An efficient high-current circuit for fast radio-frequency spectroscopy in cold atomic gases

Abstract

We design and implement a low-impedance, high-current radio-frequency (RF) circuit, enabling fast coherent coupling between magnetic levels in cold alkali atomic samples. It is based on a compact shape-optimized coil that maximizes the RF field coupling with the atomic magnetic dipole, and on coaxial transmission-line transformers that step up the field-generating current flowing in the coil by a factor $\sim\,4$ to about $7.5\,$A for $100\,$W of RF driving. This allows to obtain a RF coupling field of about $0.035\,\text{G}/\sqrt{\text{W}}$ at the atomic sample location. The system is robust and versatile, as it generates a large RF field without compromising on the available optical access, and its central resonant frequency can be adjusted in situ. Our approach provides a cost-effective, reliable solution, featuring a negligible level of interference with surrounding electronic equipment thanks to its symmetric layout. We test the circuit performance using a maximum RF power of $80\,$W at a frequency around $82\,$MHz, which corresponds to a measured Rabi frequency $Ω_R/2π\simeq 18.5\,$kHz, i.e. a $π$-pulse duration of about $27\,μ$s, between two of the lowest states of ${}^6$Li at an offset magnetic field of $770\,$G. Our solution can be readily adapted to other atomic species and vacuum chamber designs, in view of an increasing modularity of cold atom experiments.

Figures (6)

• Figure 1: Circuit concept and design. (a) A block diagram displays the five cascaded components composing the RF circuit: the generator, the step-down transformer, the matching network that compensates the coil impedance, the step-up transformer, and the 50$\,\Omega$ dummy load. (b) Full layout of the RF circuit. The step-down and step-up transformers are implemented by quarter-wave 12.5$\,\Omega$ coaxial transmission lines. They respectively decrease and increase the impedance of their "secondary" sides by a factor 16. The coil is modeled as a LR series, based on impedance measurements of the actual wire loop (see Fig. \ref{['fig:coil']}) inserted in a mock-up of the vacuum chamber. The capacitors compose the matching network together with the two 180 mm-long transmission lines bridging the tuning board and the coil (see also Fig. \ref{['fig:Realiz']}). The capacitance values shown here apply to a central frequency around 83 MHz.
• Figure 2: Coil design and realization. (a) The coil is formed by two turns of a half-annulus shaped coaxial wire loop (orange line), with an external radius $R_\mathrm{ext} \simeq 29$ mm. A clear optical aperture of 29 mm diameter, centered on the viewport remains available, used e.g. to shine a 25.4 mm-diameter beam on the atoms (pink circle). (b) Calculated B-field polarization pattern and transverse component amplitude $B_{\perp}$ in the atomic plane at $z \simeq 0.7\,R_\mathrm{ext} \simeq 20\,$mm. The in-plane component $B_{\perp}$ is dominant and quite homogeneous around the sample location $x,y=0$ (green cross). In particular, at the largest contour line, that delimits a region of about $30 \times 10 \,$mm$^2$, $B_\perp$ is reduced by only 15% with respect to its value at the atoms' position. (c) The coil has been realized using coaxial RG316 cable, and is held in shape by a 3D-printed supporting mold (gray plastic cylinder with grooves). The two lead cables visible in the bottom part of the picture connect to the coil through two capacitors C2 and C3 soldered to a cm-sized PCB [see Fig. \ref{['fig:Realiz']}(a)]. Measurements of the coil impedance are performed for simulation purposes, surrounding it with a metallic cylinder to emulate the EM environment within the re-entrant viewport.
• Figure 3: Circuit simulation results for a 100 W generator, calculated based on the components displayed in Fig. \ref{['fig:schblkconc']}(b). (a) The current (peak-to-peak) $I_1$ in the coil (blue), and the voltages (peak-to-peak) $V_1$ (magenta) and $V_2$ (green) across the matching capacitors C1 and C2, respectively, are displayed. (b)-(c) The modulus and Smith chart of the circuit $S_{11}$ parameter are shown, quantifying the power reflected back to the generator.
• Figure 4: Circuit realization and in situ measurements. (a) Sketch of the circuit boards and components. (b) Pictures of the realized matching (and tuning) network board. Capacitors C2 and C3 are hosted by a cm-sized PCB mounted vertically next to the coil within the plastic housing [see Fig. \ref{['fig:coil']}(c)]. The two coaxial cables connecting the tuning board with C2 and C3 share a common ground, preventing B-fields from being emitted at any other location on the feedline than the loop itself. Capacitors C1 and C4 are soldered on a dedicated PCB, which is housed and fixed to a breadboard outside the reentrant viewport. The tuning capacitance is realized by two capacitors C1$_{\hbox{f}}$ (fixed) and C1$_{\hbox{t}}$ (trimmer), C1 = C1$_{\hbox{f}}\,$+ C1$_{\hbox{t}}$. All fixed capacitors are ATC-100B series, while the tuning capacitance in C1 is realized with a Johanson MAV05D30. (c)-(d) The $S_{11}$ parameter measured with a vector network analyzer is found in good agreement with simulations [see Fig. \ref{['fig:simbanant1']}(c)]. The $S_{21}$ parameter quantifies the power reaching the final 50 $\Omega$ load, and equals about $-3\,$dB at the resonance (here $\simeq~$81 MHz).
• Figure 5: System performance measured with an ideal Fermi gas of $^6$Li atoms at $B_0 \simeq 770$ G. On the vertical axis, the relative population denotes the number of atoms in state $\ket{2}$ normalized to the total atom number. (a) Spectroscopy of the $\ket{2} \leftrightarrow \ket{3}$ transition. The solid line is a fit of the data with the expected sinc-function lineshape, yielding a resonance frequency $\nu_0 = 82.08908(1)$ MHz and a Rabi frequency $\Omega_R/2\pi = 410(16)$ Hz. (b)-(c) Rabi oscillations at the resonance between states $\ket{2}$ and $\ket{3}$ for RF generator powers of about 3.5 W (yellow) and 80 W (red). Solid lines are sinusoidal fits to the data, yielding Rabi frequencies $\Omega_R/2\pi = 3.909(4)$ kHz and $\Omega_R/2\pi = 18.25(23)$ kHz, respectively.