Atomic Physics 2024

Rydberg molecules, ranging from Rydberg macrodimers to Rydberg atom-ion molecules, represent significant milestones in the recent advancements of ultra- cold atomic physics. The lifetimes of these molecules are typically shorter than those of bare Rydberg atoms, indicating the involvement of non-radiative decay processes in their dynamics. Specifically, the presence of non-adiabatic coupling between electronic potential energy curves could be a significant factor in their decay. We explore this mechanism here in the Rydberg atom-ion molecule sys- tem, where a vibrational bound state can hop onto a repulsive potential curve and decay. We employ the streamlined version of the multichannel R-matrix method to compute the positions and widths of the resonance states, revealing notable alterations arising from the influence of this coupling. An extended version of the Ryd-ion dimer is a Ryd-Ryd-ion trimer system, and this is more complex since it becomes a 6 dimensional problem. The interaction between the two Rydberg atoms reveals interesting phenomena influencing the overall molec- ular configuration. Our primary objective is to provide a detailed exploration of the electronic and vibrational structure of this tri-atomic molecule.

Free electron laser facilities have sprout all over the world. These light sources can produce ultrashort pulses, already in the sub-femtosecond regime, with enough intensity to induce non-linear phenomena in gas phase atoms and molecules. One of the most fundamental non-linear processes, two-photon ionization has been object of recent experiments, exploring and exploiting new aspects of well-known light-induced physical problems such as Rabi oscillations [1] or light-induced interferences leading to asymmetric photoelectron emission from simple atoms [2,3]. The present work proposes new schemes to employ these light sources to access information on dynamical electron correlation effects in double photoionization problems. This theoretical study first explores the electron dynamics of hydrogen using strong fields that alter the molecular potential, with relatively long wavelengths, and then investigate the double ionization of helium using a two-color scheme. In the first scenario, we examine the strong variation of the ionization yield, as well as the depletion of the ground state of the H atom with the laser intensity and compare with existing data [4]. In the second scenario, although the laser intensities are large, we employ much shorter wavelengths, thus keeping the problem within a perturbative regime. We then demonstrate how the double ionization yield can be manipulated by employing a given time-delay between these pulses of different color. In both cases, we employ a numerical approach based on the numerical solution of the time-dependent Schrödinger equation (TDSE) in full dimensionality. The wave function is described using a Finite Element Method with a Discrete Variable Representation (FM-DVR), which greatly simplifies the numerical implementation. The TDSE is the solved employing a Cranck-Nicholson [5] or Lanczos propagator [6]. The scattering function, corresponding to a specific single or double ionization channel, is then extracted by an implicit propagation to infinite time using an Exterior Complex Scaling (ECS) of the electronic coordinates, followed by a Fourier transform [5,7] [1] S. Nandi et al, Nature 608, 488 (2022) [2] M. Di Fraia et al., Phys. Rev. Lett. 123, 213904 (2019) [3] D. You et al., Phys. Rev. X 10, 031070 (2020) [4] J. Rowan et al., Phys. Rev. E 101, 023313 (2020) [5] A. Palacios, T. N. Rescigno and C. W. McCurdy, Phys. Rev. A 77, 032716 (2008) [6] A. Palacios, T. N. Rescigno and C. W. McCurdy, Phys. Rev. A 79, 033402 (2009) [7] J. Feist et al., Phys. Rev. A 77, 043420 (2008)

Photon pairs generated through spontaneous parametric down-conversion constitute a well-established approach for creating entangled bipartite systems. Laguerre-Gaussian modes, which carry orbital angular momentum (OAM), are commonly used to engineer high-dimensional entangled quantum states within the spatial domain. For Hilbert spaces with dimension $d>2$, maximally entangled states (MESs) enhance the capacity and security of quantum communication protocols and increase the efficiency of quantum-computational tasks. However, directly generating MESs within well-defined high-dimensional subspaces of the infinite OAM basis remains challenging. In this work, we formalize how the spatial distribution of the pump beam and phase-matching conditions within the nonlinear crystal can be utilized to generate MESs without additional spatial filtering of OAM modes in a given subspace. We demonstrate our method with maximally entangled qutrits ($d=3$) and ququints ($d=5$).

For aggregates of molecular monomers above layered surfaces, the dipole approximation breaks down when the distance between monomers and surfaces is less than several nanometers. To overcome this problem, we employ macroscopic quantum electrodynamics and use the complete transition current density of the individual monomers. Within this framework, the resulting Master Equation for the excitonic degrees of freedom of the aggregate is derived. For example, we discuss the case of PTCDA on a KCL surface.

