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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Magnetic field effects of Rydberg Excitons in Cu2O

Johannes Thewes, Julian Heckötter, Marc Aßmann, D. Fröhlich, P. Grünwald, Stefan Scheel, M. Bayer

Published Feb 27, 2016• 1 citation

Abstract

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.

DOI: 10.1117/12.2218532

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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.

Over the past decade, Rydberg excitons in bulk Cu 2 O have emerged as a solid-state analog to atomic Rydberg systems, exhibiting exaggerated quantum optical properties including large dipole moments, strong dipole–dipole interactions, and enhanced nonlinear susceptibilities. High-resolution absorption spectroscopy has revealed elegant scaling laws with principal quantum number across temperatures from tens of mK to above 100 K. While many features follow a hydrogen-like model, non-hydrogenic effects arise from complex bandstructures and many-body interactions. This review summarizes experimental advances in accessing high- n Rydberg states and quantum phenomena arising from diverse exciton interaction mechanisms. It also discusses prospective quantum and nonlinear optical applications.

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=38

mK with principal quantum numbers up to

n=30

, corresponding to a calculated diameter of $3\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$.

A Rydberg atom has a highly excited valence electron which is weakly bound and far from the nucleus. These atoms have exaggerated properties that make them attractive candidates for quantum computation and studies of fundamental quantum mechanics. The discrete energy levels of Rydberg atoms are shifted in the presence of an electric field by the Stark effect and are similarly shifted due to a magnetic field by the Zeeman effect. These effects couple the energy levels together, creating avoiding crossings. At these avoided crossings, an electron in one energy level can jump to the other. Our goal is to be able to use these avoided crossings to put the electron in a superposition state of both energy levels. In order to achieve this we created new software that enables us to calculate the energy levels of an electron in both a magnetic and an electric field. We present energy level maps visualizing the results of the Stark and Zeeman effects.

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.

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

T=38

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.

Abstract Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon–photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu2O-filled microresonator. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as ∝ n4.4±1.8 for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly correlated photonic (polaritonic) states in a solid state system.