Long Time Energy Oscillation Between Electron Shell and Nucleus in $^{229}$Th Ions and Coherent Electron Bridge for Nuclear Quantum Battery

Abstract

The electron shell of the Thorium ion with the $M$1(8.4~eV) transition between levels and the doublet of the $^{229}$Th nucleus ground state with the similar transition represent two qubits spatially inserted one within the other. In the case of relative proximity of the energies of these transitions, weakly damped energy oscillations can be excited between qubits, namely, multiple coherent energy transfer from the electron shell to the nucleus and vice versa. This process in the $^{229}$Th ions does not require resonant (within the width of the levels) coincidence of the transition energies due to the relatively high interaction energy of the electron and nuclear currents. The electron shell ``breathes'', periodically decreasing and increasing in size. The effect can be observed in an ion trap by the intensity of light scattered by thorium-229 ions. This extends the energy range for the $^{229m}$Th$(3/2^+,8.4$~eV) isomer excitation via an electron bridge. Furthermore, the system under consideration is transformed into a nuclear quantum battery when exposed to coherent laser radiation. To ``charge'' the battery, i.e. to excite $^{229m}$Th, one can use developed methods for charging quantum batteries, in particular, coherent excitation of the electron shell followed by coherent transfer of excitation energy to the nucleus (the coherent electron bridge). This opens the way for the design of the $^{229}$Th nuclear quantum battery at the current level of technological development.