Ground Manifold Research Articles

Population Oscillations and Ubiquitous Coherences in Multilevel Quantum Systems Driven by Incoherent Radiation.

We consider incoherent excitation of multilevel quantum systems, e.g., molecules with multiple vibronic states. We show that (1) the geometric constraints of the matter-field coupling operator guarantee that noise-induced coherences will be generated in all systems with four or more incoherent transitions between energy eigenstates and (2) noise-induced coherences can lead to population oscillations due to quantum interference via coherence transfer between pairs of states in the ground and excited manifolds. Our findings facilitate the experimental detection of noise-induced coherent dynamics in complex quantum systems.

Advancing robust state estimation of wheeled robots in degenerate environments: harnessing ground manifold and motion states

State estimation is crucial for enabling autonomous mobility in mobile robots. However, traditional localization methods often falter in degraded environments, including issues like visual occlusion, lidar performance degradation, and global navigation satellite system signal interference. This paper presents a novel estimation approach for wheeled robots, exclusively utilizing proprioceptive sensors such as encoders and inertial measurement units (IMU). Initially, the motion manifolds extracted from the historical trajectories are used to assist the encoder in realizing the orientation estimation. Furthermore, a hybrid neural network is designed to categorize the robot’s operational state, and the corresponding pseudo-constraints are added to improve the estimation accuracy. We utilize an error state Kalman filter for the encoder and IMU data fusion. Lastly, comprehensive testing is conducted using both datasets and real-world robotic platforms. The findings underscore that the integration of manifold and motion constraints within our proposed state estimator substantially elevates accuracy compared to conventional approaches. Compare with the methods commonly used in engineering, the accuracy of this method is improved by more than 20%. Crucially, this methodology enables dependable estimation even in degraded environments.

WING: Wheel-Inertial Neural Odometry With Ground Manifold Constraints

WING: Wheel-Inertial Neural Odometry With Ground Manifold Constraints

Visual Localization and Mapping Leveraging the Constraints of Local Ground Manifolds

In order to improve the accuracy of simultaneous localization and mapping problem, plane motion assumption is often used for advanced ground vehicle SLAM system. However, such an assumption is not always suitable to complex and changeable road scenes. In this letter, we propose a stereo-vision based SLAM framework that tightly couples the local ground manifold constraints into accurate camera trajectory estimation. Instead of considering a planar manifold assumption, we model the road as a sequence of local planes with different slopes named local ground manifolds (LGM). The impact region of the LGM is represented as a spherical area in the map, where the vehicle’s motion is constrained by the corresponding local plane model. ORB features and road segmentations are utilized to perform the environmental reconstruction and ground manifold representation. The structures of surroundings and the plane normal of LGMs are jointly optimized with the trajectory of the vehicle within a novel point-LGM tightly-coupled bundle adjustment framework. The experiments on KITTI datasets demonstrate that the proposed ground manifold representation can greatly benefit the camera trajectory estimation.

Integrable model of topological SO(5) superfluidity

Assisted by general symmetry arguments and a many-body invariant, we introduce a phase of matter that constitutes a topological SO(5) superfluid. Key to this finding is the realization of an exactly solvable model that displays some similarities with a minimal model of superfluid $^3$He. We study its quantum phase diagram and correlations, and find exotic superfluid as well as metallic phases in the repulsive sector. At the critical point separating trivial and nontrivial superfluid phases, our Hamiltonian reduces to the globally SO(5)-symmetric Gaudin model with a degenerate ground manifold that includes quartet states. Most importantly, the exact solution permits uncovering of an interesting non-pair-breaking mechanism for superfluids subject to external magnetic fields. Nonintegrable modifications of our model lead to a strong-coupling limit of our metallic phase with a ground-state manifold that shows an extensive entropy.

