We present a comprehensive theoretical study of the resonance fluorescence spectra of an exciton-driven quantum dot (QD) placed inside a high-$Q$ semiconductor cavity and interacting with an acoustic phonon bath. We derive a quantum master equation (ME) in the polaron frame which includes exciton-phonon and exciton-cavity coupling to all orders. This work details and extends the theory used in a recent issue of {\em Physical Review Letters} (C. Roy and S. Hughes 2011: Phys. Rev. Lett. {\bf 106} 247403) to describe the QD Mollow triplet in the regime of semiconductor cavity-QED. Here we introduce two ME forms, Nakajima-Zwanzig (NZ) and time-convolutionless (TC), both to second order in the system--phonon-reservoir perturbation. In the polaron frame, these two ME forms are shown to yield equivalent population dynamics and fluorescence spectra for a continuous wave (cw) driving field. We also demonstrate that a Markov approximation is valid for computing the incoherent scattering processes and we subsequently exploit the Markovian TC ME to explore the resonance fluorescence spectra of an exciton-driven QD. Both cavity-emitted and exciton-emitted spectra are studied and these are found to have qualitatively different spectral features. Using a coherent driving field, the well known characteristics of the atomic Mollow triplet are shown to be considerably modified with electron--acoustic-phonon scattering and we highlight the key effects arising from both cavity coupling and electron-phonon coupling. Regimes of pronounced cavity feeding and anharmonic cavity-QED are exemplified, and we find that the cavity coupling depends sensitively on the exciton-cavity detuning and the temperature of the phonon bath. We show how the full width at half maximum (linewidth) of the Mollow triplet sidebands varies as a function of the square of the Rabi frequency of the cw pump.
Detailed properties of resonance fluorescence from a single quantum dot in a micropillar cavity are investigated, with particular focus on emission coherence in dependence on optical driving field power and detuning. Power-dependent series over a wide range could trace characteristic Mollow triplet spectra with large Rabi splittings of $|Ω| \leq 15$ GHz. In particular, the effect of dephasing in terms of systematic spectral broadening $\propto Ω^2$ of the Mollow sidebands is observed as a strong fingerprint of excitation-induced dephasing. Our results are in excellent agreement with prediction…
We study the resonance fluorescence spectra of a driven quantum dot placed inside a high $Q$ semiconductor cavity and interacting with an acoustic phonon bath. The dynamics is calculated using a time-convolutionless master equation obtained in the polaron frame. We demonstrate pronounced spectral broadening of the Mollow sidebands through cavity-emission which, for small cavity-coupling rates, increases quadratically with the Rabi frequency. However, for larger cavity coupling rates, this broadening dependence is found to be more complex. This field-dependent Mollow triplet broadening is prima…
Charge-neutral excitons in semiconductor quantum dots have a small finite energy separation caused by the anisotropic exchange splitting. Coherent excitation of neutral excitons will generally excite both exciton components, unless the excitation is parallel to one of the dipole axes. We present a polaron master equation model to describe two-exciton pumping using a coherent continuous wave pump field in the presence of a realistic anisotropic exchange splitting. We predict a five-peak incoherent spectrum, thus generalizing the Mollow triplet to become a Mollow quintuplet. We experimentally co…
We study the two-time correlation function and the resonance fluorescence spectrum of a semiconductor quantum dot excited by a strong off-resonant laser pulse. The obtained analytical expressions exhibit a specific detuning-dependent damping of Rabi oscillations of the dressed quantum dot as well as a detuning-dependent width of Mollow-triplet lines. In the absence of pure dephasing, the central peak of the triplet is broadened, upon increasing detuning, but the blue and red side peaks are narrowed. We demonstrate that pure dephasing processes can invert these dependences. A crossover between …
A counterpart of the Mollow triplet (luminescence lineshape of a two-level system under coherent excitation) is obtained for the case of incoherent excitation in a cavity. Its analytical expression, in excellent agreement with numerical results, pinpoints analogies and differences between the conventional resonance fluorescence spectrum and its cavity QED analogue under incoherent excitation.
