We report attosecond-scale probing of the laser-induced dynamics in molecules. We apply the method of high-harmonic spectroscopy, where laser-driven recolliding electrons on various trajectories record the motion of their parent ion. Based on the transient phase-matching mechanism of high-order harmonic generation, short and long trajectories contributing to the same harmonic order are distinguishable in both the spatial and frequency domains, giving rise to a one-to-one map between time and photon energy for each trajectory. The short and long trajectories in H2 and D2 are used simultaneously to retrieve the nuclear dynamics on the attosecond andångström scale. Compared to using only short trajectories, this extends the temporal range of the measurement to one optical cycle. The experiment is also applied to methane and ammonia molecules.There is a continuous desire to develop methods with ever-better resolution in ultrafast science. Generally, time-resolved methods rely on ultrashort laser pulses. Therefore in the past decades, substantial efforts have been paid to produce attosecond pulses based on highorder harmonic generation (HHG) [1][2][3][4]. Since the duration of attosecond pulses is comparable to the time scale of bound electrons, such sources provide an important tool for detecting the ultrafast electron dynamics inside atoms or molecules [5][6][7][8], inaugurating a new domain for time-resolved metrology and spectroscopy [9].One popular method of attosecond probing is the pump-probe measurement [2,8]. In this scheme, a physical process is first triggered by an attosecond pump pulse and subsequently probed by a near-infrared pulse (or vice versa). Then the time-dependent information can be decoded from the streaked photoelectron spectra recorded at different pump-probe delays. On the other hand, HHG itself is a sub-femtosecond nonlinear process arising from laser induced electron-ion recollisions [10]. Rich information about the electron-ion system at the time of recollision is encoded in the harmonic spectra. Extracting this information systematically is known as high-harmonic spectroscopy (HHS). HHS has been exploited to image molecular structure withångström resolution [11][12][13][14][15][16], e.g., by molecular orbital tomography [11][12][13]. Moreover, for each high-harmonic order, the freed electron spends a specific time in the continuum before recollision, resulting in the temporal chirp of HHG [17]. The ionization-recollision delay is analogous to a pump-probe delay, providing an alternative way to map the photon energy to time. Based on this property, HHS has been developed into an emerging tool for studying nuclear dynamics [18][19][20][21][22][23] and charge migration [24][25][26][27] with attosecond temporal resolution. However, according to the recollision model [10], there are two trajectories per optical half cycle contributing to each individual harmonic order. The two trajectories are referred to as the "short" and "long" trajectories. Therefore, to guarantee a one-to-one map betwee...

To generate entangled photon pairs via quantum dots (QDs), the exciton fine structure splitting (FSS) must be comparable to the exciton homogeneous line width. Yet in the (In,Ga)As/GaAs QD, the intrinsic FSS is about a few tens µeV. To achieve photon entanglement, it is necessary to Cherrypick a sample with extremely small FSS from a large number of samples, or to apply strong in-plane magnetic field. Using theoretical modeling of the fundamental causes of FSS in QDs, we predict that the intrinsic FSS of InAs/InP QDs is an order of magnitude smaller than that of InAs/GaAs dots, and better yet, their excitonic gap matches the 1.55 µm fiber optic wavelength, therefore offer efficient on-demand entangled photon emitters for long distance quantum communication. proposed that a biexciton cascade process in a selfassembled QD can be used to generate the "event-ready" entangled photon pairs, with orders of magnitude higher efficiency than the traditional parametric down conversion method [2,3,4]. This process is shown schematically in Fig. 1(a), in which a biexciton decays into two photons via two paths of different polarizations |H and |V . If the two paths are indistinguishable, the final result is a polarization entangled photon pair state [6,7](|H xx H x + |V xx V x )/ √ 2. However, early attempts[6] to generate the entangled photon pairs using the InAs/GaAs QDs were unsuccessful, because the |H -and |V -polarized photons have a small energy difference due to the asymmetric electron-hole exchange interaction in the QDs [see Fig. 1(b)]. The small energy splitting, known as the fine structure splitting (FSS), is typically about -40 ∼ +80 µeV in the InAs/GaAs QDs [8,9,10], which is much larger than the radiative linewidth (∼ 1.0 µeV) [7,11]. Such a splitting provides therefore "which way" information about the photon decay path that can destroy the photon entanglement, leaving only classically correlated photon pairs [7,11].To achieve photon entanglement, the FSS must be reduced to a value comparable to the exciton homogeneous line width. Lack of detailed understanding of the factors controlling FSS in QDs has thus far impeded the design of small FSS values in quantum systems. It was, however, * corresponding author: helx@ustc.edu.cn Due to the in-plane asymmetry, the H and V polarized photons have a small energy splitting ∆FSS, which may destroy the polarization entanglement.

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We experimentally disentangle the contributions of different quantum paths in high-order harmonic generation (HHG) from the spectrally and spatially resolved harmonic spectra. By adjusting the laser intensity and focusing position, we simultaneously observe the spectrum splitting, frequency shift and intensity-dependent modulation of harmonic yields both for the short and long paths. Based on the simulations, we discriminate the physical mechanisms of the intensity-dependent modulation of HHG due to the quantum path interference and macroscopic interference effects. Moreover, it is shown that the atomic dipole phases of different quantum paths are encoded in the frequency shift. In turn, it enables us to retrieve the atomic dipole phases and the temporal chirps of different quantum paths from the measured harmonic spectra. This result gives an informative mapping of spatiotemporal and spectral features of quantum paths in HHG.

Atomistic pseudopotential plus configuration interaction calculations of the energy needed to charge dots by either electrons or holes are described, and contrasted with the widely used, but highly simplified two-dimensional parabolic effective mass approximation (2D-EMA). Substantial discrepancies are found, especially for holes, regarding the stable electronic configuration and filling sequence which defies both Hund's rule and the Aufbau principle.