Minimum Parametrization of the Cauchy Stress Operator

When ${\cal{D}}:\xi \rightarrow \eta$ is a linear differential operator, a "direct problem " is to find the generating compatibility conditions (CC) in the form of an operator ${\cal{D}}_1:\eta \rightarrow \zeta$ such that ${\cal{D}}\xi=\eta$ implies ${\cal{D}}_1\eta=0$. When ${\cal{D}}$ is involutive, the procedure provides successive first order involutive operators ${\cal{D}}_1, ... , {\cal{D}}_n$ when the ground manifold has dimension $n$. Conversely, when ${\cal{D}}_1$ is given, a more difficult " inverse problem " is to look for an operator ${\cal{D}}: \xi \rightarrow \eta$ having the generating CC ${\cal{D}}_1\eta=0$. If this is possible, that is when the differential module defined by ${\cal{D}}_1$ is torsion-free, one shall say that the operator ${\cal{D}}_1$ is parametrized by ${\cal{D}}$ and there is no relation in general between ${\cal{D}}$ and ${\cal{D}}_2$. The parametrization is said to be " minimum " if the differential module defined by ${\cal{D}}$ has a vanishing differential rank and is thus a torsion module. The parametrization of the Cauchy stress operator in arbitrary dimension $n$ has attracted many famous scientists (G.B. Airy in 1863 for $n=2$, J.C. Maxwell in 1863, G. Morera and E. Beltrami in 1892 for $n=3$, A. Einstein in 1915 for $n=4$) . This paper proves that all these works are using the Einstein operator and not the Ricci operator. As a byproduct, they are all based on a confusion between the so-called $div$ operator induced from the Bianchi operator ${\cal{D}}_2$ and the Cauchy operator which is the formal adjoint of the Killing operator ${\cal{D}}$ parametrizing the Riemann operator ${\cal{D}}_1$ for an arbitrary $n$. Like the Michelson and Morley experiment, it is an open historical problem to know whether Einstein was aware of these previous works or not, as the comparison needs no comment.

Hopfield Neural Network Flow: A Geometric Viewpoint.

We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN). The ordinary and stochastic differential equations associated with the HNN were introduced in the literature as analog optimizers and were reported to exhibit good performance in numerical experiments. In this work, we point out that the deterministic HNN can be transcribed into Amari's natural gradient descent, and thereby uncover the explicit relation between the underlying Riemannian metric and the activation functions. By exploiting an equivalence between the natural gradient descent and the mirror descent, we show how the choice of activation function governs the geometry of the HNN dynamics. For the stochastic HNN, we show that the so-called "diffusion machine," while not a gradient flow itself, induces a gradient flow when lifted in the space of probability measures. We characterize this infinite-dimensional flow as the gradient descent of certain free energy with respect to a Wasserstein metric that depends on the geodesic distance on the ground manifold. Furthermore, we demonstrate how this gradient flow interpretation can be used for fast computation via recently developed proximal algorithms.

Protocol for optically pumping AlH+ to a pure quantum state.

We propose an optical pumping scheme to prepare trapped AlH+ molecules in a pure state, the stretched hyperfine state of the rovibronic ground manifold |X2Σ+, v = 0, N = 0 . Our scheme utilizes linearly-polarized and circularly-polarized fields of a broadband pulsed laser to cool the rotational degree of freedom and drive the population to the hyperfine state, respectively. We simulate the population dynamics by solving a representative system of rate equations that accounts for the laser fields, blackbody radiation, and spontaneous emission. In order to model the hyperfine structure, new hyperfine constants of the A2Π excited state were computed using a RASSCF wavefunction. We find that adding an infrared laser to drive the 1-0 vibrational transition within the X2Σ+ manifold accelerates the cooling process. The results show that, under optimal conditions, the population in the target state of the rovibronic ground manifold can reach 63% after 68 μs (330 ms) and 95% after 25 ms (1.2 s) with (without) the infrared laser.

