Excitons In Cu Research Articles

Microwave-optical spectroscopy of Rydberg excitons in the ultrastrong driving regime

Abstract We study the ultrastrong driving of Rydberg excitons in Cu$_2$O by a microwave field. The effect of the field is studied using optical absorption spectroscopy, and through the observation of sidebands on the transmitted laser light. A model based on Floquet theory is constructed to study the system beyond the rotating wave approximation. We obtain near quantitative agreement between theory and experiment across a 16-fold range of microwave field strengths spanning from the perturbative to the deep strong driving regime. Compared to Rydberg atoms, the large non-radiative widths of Rydberg excitons leads to new behaviour such as the emergence of an absorption continuum without ionization.

Copper plasmonics with excitons

We investigate the propagation of surface plasmons (SPPs) in a thin layer of copper surrounded by copper oxide Cu$_2$O. It is shown that particularly strong excitons in Cu$_2$O can have considerable impact on plasmon propagation, providing many opportunities for plasmon-exciton and plasmon-plasmon interactions. It is demonstrated that by the use of sufficiently thin metal layer, one can excite the so-called long range plasmons (LRSPPs) which can overcome the inherently high ohmic losses of Cu as compared to usual plasmonic metals such as silver. Analytical results are confirmed by numerical calculations.

Self-Kerr Effect across the Yellow Rydberg Series of Excitons in Cu_{2}O.

We investigate the nonlinear refraction induced by Rydberg excitons in Cu_{2}O. Using a high-precision interferometry imaging technique that spatially resolves the nonlinear phase shift, we observe significant shifts at extremely low laser intensity near each exciton resonance. From this, we derive the nonlinear index n_{2}, present the n_{2} spectrum for principal quantum numbers n≥5, and report large n_{2} values of order 10^{-3} mm^{2}/mW. Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that the saturation intensity I_{sat} decreases as n^{-7}. We explain this with the Rydberg blockade mechanism, whereby giant Rydberg interactions limit the exciton density, resulting in a maximum phase shift of 0.5rad in our setup.

Controlling Exciton-Phonon Interactions via Electromagnetically Induced Transparency.

Highly excited Rydberg states of excitons in Cu_{2}O semiconductors provide a promising approach to explore and control strong particle interactions in a solid-state environment. A major obstacle has been the substantial absorption background that stems from exciton-phonon coupling and lies under the Rydberg excitation spectrum, weakening the effects of exciton interactions. Here, we demonstrate that two-photon excitation of Rydberg excitons under conditions of electromagnetically induced transparency (EIT) can be used to control this background. Based on a microscopic theory that describes the known single-photon absorption spectrum, we analyze the conditions under which two-photon EIT permits separating the optical Rydberg excitation from the phonon-induced absorption background, and even suppressing it entir7ely. Our findings thereby pave the way for the exploitation of Rydberg blockade with Cu_{2}O excitons in nonlinear optics and other applications.

Dynamically Steered Maser Action of Rydberg Excitons in Cu2O

The Rydberg excitons in Cu2O are a promising candidate for realization of solid state maser. The highly excited states, unique to this crystal, provide the necessary energy level transitions for emission of microwaves. The achievement of population inversion is facilitated by exceptionally long lifetimes of excitons and their strong coupling to external field. Moreover, due to the strong Stark shift of excitonic energy levels, one can tune the emission wavelength on demand.

Interactions between Rydberg excitons in Cu2O

Highly-excited states of excitons in cuprous oxide have recently been observed at a record quantum number of up to $n=25$. Here, we evaluate the long-range interactions between pairs of Rydberg excitons in Cu$_2$O, which are due to direct Coulomb forces rather than short-range collisions typically considered for ground state excitons. A full numerical analysis is supplemented by the van der Waals asymptotics at large exciton separations, including the angular dependence of the potential surfaces.

Rydberg Excitons in the Presence of an Ultralow-Density Electron-Hole Plasma.

We study the Rydberg exciton absorption of Cu_{2}O in the presence of free carriers injected by above-band-gap illumination. Already at plasma densities ρ_{EH} below one hundredth electron-hole pair per μm^{3}, exciton lines are bleached, starting from the highest observed principal quantum number, while their energies remain constant. Simultaneously, the band gap decreases by correlation effects with the plasma. An exciton line loses oscillator strength when the band gap approaches its energy, vanishing completely at the crossing point. Adapting a plasma-physics description, we describe the observations by an effective Bohr radius that increases with rising plasma density, reflecting the Coulomb interaction screening by the plasma.

