We provide a unified theory of luminescence spectra of coupled light-matter systems realized with semiconductor heterostructures in microcavities, encompassing: i) the spontaneous emission case, where the system decays from a prepared (typically pure) initial state, and ii) luminescence in the presence of a continuous, incoherent pump. While the former case has been amply discussed in the literature (albeit mainly for the case of resonance), no consideration has been given to the influence of the incoherent pump. We show how, by provoking a self-consistent quantum state, the pump considerably alters the emission spectra, even at vanishing intensities. The main outcome of our analysis is to unambiguously identify strong-coupling in situations where it appears in disguise or only seems to appear. Here, we consider bosonic matter fields, in which case fully analytical solutions can be obtained. This describes the case of quantum wells or large quantum dots, or the limit of low excitation where the average populations remain much smaller than one.
In this comment we show that there is a direct connection between coherent exchange of energy among light and matter and the emission spectrum of a microcavity quantum dot system as modeled in Phys. Rev. B 79, 235325 (2009) [arXiv:0807.3194] by F. P. Laussy, E. del Valle, and C. Tejedor. To do so, we show that in their model the necessary and sufficient conditions for having eigenvalues with non-zero imaginary parts in the propagator of the bare mode populations, are the same as for having strong coupling in the emission spectrum. This amounts to saying that, whenever there is strong coupling …
We discuss the luminescence spectra of coupled light-matter systems realized with semiconductor heterostructures in microcavities in the presence of a continuous, incoherent pumping, when the matter field is Fermionic. The linear regime--which has been the main topic of investigation both experimentally and theoretically--converges to the case of coupling to a Bosonic material field, and has been amply discussed in the first part of this work. We address here the nonlinear regime, and argue that, counter to intuition, it is better observed at low pumping intensities. We support our discussion …
The emission properties of single quantum dots in planar microcavities are studied experimentally and theoretically. Fivefold Enhanced spontaneous emission outside the microcavity is found for dots in resonance with the cavity mode, relative to detuned dots, while their radiative lifetime is only marginally decreased. Using high power excitation we obtain the in-plane cavity dispersion. Near field images of the emission show spatial distributions of several microns for resonant dots, which decrease in size with the detuning from resonance. These experimental findings are explained using a simp…
We have fabricated and studied the photoluminescence from microdisks containing single, selected self-assembled quantum dots. Using two electron beam lithography exposures and a two-step selective wet etching process, the dots were positioned at the microdisks edges with sub-micron precision. The selection and positioning of quantum dots enables an optimum coupling of the dot emission to the microdisks whispering modes.
Interband absorption and luminescence of quasi-two-dimensional, circularly symmetric, N_e electron quantum dots are studied at high magnetic fields, 8<B<60 T, and low temperatures, T<<2 K. In the N_e=0 and 1 dots, the initial and final states of such processes are fixed, and thus the dependence on B of peak intensities is monotonic. For larger systems, ground state rearrangements with varying magnetic field lead to substantial modifications of the absorption and luminescence spectra. Collective effects are seen in the N_e=2 and 3 dots at "filling factors" 1/2, 1/3 and 1/5.
We present a detailed spectroscopic study of the photoluminescence quenching in an epitaxial structures containing CdSe/ZnSe quantum dots doped with low concentration of Mn$^{2+}$ ions. Our time-resolved and time-integrated experiments reveal the origin of the quenching observed in macro-photoluminescence studies of ensembles of such dots. We show that incorporation of even a few ions to an individual dot does not quench its luminescence effectively, although some fingerprints of expected spin-dependent quenching are visible. At the same time, the presence of Mn$^{2+}$ ions in the sample signi…
We have investigated micro-photoluminescence ($μ$-PL) and excitation ($μ$-PLE) spectra of a single GaAs/AlGaAs quantum dot grown on a GaAs (411)A surface. We observed sharp resonant lines in both $μ$-PL and $μ$-PLE spectra, corresponding to the discrete energy levels of the dot. When the sample was excited at one of the resonant lines, resonant luminescence lines appear not only in Stokes side but also in anti-Stokes side. We discuss the possible origins of the anomalus anti-Stokes luminescence.
