated loading of the cooled atoms into the crossed ODT, where the vertical anti-trapping potential induced by the gravity of atoms is completely canceled by using the magnetic fore µB mF gF ∂B ∂z = mg, and µB is the Bohr magneton, mF = 3 is the atomic sublevel and gF is the Land´e factor. Nevertheless, the Cs atoms have an increasing downward velocity while the magnetic field gradient increases toward to the scheduled value due to the delay of loading time of the current in the Anti-Helmholtz coils. Thus,
FIG. 1. Experimental apparatus. A pair of anti-Helmholtz coils is involved in the circuit including FETs, a Hall sensor, a Hall detector, a high-power resistor and power supply. An oscilloscope is used to detect the current in the circuit by the Hall detector. Two horizontally crossing 1064 nm laser beams at an angle of 900 form a crossed ODT, whose center overlaps at the zero point of the pair of Anti-Helmholtz coils. A pair of Helmholtz coils produces the uniform magnetic field used for the magnetically levitated loading of the crossed ODT.
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FIG. 2. The magnetic field gradient, which is recorded by using the Hall detector, as a function of the loading time for the Anti-Helmholtz coils. The blue trace marks the starting point at which the magnetic field gradient is switched on. The red line is the fitted curve by applying Eq. (2) to the experimental loading curve. The inset is the absorption image of the atoms loaded into the crossed ODT by using the magnetic levitation method.
the efficient reduction of loading time can decrease the heating effect for the cooled atoms in the magnetically levitated loading process, and then enhance the number of atoms loaded into the crossed ODT. Another pair of Helmholtz coils are used to produce a uniform magnetic field to reduce the horizontal anti-trapping potential induced by the introduction of the vertical magnetic field gradient during the loading of the crossed ODT. Affected by the long loading time, the number of atoms is limited to 9.2 × 104 , and the corresponding absorption image is shown in the inset of Fig. 2. In order to reduce the loading time of magnetic field gradient, we analyze the response function of the current in Anti-Helmholtz coils. According to Kirchhoff’s circuit laws, the instantaneous current in a RL circuit is given as di U = Ri + L . (1) dt where U is the voltage of power supply, i is the instantaneous current, and R and L are the resistance and inductance of RL circuit, respectively. When we take the initial current of i(0) = 0, the current at time t can be expressed as U i(t) = (1 − e−t/τ ). (2) R where τ = L/R is the characteristic loading time of the current, and the magnetic field gradient is proportional to the current i(t) in the Anti-Helmholtz coils. Thus, we can reduce the loading time of magnetic field gradient by increasing the resistance in the circuit. A high-power resistor of R = 0.3 Ω is used in series with the Anti-Helmholtz coils, and the characteristic time τ is reduced to 3.55 ms, as shown in Fig. 3. This characteristic time is four times less than that in Fig. 2, and this agrees with that the high-power resistor is as three times large as the resistor of the coils. In the inset of Fig. 3, the number of atoms loaded into the ODT is substantially increased compared to that in Fig. 2. Limited by the power of power supply, we can not reduce the loading time by adding two or more high-power resistors, although the heat from a high-resistance resistor can be dissipated by dividing it into two ones. For the shorter loading time, we design a loading sequence for the output voltage of power supply and the controllable voltage of the feedback circuit whose output voltage is applied to the gate of FETs. Here we set a large value for magnetic field gradient prior to arriving its scheduled value, and the corresponding variations of both the voltage UP of power supply and the controllable voltage UF with time are designed as ( UP = 1.5uP (t ≤ t0 ), uP (t > t0 ) (3) UF = 1.5uF (t ≤ t0 ), uF (t > t0 ).
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FIG. 3. The magnetic field gradient as a function of the loading time for the Anti-Helmholtz coils in series with a high-power resistor whose resistance and power are 0.3 Ω and 1000 W.
In our experiment, the values of the voltage uP and uF are set to 2.2 v and 1.5 v, and the conversion time t 0 is 0.8 ms. In this case, the variation of magnetic field gradient with the loading time is shown in Fig. 4, and the characteristic time is derived for τ = 1.2 ms. The characteristic time is reduced by a factor of 3 compared to that in Fig. 3. The controllable voltages is equivalent to additionally adding resistors without the increasing heat. We calculate the variation of magnetic field gradient with the loading time by applying Eq. (3)–(2), and theory shows excellent agreement with experiment in Fig. 4. The number of atoms loaded into the crossed ODT is increased to 1.6 × 106 , and the inset in Fig. 4 shows the corresponding absorption image. In summary, we demonstrate an approach to reduce the loading time of magnetic field gradient by combining a high-power resistor in the circuit of anti-Helmholtz coils with an overshoot loading sequence of magnetic field gradient before arriving its scheduled value according to Kirchhoff’s laws. The efficient reduction of loading time of magnetic field gradient in the vertical direction enables the enhancement of the number of atoms loaded into the crossed ODT. Our method can be extended to a
FIG. 4. The magnetic field gradient as a function of the loading time for the Anti-Helmholtz coils with a high-power resistor in the circuit and a designed loading sequence for both the output voltage U of power supply and the controllable voltage V of the feedback circuit. The green line is the theoretical loading curve, which is obtained by applying Eq. (3)–(2).
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wide investigations involved with the utilizing of a magnetic field gradient or uniform magnetic field produced by the Anti-Helmholtz or Helmholtz coils. This work has been supported by the National Key R&D Program of China (Grant No. 2017YFA0304203), the Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT13076) and the National Natural Science Foundation of China (Grant Nos. 91436108, 61378014, 61675121, 11434007 and 11422433). 1 L.
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