Waveguides for Rydberg excitons in Cu2O from strain traps

We investigate the formation of waveguides for Rydberg excitons in Cu$_\text{2}$O from cylindrical stressors as alternatives to optical traps. We show that the achievable potential depths can easily reach the meV and the trap frequencies the GHz regimes. For Rydberg excitons, we find that it is sufficient to consider only the shift of the band gap, whereas the excitonic binding energies remain almost unchanged.

Electro-optical properties of Cu2O for P excitons in the regime of Franz-Keldysh oscillations

We present the analytical method enables one to compute the optical functions i.e., reflectivity, transmission and absorption including the excitonic effects for a semiconductor crystal exposed to a uniform electric field for energy region above the gap, for external field suitable to appearance of Franz-Keldysh (FK) oscillations. Our approach intrinsically takes into account the coherence between the carriers and the electromagnetic field. We quantitatively describe the amplitudes and periodicity of FK modulations and the influence of Rydberg excitons on FK effect is also taking into account. Our analytical findings are illustrated numerically for $P$ excitons in Cu$_2$O crystal.

Тонкая структура ридберговских экситонов в закиси меди

AbstractIn 1952, E.F. Gross and N.A. Karryev discovered excitons of big radius also called the Wannier–Mott excitons. Their energy spectrum, response to external electric and magnetic fields, and also elastic deformations of a crystal were extensively studied in the 1960s–1970s. The second wave of interest to excitons in Cu_2O crystals appeared comparatively recent, in 2014, after the “giant” highly excited exciton states had been observed in this material. A theoretical description of highly excited exciton states needs, as a rule, new approaches, because, for such states, a deviation from the exactly solved hydrogen-like model becomes substantial and a numerical solution of the Schrödinger equation with allowance made for the features of the crystal energy band structure becomes extremely resource consuming. This report is a brief review of recent theoretical and experimental studies of the fine structure of the exciton energy spectrum in copper protoxide.

Phonon-assisted absorption of excitons in Cu2O

The basic theoretical foundation for the modelling of phonon assisted absorption spectra in direct bandgap semiconductors, introduced by Elliott 60 years ago using second order perturbation theory, results in a square root shaped dependency close to the absorption edge. A careful analysis of the experiments reveals that for the yellow S excitons in Cu$_2$O the lineshape does not follow that square root dependence. The reexamination of the theory shows that the basic assumptions of constant matrix elements and constant energy denominators is invalid for semiconductors with dominant exciton effects like Cu$_2$O, where the phonon assisted absorption proceeds via intermediate exciton states. The overlap between these and the final exciton states strongly determines the dependence of the absorption on the photon energy. To describe the experimental observed line shape of the indirect absorption of the yellow S exciton states we find it necessary to assume a momentum dependent deformation potential for the optical phonons.

Stress Effects on nP Yellow Excitons in Cu2O Thin Films Recrystallized Epitaxially in a Sample Gap between Paired MgO Substrates

We investigated the stress effects on nP yellow excitons in Cu2O thin films recrystallized epitaxially in a sample gap between paired MgO substrates. In such samples, it is expected that a two-dimensional compressive stress acts on Cu2O because of the slightly larger lattice constant of Cu2O than of MgO. To clarify such stress effects, we measured the X-ray diffraction and nP absorption transitions of the yellow excitonic system and analyzed the strain and stress effects. Although the detected lattice strain and the energy shift of the yellow excitonic band gap are smaller than the values expected from the lattice mismatch at the heterointerface, this can be explained self-consistently by considering strain and stress relaxations in Cu2O thin films with departing from the MgO heterointerface. Consequently, we can find that shallow trapping potentials for the yellow excitons are formed in the ∼1.3-µm-thick region interfaced with the MgO substrates.

THz quantum optics with dark excitons in Cu2O: from stimulated emission to nonlinear population control

AbstractFundamental quantum optical processes in photogenerated excitons in Cu2O are demonstrated using few‐cycle terahertz pulses and field‐sensitive electro‐optic sampling: (i) In a dilute ensemble of 3p excitons, stimulated terahertz emission from internal transitions to the energetically lower 2s state is observed at a photon energy of 6.6 meV, with a cross section of 10‐14 cm2. (ii) An optically dark, dense, and cold 1s‐paraexciton gas is prepared by two‐photon generation of electron‐hole pairs and subsequent phonon cooling. Intense multi‐terahertz fields of order MV/cm coherently promote 70% of the quasiparticles from the 1s to the 2p state via a partial internal Rabi oscillation. Electro‐optic detection monitors the Larmor precession of the Bloch vector directly in the time domain, with femtosecond resolution. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulation of optical near field of a sub‐wavelength gold slit array and its electric quadrupole interaction with 1s excitons in Cu2O