We discuss the topical and fundamental problem of strong-coupling between a quantum dot an the single mode of a microcavity. We report seminal quantitative descriptions of experimental data, both in the linear and in the nonlinear regimes, based on a theoretical model that includes pumping and quantum statistics.
We study the evolution of a quantum state of a double quantum dot system interacting with the electromagnetic environment and with the lattice modes, in the presence of a coupling between the two dots. We propose a unified approach to the simulation of the system evolution under joint impact of the two reservoirs. We discuss the sub- and superradiant radiative decay of the system, the phonon-induced decay of entanglement between the dots, and the transfer of excitation between them.
e study theoretically, the photoluminescence properties of a single quantum dot in a microcavity under incoherent excitation. We propose a microscopic quantum statistical approach providing a Lindblad (thus completely positive) description of pumping and decay mechanisms of the quantum dot and of the cavity mode. Our analytical results show that strong coupling (SC) and linewidths are largely independent on the pumping intensity (until saturation effects come into play), in contrast to previous theoretical findings. We shall show the reliable predicting character of our theoretical framework i…
Luminescence spectroscopy experiments were realized for single colloidal quantum dots CdSe/ZnS in a broad temperature range above room temperature in a nitrogen atmosphere. Broadening and shifts of spectra due to the temperature change as well as due to spectral diffusion processes were detected and analyzed. A linear correlation between the positions of maxima and the squared linewidths of the spectra was found. This dependence was explained by a model which takes into account the slow variation of the electron-phonon coupling strength.
We show that strong-coupling (SC) of light and matter as it is realized with quantum dots (QDs) in microcavities differs substantially from the paradigm of atoms in optical cavities. The type of pumping used in semiconductors yields new criteria to achieve SC, with situations where the pump hinders, or on the contrary, favours it. We analyze one of the seminal experimental observation of SC of a QD in a pillar microcavity [Reithmaier et al., Nature (2004)] as an illustration of our main statements.
We describe how complex fluctuations of the local environment of an optically active quantum dot can leave rich fingerprints in its emission spectrum. A new feature, termed "Fluctuation Induced Luminescence" (FIL), is observed to arise from extremely rare fluctuation events that have a dramatic impact on the response of the system-so called "black swan" events. A quantum dissipative master equation formalism is developed to describe this effect phenomenologically. Experiments performed on single quantum dots subject to electrical noise show excellent agreement with our theory, producing the ch…
The spectral and dispersive emission properties are analytically determined for the two-dimensional system of exciton-polaritons in microcavities excited by a resonant and coherent optical pump. New collective excitations result from the anomalous coupling between one generic polariton state and its idler, created by the scattering of two pumped polaritons. The corresponding parametric correlation is stimulated by the emitter and idler populations and drives very efficiently the luminescence. The intrinsic properties of the collective excitations determine a peculiar emission pattern.
A quantum cascade laser where the quantum wells in the active regions are replaced by quantum dots with their atom-like discrete energy levels is an interesting system to study novel features in optical spectroscopy. We study structures suitable for diagonal lasing transitions in coupled dots, and vertical lasing transitions in a single dot, in the active regions of the laser device. The luminescence spectra as a function of electron number and dot size show that for diagonal transitions, a significant amount of blue-shift in the emission spectra can be achieved by increasing electron populati…
Luminescence properties of colloidal quantum dots have found applications in imaging, light-sources, and displays. Despite wide interest, several experimental observations from these quantum dots, such as the short lifetime on the scale of microseconds and a zero-longitudinal optical phonon line in low-temperature photoluminescence spectrum, remain unexplained by existing models. Here we propose a model including the effect of solid-state environment on luminescence by capturing coherent and incoherent interactions of band-edge exciton with phonon modes. Our model predicts the formation of dre…
We present a direct experimental evidence of photo-ionized CdTe quantum dot core having luminescence "off" state at band-edge photo-excitation. We use the autocorrelation of fluorescence fluctuations from dilute colloidal solution of CdTe quantum dots in a diffraction limited detection volume to determine their photo-ionization probability. The ionization probability is in the same order of magnitude (\approx10-6) as the CdSe and CdSe/ZnS core/shell quantum dots. Further, we measured the ionization/ neutralization rates (\approx104 s-1) after addition of β-mercaptanol and found that ionization…
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…
At the occasion of the OECS conference in Madrid, we give a succinct account of some recent predictions in the spectroscopy of a quantum dot in a microcavity that remain to be observed experimentally, sometimes within the reach of the current state of the art.
