We investigate the influence of a static, uncorrelated distribution of charged impurities on the spectrum of bound excitons in the copper oxide Cu$_{\text{2}}$O. We show that the statistical distribution of Stark shifts and ionisation rates leads to the vanishing of Rydberg resonances into an apparent continuum. The appearance of additional absorption lines due to the broken rotational symmetry, together with spatially inhomogeneous Stark shifts, leads to a modification of the observed line shapes that agree qualitatively with the changes observed in the experiment.
We develop a many-body approach to the behavior of exciton bound states and the conduction electron band edge in a surrounding electron-hole plasma with a focus on the absorption spectrum of Rydberg excitons in cuprous oxide. The interplay of band edge and exciton levels is analyzed numerically, whereby the self-consistent solution is compared to the semiclassical Debye approximation. Our results provide criteria which allow to verify or rule out the different band edge models against future experimental data.
In this study we analyze the transmission spectrum of a thin plate of Cuprous Oxide in the range of the absorption of the yellow exciton states with the coherent transfer matrix method. We demonstrate that, in contrast to the usual analysis using Beer's law, which turns out to be a rather good approximation only in the spectral region of high principal quantum numbers, a consistent quantitative description over the whole spectral range under consideration is possible. This leads to new and more accurate parameters not only for the Rydberg exciton states, but also for the strengths of indirect …
We report exciton-mediated coupling between microwave and optical fields in cuprous oxide (Cu$_2$O) at low temperatures. Rydberg excitonic states with principal quantum number up to $n=12$ were observed at 4~K using both one-photon (absorption) and two-photon (second harmonic generation) spectroscopy. Near resonance with an excitonic state, the addition of a microwave field significantly changed the absorption lineshape, and added sidebands at the microwave frequency to the coherent second harmonic. Both effects showed a complex dependence on $n$ and angular momentum, $l$. All of these feature…
The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics [1, 2] to quantum optics [3, 4] and technology [5-7]. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors [8]. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two…
Experimental and theoretical investigations of excitons in cuprous oxide have revealed a significant fine-structure splitting of the excitonic Rydberg states caused by a strong impact of the valence band structure. We provide a semiclassical interpretation of that splitting by investigating the classical dynamics of the excitonic electron-hole pair beyond the hydrogen-like model. Considering the slow motion of Rydberg excitons in coordinate space compared to the fast dynamics of quasispin and hole spin we use an adiabatic approach and energy surfaces in momentum space for the computation of th…
Highly excited atoms with an electron moved into a level with large principal quantum number are fascinating hydrogen-like objects. The giant extension of these Rydberg atoms leads to huge interaction effects. Monitoring these interactions has provided novel insights into molecular and condensed matter physics problems on a single quantum level. Excitons, the fundamental optical excitations in semiconductors consisting of a negatively charged electron and a positively charged hole, are the condensed matter analogues of hydrogen. Highly excited excitons with extensions similar to Rydberg atoms …
We investigate the infrared optical transitions between excitons of the yellow, green and blue series in the cuprous oxide Cu$_{\mathrm{2}}$O. We show that in many cases the dipole approximation is inadequate and, in particular, that it breaks down in yellow-blue transitions even for moderate principal quantum numbers of $n \approx 10$. The interband matrix elements of the transition operator needed for the evaluation of the excitonic transition strengths are derived from known as well as from fitted band parameters.
