On the structure of the energy distribution function in the hopping regime

The impact of the dispersion of the transport coefficients on the structure of the energy distribution function for charge carriers far from equilibrium has been investigated in effective-medium approximation for model densities of states. The investigations show that two regimes can be observed in energy relaxation processes. Below a characteristic temperature the structure of the energy distribution function is determined by the dispersion of the transport coefficients. Thermal energy diffusion is irrelevant in this regime. Above the characteristic temperature the structure of the energy distribution function is determined by energy diffusion. The characteristic temperature depends on the degree of disorder and increases with increasing disorder. Explicit expressions for the energy distribution function in both regimes are derived for a constant and an exponential density of states.Comment: 16 page

Theory of electric-field-induced spin accumulation and spin current in the two-dimensional Rashba model

Based on the spin-density-matrix approach, both the electric-field-induced spin accumulation and the spin current are systematically studied for the two-dimensional Rashba model. Eigenmodes of spin excitations give rise to resonances in the frequency domain. Utilizing a general and physically well-founded definition of the spin current, we obtain results that differ remarkably from previous findings. It is shown that there is a close relationship between the spin accumulation and the spin current, which is due to the prescription of a quasi-chemical potential and which does not result from a conservation law. Physical ambiguities are removed that plagued former approaches with respect to a spin-Hall current that is independent of the electric field. For the clean Rashba model, the intrinsic spin-Hall conductivity exhibits a logarithmic divergency in the low-frequency regime.Comment: 19 pages including figure

Revival of Silenced Echo and Quantum Memory for Light

We propose an original quantum memory protocol. It belongs to the class of rephasing processes and is closely related to two-pulse photon echo. It is known that the strong population inversion produced by the rephasing pulse prevents the plain two-pulse photon echo from serving as a quantum memory scheme. Indeed gain and spontaneous emission generate prohibitive noise. A second $\pi$-pulse can be used to simultaneously reverse the atomic phase and bring the atoms back into the ground state. Then a secondary echo is radiated from a non-inverted medium, avoiding contamination by gain and spontaneous emission noise. However, one must kill the primary echo, in order to preserve all the information for the secondary signal. In the present work, spatial phase mismatching is used to silence the standard two-pulse echo. An experimental demonstration is presented.Comment: 13 pages, 6 figure

Controlled Compositional Disorder in Er3+:Y2SiO5 Provides a Wide-Bandwidth Spectral Hole Burning Material at 1.5mum

The subgigahertz spectral bandwidth of the lowest energy 1.5mum Er3+ I15/24--\u3eI13/24 optical transition in Er3+:Y2SiO5 has been increased to ˜22GHz by intentionally introducing compositional disorder through codoping with Eu3+ impurity ions. This illustrates a general bandwidth control technique for spectral hole burning device applications including spatial-spectral holography and quantum computing. Coherence measurements by stimulated photon echoes demonstrated that the increased disorder does not perturb the dynamical properties of the Er3+ transition and, thus, gives the desired bandwidth enhancement without penalty in other properties. The echo measurements and model analysis also show that phonon-driven spin flips of Er3+ ions in the ground state are responsible for the spectral diffusion that was observed for the optical transition. These results collectively give a better understanding of both the nature of disorder and of the ion-ion interactions in doped materials, and they also enable the high bandwidths required for signal processing and memory applications at 1.5mum based on spectral hole burning

Optical Decoherence and Spectral Diffusion at 1.5 μM in Er3+: Y2 SiO5 versus Magnetic Field, Temperature, and Er3+ Concentration

The mechanisms and effects of spectral diffusion for optical transitions of paramagnetic ions have been explored using the inhomogeneously broadened 1536 nm I15∕24→I13∕24 transition in Er3+:Y2SiO5. Using photon echo spectroscopy, spectral diffusion was measured by observing the evolution of the effective coherence lifetimes over time scales from 1μs to 20 ms for magnetic-field strengths from 0.3 to 6.0 T, temperatures from 1.6 to 6.5 K, and nominal Er3+ concentrations of 0.0015%, 0.005%, and 0.02%. To understand the effect of spectral diffusion on material decoherence for different environmental conditions and material compositions, data and models were compared to identify spectral diffusion mechanisms and microscopic spin dynamics. Observations were successfully modeled by Er3+−Er3+ magnetic dipole interactions and Er3+ electron spin flips driven by the one-phonon direct process. At temperatures of 4.2 K and higher, spectral diffusion due to Y89 nuclear spin flips was also observed. The success in describing our extensive experimental results using simple models provides an important capability for exploring larger parameter spaces, accelerating the design and optimization of materials for spatial-spectral holography, and spectral hole-burning devices. The broad insight into spectral diffusion mechanisms and dynamics is applicable to other paramagnetic materials, such as those containing Yb3+ or Nd3+

Magnetic G Tensors for the I 15/2 4 and I 13/2 4 States of Er3+: Y2 Si O5

We present the complete Zeeman g tensors for the lowest-energy I15∕24 and I13∕24 states of Er3+ doped into Y2SiO5 for both crystallographic sites deduced from orientation-dependent optical Zeeman spectroscopy over three orthogonal crystal planes. From these data, principal axes of the g tensors were determined for each crystallographic site. Along axes with maximum values, the effective g factors are 14.65 (site 1) and 15.46 (site 2) for the ground state, and 12.97 (site 1) and 13.77 (site 2) for the excited state. To minimize optical decoherence and spectral diffusion in device applications and high resolution spectroscopy, special directions for applying an external magnetic field have been found for each site, for which the ground- and excited-state g factors are equal. Among those directions, choices are presented that also maximize the ground-state splittings for all four magnetically inequivalent sites, thus optimizing the prospects for freezing out electron spin fluctuations and reducing decoherence and spectral diffusion significantly