Effects of Ground Manifold Modeling on the Accuracy of Stixel Calculations

This paper highlights the role of ground manifold modeling for stixel calculations; stixels are medium-level data representations used for the development of computer vision modules for self-driving cars. By using single-disparity maps and simplifying ground manifold models, calculated stixels may suffer from noise, inconsistency, and false-detection rates for obstacles, especially in challenging datasets. Stixel calculations can be improved with respect to accuracy and robustness by using more adaptive ground manifold approximations. A comparative study of stixel results, obtained for different ground-manifold models (e.g., plane-fitting, line-fitting in $v$ -disparities or polynomial approximation, and graph cut), defines the main part of this paper. This paper also considers the use of trinocular stereo vision and shows that this provides options to enhance stixel results, compared with the binocular recording. Comprehensive experiments are performed on two publicly available challenging datasets. We also use a novel way for comparing calculated stixels with ground truth. We compare depth information, as given by extracted stixels, with ground-truth depth, provided by depth measurements using a highly accurate LiDAR range sensor (as available in one of the public datasets). We evaluate the accuracy of four different ground-manifold methods. The experimental results also include quantitative evaluations of the tradeoff between accuracy and run time. As a result, the proposed trinocular recording together with graph-cut estimation of ground manifolds appears to be a recommended way, also considering challenging weather and lighting conditions.

Non-radiative processes and luminescence quenching in Mn4+ doped phosphors

We present the temperature dependence of the 2E→4A2 emission of Na2TiF6:Mn4+. Our results are discussed in the framework of the single configurational coordinate diagram (SCCD) model proposed by Struck and Fonger. We have critically analyzed the SCCD model and calculated the vibrational overlap integrals directly from the Manneback recurrence formulas. We have considered the physical origin of shift of the excited state parabolae in the configurational space as well as possible different slopes of the ground and excited electronic manifolds. We have compared our results with numerous results obtained for Mn4+ in other lattices available in the literature. We have found the high inconsistency between the experimental results and values obtained under the SCCD model. Moreover, we have found strong correlation between the values of experimental activation energies Enr and values of constant describing the probability of nonradiative process (i.e. frequency constant). We have considered interaction with lattice phonons described by power dependence defined by exponent α, related to dimension of phonon space and effective phonon energy ℏωeff. We found α≈7.42 and ℏωeff = 315 cm −1 for Enr < 4000 cm−1 and α≈19.73, and ℏωeff =1130 cm−1 for Enr > 4000 cm−1.

Light-induced processes in nature: Coherences in the establishment of the nonequilibrium steady state in model retinal isomerization.

Dynamics and coherences in retinal isomerization are investigated in a standard two-mode two-state model irradiated by natural incoherent light using the Markovian partial-secular Bloch-Redfield formalism. The two-mode two-state model is a minimal model of retinal that considers vibronic states on a ground and excited electronic manifold coupled to two continuous Ohmic harmonic baths. All light-induced coherent oscillations are shown to disappear as the turn-on time becomes realistically slow. Rather, an interplay between incoherent-light induced coherences and environmentally induced coherences is exposed as the system approaches a nonequilibrium steady state. The dynamics of the system reveal stable steady state coherences under realistic conditions, producing a small but robust transient enhancement of quantum yield.

Collective dipole oscillations of a spin-orbit coupled Fermi gas

The collective dipole mode is induced and measured in a spin-orbit (SO) coupled degenerate Fermi gas of 173Yb atoms. Using a differential optical Stark shift, we split the degeneracy of three hyperfine states in the ground manifold, and independently couple consecutive spin states with the equal Raman transitions. A relatively long-lived spin-orbit-coupled Fermi gas, readily being realized with a narrow optical transition, allows to explore a single-minimum dispersion where three minima of spin-1 system merge into and to monitor collective dipole modes of fermions in the strong coupling regime. The measured oscillation frequency of the dipole mode is compared with the semi-classical calculation in the single-particle regime. Our work should pave the way towards the characterization of spin-orbit-coupled fermions with large spin s >frac{1}{2} in the strong coupling regime.

Sub-Doppler Laser Cooling of 23Na in Gray Molasses on the D2 Line☆☆Supported by the National Key Research and Development Program of China under Grant No 2016YFA0301602, the National Natural Science Foundation of China under Grant Nos 11474188 and 11704234, the National Key Research and Development Program of China under Grant No 2018YFA0307601, the Fund for Shanxi ‘1331 Project’ Key Subjects

We report on the efficient gray molasses cooling of sodium atoms using the D2 optical transition at 589.1 nm. Thanks to the hyperfine split about between and in the excited state , this atomic transition is effective for the gray molasses cooling mechanism. Using this cooling technique, the atomic sample in F = 2 ground manifold is cooled from to in 3.5 ms. We observe that the loading efficiency into magnetic trap is increased due to the lower temperature and high phase space density of atomic cloud after gray molasses. This technique offers a promising route for the fast cooling of the sodium atoms in the F = 2 state.

