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arXiv:1704.00974 · Physical review. B./Physical review. B

Scaling laws of Rydberg excitons

Julian Heckötter, Marcel Freitag, D. Fröhlich, Marc Aßmann, M. Bayer, Marina A. Semina, Михаил Михайлович Глазов

Published Sep 22, 2017• 75 citations
arXivHTMLPDF

Abstract

The recent observation of excitons in highly excited states has allowed the study of Rydberg physics in cuprous oxide crystals. This opens the unique possibility to elaborate on similarities and differences between Rydberg atoms and Rydberg excitons, as done here experimentally and theoretically for quantities related to the splitting of multiplets with particular principal quantum number $n$ in zero and finite electric or magnetic fields. The authors find characteristic scaling laws with $n$ with some discrepancies between excitons and atoms, but surprisingly, they find mostly similarities, even though the underlying physics, such as the complex valence band structure, are quite different.

DOI
10.1103/physrevb.96.125142

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The recent observation of excitons in highly excited states has allowed the study of Rydberg physics in cuprous oxide crystals. This opens the unique possibility to elaborate on similarities and differences between Rydberg atoms and Rydberg excitons, as done here experimentally and theoretically for quantities related to the splitting of multiplets with particular principal quantum number nnn in zero and finite electric or magnetic fields. The authors find characteristic scaling laws with nnn with some discrepancies between excitons and atoms, but surprisingly, they find mostly similarities, even though the underlying physics, such as the complex valence band structure, are quite different.
The complex valence band structure of bulk cuprous oxide necessitates going beyond the parabolic approximation to precisely estimate exciton binding energies. The same is true for excitons in cuprous oxide quantum wells, for which many effects have been obtained so far only qualitatively within a hydrogenlike two-band model. Here, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells based on the Luttinger-Kohn model, taking into account the full complex valence band structure. Symmetry properties of the system are discussed. Numerical results based on the diagonalization of the Hamiltonian using B-spline functions reveal the energy shifts and the lifting of degeneracies due to the nondiagonal coupling terms of the complex valence band. The relative oscillator strengths of the excitonic transitions induced by circularly polarized light are also calculated.
Rydberg excitons are semiconductor analogues to Rydberg atoms, where one electron is promoted to an energy level of large principal quantum number η and which behave in a manner similar to hydrogen. Their huge spatial extent results in giant dipole moments and interaction effects, which can be used to create nonlinearities at the single excitation level. In contrast to hydrogen, the effective masses and Rydberg energies involved are moderately small, so that in contrast to Rydberg atoms the high field limit of Rydberg physics can be studied using fields strengths that can be realized in the lab. Here we investigate the effects of external magnetic fields of up to 7T on Rydberg excitons both in Faraday and Voigt geometry. In both cases complicated splitting patterns emerge. We investigate the differences between the two geometries and highlight spectroscopic features that are especially easy to access using them. We show that the large number of resonances in the spectrum renders a microscopic treatment of each individual resonance implausible. We instead demonstrate general effects introduced by the field like avoided crossings and discuss alternative approaches to the level structure in terms of collective descriptions.
Abstract Within the last few years, Rydberg excitons, bound electron–hole pairs in highly excited states, have emerged as a promising technology platform for quantum nonlinear optics, quantum information processing, and quantum sensing. The advanced device designs and sensing concepts in these fields require strong nonlinearities at the few-photon or few-carrier level. Rydberg states offer the required strong nonlinearities as the relevant physical quantities at the heart of such nonlinear effects scale strongly with the principal quantum number, n, of the excited state: For example, their polarizability scales as n7n^7n7 n 7 , resulting in an enormous sensitivity to external fields. We review recent experimental and theoretical results that pave the way toward quantum sensing of the electric fields originating from static charge carriers and strongly diluted electron–hole plasmas. We also discuss the strong nonlinear optical properties of Rydberg excitons and how they could be utilized in terms of sensing. Graphical abstract
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. We show giant Rydberg excitons at T=38T=38T=38 mK with principal quantum numbers up to n=30n=30n=30, corresponding to a calculated diameter of $3\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$.
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 to quantum optics and technology. 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. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This is made possible by two-color pump-probe experiments that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character.
Hosting giant Rydberg excitons with principal quantum numbers up to n = 30, cuprous oxide (Cu2O) provides a rare solid-state setting for exploring Rydberg physics, as exemplified by the blockade effect. Here we access the strongly interaction regime at high excitation densities (10^14-10^16/cm^3) and resolve the corresponding blockade dynamics for n = 2-7 using time-resolved spectroscopy. We find that Rydberg blockades are primarily governed by resonant dipolar interactions and that exciton recombination is coupled to the blockade itself. These findings demonstrate the potential for manipulating Rydberg exctions in the strongly interacting blockade regime in a solid state system.