Advances in Antimatter Spectroscopy and Atomic Clock Interferometry
Two independent scientific papers have been published, detailing advances in antimatter spectroscopy and atomic clock interferometry. The first reports a refined measurement of the hyperfine structure of antihydrogen, while the second describes a methodology for differential phase noise cancellation in atom interferometry.
Antihydrogen Hyperfine Splitting Measurement
Experimental Setup
Researchers at the ALPHA-2 experiment conducted measurements of the ground-state hyperfine splitting of antihydrogen. The measurement utilized a flattened magnetic field profile, designed to reduce the second axial derivative of the axial magnetic field to less than 2 T m⁻². This represents a factor of 20 reduction compared to previous work.
"This represents a factor of 20 reduction compared to previous work."
The magnetic field was intentionally depressed below the central mirror coil by approximately 5 × 10⁻⁵ T to create a shallow, centrally located absolute minimum. Electron cyclotron resonance (ECR) mapping was used to measure the axial magnetic field profile in situ, with a frequency resolution of approximately 1 ppm and a spatial resolution of approximately 1 mm.
Measurement Protocol
Two experiments were performed at magnetic fields of 1.03 T and 1.07 T. In each experiment, eight replicates of spectroscopy were conducted. Magnetic field drift was characterized at approximately -0.025 G/h for 1.03 T and -0.026 G/h for 1.07 T. Corresponding positron spin resonance frequency drifts were -72.82 ± 0.04 kHz/h (at 1.03 T) and -75.64 ± 0.05 kHz/h (at 1.07 T), consistent with expectations.
Microwave fields were produced by an Agilent E8257D signal generator, amplified, and delivered to the trap. Positron spin-flip transitions were driven by the transverse component of the microwave magnetic field. Injected powers were tuned to balance transition rates.
Data Analysis
Annihilation events were reconstructed from charged-particle products detected by a silicon vertex detector. Background separation utilized a Boosted Decision Tree classifier. The event selection efficiency was 75.7%, and the cosmic ray misidentification rate was 37.4 × 10⁻³ s⁻¹.
Analysis fitted the frequency distributions with an empirical model that included a base lineshape and a resolution function. Onset frequencies for the two transitions were extracted per replicate. The hyperfine splitting was obtained from the difference in onset frequencies, accounting for magnetic field drift via a linear model with a common slope. Simultaneous maximum likelihood fits to eight replicates were performed for each field.
Simulations of antihydrogen motion and microwave interaction informed the lineshape model. Systematic uncertainties were evaluated for reproducibility, signal model, binning, and B-drift. Signal model uncertainties included alternative base functions and resolution function forms. Reproducibility was assessed by repeating the fit with shape parameters from high-statistics samples. Short-time deviations from linear magnetic field drift were studied using Gaussian Process Regression and auxiliary data.
Validation included Monte Carlo pseudo-experiments and cross-checks using peak frequencies. Alternative background treatments applying tighter selections did not produce statistically significant deviations.
Atom Interferometry with Differential Phase Noise Cancellation
Cooling Sequence
Strontium-87 atoms were collected over 1.5 seconds using the ¹S₀ → ¹P₁ transition at 461 nm with a field gradient of 3.5 mT/cm during the "blue MOT" stage. Repump lasers at 679 nm and 707 nm recycled atoms from the ³P₂ manifold. Subsequently, atoms were captured on the ¹S₀ (F=9/2) to ³P₁ (F'=11/2) transition at 689 nm with a gradient of 390 μT/cm during the "red MOT" stage. Sidebands at 1,463.265 MHz were applied. Intensity was set at 1,800 I_sat for 220 ms, then ramped linearly from 490 to 40 I_sat over 100 ms. A seventh 'up' beam supported against gravity. This process brought atoms to 2 μK and compressed them.