Enantiopure Benzamidinate/Cyclooctatetraene Complexes of the Rare-Earth Elements: Synthesis, Structure, and Magnetism

Novel chiral rare-earth half sandwich complexes containing the chiral amidinate ligand, (S,S)-N,N′-bis(1-phenylethyl)benzamidinate ((S)-PEBA) or the tBu analogue (S,S)-N,N′-bis(1-phenylethyl) pivalamidinate ((S)-PETA) and the cyclooctatetraene dianion (C8H8)2– (COT) were synthesized. All complexes were fully characterized and the solid state structures were established by single-crystal crystallography. Magnetic property measurements indicated that the complex [{(S)-PETA}Er(COT)(THF)] is a typical field-induced single-molecule magnet (SMM), of which the magnetic properties are in reasonable agreement with high-level quantum chemical calculations. Due to predominantly electrostatic ligand field effects, the relativistic J = 15/2 ground manifold of Er(III) is split into 8 Kramers doublets spanning a range of ∼500 cm–1, representable by means of higher order spin tensor operators. According to the quantum chemical calculations as well as from analysis of the experimental data, the magnetic relaxation pathway...

Spin-orbit-coupled Bose-Einstein condensates of rotating polar molecules

An experimental proposal for realizing spin-orbit (SO) coupling of pseudospin-1 in the ground manifold $^1\Sigma(\upsilon=0)$ of (bosonic) bialkali polar molecules is presented. The three spin components are composed of the ground rotational state and two substates from the first excited rotational level. Using hyperfine resolved Raman processes through two select excited states resonantly coupled by a microwave, an effective coupling between the spin tensor and linear momentum is realized. The properties of Bose-Einstein condensates for such SO-coupled molecules exhibiting dipolar interactions are further explored. In addition to the SO-coupling-induced stripe structures, the singly and doubly quantized vortex phases are found to appear, implicating exciting opportunities for exploring novel quantum physics using SO-coupled rotating polar molecules with dipolar interactions.

Coherent spin dynamics in a gadolinium-dopedCaWO4crystal

We report the first observation of Rabi oscillations in the spin-7/2 ensemble of trivalent gadolinium ions hosted in CaWO$_4$ single crystal. A number of transitions within the lowest electronic multiplet $^8S_{7/2}$ of Gd$^{3+}$ ion are studied using a combination of continuous-wave and pulsed electron paramagnetic resonance spectroscopy. The corresponding Rabi damping curves and the spin coherence times are detected at varying strengths of the microwave field. These data are well reproduced by a theoretical model which accounts for the intrinsic inhomogeneity of the microwave field within the microwave resonator and the magnetic dipole interactions in the diluted spin ensemble. The results indicate that the studied 8-level ground manifold of Gd$^{3+}$ ion can represent an effective three qubit quantum system.

State-Selective Excitation of Quantum Systems via Geometrical Optimization

We lay out the foundations of a general method of quantum control via geometrical optimization. We apply the method to state-selective population transfer using ultrashort transform-limited pulses between manifolds of levels that may represent, e.g., state-selective transitions in molecules. Assuming that certain states can be prepared, we develop three implementations: (i) preoptimization, which implies engineering the initial state within the ground manifold or electronic state before the pulse is applied; (ii) postoptimization, which implies engineering the final state within the excited manifold or target electronic state, after the pulse; and (iii) double-time optimization, which uses both types of time-ordered manipulations. We apply the schemes to two important dynamical problems: To prepare arbitrary vibrational superposition states on the target electronic state and to select weakly coupled vibrational states. Whereas full population inversion between the electronic states only requires control at initial time in all of the ground vibrational levels, only very specific superposition states can be prepared with high fidelity by either pre- or postoptimization mechanisms. Full state-selective population inversion requires manipulating the vibrational coherences in the ground electronic state before the optical pulse is applied and in the excited electronic state afterward, but not during all times.