Highly electronically excited atomic impurities within a BEC typically have interactions characterised by a scattering length that may rival or even surpass the average spacing between the surrounding bosons. The significance of these interactions depends on the thermal de Broglie wavelength; for shorter lengths, the system exhibits a rich absorption spectrum which extends typical polaron physics. However, within a dense bath, the absorption spectrum consists only of a broad single Gaussian, indicating an almost classical behaviour. Beyond altering interaction ranges, scattering length and interaction strength, the electronic angular states of the impurity can be manipulated, breaking the spherical symmetry of the interactions. In free space, this manipulation leads to the emergence of l(l+1) degenerate electronic potential energy surfaces, introducing non-additive interactions. Our investigation delves into the impact of these anisotropic and non-additive interactions on the absorption spectrum of a Rydberg impurity within an ideal BEC.

Periodic driving of systems of particles can create crystalline structures in time. Such systems can be used to study solid-state physics phenomena in the time domain. In addition, it is possible to engineer the wave-number band structure of optical systems and to realize photonic time crystals by periodic temporal modulation of the material properties of the electromagnetic wave propagation medium. We introduce here a versatile averaged-permittivity approach which empowers emulating various condensed matter phases in the time dimension in a traveling wave resonator. This is achieved by utilizing temporal modulation of permittivity within a small segment of the resonator and the spatial shape of the segment. The required frequency and depth of the modulation are experimentally achievable, opening a pathway for research into the practical realisation of crystalline structures in time utilising microwave and optical systems.

Spontaneous time-translation symmetry breaking had not attracted much attention until Wilczek introduced the concept of time crystals. Despite this particular realization being prohibited by the ,,no-go'' theorem, the idea inspired a new version of time crystals, i.e. the discrete time crystals (DTCs). In general, a DTC is a periodically driven quantum many-body system that spontaneously breaks the discrete time-translation symmetry of the Hamiltonian due to particle interactions and starts evolving with a period s-times, where s is integer, longer than the period of the external driving. One platform for realizing DTC consists of a single ultracold atomic cloud, i.e. weakly interacting bosons, bouncing resonantly on a periodically driven atom mirror. In our work, we extend this concept by considering two distinct ultracold atomic clouds. In our setup, atoms in different clouds interact with infinite repulsive strength, while atoms within each cloud interact attractively. The system is one-dimensional and placed in a gravitational field, with the lower atomic cloud bouncing on an oscillating mirror. Due to the infinite repulsive inter-species interaction, the lower cloud effectively acts as a driving force for the upper cloud. We investigate how sufficiently strong intra-species interactions can induce discrete time-translation symmetry breaking, leading to the formation of a complex DTC.

Authors: Zeinab Hardani, Manfred Lein Affiliation: Leibniz Universität Hannover, Germany Abstract: In the high harmonic generation (HHG) process, the knowledge of the Coulomb potential effect allows us to accurately adjust the phase of the induced dipole, thereby defining the shape of the XUV radiation [1]. To this end, we study the phase in HHG [2], which has three contributions: the "strong-field phase" calculated within the strong-field approximation (SFA) [3], the "Coulomb phase" from the additional Coulomb effect on electron trajectories, and the target-specific "recombination phase" due to the transition dipole in photo-recombination. We perform a numerical solution of the time-dependent Schrödinger equation (TDSE) in one dimension for a model argon atom subject to an intense few-cycle laser pulse, obtaining the time-dependent dipole acceleration. The phase for the short trajectory of HHG is then evaluated via time-frequency analysis of the dipole acceleration [4], specifically focusing on the Coulomb phase shifts as the laser intensity is varied [5]. To isolate the Coulomb phase, we subtract the calculated SFA phase from the total TDSE phase. Our results show agreement with the analytical R-matrix (ARM) approach [6]. Additionally, we perform a recombination phase calculation by solving the TDSE for the model argon atom, where we isolate this phase by subtracting the total TDSE phase of the p orbital from that of an s orbital with the same ionization potential. We compare the resulting recombination phase differences with those obtained from exact continuum states [7], observing a phase shift around the Cooper minimum of the model atom. References: [1] Shafir, D., Fabre, B., Higuet, J., Soifer, H., Dagan, M., Descamps, D., Mével, E., et al. "Role of the ionic potential in high harmonic generation." Phys. Rev. Lett. 108, 203001 (2012). [2] Salieres, P., L'huillier, A., Antoine, P., Lewenstein, M. "Study of the spatial and temporal coherence of high-order harmonics." Adv. At. Mol. Opt. Phys. 41, 83-142 (1999). [3] Lewenstein, M., Balcou, P., Ivanov, M. Yu., L’huillier, A., Corkum, P. B. "Theory of high-harmonic generation by low-frequency laser fields." Phys. Rev. A 49, 2117 (1994). [4] Yue, S., Liu, J., Xue, S., Du, H., Lein, M. "Observing the Coulomb shifts of ionization times in high-order harmonic generation." Phys. Rev. A 107, 063102 (2023). [5] Azoury, D., Krüger, M., Barry D. Bruner, B. D., Smirnova, O., Dudovich, N. "Direct measurement of Coulomb-laser coupling", Sci. Rep. 11, 495 (2021). [6] Torlina, L., Smirnova, O. "Coulomb time delays in high harmonic generation." New J. Phys. 19, 023012 (2017). [7] Chacon, A., Lein, M., Ruiz, C. "Retrieval of the amplitude and phase of the dipole matrix element by attosecond electron-wave-packet interferometry." Phys. Rev. A 87, 023408 (2013).