We numerically investigate the odd parity states of the green exciton series in cuprous oxide. Taking into account the coupling to the yellow series and especially to the yellow continuum, the green excitons are quasi-bound resonances with a finite lifetime which cannot be described with Hermitian operators. To calculate their positions and linewidths, we use the method of complex-coordinate rotation, leading to a non-Hermitian complex eigenvalue problem. We find that the behavior of the dominant P states is very well approximated by a modified Rydberg formula using a negative quantum defect. …
The complete theoretical description of experimentally observed magnetoexcitons in cuprous oxide has been achieved by F. Schweiner et al [Phys. Rev. B 95, 035202 (2017)], using a complete basis set and taking into account the valence band structure and the cubic symmetry of the solid. Here, we extend these calculations by investigating numerically the autoionising resonances of cuprous oxide in electric fields and in parallel electric and magnetic fields oriented in [001] direction. To this aim we apply the complex-coordinate-rotation method. Complex resonance energies are computed by solving …
Excitons with a radius of a few lattice constants can be affected by strong central-cell corrections, leading to significant deviations of the optical spectrum from the hydrogen-like Rydberg series, and also to an enhancement of the exciton mass. We present an approach to this situation based on a lattice model that incorporates the effects of a non-parabolic band structure, short distance corrections to the Coulomb interaction between electrons and holes, spin-orbit and exchange coupling. The lattice model allows for observation of the crossover from large radius Wannier to small radius Frenk…
Charge impurities in graphene can host an infinite family of Rydberg-like resonance states of massless Dirac particles. These states, appearing for supercritical charge, are described by Bohr-Sommerfeld quantization of collapsing classical trajectories that descend on point charge, in analogy to Rydberg states relation with planetary orbits. We argue that divalent and trivalent charge impurities in graphene is an ideal system for realization of this atomic collapse regime. Strong coupling of these states to the Dirac continuum via Klein tunneling leads to striking resonance effects with direct…
Rydberg excitons are, with their ultrastrong mutual interactions, giant optical nonlinearities, and very high sensitivity to external fields, promising for applications in quantum sensing and nonlinear optics at the single-photon level. To design quantum applications it is necessary to know how Rydberg excitons and other excited states relax to lower-lying exciton states. Here, we present photoluminescence excitation spectroscopy as a method to probe transition probabilities from various excitonic states in cuprous oxide, and we show giant Rydberg excitons at $T=38$ mK with principal quantum n…
We theoretically investigate the nonlinear optical transmission through a cuprous oxide crystal for wavelengths that cover the series of highly excited excitons, observed in recent experiments. Since such Rydberg excitons have strong van der Waals interactions, they can dynamically break the conditions for resonant exciton creation and dramatically modify the refractive index of the material in a nonlinear manner. We explore this mechanism theoretically and determine its effects on the optical properties of a semiconductor for the case of degenerate pair-state asymptotes of Rydberg excitons in…
In one dimensional chains of trapped Rydberg excitons in cuprous oxide semiconductor the topological spin phase has been recently predicted [Phys. Rev. Lett. 123, 126801 (2019); arXiv:1903.11951]. This phase is characterized by the diluted antiferromagnetic order of $p$-shell exciton angular momenta-$1$ and the edge states behaving akin spin-$1/2$ fermions. Here we study the properties of the ground state in the finite chains and its fine structure resulting from the effective interaction of the edge spins. We demonstrate that these edge states can detected optically via the enhancement of the…
The observation of giant Rydberg excitons in cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ up to a principal quantum number of $n=25$ by T.~Kazimierczuk \emph{et al.} [Nature \textbf{514}, 343, (2014)] inevitably raises the question whether these quasi-particles must be described within a multi-polariton framework since excitons and photons are always coupled in the solid. In this paper we present the theory of exciton-polaritons in $\mathrm{Cu_{2}O}$. To this end we extend the Hamiltonian which includes the complete valence band structure, the exchange interaction, and the central-cell correc…
For low-density plasmas, the classical limit described by the Debye-Hückel theory is still considered as an appropriate description even though a clear experimental proof of this paradigm is lacking due to the problems in determining the plasma-induced shift of single-particle energies in atomic systems. We show that Rydberg excitons in states with a high principal quantum number are highly sensitive probes for their surrounding making it possible to unravel accurately the basic properties of low-density non-degenerate electron-hole plasmas. To this end, we accurately measure the parameters of…
We present a study of even parity Rydberg exciton states in cuprous oxide using time-resolved second harmonic generation (SHG). Excitonic states with principal quantum number n = 5 - 12 were excited by nanosecond pulses around 1143 nm. Using time-resolved single-photon counting, the coherently generated second harmonic was isolated both temporally and spectroscopically from inelastic emission due to lower-lying free and bound excitonic states, which included narrow resonances at 1.99 eV associated with an exceptional lifetime of 641 $\pm$ 7 $μ$s. The near transform-limited excitation bandwidth…