We present both experimental and theoretical investigations of a laser-driven quantum dot (QD) in the dressed-state regime of resonance fluorescence. We explore the role of phonon scattering and pure dephasing on the detuning-dependence of the Mollow triplet and show that the triplet sidebands may spectrally broaden or narrow with increasing detuning. Based on a polaron master equation approach which includes electron-phonon interaction nonperturbatively, we derive a fully analytical expression for the spectrum. With respect to detuning dependence, we identify a crossover between the regimes o…
Applying high power continuous-wave resonant s-shell excitation to a single self-assembled In- GaAs quantum dot, we demonstrate the generation of post-selected single-indistinguishable photons from the Mollow triplet sidebands. A sophisticated spatial filtering technique based on a double Michelson interferometer enabled us to separate the spectrally close lying individual Mollow components and perform almost background free two-photon interference measurements. Showing high consistency with the results of an independent determination of the emission coherence of 250 +/- 30 ps, our analysis re…
We experimentally demonstrate that the Mollow triplet sidebands of a quantum dot strongly coupled to a cavity exhibit anomalous power induced broadening and enhanced emission when one sideband is tuned over the cavity frequency. We observe a nonlinear increase of the sideband linewidth with excitation power when the Rabi frequency exceeds the detuning between the quantum dot and the cavity, consistent with a recent theoretical model that accounts for acoustic phonon-induced processes between the exciton and the cavity. In addition, the sideband tuned to the cavity shows strong resonant emissio…
Emission from a resonantly excited quantum emitter is a fascinating research topic within quantum optics and a useful source for different types of quantum light fields. The resonance spectrum consists of a single spectral line below saturation of a quantum emitter which develops into a triplet at powers above saturation of the emitter. The spectral properties of the triplet strongly depends on pump power and detuning of the excitation laser. The three closely spaced photon channels from the resonance fluorescence have different photon statistical signatures. We present a detailed photon-stati…
We analyze a photon transport through an 1D open waveguide side coupled to the $N$-photon microwave cavity with embedded artificial two- level atom (qubit). The qubit state is probed by a weak signal at the fundamental frequency of the waveguide. Within the formalism of projection operators and non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme to obtain the photon wavefunction which allows for the calculation of the probability amplitudes of the spontaneous transitions between the levels of two Rabi doublets in $N$- photon cavity. We obtain analytic expressions fo…
Although individual spins in quantum dots have been studied extensively as qubits, their investigation under strong resonant driving in the scope of accessing Mollow physics is still an open question. Here, we have grown high quality positively charged quantum dots embedded in a planar microcavity that enable enhanced light-matter interactions. Under a strong magnetic field in the Voigt configuration, individual positively charged quantum dots provide a double-lambda level structure. Using a combination of above-band and resonant excitation, we observe the formation of Mollow triplets on all o…
Using a realistic quantum master equation we show that the resonance fluorescence spectra of a two-level artificial atom (quantum dot) can be tuned by adjusting its photonic local density of states via biasing of one or more graphene monolayers. The structured photon reservoir is included using a photon Green function theory which fully accounts for the loss and dispersion. The field-driven Mollow triplet spectrum can be actively controlled by the graphene bias in the THz frequency regime. We also consider the effect of a dielectric support environment, and multiple graphene layers, on the emi…
We investigate temperature-dependent resonance fluorescence spectra obtained from a single self-assembled quantum dot. A decrease of the Mollow triplet sideband splitting is observed with increasing temperature, an effect we attribute to a phonon-induced renormalisation of the driven dot Rabi frequency. We also present first evidence for a non-perturbative regime of phonon coupling, in which the expected linear increase in sideband linewidth as a function of temperature is cancelled by the corresponding reduction in Rabi frequency. These results indicate that dephasing in semiconductor quantum…
