Using a semi-classical approach, we derive a fully analytical expression for the ionization rate of excitons in two-dimensional materials due to an external static electric field, which eliminates the need for complicated numerical calculations. Our formula shows quantitative agreement with more sophisticated numerical methods based on the exterior complex scaling approach, which solves a non-hermitian eigenvalue problem yielding complex energy eigenvalues, where the imaginary part describes the ionization rate. Results for excitons in hexagonal boron nitride and the $A-$exciton in transition metal dichalcogenides are given as a simple examples. The extension of the theory to include spin-orbit-split excitons in transition metal dichalcogenides is trivial.
We show that two initially non-resonant quantum dots may be brought into resonance by the application of a single detuned laser. This allows for control of the inter-dot interactions and the generation of highly entangled excitonic states on the picosecond timescale. Along with arbitrary single qubit manipulations, this system would be sufficient for the demonstration of a prototype excitonic quantum computer.
The optical Stark effect is a tell-tale signature of coherent light-matter interaction in excitonic systems, wherein an irradiating light beam tunes exciton transition frequencies. Here we show that, when excitons are placed in a nanophotonic cavity, the excitonic Stark effect can become highly nonlinear, exhibiting multi-valued and hysteretic Stark shifts that depend on the history of the irradiating light. This multistable Stark effect (MSE) arises from feedback between the cavity mode occupation and excitonic population, mediated by the Stark-induced mutual tuning of the cavity and excitoni…
The emission spectrum of exciton complexes formed in individual self-assembled quantum dots (QDs) embedded into a p-n junction is theoretically studied using an effective mass model. We calculate the particle Coulomb interactions, eletron-hole overlaps and transition energies of exciton complexes for the different strength and direction of electric field. Both redshifts and blueshifts are observed in exciton, trions and biexciton. The Stark effect may be applied to manipulate the spontaneous emission rate of individual QDs embedded in microcavities.
We compute binding energies, Stark shifts, electric-field-induced dissociation rates, and the Franz-Keldysh effect for excitons in phosphorene in various dielectric surroundings. All three effects show a pronounced dependence on the direction of the in-plane electric field, with the dissociation rates in particular decreasing by several orders of magnitude upon rotating the electric field from the armchair to the zigzag axis. To better understand the numerical dissociation rates, we derive an analytical approximation to the anisotropic rates induced by weak electric fields, thereby generalizin…
We calculate the excitonic spectrum of few-layer black phosphorus by direct diagonalization of the effective mass Hamiltonian in the presence of an applied in-plane electric field. The strong attractive interaction between electrons and holes in this system allows one to investigate the Stark effect up to very high ionizing fields, including also the excited states. Our results show that the band anisotropy in black phosphorus becomes evident in the direction dependent field induced polarizability of the exciton.
We report on the observation of spin dependent optically dressed states and optical Stark effect on an individual Mn spin in a semiconductor quantum dot. The vacuum-to-exciton or the exciton-to-biexciton transitions in a Mn-doped quantum dot are optically dressed by a strong laser field and the resulting spectral signature is measured in photoluminescence. We demonstrate that the energy of any spin state of a Mn atom can be independently tuned using the optical Stark effect induced by a control laser. High resolution spectroscopy reveals a power, polarization and detuning dependent Autler-Town…
Resonant transfer of energy between excited states in a system of two semiconductor quantum dots is studied theoretically. The model Hamiltonian has been formulated, which allowed describe the impact on the dynamics of the resonant laser pulse, the Coulomb interaction, the static Stark effect, and the relaxation of the exciton states. Examples of calculations for efficiency of the energy transfer under different excitation conditions are presented. The control of the process by the level shift in a constant electric field is demonstrated.
