Abstract:Single quantum emitters (SQEs) are at the heart of quantum optics 1 We assign this fine structure to two excitonic eigen-modes whose degeneracy is lifted by a large ~0.71 meV coupling, likely due to the electron-hole exchange interaction in presence of anisotropy 8 . Magneto-optical measurements also reveal an exciton g-factor of ~8.7, several times larger than that of delocalized valley excitons 9-12 . In addition to their fundamental importance, establishing new SQEs in 2D quantum materials could give rise to practical advantages in quantum information processing, such as efficient photon extraction and high integratability and scalability. Here, we report the first observation of photon antibunching from localized SQEs in tungsten-diselenide (WSe2) monolayers. WSe2 monolayers are grown on top of a 300 nm SiO2 on silicon substrate by physical vapor transport 26 , a scalable synthesis approach (see Methods).For the optical experiments, the monolayers are held in vacuum inside a cryostat at 4.2 K, where a magnetic field is applied perpendicular to the sample plane (Faraday geometry).Experiments are performed in the reflection geometry where a confocal microscope allows 3 for both laser excitation with a beam focal spot of ~1 µm and collection of the emission (see Methods and Supplementary Fig. S1).The WSe2 monolayer is excited using a continuous-wave (cw) laser at a wavelength of 637 nm. Figure 1a shows the emergence of sharp spectral lines, which are red shifted by ~40-100 meV from the PL of the delocalized valley excitons (see right inset of Fig. 1a). With an excitation power of 6 µW, the peak intensity of the sharp lines are ~500 times stronger than the delocalized valley excitons. The left inset of Fig. 1a shows the fine structure of the highestintensity line (we call SQE1), which is composed of a doublet. The red lines are Lorentzian fits which yield linewidths of ~112 µeV and ~122 µeV (FWHM) and a splitting of 0.68 meV.A statistical histogram on 92 randomly localized emitters from 15 different monolayers is presented in Fig. 1b, yielding linewidths ranging from 58 µeV to 500 µeV, with an average spectral linewidth of 130 µeV, roughly two orders of magnitude smaller than the linewidth of the delocalized exciton PL. The linewidth of these emitters increases dramatically when the temperature is increased (see Supplementary Fig. S2).The sharp lines are highly spatially localized. Figure 1c illustrates a scanning confocal microscope image of the PL from the emission line centered at 1.7186 eV. The isolated bright spots show that the emission is from localized sites, which are likely excitons bound to atomic defects. These sharp lines show strong saturation behavior as a function of laser power. We investigate the power dependence of the SQE1 peak at 1.7156 eV (left inset of Fig. 1a) as an example. Figure 1d shows the integrated counts as a function of excitation power, demonstrating a pronounced saturation behavior similar to an atom-like two-level system.Under excitation with a 3-ps pulsed laser at ...

Single photon sources based on semiconductor quantum dots offer distinct advantages for quantum information, including a scalable solid-state platform, ultrabrightness, and interconnectivity with matter qubits. A key prerequisite for their use in optical quantum computing and solid-state networks is a high level of efficiency and indistinguishability. Pulsed resonance fluorescence (RF) has been anticipated as the optimum condition for the deterministic generation of high-quality photons with vanishing effects of dephasing. Here, we generate pulsed RF single photons on demand from a single, microcavity-embedded quantum dot under s-shell excitation with 3-ps laser pulses. The π-pulse excited RF photons have less than 0.3% background contributions and a vanishing two-photon emission probability. Non-postselective Hong-Ou-Mandel interference between two successively emitted photons is observed with a visibility of 0.97(2), comparable to trapped atoms and ions. Two single photons are further used to implement a high-fidelity quantum controlled-NOT gate.Single photons have been proposed as promising quantum bits (qubits) for quantum communication [1], linear optical quantum computing [2, 3] and as messengers in quantum networks [4]. These proposals primarily rely upon a high degree of indistinguishability between individual photons to obtain the Hong-Ou-Mandel (HOM) type interference [5] which is at the heart of photonic controlled logic gates and photon-interference-mediated quantum networking [1][2][3][4].Among different types of single-photon emitters [6, 7], quantum dots (QDs) are attractive solid-state devices since they can be embedded in high-quality nanostructure cavities and waveguides to generate ultra-bright sources of single and entangled photons [7][8][9][10]. QDs also provide a light-matter interface [11][12][13] and can in principle be scaled to large quantum networks [14]. Two-photon HOM interference experiments using photons from a single QD [5,15,17], as well as from independent sources [18,19], have not only demonstrated the potential of QDs as single-photon sources, but also revealed the level of dephasing arising from incoherent excitation. The method of incoherent pumping (via above band-gap or p-shell excitation) typically causes reduced photon coherence times due to homogeneous broadening of the excited state [5] and uncontrolled emission time jitter from the nonradiative high-level to s-shell relaxation [6], leading to a decrease of photon indistinguishability.To eliminate these dephasings, an increasing effort has been devoted to s-shell resonant optical excitation of QDs. The Mollow triplet spectra and photon correlations of the resonance fluorescence (RF) have been measured [1][2][3]21]. Under continuous-wave (CW) laser excitation, a high degree of indistinguishability for continuously generated RF photons has been demonstrated through post-selective HOM interference [25]. However, in the CW regime, as the emission time of the RF photons is uncontrolled, the HOM interference relies on th...