We study (In,Ga)(As,Sb)/GaAs quantum dots embedded in a GaP (100) matrix, which are overgrown by a thin GaSb capping layer with variable thickness. Quantum dot samples are studied by temperature-dependent photoluminescence, and we observe that the quantum dot emission shows anomalous temperature dependence,~i.e., increase of energy with temperature increase from 10~K to $\sim$70~K, followed by energy decrease for larger temperatures. With the help of fitting of luminescence spectra by Gaussian bands with energies extracted from eight band ${\bf k}\cdot{\bf p}$ theory with multiparticle correct…
Spin relaxation of electrons doped in InP quantum dots was studied by means of luminescence pump-probe and Hanle measurements. Optical pumping makes spins of doped electrons to be oriented in parallel to the helicity of the circularly polarized excitation. The luminescence pump-probe showed the spin orientation of the doped electrons decay on a millisecond time-scale. Hanle measurement clarified the spin dephasing relaxation time of doped electrons is 1.7 ns which is explained by the frozen fluctuation of nuclear spins.
We have recently developed a self-consistent theory of Strong-Coupling in the presence of an incoherent pumping [arXiv:0807.3194] and shown how it could reproduce quantitatively the experimental data [PRL 101, 083601 (2008)]. Here, we summarize our main results, provide the detailed analysis of the fitting of the experiment and discuss how the field should now evolve beyond merely qualitative expectations, that could well be erroneous even when they seem to be firmly established.
CdSe quantum dots (QDs) with different organic linker molecules are attached to ZnO nanowires (NWs) to study the luminescence dynamics and the electron tunneling from the QDs to the nanowires in time-resolved photoluminescence (PL) and photoconductivity measurements. The PL transients of the QD luminescence indicate two different recombination channels: the direct recombination inside the QD core and the recombination via QD surface defect states. After linking the QDs to the ZnO NW surface, photo-induced electron tunneling from an excited state of the QD into the conduction band of the nanowi…
Quantum dots play a promising role in the development of novel optical and biosensing devices. In this study, we investigated steady-state and time-dependent luminescence properties of InGaP/ZnS core/shell colloidal quantum dots in a solution phase at room temperature. The steady state experiments exhibited an emission maximum at 650 nm with full width at half maximum of ~ 85 nm, and strong first-excitonic absorption peak at 600 nm. The time-resolved luminescence measurements depicted a bi-exponential decay profile with lifetimes of τ1\sim 47 ns and τ 2\sim 142 ns at the emission maximum. Addi…
The light emission rate of a single quantum dot can be drastically enhanced by embedding it in a resonant semiconductor microcavity. This phenomenon is known as the Purcell effect, and the coupling strength between emitter and cavity can be quantified by the Purcell factor. The most natural way for probing the Purcell effect is a time-resolved measurement. However, this approach is not always the most convenient one, and alternative approaches based on a continuous-wave measurement are often more appropriate. Various signatures of the Purcell effect can indeed be observed using continuous-wave…
We study the luminescence dynamics of telecom wavelength InAs quantum dots grown on InP(111)A by droplet epitaxy. The use of the ternary alloy InAlGaAs as a barrier material leads to photon emission in the 1.55 $μ$m telecom C-band. The luminescence decay is well described in terms of the theoretical interband transition strength without the impact of nonradiative recombination. The intensity autocorrelation function shows clear anti-bunching photon statistics. The results suggest that our quantum dots are useful for constructing a practical source of single photons and quantum entangled photon…
The quantum-jump approach is used for a theoretical description of resonance luminescence from a {\em single} semiconductor quantum dot in contact with its solid-state environment. For continuous excitation of the single-exciton groundstate the luminescence exhibits bright periods, where photons are spontaneously emitted from the exciton decay, which are interrupted by dark periods when one electron or hole suffers a spin flip. It is shown that continuously monitored resonance luminescence provides a very sensitive measure of such rare single scattering events in quantum dots.