When a detuned and strong laser pulse acts on an optical transition, a Stark shift of the corresponding energies occurs. We analyze how this optical Stark effect can be used to prepare and control the dark exciton occupation in a semiconductor quantum dot. The coupling between the bright and dark exciton states is facilitated by an external magnetic field. Using sequences of laser pulses, we show how the dark exciton and different superposition states can be prepared. We give simple analytic formulas, which yield a good estimate for optimal preparation parameters. The preparation scheme is qui…
We investigate electric-field induced redshifts of photoluminescence from individual single-walled carbon nanotubes. The shifts scale quadratically with field, while measurements with different excitation powers and energies show that effects from heating and relaxation pathways are small. We attribute the shifts to the Stark effect, and characterize nanotubes with different chiralities. By taking into account exciton binding energies for air-suspended tubes, we find that theoretical predictions are in quantitative agreement.
We propose a coherent control scheme based on the optical Stark effect in optically generated excitons in quantum dot molecules (QDMs). We show that, by the combined action of voltage bias detuning sweeps and Rosen-Zener pulsed interactions, it is possible to dynamically generate and modify an anticrossing gap that emerges between the dressed energy levels of long-lived, spatially indirect excitons. We perform numerical and analytic non-perturbative calculations based on the Bloch-Feshbach formalism, which demonstrate that this effect induces a mechanism of coherent population trapping of indi…
We investigate and compare experimental and numerical excitonic spectra of the yellow series in cuprous oxide Cu$_2$O in the Voigt configuration and thus partially extend the results from Schweiner et al. [Phys. Rev. B 95, 035202 (2017)], who only considered the Faraday configuration. The main difference between the configurations is given by an additional effective electric field in the Voigt configuration, caused by the motion of the exciton through the magnetic field. This Magneto-Stark effect was already postulated by Gross et al. and Thomas et al. in 1961 [Sov. Phys. Solid State 3, 221 (1…
We present Floquet-Keldysh non-equilibrium dynamical mean field calculations (DMFT) with an iterative perturbative solver (IPT) for high pump-power induced Stark states yielding a closing gap within semiconductor bulk and nano-cavities. Our model predicts unusual broadening of bands in systems like ZnO random lasers. This can be explained as an exciton-polariton coupling within the single crystalline pillar meeting the Mie resonance condition. Extraordinary enhancement of the lifetime of electronic states within the gap can lead to stable lasing modes and gain narrowing.
We calculate the optical properties of carbon nanotubes in an external static electric field directed along the tube axis. We predict strong Franz-Keldysh oscillations in the first and second band-to-band absorption peaks, quadratic Stark effect of the first two excitons, and the field dependence of the bound exciton ionization rate for a wide range of tube chiralities. We find that the phonon assisted mechanism dominates the dissociation rate in electro-optical devices due to the hot optical phonons. We predict a quadratic dependence of the Sommerfeld factor on the electric field and its incr…
We theoretically investigate excitons in MoS$_2$ monolayers in an applied in-plane electric field. Tight-binding and Bethe-Salpeter equation calculations predict a quadratic Stark shift, of the order of a few meV for fields of 10 V/$μ$m, in the linear absorption spectra. The spectral weight of the main exciton peaks decreases by a few percent with an increasing electric field due to the exciton field ionization into free carriers as reflected in the exciton wave functions. Subpicosecond exciton decay lifetimes at fields of a few tens of V/$μ$m could be utilized in solar energy harvesting and p…
Monolayer transition metal dichalcogenide semiconductors host strongly bound two-dimensional excitonic complexes, and form an excellent platform for probing many-body physics through manipulation of Coulomb interaction. Quantum confined Stark effect is one of the routes to dynamically tune the emission line of these excitonic complexes. In this work, using a high quality graphene/hBN/WS$_2$/hBN/Au vertical heterojunction, we demonstrate for the first time, an out-of-plane electric field driven change in the sign of the Stark shift from blue to red for four different excitonic species, namely, …
We present experimental observations of a non-resonant dynamic Stark shift in strongly coupled microcavity quantum well exciton-polaritons - a system which provides a rich variety of solid-state collective phenomena. The Stark effect is demonstrated in a GaAs/AlGaAs system at 10K by femtosecond pump-probe measurements, with the blue shift approaching the meV scale for a pump fluence of 2 mJcm^-2 and 50 meV red detuning, in good agreement with theory. The energy level structure of the strongly coupled polariton Rabi-doublet remains unaffected by the blue shift. The demonstrated effect should al…