Reminiscent of the bound character of a qubit's dynamics confined on the Bloch sphere, the observation of a Mollow triplet in the resonantly driven qubit fluorescence spectrum represents one of the founding signatures of Quantum Electrodynamics. Here we report on its observation in a hybrid spin-nanomechanical system, where a Nitro-gen Vacancy spin qubit is magnetically coupled to the vibrations of a Silicon Carbide nanowire. A resonant microwave field turns the originally parametric hybrid interac-tion into a resonant process, where acoustic phonons are now able to induce transitions between …
We present a theoretical study of the resonance fluorescence spectra of an optically driven quantum dot placed near a single metal nanoparticle. The metallic reservoir coupling is calculated for an 8-nm metal nanoparticle using a time-convolutionless master equation approach where the exact photon reservoir function is included using Green function theory. By exciting the system coherently near the nanoparticle dipole mode, we show that the driven Mollow spectrum becomes highly asymmetric due to internal coupling effects with higher-order plasmons. We also highlight regimes of resonance squeez…
Resonant excitation of solid state quantum emitters has the potential to deterministically excite a localized exciton while ensuring a maximally coherent emission. In this work, we demonstrate the coherent coupling of an exciton localized in a lithographically positioned, site-controlled semiconductor quantum dot to an external resonant laser field. For strong continuous-wave driving we observe the characteristic Mollow triplet and analyze the Rabi splitting and sideband widths as a function of driving strength and temperature. The sideband widths increase linearly with temperature and the squ…
The study of light-matter interaction at the quantum scale has been enabled by the cavity quantum electrodynamics (CQED) architecture, in which a quantum two-level system strongly couples to a single cavity mode. Originally implemented with atoms in optical cavities, CQED effects are now also observed with artificial atoms in solid-state environments. Such realizations of these systems exhibit fast dynamics, which makes them attractive candidates for devices including modulators and sources in high-throughput communications. However, these systems possess large photon out-coupling rates that o…
We introduce a nanowire-based photonic crystal waveguide system capable of controllably mediating the photon coupling between two quantum dots which are macroscopically separated. Using a rigorous Green-function-based master equation approach, our two-dot system is shown to provide a wide range of interesting quantum regimes. In particular, we demonstrate the formation of long-lived entangled states and study the resonance fluorescence spectrum which contains clear signatures of the coupled quantum dot pair. Depending upon the operating frequency, one can obtain a modified Mollow triplet spect…
A theoretical investigation is presented of the statistics of excitons in quantum dots (QDs) of different sizes. A formalism is developed to build the exciton creation operator in a dot from the single exciton wavefunction and it is shown how this operator evolves from purely fermionic, in case of a small QD, to purely bosonic, in case of large QDs. Nonlinear optical emission spectra of semiconductor microcavities containing single QDs are found to exhibit a peculiar multiplet structure which reduces to Mollow triplet and Rabi doublet in fermionic and bosonic limits, respectively.
Excitons are composite bosons that can feature spin singlet and triplet states. In usual semiconductors, without an additional spin-flip mechanism, triplet excitons are extremely inefficient optical emitters. Large spin-orbit coupling in transition metal dichalcogenides (TMDs) couples circularly polarized light to excitons with selective valley and spin. Here, we demonstrate electrically controlled brightening of spin-triplet interlayer excitons in a MoSe$_2$/WSe$_2$ TMD van der Waals (vdW) heterostructure. The atomic registry of vdW layers in TMD heterostructures provides a quasi-angular mome…
We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting qubit. The ground to first excited state transition of the qubit is strongly pumped while the resulting dressed qubit spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive read-out of the qubit coupled off-resonantly to a microwave transmission line resonator. The observed frequencies of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher …
