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Probing Nuclear Sizes through Precision Spectroscopy of Ultracold Bosonic and Fermionic Helium

Yuri van der Werf

Published Nov 25, 2023• 0 citations
Publisher

Abstract

The helium atom, being a calculable system with narrow transitions that can be measured precisely, is an excellent candidate for testing state-of-the-art Quantum Electrodynamics calculations. This thesis presents a series of precise spectroscopic measurements on a narrow transition in ultracold trapped quantum gases of helium, using both the 3-He and 4-He isotopes, which exhibit distinctly different quantum-statistical behaviour in this ultracold regime. From the shift of this transition between the two isotopes, the difference in their nuclear charge radii is extracted, which is used as a benchmark quantity for comparison with other measurements and tests of Quantum Electrodynamics theory.

DOI
10.5463/thesis.364

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The helium atom, being a calculable system with narrow transitions that can be measured precisely, is an excellent candidate for testing state-of-the-art Quantum Electrodynamics calculations. This thesis presents a series of precise spectroscopic measurements on a narrow transition in ultracold trapped quantum gases of helium, using both the 3-He and 4-He isotopes, which exhibit distinctly different quantum-statistical behaviour in this ultracold regime. From the shift of this transition between the two isotopes, the difference in their nuclear charge radii is extracted, which is used as a benchmark quantity for comparison with other measurements and tests of Quantum Electrodynamics theory.
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Precision spectroscopy of simple atomic systems has refined our understanding of the fundamental laws of quantum physics. In particular, helium spectroscopy has played a crucial role in describing two-electron interactions, determining the fine-structure constant and extracting the size of the helium nucleus. Here we present a measurement of the doubly forbidden 1557-nanometer transition connecting the two metastable states of helium (the lowest energy triplet state 2 (3)S(1) and first excited singlet state 2 (1)S(0)), for which quantum electrodynamic and nuclear size effects are very strong. This transition is weaker by 14 orders of magnitude than the most predominantly measured transition in helium. Ultracold, submicrokelvin, fermionic (3)He and bosonic (4)He atoms are used to obtain a precision of 8 × 10(-12), providing a stringent test of two-electron quantum electrodynamic theory and of nuclear few-body theory.
Exotic helium atoms act as unique atomic traps for heavy, negatively charged particles, protecting them from nuclear annihilation and nuclear capture on timescales long enough to enable high-precision laser spectroscopy. Such measurements serve as stringent tests of three-body quantum electrodynamics and offer a direct route to determining fundamental particle masses. Motivated by upcoming spectroscopic efforts targeting pionic (π− 4He+π^{-\,4}\mathrm{He}^+π−4He+) and kaonic (K− 4He+K^{-\,4}\mathrm{He}^+K−4He+) helium, we present a rigorous theoretical evaluation of the collisional and density effects governing these systems. Using an ab initio potential energy surface and coupled-channel quantum scattering calculations, we study the collisional stability of the candidate metastable states against inelastic quenching in a cryogenic helium buffer gas. Furthermore, we provide theoretical reference values for the pressure broadening and pressure shift coefficients of the targeted transitions. These results establish an essential benchmark for future experiments, paving the way for refined determinations of the pion and kaon masses.
A series of magic wavelengths for the 23S1 → 23PJ (J = 0, 1, 2) transitions in helium is determined with high precision using the relativistic configuration interaction combined with the radiative potential method. The calculation explicitly incorporates relativistic, finite nuclear mass, and quantum electrodynamic corrections through the inclusion of mass shift and radiative potential operators into the Dirac-Coulomb-Breit Hamiltonian. The resulting magic wavelengths lie entirely within the visible spectrum (400-700 nm) and converge to seven significant digits, making them directly accessible for experimental verification. These accurate predictions serve as benchmarks for testing atomic structure theory and support the development of state-insensitive optical trapping schemes in precision spectroscopy.
Trapped gases of ultracold metastable helium atoms are a unique experimental sys- tem. The trapped cloud’s low temperatures, the ability to selectively trap and ma- nipulate individual atomic states and the isolation provided in a vacuum chamber are all conducive to the measurement of precision atomic parameters, such as atomic transition rates. Due to it’s atomic structure helium - the simplest multi-electron atom - is a favourite test-bed for precision QED theoretical calculations compared to experimentally determined parameters. This thesis reports on a number of tran- sition rates measured for the first time with high accuracy, including the first excited metastable state lifetime, found to be 7870(510)s, the longest of any neutral atomic species yet measured. Transition rates from the 23P level to the ground state were also measured for the first time and found to be in excellent agreement with theory. Further cooling of helium produces a Bose-Einstein condensate (BEC), where all atoms are in an identical quantum state, the analogue of an optical laser. One par- ticularly interesting property a BEC posesses is long-range coherence to all orders, meaning all component particles are described by a single wavefunction. While first order coherence is measured in an interference experiment like Young’s double slit, higher order coherence is the ability for correlations to exist between groups of two, three or more particles, quantified by the measurement of correlation functions. Prior to the work in this thesis correlation functions for atoms had only been measured for second order. Here we develop a new technique which we use to show that a BEC is coherent to second and third order to 0.1% accuracy, compared to a thermal cloud which we show is incoherent. At small inter-particle spacings, there is an enhanced probability of measuring double and triple events in the thermal cloud (termed bunching). A drawback of all previous atomic correlation measurements is that the small de-Broglie wavelengths compared to the detector resolution leads to a significant reduction in the measured bunching amplitudes compared to theory. By altering our trapping configuration and temperature we are able to measure a two-particle bunching amplitude which is 88% of the theoretical maximum. This system also allowed the measurement of correlations up to 5th order in thermal gases. The near ideal bunching allowed us to demonstrate perturbations to the correlation functions due to the 1D nature of the system. These advances should lead to correlation measurements being used as a probe to characterise more exotic system properties such as low dimensionality, engineered quantum states and paticle pairing. Finally, a waveguide was created using a dipole laser beam and used to guide atoms in analogy to an optical laser in a fibre. Guided ‘atom lasers’ are likely to be important components for practical devices such as precision sensors. We demonstrate that a guided atom laser has a gaussian profile matching the lowest transverse mode of the waveguide and is first and second order coherent. In contrast guided thermal atoms show matter-wave speckle and are incoherent.
The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-Tc_cc​ superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-1/21/21/2 Fermi gas and the Bose with short-range interactions. Using fermionic 6^66Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of 7^77Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.