Dipole Trap and State Preparation
Two crossed optical dipole traps at 1064 nm and 813 nm were used, separated vertically by 1 mm. A transparency beam at 488 nm protected atoms from scattered 689-nm light. After the red MOT, dipole traps and repumpers were switched on. A 100-ms top-trap loading stage optimized parameters to load the upper trap. The red MOT was then released for 3 ms to allow atoms to fall to the bottom trap, followed by a 100-ms bottom-trap loading stage.
After loading, atoms were optically pumped to the stretched state M_F=9/2 using a 20-ms pulse of circularly polarized 689-nm light in a 38-μT horizontal bias field. The bias field was then ramped to 31 μT.
Velocity Selection and Interferometry
A clock beam at 698 nm, directed vertically upwards with a waist of 600 μm and a linewidth below 2 Hz, was used for velocity selection. A 200-μs π pulse at 20 mW excited slow atoms to ³P₀. Ground-state atoms were pushed away with a 461-nm pulse, leaving slow atoms in ³P₀. A subsequent 44-μs Rabi π pulse achieved 90% de-excitation.
The clock atom interferometry sequence involved three resonant pulses (π/2 – π – π/2) on the 698-nm transition with a π-pulse time of 44 μs and a dark time of 200 μs. The phases of the pulses were set to 0, φ, and 4φ, with φ scanned from 0 to 2π in 100 steps. For high laser noise samples, additional random phase steps were applied during dark times.
Phase Noise and Analysis
The variance of the interferometer laser phase was calculated from the spectral density of frequency fluctuations. For a thermal-noise-limited laser with flicker noise, the standard deviation was 710 mrad for T=5 s, motivating noise cancellation.
A horizontal 689-nm Stark-shifting pulse (30 μs) was applied to the top interferometer during the gap between the first π/2 and π pulses, inducing a bias differential phase φ_Stark.
Electronic signals were produced via the ARTIQ platform (FPGA-based). Control software was Python-based and open-source.
Phase Extraction and Data Filtering
Unbinned maximum-likelihood analysis was used for phase extraction. For each shot, per-shot likelihood integrated over the common phase φ using a uniform prior. Response functions were sinusoidal fringe models parameterized by offsets and contrasts. In differential-phase stability analysis mode, δφ was estimated as piecewise constant over consecutive blocks of 141 shots. In oscillatory-signal analysis mode, δφ was parameterized as δφ(t)=δφ₀ + S sin(ωt) + C cos(ωt). Signal significance was quantified via a likelihood-ratio test against the null hypothesis.
Runs where laser locks failed or atom counts were below 60% of the median were excluded.
Atom Number Calibration and Noise Levels
Fluorescence from an EMCCD was calibrated via absorption imaging. Absorption cross sections for ⁸⁷Sr were determined via spectroscopy of the three ¹S₀ → ¹P₁ hyperfine transitions. The uncertainty in atom number was 8%. Median atom numbers were 3,100 (with an uncertainty of 210) in the top trap and 2,040 (with an uncertainty of 160) in the bottom trap.
Maximum-likelihood phase extraction applied to low laser noise (LLN) and high laser noise (HLN) datasets yielded per-block standard deviations of σ_LLN = 3.69 ± 0.19 mrad and σ_HLN = 3.89 ± 0.20 mrad. The standard error of the mean was 260 ± 13 μrad (LLN) and 275 ± 14 μrad (HLN).
"The theoretical standard quantum limit (SQL) was defined as the Cramér–Rao bound for per-shot phase noise σ_δφ."
The theoretical standard quantum limit (SQL) was defined as the Cramér–Rao bound for per-shot phase noise σ_δφ, computed using the likelihood model with only quantum projection noise. The result was 43.5 ± 1.6 mrad per shot, corresponding to 258 ± 10 μrad over the full dataset.
Synthetic datasets replicated experimental conditions. The unbinned maximum-likelihood estimator was validated to be unbiased. Overlapping Allan deviations from 5,100 simulations provided an SQL reference. Statistical tests (with p=0.82 for HLN and p=0.65 for LLN) indicated no significant deviation from the SQL prediction.