In this theoretical study, we focus on delocalized electronic excitonic states in molecular aggregates, particularly those exhibiting topological phases. It has been shown that a two-dimensional molecular aggregate, composed of two different sublattices and complex transition dipole moments, possesses topological edge states [1]. However, these states are predominantly ’dark’ in traditional far-field absorption spectra. We consider a typical scattering scanning optical near-field microscopy (s-SNOM) setup, where the aggregate interacts with the near field stemming from a metallic tip [2, 3]. With the help of s-SNOM, we can not only excite these dark states but also record spatially resolved absorption spectra, revealing clear signatures of both excitonic edge states and bulk states. Moreover, we look at reconstruction of the eigenstate wavefunctions from the near-field absorption spectra using convolution neural networks (CNNs). The reconstruction is studied in the presence of diorder in the Hamiltonian and noise added to the spectra. [1] J.Y. Zhou, S. K. Saikin, N.Y. Yao and A. Aspuru-Guzik, Nature materials 13, 1026-1032 (2014) [2] X. Gao and A. Eisfeld, J. Phys. Chem. Lett. 9, 6003 (2018) [3] S. Nayak, F. Zheng and A. Eisfeld, J. Chem. Phys. 155, 134701 (2021)

Ionization of targets such as atoms, ions, and molecules by charged projectiles such as electrons / positrons has been studied from a long time and has various applications; few may be listed as diagnostics of fusion plasmas, modeling of physics and chemistry related to atmosphere, understanding the effect of ionizing radiation on biological tissues etc. The detailed information about this kind of collision processes are obtained from cross sections. Particularly, the triple differential cross section (TDCS) obtained through the coincidence study has been of interest since the pioneering work of Ehrhardt group [1]. Coincidence study of TDCS has been of particular interest since it provides full information about the collision dynamics and momentum vectors of all the free particles involved in the ionization are determined. Good amount of ionization cross section studies have been reported for the atomic targets [2]. From last decade the molecular targets have also been studied for the ionization processes [2, 3] as well as electron momentum spectroscopy studies [4]. We report the results of our recent work on calculation of electron impact ionization triple differential cross sections for atomic (Ar, Xe) [5, 6] and molecular (N2, H2O and CO2) [7-9] targets. We will review briefly the status of charged particle ionization processes from targets with introductory idea about the theoretical formalism involved and results for the electron impact ionization of atomic and molecular targets will be discussed. References: [1] H. Ehrhardt, K. H. Hesselbacher, K. Jung, and K. Willmann, J. Phys. B 5, 1559 (1972). [2] D. H. Madison and O. Al-Hagan, J. At. Mol. Opt. Phys. 2010, 367180 (2010). [3] E. Ali, K. Nixon, A. J. Murray, C. G. Ning, J. Colgan and D. Madison, Phys. Rev. A 92, 042711 (2015). [4] N. Watanabe, S. Yamada and M. Takahashi, Phys. Chem. Chem. Phys. 20, 1063 (2018). [5] G. Purohit, Nuclear Inst. and Methods in Physics Research B 487, 52 (2021). [6] A Pandey , D Kato, W Quint and G Purohit, J. Phys. B: At. Mol. Opt. Phys. 56, 245201 (2023). [7] A. Pandey and G. Purohit, Atoms 10 (2), 50 (2022). [8] A Pandey, G Purohit, Nuclear Inst. and Methods in Physics Research B 547, 165222, (2024). [9] A. Pandey and G. Purohit, J. Phys. B: At. Mol. Opt. Phys. 57, 105201 (2024)