We study the effect of an electric-field on an electron-hole pair in an asymmetric system of vertically coupled self-assembled quantum dots taking into account their non-perfect alignment. We show that the non-perfect alignment does not qualitatively influence the exciton Stark effect for the electric field applied in the growth direction, but can be detected by application of a perpendicular electric field. We demonstrate that the direction of the shift between the axes of non-aligned dots can be detected by rotation of a weak electric field within the plane of confinement. Already for a near…
We demonstrate electrical control of the A-exciton interband transition in mono- and few-layer $MoS_{2}$ crystals embedded into photocapacitor devices via the DC Stark effect. Electric field dependent low-temperature photoluminescence spectroscopy reveals a significant tuneability of the A-exciton transition energy, up to $\sim 16 meV$, from which we extract the mean DC exciton polarisability $<\barβ>_{N} = (0.58 \pm 0.25) \cdot 10^{-8} DmV^{-1}$. The exciton polarisability is shown to be layer-independent, indicating a strong localisation of both electron and hole wave functions in each indiv…
In this paper, we study the exciton absorption spectra in InGaAs prolate ellipsoidal quantum dots when a strong pump laser resonant with electron quantized levels is active. Our obtained results by renormalized wavefunction theory show that, under suitable conditions, the initial exciton absorption peak is split into two new peaks as the evidence of the existence of the three-level optical Stark effect of excitons. We have suggested an explanation of the origin of the effect as well as investigating the effect of pump field energy, size, and geometric shape of the quantum dots on effect charac…
Transition metal dichalcogenides (TMDs) constitute a versatile platform for atomically thin optoelectronics devices and spin-valley memory applications. In monolayers optical absorption is strong, but the transition energy is not tunable as the neutral exciton has essentially no out-of-plane electric dipole. In contrast, interlayer exciton transitions in heterobilayers are widely tunable in applied electric fields, but their coupling to light is considerably reduced. Here, we show tuning over 120 meV of interlayer excitons with high oscillator strength in bilayer MoS2. These shifts are due to …
We report on the experimental and theoretical investigation of magnetic-field-induced second harmonic generation (SHG) and two-photon absorption (TPA) of excited exciton states ($n \geq 3$) of the yellow series in Cu$_2$O. In this centrosymmetric material, SHG can occur due to constructive interplay of electric dipole and electric quadrupole/magnetic dipole transitions for light propagating along the low-symmetry directions [111] or [112]. By application of a magnetic field in Voigt configuration, SHG gets also allowed for excitation along the [110]-axis and even the high-symmetry cubic direct…
Photoexcited intralayer excitons in van der Waals heterostructures (vdWHs) with type-II band alignment have been observed to tunnel into interlayer excitons on ultrafast timescales. Such interlayer excitons have sufficiently long lifetimes that inducing dissociation with external in-plane electric fields becomes an attractive option of improving efficiency of photocurrent devices. In the present paper, we calculate interlayer exciton binding energies, Stark shifts, and dissociation rates for six different transition metal dichalcogenide (TMD) vdWHs using a numerical procedure based on exterior…
The $k\cdot p$ effective mass approximation (EMA) predicts large, nearly size-independent exciton oscillator strengths in quantum confined semiconductors. Yet, experimental reports have concluded that the total oscillator strength of the lowest-energy (1S$_{3/2}$1S$_{\text{e}}$) excitons in strongly confined CdSe NQDs is small and strongly size-dependent. Using the optical Stark effect, we show that the oscillator strength of the 1S$_{3/2}$1S$_{\text{e}}$ excitonic absorption peak in CdSe NQDs follows the predictions of the EMA. These oscillator strengths enable helicity-selective unsaturated …
The optics of dangling-bond-free van der Waals heterostructures containing transition metal dichalcogenides are dominated by excitons. A crucial property of a confined exciton is the quantum confined Stark effect (QCSE). Here, such a heterostructure is used to probe the QCSE by applying a uniform vertical electric field across a molybdenum disulfide (MoS$_2$) monolayer. The photoluminescence emission energies of the neutral and charged excitons shift quadratically with the applied electric field provided the electron density remains constant, demonstrating that the exciton can be polarized. St…
In 1H monolayer transition metal dichalcogenide, the inversion symmetry is broken, while the reflection symmetry is maintained. On the contrary, in the bilayer, the inversion symmetry is restored, but the reflection symmetry is broken. As a consequence of these contrasting symmetries, here we show that bilayer WS$_2$ exhibits a quantum confined Stark effect (QCSE) that is linear with the applied out-of-plane electric field, in contrary to a quadratic one for a monolayer. The interplay between the unique layer degree of freedom in the bilayer and the field driven partial inter-conversion betwee…
