E. Poem

Polarization sensitive spectroscopy of charged quantum dots

We present an experimental and theoretical study of the polarized photoluminescence spectrum of single semiconductor quantum dots in various charge states. We compare our high resolution polarization sensitive spectral measurements with a many-carrier model which we developed for this purpose. The model considers both the isotropic and anisotropic exchange interactions between all participating electron-hole pairs. With this addition, we calculate both the energies and polarizations of all optical transitions between collective, quantum dot confined charge-carrier states. We succeed in identifying most of the measured spectral lines. In particular, the lines resulting from singly, doubly, and triply negatively charged excitons and biexcitons. We demonstrate that lines emanating from evenly charged states are linearly polarized. Their polarization direction does not necessarily coincide with the traditional crystallographic direction. It depends on the shells of the single carriers, which participate in the recombination process.

Complete control of a matter qubit using a single picosecond laser pulse

We demonstrate for the first time that a matter physical two level system, a qubit, can be fully controlled using one ultrafast step. We show that the spin state of an optically excited electron, an exciton, confined in a quantum dot, can be rotated by any desired angle, about any desired axis, during such a step. For this we use a single, resonantly tuned, picosecond long, polarized optical pulse. The polarization of the pulse defines the rotation axis, while the pulse detuning from a non-degenerate absorption resonance, defines the magnitude of the rotation angle. We thereby achieve a high fidelity, universal gate operation, applicable to other spin systems, using only one short optical pulse. The operation duration equals the pulse temporal width, orders of magnitude shorter than the qubit evolution life and coherence times.

Optically induced rotation of an exciton spin in a semiconductor quantum dot.

We demonstrate control over the spin state of a semiconductor quantum dot exciton using a polarized picosecond laser pulse slightly detuned from a biexciton resonance. The control pulse follows an earlier pulse, which generates an exciton and initializes its spin state as a coherent superposition of its two nondegenerate eigenstates. The control pulse preferentially couples one component of the exciton state to the biexciton state, thereby rotating the excitons spin direction. We detect the rotation by measuring the polarization of the exciton spectral line as a function of the time difference between the two pulses. We show experimentally and theoretically how the angle of rotation depends on the detuning of the second pulse from the biexciton resonance.A polarized picosecond laser pulse, which couples the bright exciton states to biexciton resonant states, is used to manipulate the exciton spin. We directly demonstrate this novel knob in a picosecond time-resolved two pulses experiment.