We demonstrate deterministic and robust generation of pulsed resonance fluorescence single photons from a single InGaAs quantum dot using the method of rapid adiabatic passage. Comparative study is performed with transform-limited, negatively chirped and positively chirped pulses, identifying the last one to be the most robust against fluctuation of driving strength. The generated single photons are background free, have a vanishing twophoton emission probability of 0.3% and a raw (corrected) two-photon Hong-Ou-Mandel interference visibility of 97.9% (99.5%), reaching a precision that places single photons at the threshold for fault-tolerant surface-code quantum computing. The single-photon source can be readily scaled up to multi-photon entanglement and used for quantum metrology, boson sampling and linear optical quantum computing.Photons offer an appealing platform for quantum information processing because of their fast transmission, low decoherence, and the ease of implementing precise single-qubit operations [1,2] [9]. Yet, scaling up from these small-scale demonstrations to more, practically useful, photons appears challenging due to the probabilistic generation and high-order emission of photon pairs in parametric down conversion [2].To overcome these shortcomings, an increasing effort has turned to single quantum emitters [10]. Self-assembled quantum dots (QDs) on scalable semiconductor chips are promising single-photon emitters with high quantum efficiency [11]. Further, QDs can be embedded in monolithic nanocavities to enhance light-matter interaction and photon extraction [12]. Since the first observation of photon antibunching from QDs [13], numerous experiments have demonstrated single-photon emission [11,12,[14][15][16].Scalable photonic quantum technologies place stringent demands on the single-photon sources. One of the key requirements is deterministic single-photon generation, that is, the source should emit one-and only one-photon upon each pulsed excitation. To this end, ultrafast laser pulses have been used to resonantly excite a QD two-level system to generate on-demand resonance fluorescence (RF) single photons and observe Rabi oscillation (RO) [16]. Under a π pulse excitation, the two-level system is deterministically prepared in the excited state, followed by radiative emission of a single photon. However, using this technique, the efficiency of singlephoton generation is sensitive to the variation of pulse area, which can be caused by fluctuation of experimental parameters such as the excitation power and dipole moment.A more robust method of excited state preparation in a twolevel system is rapid adiabatic passage (RAP) with frequencychirped pulses. Unlike RO, adiabatic popular transfer is largely unaffected by the variation in the optical field, interaction time, and atomic dipole moment. Previous experiments have used negatively chirped pulses to demonstrate population transfer in single QDs, where the exciton population is read out by photocurrent [17] or probabilistic photon emiss...

Single photon sources based on semiconductor quantum dots offer distinct advantages for quantum information, including a scalable solid-state platform, ultrabrightness, and interconnectivity with matter qubits. A key prerequisite for their use in optical quantum computing and solid-state networks is a high level of efficiency and indistinguishability. Pulsed resonance fluorescence (RF) has been anticipated as the optimum condition for the deterministic generation of high-quality photons with vanishing effects of dephasing. Here, we generate pulsed RF single photons on demand from a single, microcavity-embedded quantum dot under s-shell excitation with 3-ps laser pulses. The π-pulse excited RF photons have less than 0.3% background contributions and a vanishing two-photon emission probability. Non-postselective Hong-Ou-Mandel interference between two successively emitted photons is observed with a visibility of 0.97(2), comparable to trapped atoms and ions. Two single photons are further used to implement a high-fidelity quantum controlled-NOT gate.