Transition metal dichalcogenides (TMDCs) heterostructure with a type II alignment hosts unique interlayer excitons with the possibility of spin-triplet and spin-singlet states. However, the associated spectroscopy signatures remain elusive, strongly hindering the understanding of the Moire potential modulation of the interlayer exciton. In this work, we unambiguously identify the spin-singlet and spin-triplet interlayer excitons in the WSe2/MoSe2 hetero-bilayer with a 60-degree twist angle through the gate- and magnetic field-dependent photoluminescence spectroscopy. Both the singlet and tripl…
Two-dimensional (2D) layered hybrid perovskites provide an ideal platform for studying the properties of excitons. Here, we report on a strong triplet-exciton and longitudinal-optical (LO) phonon coupling in 2D (C6H5CH2CH2NH3, PEA)2PbBr4 perovskites. The triplet excitons exhibit strong photoluminescence (PL) in thick perovskite microflakes, and the PL is not detectable for monolayer microflakes. The coupling strength of the triplet exciton-LO phonon is approximately two to three times greater than that of the singlet exciton-LO phonon with a LO phonon energy of about 21 meV. This difference mi…
Excitons are composite bosons that can feature spin singlet and triplet states. In usual semiconductors, without an additional spin-flip mechanism, triplet excitons are extremely inefficient optical emitters. Transition metal dichalcogenides (TMDs), with their large spin-orbit coupling, have been of special interest for valleytronic applications for their coupling of circularly polarized light to excitons with selective valley and spin$^{1-4}$. In atomically thin MoSe$_2$/WSe$_2$ TMD van der Waals (vdW) heterostructures, the unique atomic registry of vdW layers provides a quasi-angular momentu…
Photophysics of single-wall carbon nanotubes (SWCNTs) is intensively studied due to their potential application in light harvesting and optoelectronics. Excited states of SWCNTs form strongly bound electron-hole pairs, excitons, of which only singlet excitons participate in application relevant optical transitions. Long-living spin-triplet states hinder applications but they emerge as candidates for quantum information storage. Therefore knowledge of the triplet exciton energy structure, in particular in a SWCNT chirality dependent manner, is greatly desired. We report the observation of light…
We show theoretically that the emission spectrum of a single large quantum dot strongly coupled to a single photon mode in a microcavity can be qualitatively different from the spectrum obtained with an atom in a cavity. Instead of the well-known Mollow triplet we predict appearance of multiplets with the number of peaks a function of the quantum dot size and pumping intensity. The mutiplets can appear if the quantum dot is larger than the exciton Bohr radius, so that excitons are confined as whole particles in the dot. In this case the Pauli principle is relaxed and one can accommodate more t…
We report on single-object spectroscopic studies of a characteristic set of three resonances which appear in GaAlAs/AlAs quantum dot structures. The experiments included the photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy, photon-correlation measurements, analysis of the linear polarization of the emission spectra as well as the PL and PLE spectroscopy performed as a function of magnetic field. The investigated resonances are assigned to three different states of a positively charged exciton: a singlet ground state, a conventional triplet state (involving an electron…
Two-dimensional semiconductors feature valleytronics phenomena due to locking of the spin and momentum valley of the electrons. However, the valley polarization is intrinsically limited in monolayer crystals by the fast intervalley electron-hole exchange. Hetero-bilayer crystals have been shown to have a longer exciton lifetime and valley depolarization time. But the reported valley polarization was low; the valley selection rules and mechanisms of valley depolarization remains controversial. Here, we report singlet and brightened triplet interlayer excitons both with over 80% valley polarizat…
Exciton-polaritons are quasiparticles with mixed photon and exciton character that demonstrate rich quantum phenomena, novel optoelectronic devices and the potential to modify chemical properties of materials. Organic semiconductors are of current interest for their room-temperature polariton formation. However, within organic optoelectronic devices, it is often the 'dark' spin-1 triplet excitons that dominate operation. These triplets have been largely ignored in treatments of polariton physics. Here we demonstrate polariton population from the triplet manifold via triplet-triplet annihilatio…
A theory of charged excitons X- in a dilute 2D electron gas in a high magnetic field is presented. In contrast to previous calculations, three bound X- states (one singlet and two triplets) are found in a narrow and symmetric GaAs quantum well. The singlet and a "bright" triplet are the two optically active states observed in experiments. The bright triplet has the binding energy of about 1 meV, smaller than the singlet and a "dark" triplet. The interaction of bound X-'s with a dilute 2D electron gas is investigated using exact diagonalization techniques. It is found that the short-range chara…