We study the evolution of photoluminescence (PL) from homogeneous and inhomogeneous ensembles of a few coupled QDs. We discuss the relation between signals from a given QD ensemble under strong and weak excitation (full inversion and linear response regimes): A system homogeneous enough to manifest superradiant emission when strongly inverted shows a non-exponential decay of the PL signal under spatially coherent weak excitation. In an inhomogeneous ensemble the PL decay is always nearly exponential with a qualitatively different form of the time dependence in the two excitation regimes and wi…
Quantum dots have found applications across the semiconductor and biotechnology industries, improving energy efficiency, color purity, and imaging capability. However, the standard quantum dot relies on a heavy metal architecture, which has undesirable environmental impacts. Thus, alternative material systems are desirable. One strategy is the ZnS-AgInS2 (ZAIS) quantum dot which has a metal dichalcogenide chemical structure. Unlike heavy metal quantum dots, these nanoparticles luminesce even when defects are present, and their emission wavelength is tuned by varying the relative composition. P…
We describe the optical emission and the carrier dynamics of an ensemble of self-assembled GaAs quantum dots embedded in GaP(001). The QD formation is driven by the 3.6 % lattice mismatch between GaAs and GaP in Stranski-Krastanow mode after deposition of more than 1.2 monolayers of GaAs. The quantum dots have an areal density between 6 and 7.6x1010 per cm-2 and multimodal size distribution. The luminescence spectra show two peaks in the range of 1.7 and 2.1 eV. The samples with larger quantum dots have red emission and show less thermal quenching compared to the samples with smaller QDs. The …
The influence of a distributed Bragg reflector composed of ZnTe, MgTe, and MgSe superlattices on photoluminescence of self assembled CdTe quantum dots (QD) emitting in the yellow spectral range is investigated. In the case of QDs grown on a distributed Bragg reflector the photoluminescence intensity is enhanced by more than one order of magnitude, whereas the single QD lines are broadened as compared to the case of QDs grown on a ZnTe buffer. Structural and chemical analysis reveal an unintentional formation of a thin ZnSe layer induced by the growth interruption needed for the deposition of t…
We investigate polarization properties of neutral exciton emission in single self-assembled InAs/GaAs quantum dots. The in-plane shape and strain anisotropy strongly couple the heavy and light hole states and lead to large optical anisotropy with non-orthogonal linearly polarized states misaligned with respect to the crystallographic axes. Owing to a waveguiding experimental configuration, luminescence polarization along the growth axis has been observed revealing the presence of shear components of the deformation tensor out of the growth plane. Resonant luminescence experiments allowed deter…
We report on our theoretical studies of the luminescence spectra of a quantum cascade laser where the quantum wells in the active regions are replaced by parabolic quantum dots. We analyze the influence of shape and size of the dots on the luminescence spectra. The emission spectra have interaction induced blueshift which increases almost linearly with increasing electron number. The blueshift is smaller for larger and non-circular dots. For large dots, shape of the emission line has weak dependence on the shape of quantum dots.
