Research Projects

In stark contrast to classical physics where confined particles can have exactly zero energy, quantum theory exhibits a finite zero-point energy (ZPE) that represents the lowest possible energy state of a system. This energy is an inherent feature of quantum systems, arising from the Heisenberg uncertainty principle. One significant remark comes from Feynman lectures, ``The vacuum is not empty. It is filled with fluctuating fields. The ZPE is the lowest energy state of these quantum fluctuations, and its consequences are observable, as in the Casimir effect.'' However, the ZPE associated with an electromagnetic quantum-mechanical oscillator such as a confined particle, remains largely unexplored experimentally. We propose to directly measure the absolute value of the ZPE of a confined particle with high precision. This is possible via laser photo-detachment spectroscopy of hydrogen anions (H⁻) that are confined by the electromagnetic fields of a Penning trap. Both the electron that is bound in the anion before detachment and the electron that remains bound in the trap after detachment are fully quantum-mechanical bound systems. The detached electron in the trap behaves as a quantum-mechanical oscillator with energy levels (N + 1/2)ħω₊, where the electron’s motional frequency ω₊ can be controlled by adjusting the magnetic field strength. In the ground state, where N=0, the ZPE ħω₊/2 of the confined electron leads to a measurable shift in the photo-detachment threshold compared to the free-particle case. This shift can be detected with high precision using laser photo-detachment spectroscopy. The photon energy hv required to detach the electron is given by the electron affinity Eₐ=0.754195(19) eV of the H⁻ anion. However, when the detached electron is not free to go to the continuum, but remains confined for example in a Penning trap, where it occupies the quantum-mechanical ground state of oscillation in the trap's harmonic potential, the ZPE ħω₊/2 of the confined electron adds to this energy threshold, i.e. hν = Eₐ + (ħω₊/2). A measurement of the photo-detachment cross section as a function of photon energy in the trap yields the threshold value Eₐ + (ħω₊/2). Subtracting the well-known free-particle value Eₐ, provides a direct measurement of the ground-state ZPE ħω₊/2. The hydrogen anion is ideal for this experiment due to its simplicity; It consists of one proton and two electrons with the simplest possible electronic configuration ¹S₀ and no excited bound states. The detachment energy of approximately 0.75 eV corresponds to a laser wavelength of around 1644 nm, which is commercially available. Additionally, H⁻ ions can be efficiently produced within the trap via electron-impact dissociation of molecular hydrogen, simplifying the overall experimental procedure. Understanding ZPE contributes to various fields, such as the role of quantum fluctuations in superfluidity and the potential link to the cosmological constant problem in cosmology.

Quantum Mechanics, Penning Trap, Hydrogen Anion, Ground-State Energy, Harmonic Oscillator, Photo-detachment Spectroscopy