Ultracold atoms in optical tweezer arrays emerged as a powerful platform for quantum simulation, quantum computation, and quantum sensing. The accurate, fully correlated theoretical description of such systems adopting realistic atom-atom interaction potentials is challenging, if the trap dimension is similar to the effective atom-atom interaction length. Inspired by the quantum-chemistry approaches for describing the electrons in molecules, a configuration-interaction (CI) approach adopting trap-well centered Gaussian-type orbitals appears appealing, especially since the tweezer potential is, in contrast to the Coulombic potential of the nuclei in molecules, short ranged and almost harmonic. However, the tremendous amount of six-dimensional atom-atom interaction integrals occurring in a CI calculation needs to be efficiently and accurately handled. In this work it is shown that these integrals can be reduced to linear combinations of one-dimensional master integrals. Adopting analytic model potentials for describing the atom-atom interaction, these master integrals can even be expressed via hypergeometric functions. First results of the new approach will be presented on the poster. This includes a validation of the approach as well as a comparison of different model potentials describing the atom-atom interaction.

An operator that generates an approximate symmetry of long-range Rydberg molecules (LRRMs) formed by two alkali atoms, one in a Rydberg state and the other in the ground state, is identified. This is first done by evaluating the natural orbitals associated with a variational calculation of the binding wave function within the Born-Oppenheimer description of the molecule including $s$ and $p$ Fermi pseudopotential and the hyperfine structure energy terms. The resulting orbitals with the highest occupation number are shown to be identical to those obtained by a perturbative model for high angular momentum—trilobite and butterfly—LRRMs. Whenever the slight dependence of the quantum defects of the Rydberg electron on its total momentum $\vec{j}$ can be neglected, the symmetry operator of the high angular momentum LRRMs orbitals is identified as the sum of the spin of the Rydberg electron $\vec{s}_1$, spin of the valence electron $\vec{s}_2$ and the spin of nucleus $\vec{i}$, of the ground-state atom, $\vec{N}=\vec{s}_1+\vec{s}_2+\vec{i}$. The spin orbitals that diagonalize $\vec{N}$ define compact basis sets for the description of LRRMs. The expected consequences of this approximate spin-symmetry on the spectra of LRRMs are briefly described.

Scattering properties and time delays for non-symmetric potentials are discussed paradigmatically in one dimension in comparison to symmetric ones. Only for the latter the Wigner and Smith time delays coincide. We further discuss the importance of the potential position and give a criterion how to identify a potential with intrinsic symmetry which behaves like an asymmetric one if it is merely offset from the scattering center.

Quantum reflection is a phenomenon where a quantum particle reflects off of a step-like potential remaining bound. This behavior is exhibited in ultralong-range Rydberg molecules, which abound with almost step-like drops at points where potential curves narrowly avoid each other. Despite such a potential landscape, there are numerous resonance states bound by quantum reflection, within Born-Oppenheimer approximation. However, when potential curves come close to each other, they become coupled, leading to significant non-adiabatic couplings. On the poster I will present their influence on molecular binding, recently studied in our work.

A convenient method to describe light matter interaction in cavity resonators is to reduce the involved degrees of freedom to the absolute minimum. In the context of a localized quantum emitter in a lossy cavity, the so-called pseudomode approach condenses the effect of the electromagnetic field on the emitter’s dynamics in a discrete set of effective modes. These modes absorb the strongly-coupling field’s degrees of freedom and the weakly-coupling ones are usually represented as an external “environment”, allowing one to efficiently describe the emitter’s dynamics, e.g. by Markovian Lindblad master equations. This system-environment separation becomes ever more difficult, though, as the system’s complexity and/or the number of strongly coupled degrees of freedom increase. Here, we construct a fully analytical and non-perturbative pseudomode model for open cavities by “reverse-engineering” from the exact, position-resolved spectral density within the cavity. This subsequently guarantees the construction of an optimal set of modes that efficiently captures the emitter’s dynamics. Our method thus generalizes the application of the standard pseudomodes to more complex targets such as condensed matter or extended atomic systems and even to very leaky open cavities.