Electric field-controlled, two-dimensional (2D) exciton dynamics in transition metal dichalcogenide monolayers is a current research focus in condensed matter physics. We have experimentally investigated the spectral and temporal properties of the A-exciton in a molybdenum diselenide (MoSe2) monolayer under controlled variation of a vertical, electric dc field at room temperature. By using steady-state and time-resolved photoluminescence spectroscopies, we have observed dc field-induced spectral shifts and linewidth broadenings that are consistent with the shortening of the exciton's non-radia…
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.
As the field of metal halide perovskites (MHP) matures, state-of-the-art techniques to measure basic properties such as the band gap and exciton binding energy continue to produce inconsistent values. This issue is persistent even for 2D MHPs wherein the large separation between exciton and continuum states should make such measurements more straightforward. In this study, we revert to the established theory of a 2D Wannier exciton in a uniform electric field to analyze the electroabsorption response of an archetypal 2D MHP system, phenethylammonium lead iodide (PEA2PbI4). The high level of ag…
We report on the theoretical and experimental investigation of valley-selective optical Stark and Bloch-Siegert shifts of exciton resonances in monolayers WSe$_2$ and MoS$_2$ induced by strong circularly polarized nonresonant optical fields. We predict and observe transient shifts of both 1sA and 1sB exciton transitions in the linear interaction regime. The theoretical description is based on semiconductor Bloch equations. The solutions of the equations are obtained with a modified perturbation technique, which takes into account many-body Coulomb interaction effects. These solutions allow to …
We investigate the near infrared interband absorption of semiconductor quantum wells driven by intense terahertz radiation in the regime of ultrastrong coupling, where the Rabi frequency is a significant fraction of the frequency of the strongly driven transition. With the driving frequency tuned just below the lowest frequency transition between valence subbands, a particularly interesting phenomenon is observed. As the THz power increases, a new peak emerges above the frequency of the undriven exciton peak which grows and eventually becomes the larger of the two. This reversal of relative pe…
Coherent optical dressing of quantum materials offers technological advantages to control their electronic properties, such as the electronic valley degree of freedom in monolayer transition metal dichalcogenides (TMDs). Here, we observe a new type of optical Stark effect in monolayer WS2, one that is mediated by intervalley biexcitons under the blue-detuned driving with circularly polarized light. We found that such helical optical driving not only induces an exciton energy downshift at the excitation valley, but also causes an anomalous energy upshift at the opposite valley, which is normall…
The effect of external electric field on electron-hole correlation in GaAs quantum dots is investigated. The electron-hole Schrodinger equation in the presence of external electric field is solved using explicitly correlated full configuration interaction (XCFCI) method and accurate exciton binding energy and electron-hole recombination probability are obtained. The effect of the electric field was included in the 1-particle single component basis functions by performing variational polaron transformation. The quality of the wavefunction at small inter-particle distances was improved by using …
We show how to compute the optical functions of Wide Parabolic Quantum Wells (WPQWs) exposed to uniform electric F applied in the growth direction, in the excitonic energy region. The effect of the coherence between the electron-hole pair and the electromagnetic field of the propagating wave including the electron-hole screened Coulomb potential is adopted, and the valence band structure is taken into account in the cylindrical approximation. The role of the interaction potential and of the applied electric field, which mix the energy states according to different quantum numbers and create sy…
The interactions between the excited states of a single chromophore with static and dynamic electric fields confined to a plasmonic cavity of picometer dimensions are investigated in a joint experimental and theoretical effort. In this configuration, the spatial extensions of the confined fields are smaller than the one of the molecular exciton, a property that is used to generate fluorescence maps of the chromophores with intra-molecular resolution. Theoretical simulations of the electrostatic and electrodynamic interactions occurring at the chromophore-picocavity junction are able to reprodu…