We report the first theoretical calculations of excited state absorptions (ESAs) from the singlet and triplet excitons, as well as the key intermediate in the singlet fission (SF) process, the spin singlet multiexciton triplet-triplet state, for solid pentacene with herringbone crystal structure. Our goal is to compare theoretical results against ultrafast transient photoinduced absorption (PA) measurements and their interpretations, which have remained controversial. We show that the elusive triplet-triplet state absorbs both in the visible and near infrared (NIR), at or close to the PA energ…
We use a laser-driven single (In,Ga)As quantum dot (QD) in the dressed state regime of resonance fluorescence ($T = 4$ K) to observe the four $D_1$-transition lines of alkali atomic cesium ($Cs$) vapor at room temperature. We tune the frequency of the dressing continuous-wave laser in the vicinity of the bare QD resonance $\sim 335.116$ THz ($\sim 894.592$ nm) at constant excitation power and thereby controllably tune the center and side channel frequencies of the probe light, i.e. the Mollow triplet. Resonances between individual QD Mollow triplet lines and the atomic hyperfine-split transiti…
We investigate the optical properties of spin-triplet interlayer excitons in heterobilayer transition metal dichalcogenides in comparison with the spin-singlet ones. Surprisingly, the optical transition dipole of the spin-triplet exciton is found to be in the same order of magnitude to that of the spin-singlet exciton, in sharp contrast to the monolayer excitons where the spin triplet species is considered as dark compared to the singlet. Unlike the monolayer excitons whose spin-conserved (spin-flip) transition dipole can only couple to light of in-plane (out-of-plane) polarization, such restr…
The fluorescence spectrum of a strongly pumped two level system is characterised by the Mollow triplet that has been observed in a variety of systems, ranging from atoms to quantum dots and superconducting qubits. We theoretically studied the fluorescence of a strongly pumped intersubband transition in a quantum well. Our results show that the many-electron nature of such a system leads to a modification of the usual Mollow theory. In particular, the intensity of the central peak in the fluorescence spectrum becomes a function of the electron coherence, allowing access to the coherence time of…
Unveiling the Spin-Valley Structure of Dipolar Exciton Ladders in R-stacked WSe$_2$/WS$_2$ Moiré Heterobilayers
Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University（赫瑞-瓦特大学光子与量子科学研究所）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料纳米结构研究中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（电子与光学材料研究中心）
研究 R 堆叠 WSe₂/WS₂ 莫尔异质双层中偶极激子阶梯的自旋-谷结构，用螺旋度分辨磁光致发光确定其微观起源，明确不同电荷填充时各激子态情况，建立超越简单占据数物理的自旋-谷分辨图像。
We show that the energy differences between the lowest optical singlet exciton and the lowest triplet exciton in semiconducting single-walled carbon nanotubes with diameter $\sim 1$ nm and graphene nanoribbons with widths $\sim 2$ nm are an order of magnitude smaller than in the $π$-conjugated polymer poly(para-phenylenevinylene). Our calculated energy gaps between the singlet and triplet excitons are in excellent agreement with the measured values in three different nanotubes with diameters close to 1 nm. The spatial extent of the triplet exciton is nearly the same as that of the singlet exci…
We present a generic theory of primary photoexcitations in low band gap donor-acceptor conjugated copolymers. Because of the combined effects of strong electron correlations and broken symmetry, there is considerable mixing between a charge-transfer exciton and an energetically proximate triplet-triplet state with an overall spin singlet. The triplet-triplet state, optically forbidden in homopolymers, is allowed in donor-acceptor copolymers. For an intermediate difference in electron affinities of the donor and the acceptor, the triplet-triplet state can have stronger oscillator strength than …
Quantifying the spin-spin interactions which influence electronic transitions in organic semiconductors is crucial for understanding their magneto-optoelectronic properties. By combining a theoretical model for three spin interactions in the coherent regime with pulsed electrically detected magnetic resonance experiments on MEH-PPV diodes, we quantify the spin-coupling within complexes comprising three spin-half particles. We determine that these particles form triplet-exciton:polaron pairs, where the polaron:exciton exchange is over 5 orders of magnitude weaker (less than 170 MHz) than that w…