AbstractLaight propagation through a gold film with a periodically structured 50 nm width slit array into Cu2O has been calculated with a FDTD (Finite Difference Time Domain) method with a 5 nm mesh‐grid. Owing to the presence of a guided mode in the slit and a surface plasmon mode at the gold/Cu2O interface, optical near field generation in Cu2O are efficient in the case where the polarization of the incident light is perpendicular to the slit. The efficiency of the electric quadrupole (E2) transition of the 1s ‐exciton in Cu2O, which is modified by the field gradient of the excitation light, is evaluated for the calculated optical near field. Slit period dependences of the near field generation and the E2 transition efficiency are examined for a 50 nm thick array film. The enhancement of the effective E2 transition efficiency in the volume of 50 nm thickness above the film relative to the efficiency by the plane wave excitation is found to reach a factor 28 at the slit period of 110 nm. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

High resolution spectroscopy of excitons in Cu2O

AbstractThe lowest ortho‐ and paraexcitons of Cu2O are studied by high‐resolution spectroscopy. After a detailed description of the experimental setup, the quadrupole polariton is extended to a two‐oscillator resonance. As an example, the group velocity of the M = ±1 orthoexciton components in a magnetic field of 0.1 T is measured and fitted to a two‐oscillator model with f (oscillator strength) as the only fit parameter. The paraexciton resonance is measured in a magnetic field of 10 T. Its oscillator strength is by almost a factor 200 lower than the oscillator strength of the orthoexciton. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

K‐dependent exchange interaction of quadrupole excitons in Cu2O

AbstractThe long‐ and short‐range exchange interaction for the quadrupole allowed transition to the yellow 1S orthoexciton in Cu2O is derived. While the three orthoexciton states still remain degenerate, when treating the exchange up to the order of K‐linear terms, a fine structure arises when K‐quadratic terms are included. This splitting is investigated experimentally by high resolution spectroscopy. Exchange contributions of few μeV are resolved and compared to theory. The impact of strain on the exciton fine structure is discussed and evaluated.

Two-photon diagnostics of stress-induced exciton traps and loading of1s-yellow excitons inCu2O

Two-photon spectroscopy is applied to stress-induced exciton traps for 1 yellow excitons in Cu 2 O crystals at 1.6 K. The resonance emission lines associated with orthoexcitons and paraexcitons are used to measure the shape and depth of the traps for respective species of excitons. The luminescence from paraexcitons shows well-resolved structure suggesting their drift motion toward the bottom of the trap. The transit time of the drift is evaluated to be 0.2 μs from the peak energy of the structure. This value is comparable to the decay time of paraexciton luminescence of 0.3 μs under 2.4 kbar stress measured by time-resolved spectroscopy. The decay time under the stress is slightly shorter than that with zero stress (0.6 μs), but is enough to establish the cooling of the paraexciton system.

1s TO 2p TRANSITIONS OF EXCITONS IN Cu 2 O

Infrared transitions of excitons in Cu 2 O from the 1s to 2p levels have been investigated with a pump-probe experiment. 1s densities around 10 15 /cm 3 have been created by pumping with a cw-laser and the induced 1s M 2p absorption has been probed simultaneously. The main experimental finding is that there is a splitting of , 3.7 v meV in the 2p level scheme, which has not been reported so far. Analyzing the linewidth and shape of the transitions, we find that the effective mass of the 1s state might have been overestimated in earlier studies.

Bose-Einstein condensation of excitons inCu2O

We present a parameter-free model which estimates the density of excitons in Cu$_2$O, related to experiments that have tried to create an excitonic Bose-Einstein condensate. Our study demonstrates that the triplet-state excitons move along adiabats and obey classical statistics, while the singlet-state excitons are a possible candidate for forming a Bose-Einstein condensate. Finally we show that the results of this study do not change qualitatively in a two-dimensional exciton gas, which can be realized in a quantum well.

SPATIALLY DEPENDENT AMPLIFICATION OF AN EXCITONIC BOSE-EINSTEIN CONDENSATE IN Cu2O

Experimental results are presented on the spatial dependence of amplification of a travelling Bose-Einstein condensate of excitons in Cu 2 O . The exciton condensate is created at T = 1.8 K by high intensity pulsed laser illumination (λ = 532 nm). Amplification of the moving condensate is triggered by the local, time-delayed injection of thermal excitons created by a lateral laser pulse tuned at the 1S orthoexciton resonance (λ = 609.48 nm), perpendicular to the path of the condensate. The amplification factor depends on the trigger time of the lateral laser pulse and is related to the stimulated scattering into the condensate of non-condensed excitons present in the crystal volume. A spatial correlation is also observed between the amplification factor and the optical attenuation of the lateral laser radiation induced by the passing condensate.