This letter assigns the Faraday rotation in photoexcited semiconductors to ``Pauli interactions'', \emph{i}. \emph{e}., carrier exchanges, between the real excitons present in the sample and the virtual excitons coupled to the $σ_{\pm}$ parts of a linearly polarized light. While \emph{direct Coulomb} interactions scatter bright excitons into bright excitons, whatever their spins are, \emph{Pauli} interactions do it for bright excitons \emph{with same spin only}. This makes these Pauli interactions entirely responsible for the refractive index difference, which comes from processes in which the…
A new degree of freedom, the valley pseudospin, emerges in atomically thin two-dimensional transition metal dichalcogenides (MX2) and has attracted great scientific interest. The capability to manipulate the valley pseudospin, in analogy to the control of spin in spintronics, can open up exciting opportunities in valleytronics. Here we demonstrate that an ultrafast and ultrahigh valley pseudomagnetic field can be generated using circularly polarized femtosecond pulses to selectively control the valley degree of freedom in monolayer MX2. Employing ultrafast pump-probe spectroscopy, we observed …
The study of two-dimensional (2D) van der Waals materials has been an active field of research in the development of new optoelectronics and photonic applications over the last decade. Organic-inorganic layered perovskites are currently some of the most promising 2D van der Waals materials, due to their exceptional optical brightness and enhanced excitonic effects. However, low crystal quality and spectral diffusion usually broaden the exciton linewidth, obscuring the fine structure of the exciton in conventional photoluminescence experiments. Here, we propose a mechanical approach for reducin…
Indirect excitons in coupled quantum wells have long radiative lifetimes and form a cold quasi-two-dimensional population suitable for studying collective quantum effects. Here we report the observation of the exciton Mott transition from an insulating (excitons) to a conducting (ionized electron-hole pairs) phase, which occurs gradually as a function of carrier density and temperature. The transition is inferred from spectral and time-resolved photoluminescence measurements around a carrier density of $2\times10^{10} \mathrm{cm}^{-2}$ and temperatures of $12-16 \mathrm{K}$. An externally appl…
We report experimental evidence of excitonic spin-splitting, in addition to the conventional Zeeman effect, produced by a combination of the Rashba spin-orbit interaction, Stark shift and charge screening. The electric-field-induced modulation of the spin-splitting are studied during the charging and discharging processes of p-type GaAs/AlAs double barrier resonant tunneling diodes (RTD) under applied bias and magnetic field. The abrupt changes in the photoluminescence, with the applied bias, provide information of the charge accumulation effects on the device.
Demonstrating the quantum-confined Stark effect (QCSE) in silicon nanocrystals (NCs) embedded in oxide has been rather elusive, unlike the other materials. Here, the recent experimental data from ion-implanted Si NCs is unambiguously explained within the context of QCSE using an atomistic pseudopotential theory. This further reveals that the majority of the Stark shift comes from the valence states which undergo a level crossing that leads to a nonmonotonic radiative recombination behavior with respect to the applied field. The polarizability of embedded Si NCs including the excitonic effects …
We investigate the magneto-optical properties of excitons bound to single stacking faults in high-purity GaAs. We find that the two-dimensional stacking fault potential binds an exciton composed of an electron and a heavy-hole, and confirm a vanishing in-plane hole $g$-factor, consistent with the atomic-scale symmetry of the system. The unprecedented homogeneity of the stacking-fault potential leads to ultra-narrow photoluminescence emission lines (with full-width at half maximum ${\lesssim 80~μ\text{eV} }$) and reveals a large magnetic non-reciprocity effect that originates from the magneto-S…
We develop a theoretical background to treat exciton states of semiconductor single-walled carbon nanotubes (SWCNTs) in presence of a periodic potential induced by the surface acoustic wave (SAW) propagating along semiconducting SWCNT. The formalism naturally accounts for the electronic bands splitting into the Floquet sub-bands brought about by the Bragg scattering on the SAW potential. Optically induced transitions within the Floquet states and formation of correlated electron-hole pairs, i.e., exciton states, are examined numerically. We discuss dynamical formation of new van Hove singulari…
We demonstrate an electrostatic trap for indirect excitons in a field-effect structure based on coupled GaAs quantum wells. Within the plane of a double quantum well indirect excitons are trapped at the perimeter of a SiO2 area sandwiched between the surface of the GaAs heterostructure and a semitransparent metallic top gate. The trapping mechanism is well explained by a combination of the quantum confined Stark effect and local field enhancement. We find the one-dimensional trapping potentials in the quantum well plane to be nearly harmonic with high spring constants exceeding 10 keV/cm^2.