By direct absorption spectroscopy and comparison to photoluminescence (PL), we investigate negatively charged excitons in dilute two-dimensional electron systems at temperatures down to T=40 mK in the regime of the fractional quantum Hall effect. At very low temperatures, for filling factor ν< 1/3, an additional excitation appears in the PL spectrum, between the well-known singlet and triplet excitons. The observation of a similar excitation by PL was reported very recently [G. Yusa et al., cond-mat0103561], and the excitation was assigned, in spite of a PL intensity similar to that of the neu…
Charged magneto-excitons X- in a dilute 2D electron gas in narrow and symmetric quantum wells are studied using exact diagonalization techniques. An excited triplet X- state with a binding energy of about 1 meV is found. This state and the singlet are the two optically active states observed in photoluminescence (PL). The interaction of X-'s with electrons is shown to have short range, which effectively isolates bound X- states from a dilute e-h plasma. This results in the insensitivity of PL to the filling factor nu. For the "dark" triplet X- ground state, the oscillator strength decreases ex…
Transition-metal dichalcogenides can be easily produced as atomically thin sheets, exhibiting the possibility to optically polarize and read out the valley pseudospin of extremely stable excitonic quasiparticles present in these 2D semiconductors. Here, we investigate a monolayer of tungsten disulphide in high magnetic fields up to 30\,T via photoluminescence spectroscopy at low temperatures. The valley degeneracy is lifted for all optical features, particularly for excitons, singlet and triplet trions, for which we determine the g factor separately. While the observation of a diamagnetic shif…
We present a comparative theoretical study of magnetic resonance within the polaron pair recombination (PPR) and the triplet exciton-polaron quenching (TPQ) models. Both models have been invoked to interpret the photoluminescence detected magnetic resonance (PLDMR) in $π$-conjugated materials. We show that resonance lineshapes calculated within the two models differ dramatically in several regards. First, in the PPR model, the lineshape exhibits unusual behavior upon increasing the microwave power: it evolves from fully positive at weak power to fully negative at strong power. In contrast, in …
We detect a novel radiative cascade from a neutral semiconductor quantum dot. The cascade initiates from a metastable biexciton state in which the holes form a spin-triplet configuration, Pauli-blockaded from relaxation to the spin-singlet ground state. The triplet biexciton has two photon-phonon-photon decay paths. Unlike in the singlet-ground state biexciton radiative cascade, in which the two photons are co-linearly polarized, in the triplet biexciton cascade they are crosslinearly polarized. We measured the two-photon polarization density matrix and show that the phonon emitted when the in…
We show that optical transitions of charged excitons in semiconductor heterostructures are governed in magnetic fields by a novel exact selection rule, a manifestation of magnetic translations. It is shown that the spin-triplet ground state of the quasi-two-dimensional charged exciton X- --- a bound state of two electrons and one hole --- is optically inactive in photoluminescence at finite magnetic fields. Internal bound-to-bound X- triplet transition has a specific spectral position, below the electron cyclotron resonance, and is strictly prohibited in a translationally-invariant system. The…
In photovoltaics (PVs) and artificial photosynthetic systems based on excitons, the question of how energy must be lost in overcoming the Coulomb barrier, converting excitons to free charges, is fundamental, as it determines the achievable open-circuit voltage or over-potential1-3. Here, using transient and steady-state optical spectroscopy we study a model system, pentacene/C60, where pentacene triplet excitons are dissociated to form charge transfer states, which we show to be degenerate in energy with the triplet excitons. We directly track these charge transfer states undergoing efficient …
The surprising recent observation of highly emissive triplet-states in lead halide perovskites accounts for their orders-of-magnitude brighter optical signals and high quantum efficiencies compared to other semiconductors. This makes them attractive for future optoelectronic applications, especially in bright low-threshold nano-lasers. Whilst non-resonantly pumped lasing from all-inorganic lead-halide perovskites is now well-established as an attractive pathway to scalable low-power laser sources for nano-optoelectronics, here we showcase a resonant optical pumping scheme on a fast triplet-sta…