Revealing the Cu2+ ions localization at low symmetry Bi sites in photorefractive Bi12GeO20 crystals doped with Cu and V by high frequency EPR

The sites of incorporation of Cu2+ impurity ions in Bi12GeO20 single crystals co-doped with copper and vanadium have been investigated by electron paramagnetic resonance (EPR). While the X-band EPR spectra consist of a simple broad (ΔB ∼50mT) line with anisotropic lineshape, the W-band EPR spectra exhibit well resolved, strongly anisotropic lines, due to transitions within the 3d9–2D ground manifold of the Cu2+ ions. The most intense group of lines, attributed to the dominant Cu2+(I) center, displays a characteristic four components hyperfine structure for magnetic field orientations close to a 〈110〉 direction. The g and A tensor main axes are very close to one of the 12 possible sets of orthogonal 〈1−10〉, 〈00−1〉 and 〈110〉 crystal directions. Several less intense lines, with unresolved hyperfine structure and similar symmetry properties, mostly overlapped by the Cu2+(I) spectrum, were attributed to Cu2+(II) centers. The two paramagnetic centers are identified as substitutional Cu2+ ions at Bi3+ sites with low C1 symmetry, very likely resulting from different configurations of neighboring charge compensating defects.

Quantum Control in the Cs6S1/2Ground Manifold Using Radio-Frequency and Microwave Magnetic Fields

We implement arbitrary maps between pure states in the 16-dimensional Hilbert space associated with the ground electronic manifold of ^{133}Cs. This is accomplished by driving atoms with phase modulated radio-frequency and microwave fields, using modulation waveforms found via numerical optimization and designed to work robustly in the presence of imperfections. We evaluate the performance of a sample of randomly chosen state maps by randomized benchmarking, obtaining an average fidelity >99%. Our protocol advances state-of-the-art quantum control and has immediate applications in quantum metrology and tomography.

Magneto-optical activity off−ftransitions and properties of4fstates in single-crystal DyFe3(BO3)4

Magnetic circular dichroism and polarized optical absorption spectra of single-crystal DyFe${}_{3}$(BO${}_{3}$)${}_{4}$ were measured in the region of the crystal transparency from 8700 to 16 000 cm${}^{\ensuremath{-}1}$ in the temperature range from 90 K up to room temperature. Spectra of d-d and f-f transitions were separated, and f-f transitions ${}^{6}$${H}_{15/2}$ \ensuremath{\rightarrow} ${}^{6}$(${F}_{9/2}$+${H}_{7/2}$), ${}^{6}$${F}_{7/2}$, ${}^{6}$${F}_{5/2}$, and ${}^{6}$${F}_{3/2}$ were studied. From these measurements, temperature dependences of the paramagnetic magneto-optical activity (MOA) of the electric dipole-forbidden f-f transitions were obtained. It was revealed that, in contrast to allowed transitions, temperature dependences of the MOA of some f-f transitions substantially deviate from the Curie-Weiss law. The theories of MOA of allowed and f-f transitions were considered and the experimental results obtained were accounted for. Circular polarizations in magnetic field and linear polarizations of absorption lines were determined. The Zeeman splitting of some absorption lines were found. Symmetries of the crystal field states were analyzed on the bases of the obtained results in ${D}_{3}$ local symmetry approximation. A small splitting (\ensuremath{\approx}16.5 cm${}^{\ensuremath{-}1}$) between the two lowest sublevels of the ground manifold was detected, and symmetries of these states were identified as ${E}_{1/2}$ ($M$ $=$ \ifmmode\pm\else\textpm\fi{}13/2) and ${E}_{3/2}$ ($M$ $=$ \ifmmode\pm\else\textpm\fi{}15/2), respectively. Deviation of the local symmetry of the Dy${}^{3+}$ ion from ${D}_{3}$ is small, and it was revealed that polarizations of the majority of absorption lines can be accounted for in the ${D}_{3}$ symmetry. This also testifies that in the process of some other electron transitions, the equilibrium configuration of the local environment deviates from ${D}_{3}$ symmetry stronger than it does in the ground state. In addition, it has been shown that the distortions depend not only on the excited but also on the initial state.