The optically induced spin dynamics of a single Mn atom embedded into a single semiconductor quantum dot can be strongly influenced by using the optical Stark effect. The exchange interaction gives rise to simultaneous spin flips between the quantum dot electron and Mn. In the time domain these flips correspond to exchange induced Rabi oscillations, which are typically off-resonant. By applying a detuned laser pulse, the states involved in the flipping can be brought into resonance by means of the optical Stark effect increasing the amplitude of the Rabi oscillations to one. In this paper we s…
Generation of photocurrents in semiconducting materials requires dissociation of excitons into free charge carriers. While thermal agitation is sufficient to induce dissociation in most bulk materials, an additional push is required to induce efficient dissociation of the strongly bound excitons in monolayer transition-metal dichalcogenides (TMDs). Recently, static in-plane electric fields have proven to be a promising candidate. In the present paper, we introduce a numerical procedure, based on exterior complex scaling, capable of computing field-induced exciton dissociation rates for a wider…
Recently, we suggested an unconventional approach [the so-called Internal-Field-Guarded-Active-Region Design (IFGARD)] for the elimination of the crystal polarization field induced quantum confined Stark effect (QCSE) in polar semiconductor heterostructures. And in this work, we demonstrate by means of micro-photoluminescence techniques the successful tuning as well as the elimination of the QCSE in strongly polar $[000\bar{1}]$ wurtzite GaN/AlN nanodiscs while reducing the exciton life times by more than two orders of magnitude. The IFGARD based elimination of the QCSE is independent of any s…
Exciton spectra of monolayer transition metal dichalcogenides (TMDs) in various dielectric environments are studied. The screened hydrogen model (SHM) [Phys. Rev. Lett. 116, 056401 (2016)] is examined by comparing its exciton spectra with the radial equation (RE) solutions. While the SHM is found to describe the nonhydrogenic exciton Rydberg series reasonably well, it fails to account for the linear decrease of the exciton energy with the orbital quantum number $m$. The exciton Bohr orbit shrinks as $\lvert m\rvert$ becomes larger resulting in increased strength of the electron-hole interactio…
The Berry phase of Bloch states can have profound effects on electron dynamics lead to novel transport phenomena, such as the anomalous Hall effect and the valley Hall effect. Recently, it was predicted that the Berry phase effect can also modify the exciton states in transition metal dichalcogenide monolayers, and lift the energy degeneracy of exciton states with opposite angular momentum through an effective valley-orbital coupling. Here, we report the first observation and control of the Berry-phase induced splitting of the 2p-exciton states in monolayer molybdenum diselenide using the intr…
We optimized the performance of quantum confined Stark effect QCSE based voltage nanosensors. A high throughput approach for single particle QCSE characterization was developed and utilized to screen a library of such nanosensors. Type II ZnSe CdS seeded nanorods were found to have the best performance among the different nanosensors evaluated in this work. The degree of correlation between intensity changes and spectral changes of the excitons emission under applied field was characterized. An upper limit for the temporal response of individual ZnSe CdS nanorods to voltage modulation was char…