Spectroscopy and Dynamics of Er3+: Y2 Si O5 at 1.5 μM

We present the results of detailed site-selective spectroscopy performed on the I15∕24↔I13∕24 transition of Er3+:Y2SiO5 at 1.5μm. New determinations of the I13∕24 and I15∕24 crystal-field-level structure for the two crystallographically inequivalent Er3+ sites have been made. The fluorescence dynamics of the metastable I13∕24:Y1 excited state was investigated, showing exponential decays for Er3+ at both crystallographic sites with fluorescence lifetimes of 11.4ms for site 1 and 9.2ms for site 2. Exceptionally sharp inhomogeneous absorption lines of 180, 390, and 510MHz were observed in 0.0015% Er3+:Y2SiO5, 0.005% Er3+:Y2SiO5, and 0.02% Er3+:Y2SiO5 crystals, respectively. The g-values for the lowest energy I15∕24 (Z1) and I13∕24 (Y1) doublets were measured to be 5.5 and 4.6 for site 1 and 15.0 and 12.9 for site 2 when the magnetic field was oriented along the crystal’s D1 axis

Material Optimization of Er3+Y2SiO5 at 1.5 μm for Optical Processing, Memory, and Laser Frequency Stabilization Applications

Spatial-spectral holography using spectral hole burning materials is a powerful technique for performing real-time, wide-bandwidth information storage and signal processing. For operation in the important 1.5 μm communication band, the material Er3+:Y2SiO5 enables applications such as laser frequency stabilization, all-optical correlators, analog signal processing, and data storage. Site-selective absorption and emission spectroscopy identified spectral hole burning transitions and excited state T1 lifetimes in the 1.5 μm spectral region. The effects of crystal temperature, Er3+-dopant concentration, magnetic field strength, and crystal orientation on spectral diffusion were explored using stimulated photon echo spectroscopy, which is the “prototype” interaction mechanism for device applications. The performance of Er3+:Y2SiO5 and related Er3+ materials has been dramatically enhanced by reducing the effect of spectral diffusion on the coherence lifetime T2 through fundamental material design coupled with the application of an external magnetic field oriented along specific directions. A preferred magnetic field orientation that maximized T2 by minimizing the effects of spectral diffusion was determined using the results of angle-dependent Zeeman spectroscopy. The observed linewidth broadening due to spectral diffusion was successfully modeled by considering the effect of one-phonon (direct) processes on Er3+ - Er3+ interactions. The reported studies improved our understanding of Er3+ materials, explored the range of conditions and material parameters required to optimize performance for specific applications, and enabled measurement of the narrowest optical resonance ever observed in a solid—with a homogeneous linewidth of 73 Hz. With the optimized materials and operating conditions, photon echoes were observed up to temperatures of 5 K, enabling 0.5 GHz bandwidth optical signal processing at 4.2 K and providing the possibility for operation with a closed-cycle cryocooler

Effects of Magnetic Field Orientation on Optical Decoherence in Er3+: Y2 SiO5

The influence of the anisotropic Zeeman effect on optical decoherence was studied for the 1.54 μm telecom transition in Er3+:Y2SiO5 using photon echo spectroscopy as a function of applied magnetic field orientation and strength. The decoherence strongly correlates with the Zeeman energy splittings described by the ground- and excited-state g factor variations for all inequivalent Er3+ sites, with the observed decoherence times arising from the combined effects of the magnetic dipole-dipole coupling strength and the ground- and excited-state spin-flip rates, along with the natural lifetime of the upper level. The decoherence time was maximized along a preferred magnetic field orientation that minimized the effects of spectral diffusion and that enabled the measurement of an exceptionally narrow optical resonance in a solid—demonstrating a homogeneous linewidth as narrow as 73 Hz

Measuring the Accuracy of Object Detectors and Trackers

The accuracy of object detectors and trackers is most commonly evaluated by the Intersection over Union (IoU) criterion. To date, most approaches are restricted to axis-aligned or oriented boxes and, as a consequence, many datasets are only labeled with boxes. Nevertheless, axis-aligned or oriented boxes cannot accurately capture an object's shape. To address this, a number of densely segmented datasets has started to emerge in both the object detection and the object tracking communities. However, evaluating the accuracy of object detectors and trackers that are restricted to boxes on densely segmented data is not straightforward. To close this gap, we introduce the relative Intersection over Union (rIoU) accuracy measure. The measure normalizes the IoU with the optimal box for the segmentation to generate an accuracy measure that ranges between 0 and 1 and allows a more precise measurement of accuracies. Furthermore, it enables an efficient and easy way to understand scenes and the strengths and weaknesses of an object detection or tracking approach. We display how the new measure can be efficiently calculated and present an easy-to-use evaluation framework. The framework is tested on the DAVIS and the VOT2016 segmentations and has been made available to the community.Comment: 10 pages, 7 Figure