Radiative cascades from charged semiconductor quantum dots

We measured, for the first time, two photon radiative cascades due to sequential recombination of quantum dot confined electron hole pairs in the presence of an additional spectator charge carrier. We identified direct, all optical cascades involving spin blockaded intermediate states, and indirect cascades, in which non radiative relaxation precedes the second recombination. Our measurements provide also spin dephasing rates of confined carriers. Semiconductor quantum dots (QDs) strongly localize charge carriers, and discretize their energy level spectrum, in a similar way to electrons in atoms. Radiative cascades in neutral QDs [1, 2, 3, 4] demonstrated their potential as deterministic sources for polarization entangled photon pairs [5, 6]. The neutral radiative cascade [7, 8] leaves the QD empty of charge carriers. This is essential for entangling the emitted two photons, since otherwise the remaining carrier’s spin betrays the required “which path” ambiguity [9, 10]. Neutrality prevents, however, the important benefit of correlating between the emitted photons’ polarizations (“flying qubits”) and the local carrier’s spins (“anchored qubits”). The situation is drastically different in charged QDs, where quantum correlations exist between the flying and anchored qubits. Here we report on two-photon radiative cascades in the presence of an additional hole. The energy levels of a positively charged QD [11, 12] containing up to three holes and two electrons are schematically described in Fig. 1(a). The figure presents also the relevant optical and non-optical total-spin conserving transitions between these levels. The two photon radiative cascades start from the ground level of the three hole and two electron state. The unpaired hole’s spin projection along the growth axis determines the total spin of the two Kramers’ degenerate states (for simplicity only one state is drawn in Fig. 1(a)). Radiative recombination of first level electron-hole (e-h) pair leaves three unpaired charge carriers within the QD. There are 8 possible different spin configurations for the remaining carriers. These configurations form 4 energy levels of Kramers’ pairs [11, 12]. The three lowest levels are those in which the two unpaired holes are in spin-triplet states. Those states are separated from the highest energy level in which the holes are in a singlet spin state by the hole-hole isotropic exchange interaction, which is significantly stronger than the e-h exchange interaction. The later removes the degeneracy between the triplet states as shown in Fig. 1(a). The lowest triplet level cannot be reached optically. The optical transitions into the other levels are optically allowed. The circular polarization of the emitted photons are indicated in the figure. It depends on the spins of the annihilated electron hole pair. The measured emission contains also linear components (see Fig. 1(c)), due to the anisotropic e-h exchange interaction [11, 12]. The relaxation proceeds by radiative recombination of the remaining first level e-h pair, leaving thus only one hole in its second level. The hole can then quickly relax non-radiatively to its ground level. There is a fundamental difference between the singlet and triplet intermediate states. While in the later, due to Pauli’s exclusion principle, radiative recombination must occur before the excited hole can relax to its ground state (resulting in two “direct” cascades), in the former non-radiative relaxation of the excited hole state may occur prior to the radiative recombination (resulting in one “direct” and one “indirect” cascade). Figure 1. (a) Schematic description of the energy levels of a singly positively charged QD. Vertical (curly) arrows indicate radiative (nonradiative) transitions between these levels. State occupation and spin wavefunctions are described to the left of each level where ↑ (⇓) represents an electron (hole) with spin up (down). A short blue (long red) arrow represents a carrier in its first (second) level. S (T) stands for two holes’ singlet (triplet) state and 0 (1) for Sz = 0 (Sz = ±1) total holes’ pseudo-spin projection on the QD growth direction. The ground staste singlet is indicated by SG. Only one out of two (Kramers’) degenerate states is described. (b) Measured PL spectrum on which the actual transitions are identified. Excitonic (biexcitonic) transitions are highlighted yellow (orange). Transitions which are not discussed here are marked by gray letters. (c) Measured degree of linear polarization spectrum, along the in-plane symmetry axes of the QD. Positive (negative) value represents polarization along the QD’s major (minor) axis. The studied sample contains InGaAs QDs in the middle of a 1λ microcavity [5]. For the optical measurements the sample was placed inside a tube immersed in liquid Helium, maintaining sample temperature of 4.2K. A X60, 0.85 NA, in-situ microscope objective was used to both focus the exciting beam on the sample surface and to collect the emitted light. The polarization of the emitted light was analyzed using two computer controlled liquid crystal variable retarders and a linear polarizer. In Fig. 1(b) we present the spectrum measured under non-resonant cw excitation with 1 μW of HeNe laser light (1.96 eV). The corresponding degree of linear polarization is presented in Fig. 1(c). The spectral lines participating in the radiative cascades described in Fig. 1(a) are clearly identified spectrally in the single QD PL and linear polarization spectra, and are highlighted orange (yellow) for biexcitonic (excitonic) transitions. For polarization-sensitive time-resolved intensity-correlation measurements, we used a HanburyBrown and Twiss like apparatus [5]. In Fig. 2 we present the measured and calculated intensity correlation functions for photon pairs emitted in the four spin-conserving radiative cascades outlined in Fig. 1(a). The measured data clearly reveal the sequence of the radiative events, reassuring the interpretations of Fig. 1. In Fig. 3 we present measured and calculated intensity correlation functions between different radiative cascades. Since spin blockading prevents the relaxation of the second level hole to its first level, they provide an estimate for the rate by which the hole spin’s scatters [13]. Fast scattering would give rise to a peak in the correlation function, because then the photon emissions preceeding and succeeding the scattering process would mostly happen one right after the other. Scattering rate slower than the radiative recombination rate and/or the optical generation rate would give rise to a dip in the correlation function, since the second photon would most probably be emitted only after additional recombination and generation of e-h pairs. In Fig. 3 (a) and (c) we probe possible transitions from the singlet Figure 2. Measured and calculated timeresolved, polarization sensitive intensity correlation functions, for the 4 radiative cascades described in Fig. 1. The states involved in the first (second) photon emission are illustrated to the left (right) side of each panel. All symbols and labels are as in Fig. 1. Solid Blue (red) line stands for measured cross(co-) circularly polarized photons. Dashed lines represent the corresponding calculated functions. The bar presents the acquisition rate in coincidences per time bin (80 ps) per hour. Figure 3. Measured and calculated timeresolved, polarization sensitive intensity correlation functions, across the radiative cascades. (a) [(c)] Correlations between the singlet biexciton transition and the exciton transition from the T0, [T1] state. (b) [(d)] Correlations between the T0, [T1] biexciton transition and the ground X exciton transition. All symbols and labels are as in Fig. 1. The meanings of all line types and colors are as in Fig. 2. intermediate state to the triplet T0 and T1 intermediate states, respectively. In (b) and (d) we probe possible transitions from the triplet T0 and T1 intermediate states, respectively, to the singlet ground state. Assuming that relaxation from the intermediate triplet states to the ground singlet states must be preceded by transition to the intermediate singlet states, these measurements provide quantitative estimation for the reverse of the processes described in (a) and (c). From the measured data in Fig. 3 one clearly notes that transition between the two holes’ singlet state to the T1 triplet state (Fig. 3c) and vice versa (Fig. 3d) are forbidden, while transitions between the singlet and the T0 triplet states (Fig. 3a) and vice versa (Fig. 3b) are partially allowed. This means that the holes spin projection on the QD’s growth axis is conserved during the relaxation while their in-plane spin projection scatters [13]. The difference between the scattering rates from the singlet to triplet state and that from the triplet to singlet is due to the energy difference between these two states (∼4 meV), which is much larger than the ambient thermal energy (∼0.5 meV). Our model is composed of a set of coupled rate equations for the time-dependent probabilities of finding the system in one of its many-carriers-states [2]. We include all the states as described in Fig. 1(a), together with their Kramers conjugates. In addition, we include four more states representing charged multiexcitons up to 6 e-h pairs [2]. There are clear spectral evidences for processes in which the QD changes its charge state and becomes neutral due to optical depletion [14, 15, 16] (see Fig. 1(b)). These observations are considered in our model by introducing one additional state which represents a neutral QD. The transition rates between the states include radiative rate (γr = 1.25ns −1 deduced directly from the PL decay of the exciton lines) and non-radiative spin-conserving rate (ΓS→S = 35γr, deduced from the intensity ratios of the relevant PL lines). We also include the rates for optical generation of e-h pairs (Ge = 1γr, forced by equating