Emission spectra of quantum dot arrays in zero-dimensional microcavities are studied theoretically, and it is shown that they are determined by the competition between the formation of the collective superradiant mode and inhomogeneous broadening. The random sources method for the calculation of photoluminescence spectra under a non-resonant pumping is developed, and a microscopic justification of the random sources method within a framework of the standard diagram technique is given. The emission spectra of a microcavity are analyzed with allowance for the spread of exciton states energies ca…
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 compare three different notions of concurrence to measure the polarization entanglement of two-photon states generated by the biexciton cascade in a quantum dot embedded in a microcavity. We focus on the often-discussed situation of a dot with finite biexciton binding energy in a cavity tuned to the two-photon resonance. Apart from the time-dependent concurrence, which can be assigned to the two-photon density matrix at any point in time, we study single- and double-time integrated concurrences commonly used in the literature that are based on different quantum state reconstruction schemes.…
A theory of optical emission of quantum dot arrays in quantum microcavities is developed. The regime of the strong coupling between the quantum dots and photonic mode of the cavity is considered. The quantum dots are modeled as two-level systems. In the low pumping (linear) regime the emission spectra are mainly determined by the superradiant mode where the effective dipoles of the dots oscillate in phase. In the non-linear regime the superradiant mode is destroyed and the emission spectra are sensitive to the parity of quantum dot number. Further increase of the pumping results in the line wi…
Time-resolved microphotoluminescence study is presented for quantum dots which are formed in the InAs/GaAs wetting layer. These dots are due to fluctuations of In composition in the wetting layer. They show spectrally sharp luminescence lines with a low spatial density. We identify lines related to neutral exciton and biexciton as well as trions. Exciton emission antibunching (second order correlation value of g^2(0)=0.16) and biexciton-exciton emission cascade prove non-classical emission from the dots and confirm their potential as single photon sources.
In this chapter we will discuss the technology and experimental techniques to realize quantum dot (QD) single photon sources combining high outcoupling efficiencies and highest degrees of non-postselected photon indistinguishability. The system, which is based on ultra low density InAs QDs embedded in a quasi planar single sided microcavity with natural photonic traps is an ideal testbed to study quantum light emission from single QDs. We will discuss the influence of the excitation conditions on the purity of the single photon emission, and in particular on the degree of indistinguishability …
Experimental results obtained previously for the photoluminescence efficiency (PL$_{eff}$) of Ge quantum dots (QDs) are theoretically studied. A $\log$-$\log$ plot of PL$_{eff}$ versus QD diameter ($D$) resulted in an identical slope for each Ge QD sample only when $E_{G}\sim (D^2+D)^{-1}$. We identified that above $D\approx$ 6.2 nm: $E_{G}\sim D^{-1}$ due to a changing effective mass (EM), while below $D\approx$ 4.6 nm: $E_{G}\sim D^{-2}$ due to electron/ hole confinement. We propose that as the QD size is initially reduced, the EM is reduced, which increases the Bohr radius and interface sca…
Using an approximate time-dependent density functional theory method, we calculate the absorption and luminescence spectra for hydrogen passivated silicon nanoscale structures with large aspect ratio. The effect of electron confinement in axial and radial directions is systematically investigated. Excited state relaxation leads to significant Stokes shifts for short nanorods with lengths less than 2 nm, but has little effect on the luminescence intensity. The formation of self-trapped excitons is likewise observed for short nanostructures only; longer wires exhibit fully delocalized excitons w…
We present a consistent theoretical description of few-particle effects in the optical spectra of semiconductor quantum dots, based on a direct-diagonalization approach. We show that, because of the strong Coulomb interaction among electrons and holes, each configuration of the confined few-particle system leads to its characteristic signature in the optical spectra. We discuss quantitative predictions and comparison with experiments for both absorption and luminescence.
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.
