Generation of strong ultralow-phase-noise microwave fields with tunable ellipticity for ultracold polar molecules

TL;DR

The paper tackles the challenge of stabilizing ultracold polar molecules by providing a robust microwave platform that delivers strong near-field fields with ultralow phase-noise and tunable polarization. The authors design and characterize a dual-feed rectangular waveguide antenna, develop a home-built near-field probe for field calibration, and implement notch-filter phase-noise measurements to reach $-170$ dBc/Hz at 20 MHz. They demonstrate high Rabi frequencies up to $71.1$ MHz, corresponding to $6.9$ kV/m, and achieve ultralow one-body losses ($\tau_{1B}=9.6$ s) with field-linked resonances and tetramer formation, enabling evaporative cooling to deep quantum degeneracy. The work provides a practical, scalable framework for MW-based control in ultracold molecular systems and could benefit other quantum platforms that require precise, low-noise MW control.

Abstract

Microwave(MW) fields with strong field strength, ultralow phase-noise and tunable polarization are crucial for stabilizing and manipulating ultracold polar molecules, which have emerged as a promising platform for quantum sciences. In this letter, we present the design, characterization, and performance of a robust MW setup tailored for precise control of molecular states. This setup achieves a high electric field intensity of 6.9 kV/m in the near-field from a dual-feed waveguide antenna, enabling a Rabi frequency as high as 71 MHz for the rotational transition of sodium-potassium molecules. In addition, the low noise signal source and controlled electronics provide ultralow phase-noise and dynamically tunable polarization. Narrow-band filters within the MW circuitry further reduce phase-noise by more than 20 dB at 20 MHz offset frequency, ensuring prolonged one-body molecular lifetimes up to 10 seconds. We also show practical methods to measure the MW field strength and polarization using a simple homemade dipole probe, and to characterize phase-noise down to -170 dBc/Hz with a commercial spectrum analyser and a notch filter. Those capabilities allowed us to evaporatively cool our molecular sample to deep quantum degeneracy. Furthermore, the polarization tunability enabled the observation of field-linked resonances and facilitated the creation of field-linked tetramers.These techniques advance the study of ultracold polar molecules and broaden the potential applications of MW tools in other platforms of quantum sciences.

Figures (7)

• Figure 1: (a) Sketch of the experimental setup. The dual-feed rectangular waveguide antenna, positioned 5 mm below the glass cell, radiates circularly polarized microwave. Molecules are in vacuum inside the glass cell. Details on the choice of antenna geometry is provided in main text. The hole at the rear end allows the imaging beam to pass through and address molecules. (b) Dressed state configuration of $^{23}\text{Na}^{40}\text{K}$. The $\sigma^-$ polarized MW field couples $|J=0, m_J=0\rangle$ and $|J=1, m_J=-1\rangle$, forming the dressed states $|+\rangle$ and $|-\rangle$. The remaining states in $|J=1\rangle$ manifold act as spectator states, denoted as $|0\rangle$. Because the MW is blue-detuned by $\Delta$ relative to the transition frequency at 5.64 GHz, molecules predominantly occupy the $|+\rangle$ state. (c) Adiabatic intermolecular potential curves for selected dressed state combinations. Molecules in the $|+\rangle$ state experience the repulsive potential at short range and are therefore shielded from sticky collision Bause2023. Residual losses arise when the molecules either tunnel through the repulsive barrier(two-body) or transition to lower lying unshielded dressed states (one-body) Schindewolf2022.
• Figure 2: (a) Spatial distribution of on-axis MW field strength for a single feed. We show the the position of the dummy glass cell and electrodes as well as the nominal position of the molecules as gray background, solid and dashed lines, respectively. Blue (orange) data points are measured without (with) glass cell in place. The blue (orange) line is the simulated field strength without (with) the glass cell. The dashed line is the Gaussian beam approximation from Eq. \ref{['eq:gaussian_beam']}. Insets show a two dimensional cut of the field strength distribution with and without the glass cell. (b) Relative MW field strength $\tilde{E}=E_i/\max(E_i)$ for each feed $i\in \{1, 2\}$ at 22 mm distance from the antenna opening as a function of azimuthal angle $\theta$, without the glass cell. The maximum and minimum field strengths yield extinction ratios of 7.5 and 10.9 for feed 1 and 2, respectively. Blue (orange) dots correspond to feed 1 (2), dashed curves are fits to the function $\max(\tilde{E_i})\times|\cos(\theta + \phi_i)| + \min(\tilde{E_i})$, yielding offset phases of $\phi_1=$ 97.6° and $\phi_2=$ 8.7°. The results confirm near-linear polarization and a $\pi$/2 phase difference between the two feeds.
• Figure 3: (a) Circuitry of the probe. Circuit consisting of dipole antenna, a diode and low-pass filter to convert the RMS field strength to a dc voltage and a 20 cm long carbon wire to physically separate the probe from the metallic connector and measuring device (schematic is adapted from Ref. Vzivkovic2011). (b) Image of the probe attached to a rotational mount to measure polarization purity of an electric field. (c) Calibration of the probe in an anechoic chamber. The probe response is plotted against the simulated electric field strength at a distance of 36 cm from an open-ended rectangular waveguide (antenna). Data points represent measurements at various input power levels. The RMS value of the electric field strength was simulated based on the known antenna geometry and measured probe distance. The solid line represents a fit to the data, described by Eq. \ref{['eq:probe_response_function']} with the parameters described in the main text. (d) Image of the calibration setup consisting of the waveguide antenna and probe in it's far field, inside anechoic chamber at TUM.
• Figure 4: (a) Control electronics for the MW setup. A control computer is used to program the signal source to output a signal with constant frequency and amplitude. The control voltage to Voltage Controlled Phase Shifter (VCPS) in path 2 as well as the reference voltages for the feedback loops are provided from arbitrary waveform generators. (b) Schematic of the detection board. The detection board splits part of the signal after power amplifier. One part is mixed with a signal from the other path to monitor the relative phase between the two feeds. The rest of the power is fed into a logarithmic photodiode that outputs a voltage proportional to the RMS value of the signal. A feedback loop (gray inset) is employed to steer the control voltage of the VCA, with reference input provided by an arbitrary waveform generator.
• Figure 5: (a) Setup for the phase-noise measurement. The MW signal from the SMA100B source is amplified by Kuhne KU PA 510590-10A amplifier and passed through a band-pass filter QFB-5650.5-5651.5-13 before being sent to another filter of same kind through circulator QCC1523C-5000-6000-60-S-1. We divert the reflection of the bandpass filter to the spectrum analyser, effectively extending the dynamic range of the analyser. (b) Transfer function of the ""*Notch filter comprised of the filter and the circulator. The reflected power spectral density is -22 dB suppressed within the pass band of the filter. This is measured with a vector network analyser. (c) Phase-noise of the signal source followed by amplifier and a bandpass filter with (blue) and without (green) the Notch filter as a function of frequency offset from the carrier. The carrier is measured to be 10.25 dBm.