Radiative cascade from quantum dot metastable spin-blockaded biexciton

We detect a radiative cascade which initiates from a metastable biexciton state in a neutral semiconductor quantum dot. In this biexciton, the heavy 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 colinearly polarized, in the triplet-biexciton cascade they are cross-linearly polarized. We measured the two-photon polarization density matrix and show that the phonon emitted when the intermediate exciton relaxes from excited to ground state, preserves the exciton’s spin. The phonon, thus, does not carry with it any which-path information other than its energy. Nevertheless, entanglement distillation by spectral filtering was found to be rather ineffective for this cascade. This deficiency results from the opposite sign of the anisotropic electron-hole exchange interaction in the excited exciton relative to that in the ground exciton.

Correlated and entangled pairs of single photons from semiconductor quantum dots

Entangled photon pairs are emitted from a biexciton decay cascade of single quantum dots when spectral filtering is applied. We show this by experimentally measuring the density matrix of the polarization state of the photon pair emitted from a continuously pumped quantum dot. The matrix clearly satisfies the Peres criterion for entanglement. By applying in addition a temporal window, the quantum dot becomes an entangled light source.

Electron-hole spin flip-flop in semiconductor quantum dots

We use temporally resolved intensity cross-correlation measurements to identify the biexciton-exciton radiative cascades in a negatively charged QD. The polarization sensitive correlation measurements show unambiguously that the excited two-electron triplet states relax nonradiatively to their singlet ground state via a spin nonconserving flip-flop with the ground state heavy hole. We explain this mechanism in terms of resonant coupling between the confined electron states and an LO phonon. This resonant interaction together with the electron-hole exchange interaction provides an efficient mechanism for this otherwise spin-blockaded, electronic relaxation.

Two-photon photoluminescence excitation spectroscopy of single quantum dots

We present experimental and theoretical study of single semiconductor quantum dots excited by two non-degenerate, resonantly tuned variably polarized lasers. The first laser is tuned to excitonic resonances. Depending on its polarization it photogenerates a coherent single exciton state. The second laser is tuned to biexciton resonances. By scanning the energy of the second laser for various polarizations of the two lasers, while monitoring the emission from the biexciton and exciton spectral lines, we map the biexciton photoluminescence excitation spectra. The resonances rich spectra of the second photon absorption are analyzed and fully understood in terms of a many carrier theoretical model which takes into account the direct and exchange Coulomb interactions between the quantum confined carriers.

Polarization memory in single quantum dots

Abstract We measured the polarization memory of excitonic and biexcitonic optical transitions from single quantum dots at either positive, negative or neutral charge states. Positive, negative and no circular or linear polarization memory was observed for various spectral lines, under the same quasi-resonant excitation below the wetting layer bandgap. We developed a model which explains both qualitatively and quantitatively the experimentally measured polarization spectrum for all these optical transitions. We consider quite generally the loss of spin orientation of the photogenerated electron–hole pair during their relaxation towards the many-carrier ground states. Our analysis unambiguously demonstrates that while electrons maintain their initial spin polarization to a large degree, holes completely dephase.

Two-photon resonance spectroscopy of single quantum-dots

We study two photon absorption resonances in single semiconductor quantum dots, using polarization sensitive two beam time resolved spectroscopy. The rich spectrum of the biexciton resonances is fully understood, for the first time.