P6 Nuclear excitation with twisted light combs

The lowest known nuclear excited state in 229Th is long-lived and thus termed a nuclear isomer. Due to the small excitation energy, there is a strong coupling to the electronic shell and a very narrow estimated radiative width of 10-19. Thus, nuclear spectroscopy on this transition is very challenging. The aim of this project is to address new avenues for nuclear excitation of the 229Th nuclear clock transition from the theory side via two objectives.

The key main goal of the first phase of the overarching “nuclear pillar” of COMB.AT is the excitation of the 229Th isomer using laser light and a determination of the transition wavelength to GHz resolution. The particular goal of project P6 is to tackle from the theory side the challenges of the weak photoexcitation cross section and to support the experimental efforts of projects P4 and P5. To this end, the team of P6 will follow two strategies, which lead to two sets of objectives:

Theoretical calculations for coupling of the isomeric transition to laser beams carrying OAM: The fundamental question here is whether OAM beams can increase the efficiency of the direct radiative excitation of the isomeric state and allow for selective driving in targets displaying nuclear hyperfine splitting. The starting point will be the calculation of nuclear photoabsorption cross sections for Bessel modes, as a counterpart to the so-far existing studies of plane wave absorption. This will be extended to Bessel-Gauss and the more realistic Laguerre-Gaussian beams carrying OAM. The calculations will be detailed for two scenarios:

  1. a large number of 229Th nuclei embedded in VUV-transparent crystals, which display quadrupole hyperfine splitting. The team of P6 will calculate numerically the sublevel populations and level polarization for the quadrupole splitting case in Th-doped VUV transparent crystals relevant for the NQRS Methodology pursued in P5,
  2. few 229Th trapped ions without quadrupole splitting.  Here the researchers of P6 will investigate the spatial separation of multipole channels (M1 and E2) for direct photo absorption of single Th ions.

This first objective is of particular interest for the collaboration with the experimental partners in P4 and P5. Use of specific light polarisations or OAM can be used for selectively addressing hyperfine levels of the 229Th isomeric or ground states.

Theoretical calculations for driven electronic bridge process in VUV-transparent Th-doped crystals using a frequency comb source: This part of the project will investigate the coupling of photons to the nucleus via the intermediate coupling between atomic and nuclear degrees of freedom. The goal is to study driven EBR processes where the external photon is either carrying OAM, or is generated by a frequency comb simultaneously involved either directly or after frequency upconversion also in the preparation of the excited atomic state. The developed formalism will be applied to both the VUV-transparent crystal as well as the trapped Th ion scenario. The resulting objectives here are

  1. deduce the cross section for photon-driven EBR processes (in stimulation and absorption schemes) that make use of twisted light beams, with focus on the spatial pattern of M1 and E2 channels.
  2. theoretical results for the symmetric and asymmetric 2-photon EBR excitation pursued experimentally with frequency comb sources in subproject P5.
  3. combining the coherent pulse propagation results from the two beforementioned objectives, study of driven 2-photon EBR schemes with comb photons carrying OAM.

These objectives are supported by the following method developments:

Interaction and photoexcitation of nuclei with twisted light: The starting point for the first objective will be the determination of the interaction matrix elements for twisted photons driving the nuclear transition. Here the team of P6 will focus first on Bessel beams. The Bessel beam introduces a spatial dependence of the photoabsorption amplitudes similar to the one identified for the case of atomic photoabsorption. The goal of our researchers is to determine and investigate this spatial pattern for the relevant M1 and E2 multipoles, and identify topological charge values and spatial regions over which an increased efficiency of photoabsorption can be achieved.

The interaction matrix elements will be a key input for the development of a coherent pulse propagation formalism for twisted light wave fronts. Our developed formalism based on the Maxwell-Bloch equations will be applied to determine the excited state population for the hyperfine split thorium level system. We expect that a broadband twisted light pulse addressing all hyperfine sublevels in a 229Th:CaF2 crystal may lead to a different final polarization of the sublevel population.

Driven electronic bridge processes with combs and OAM beams: Based on Adriana Palffy-Buß’ experience on the theory of driven EBR in the crystal environment, the researchers of P6 will develop in the first stage the formalism of driven EBR using twisted light beams carrying OAM.

In a second stage of the project, the team will focus on propagation of photons from a VUV-frequency comb through the Th-doped VUV-transparent crystal, with driving of the EBR process. To this end the researchers of P6 will develop a formalism describing a several-step process with absorption of two comb photons. In the considered scenario the first comb thereby searches for the defect state resonance while the second comb searches for the energy mismatch between defect state and nuclear transition energy to drive the electronic bridge process.

This scheme, either in the symmetric or asymmetric version (depending on the frequencies of the two photons) will be investigated experimentally in project P5, using the laser developed in project P4.

The final part of the project will combine the two aspects of comb and OAM-carrying photons and investigate the driven EBR rates for frequency combs with specially designed wave fronts which carry OAM. All EBR rates will be calculated for several VUV-transparent crystals.

Team of P6

The theoretical worked planned in subproject P6 will be performed at the Institute for Theoretical Physics and Astrophysics of UniWUE in the group of PI Adriana Palffy-Buß. UniWUE is a leading university in the fields of quantum phenomena in novel materials and solid-state research.

The following personnel were already part of the PIs research group before the start of the SFB COMB.AT:

  • Adriana Palffy-Buß (Professor): PI of the subproject P6
  • Tobias Kirschbaum: PhD student

Adriana Palffy-Buß, the PI of subproject P6, has been directly involved in theoretical calculations for nuclear structure predictions of the isomer properties, quantum optics schemes with x-rays for coherent population of the isomer, as well as the coupling of the isomer to the atomic shell in the processes of internal conversion and electronic bridge in ions and VUV-transparent crystals.

For the SFB COMB.AT two PhDs will be hired to work on the two different objectives of P6. The first graduate student will start at the beginning of COMB.AT and focus on the interaction of the 229Th nucleus with vortex beams leading to photoexcitation of the isomer. The results of this first objective are also relevant for the second objective. This PhD student will determine the interaction matrix elements, develop the coherent pulse propagation formalism for vortex beams, and support numerically the experimental efforts in project P5 for nuclear photoexcitation in Th-doped VUV transparent crystals. 

The second graduate student should start after the first half year of COMB.AT and develop in parallel the theory of driven EBR with two frequency comb sources. Later on, they will also investigate driven EBR using photons from twisted light beams carrying OAM.