We study an impact of the fine structure of the heavy--hole ground state exciton confined in semiconductor quantum dots on the photoluminescence polarization dynamics solving the relevant system of the rate equations. The presence of the dark excitons is usually ignored and the polarization decay is assumed to be caused by direct transitions within the radiative doublet. We demonstrate that in strongly confined quantum dots the dark excitons, which are energetically well below the bright excitons, have actually a decisive effect on the polarization dynamics due to their persistent nature. The …
We study theoretically the radiative recombination of excitons in double quantum dots in the presence of carrier-phonon coupling. We show that the phonon-induced pure dephasing effects and transitions between the exciton states strongly modify the spontaneous emission process and make it sensitive to temperature, which may lead to non-monotonic temperature dependence of the time-resolved luminescence. We show also that under specific resonance conditions the biexcitonic interband polarization can be coherently transferred to the excitonic one, leading to an extended life time of the total cohe…
We have studied the size dependence of the exciton g-factor in self-assembled InAs/InP quantum dots. Photoluminescence measurements on a large ensemble of these dots indicate a multimodal height distribution. Cross-sectional Scanning Tunneling Microscopy measurements have been performed and support the interpretation of the macro photoluminescence spectra. More than 160 individual quantum dots have systematically been investigated by analyzing single dot magneto-luminescence between 1200nm and 1600 nm. We demonstrate a strong dependence of the exciton g-factor on the height and diameter of the…
Measured and calculated results are presented on the emission properties of a new class of emitters operating in the cavity quantum electrodynamics regime. The structures are based on high-finesse GaAs/AlAs micropillar cavities, each with an active medium consisting of a layer of InGaAs quantum dots and distinguishing feature of having substantial fraction of spontaneous emission channeled into one cavity mode (high-beta factor). This paper shows that the usual criterion for lasing with a conventional (low-beta factor) cavity, a sharp nonlinearity in an input-output curve accompanied by notice…
Most optical quantum devices require deterministic single-photon emitters. Schemes so far demonstrated in the solid state imply an energy relaxation which tends to spoil the coherent nature of the time evolution, and with it the photon indistinguishability. We focus our theoretical investigation on semiconductor quantum dots embedded in microcavities. Simple and general relations are identified between the photon indistinguishability and the collection efficiency. The identification of the key parameters and of their interplay provides clear indications for the device optimization.
The origin of visible light emission from nanostructures has been a subject of an intense debate since the early work by L. E. Brus and A. P. Alivisatos in 1980s. The intense research that followed has paved the way towards applications of quantum structures in optoelectronics and in bio-sensing and contributed to the development of nanotechnology. The major new challenge is in accessing the structural, electronic and optical properties of quantum dots on a nanoparticle scale in order to understand complex relationships between structural motifs and their contributions to the relevant physical…
A theoretical interpretation of the photoluminescence excitation spectra of self-organized polar GaN/(Al,Ga)N quantum dots is proposed. A numerical method assuming a realistic shape of the dots and including the built-in electric field effects is developed to calculate their energy structure and hence their optical absorption. The electron and hole spectra show the existence of a set of quasi-bound states that does not originate from the wetting layer, and plays a crucial role in the observed absorption spectrum of the GaN/(Al,Ga)N dots. Transitions involving these quasi-bound states and wetti…
We study the relationship between the circular polarization of photoluminescence and the magnetic field-induced spin-polarization of the recombining charge carriers in bulk Si and Ge/Si quantum dots. First, we quantitatively compare experimental results on the degree of circular polarization of photons resulting from phonon-assisted radiative transitions in intrinsic and doped bulk Si with calculations which we adapt from recently predicted spin-dependent phonon-assisted transition probabilities in Si. The excellent agreement of our experiments and calculations quantitatively verifies these sp…
Colloidal core/shell InP/ZnSe quantum dots (QDs), recently produced using an improved synthesis method, have a great potential in life-science applications as well as in integrated quantum photonics and quantum information processing as single-photon emitters. Single-particle spectroscopy of 10-nm QDs with 3.2-nm cores reveals strong photon antibunching attributed to fast (70-ps) Auger recombination of multiple excitons. The QDs exhibit very good photostability under strong optical excitation. We demonstrate that the antibunching is preserved when the QDs are excited above the saturation inten…