We investigate temperature-dependent resonance fluorescence spectra obtained from a single selfassembled quantum dot. A decrease of the Mollow triplet sideband splitting is observed with increasing temperature, an effect we attribute to a phonon-induced renormalization of the driven dot Rabi frequency. We also present first evidence for a nonperturbative regime of phonon coupling, in which the expected linear increase in sideband linewidth as a function of temperature is canceled by the corresponding reduction in Rabi frequency. These results indicate that dephasing in semiconductor quantum dots may be less sensitive to changes in temperature than expected from a standard weak-coupling analysis of phonon effects. DOI: 10.1103/PhysRevLett.113.097401 PACS numbers: 78.67.Hc, 71.38.-k, 78.47.-p Self-assembled semiconductor quantum dots (QDs) provide a promising platform for quantum information processing using single spins [1,2] and photons [3][4][5][6]. Such applications require QD quantum coherence to be preserved on time scales sufficient for performing high fidelity quantum operations, and for emitted single photons to possess a large degree of indistinguishability [7][8][9]. Indistinguishable photons can be produced by s-shell resonant optical excitation of a single QD [10][11][12], wherein an electron-hole pair is created directly without any relaxation from higher states, which would otherwise cause inhomogeneous broadening in the QD emission spectrum. The coherence time (T 2 ) of such photons is able to approach the Fourier transform limit, T 2 ¼ 2T 1 (with T 1 the QD radiative lifetime) at low temperatures (∼4 K) and weak driving strengths [13].As the intensity of the pump laser increases, however, an additional power dependent dephasing contribution arises, even at low temperatures [14][15][16][17][18][19][20][21][22][23][24]. This is often termed excitation induced dephasing (EID), which commonly originates from deformation potential coupling of QD excitons to longitudinal acoustic (LA) phonons. As the driving strength increases, so does the energy splitting of the excitonic dressed states, and excitations are then able to scatter with the increased density of phonons around this energy scale in the bulk semiconductor lattice. Driving dependence is thus a pronounced characteristic of EID, as was observed in Refs. [14,15], where QD excitonic Rabi oscillations were measured via photocurrents, and in Refs. [16,17] through driven QD optical emission.Besides EID, another direct manifestation of the phonon influence on a driven dot can be found in the dependence of its properties on temperature. In fact, an idealized two-level system (e.g., an isolated atom) should not show any change in emission behavior with temperature over the usual experimental range, in contrast to the response to changes PRL 113,

This Letter reports all-optically tunable and highly indistinguishable single Raman photons from a driven single quantum dot spin. The frequency, linewidth, and lifetime of the Raman photons are tunable by varying the driving field power and detuning. Under continuous-wave excitation, subnatural linewidth single photons from off-resonant Raman scattering show an indistinguishability of 0.98(3). Under π pulse excitation, spin- and time-tagged Raman fluorescence photons show an almost vanishing multiphoton emission probability of 0.01(2) and a two-photon quantum interference visibility of 0.95(3). Lastly, Hong-Ou-Mandel interference is demonstrated between two single photons emitted from remote, independent quantum dots with an unprecedented visibility of 0.87(4).

The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α, −α}, α ∈ [0, 1), are called equiangular. The problem of determining the maximum size of s-distance sets in various spaces has a long history in mathematics. We suggest a new method of bounding the size of an s-distance set in compact two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-distance set in R n , n ≥ 7, is n(n+1) 2 with possible exceptions for some n = (2k + 1) 2 − 3, k ∈ N. We also prove the universal upper bound ∼ 2 3 na 2 for equiangular sets with α = 1 a and, employing this bound, prove a new upper bound on the size of equiangular sets in all dimensions. Finally, we classify all equiangular sets reaching this new bound.

A finite collection of unit vectors S ⊂ R n is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We prove that if a = −b, then a two-distance set that forms a tight frame for R n is a spherical embedding of a strongly regular graph. We also describe all two-distance tight frames obtained from a given graph. Together with an earlier work by S. Waldron (2009) [22] on the equiangular case, this completely characterizes two-distance tight frames. As an intermediate result, we obtain a classification of all twodistance 2-designs.