Spatial Wave Function Research Articles

High-Fidelity Manipulation of the Quantized Motion of a Single Atom via Stern–Gerlach Splitting**Supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0304501, 2016YFA0302800 and 2016YFA0302002), the Key Research Program of Frontier Science of the Chinese Academy of Sciences (CAS) (Grant No. ZDBSLY- SLH012), the National Natural Science Foundation of China (Grant No. 11774389), the Strategic Priority

We demonstrate high-fidelity manipulation of the quantized motion of a single 87Rb atom in an optical tweezer via microwave couplings induced by Stern–Gerlach splitting. The Stern–Gerlach splitting is mediated by polarization gradient of a strongly focused tweezer beam that functions as fictitious magnetic field gradient. The spatial splitting removes the orthogonality of the atomic spatial wavefunctions, thus enables the microwave couplings between the motional states. We obtain coherent Rabi oscillations for up to third-order sideband transitions, in which a high fidelity of larger than 0.99 is obtained for the spin-flip transition on the first order sideband after subtraction of the state preparation and detection error. The Stern–Gerlach splitting is measured at a precision of better than 0.05 nm. This work paves the way for quantum engineering of motional states of single atoms, and may have wide applications in few body physics and ultracold chemistry.

Spin-structures of the Bose-Einstein condensates with three kinds of spin-1 atoms

We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins SA, SB and SC of the three species, the spin-structures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each other, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of SA, SB and SC, the spin-structures can be further classified into four kinds, namely, p + p + p (all atoms of each species are in singlet-pairs), one species in f (fully polarized) and two species in q (a mixture of polarized atoms and singlet-pairs), two in f and one in q, and f + f + f. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-structure have been specified. A number of spin-structure-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predict.

Novel mechanism for weak magnetization with high Curie temperature observed in H-adsorption on graphene

To elucidate the physics associated with the magnetism observed in nominally nonmagnetic materials containing only sp-electrons, we have developed an extreme model to simulate the adsorption of H (in a straight-line form) on graphene. Our first principles calculations for the model result in a ferromagnetic ground state at a high temperature with a magnetic moment of one Bohr magneton per H atom. The removal of p z-orbitals from sublattice B of graphene introduces p z-vacancies. The p z-vacancy-induced states are created not because of the variations in interatomic interactions but because of the p z-orbital imbalance between two sublattices (A and B) of the conjugated p z-orbital network. Therefore, some critical requirements should be satisfied to create these states (denoted as ) to avoid further imbalances and to minimally affect the conjugated p z-orbital network. The requirements for the creation of can be given as follows: (1) consists of p z-orbitals of only the atoms in sublattice A, (2) the spatial wavefunction of is antisymmetric, and (3) in principle, extends over the entire crystal without decaying, unless other p z-vacancies are encountered. Both the origin of spin polarization and the magnetic ordering of the model can be attributed to the aforementioned requirements.

Direct measurement of the two-dimensional spatial quantum wave function via strong measurements

Wavefunction is the foundation of quantum theory, which is assumed to give a complete description of a quantum system. For a long time, wavefunction is introduced as an abstract element of the theory and there lacks effective ways to measure it directly. The situation, however, is somewhat changed when Lundeen et al. reported the direct measurement of the quantum wavefunction via weak measurements, which gives the wavefunction a clearly operational definition [Nature 474, 188 (2011)]. The weak measurement method requires sequential measurements of conjugate observables position and momentum with the position measurement is weak enough. Surprisingly, the recent research by Vallone and Dequal shows that performing sequential strong measurements realizes the same target, in which case no approximation has to be made compared to the case of weak measurements[Phys. Rev. Lett. 116, 040502 (2016)]. Here we experimentally report the direct measurement of the two-dimensional transverse wavefunction of photons via strong measurements for the first time, which implies that an accurate and clear operational definition can be given to wavefunction. We have measured the Gaussian and Laguerre-Gaussian of l = 1 spatial wavefunctions of photons with R-square are 0.97 and 0.93 respectively. As a potentially important application, we show that the direct measurement of two-dimensional wavefunction provides an alternative way to realize digital holography of three-dimensional objects. The results presented here will not only deepen our understanding of abstract wavefunction but also have significant applications in quantum information processing and quantum imaging.

Spatial Wavefunction Characterization of Femtosecond Pulses at Single-Photon Level.

Reading quantum information of single photons is commonly realized by quantum tomography or the direct (weak) measurement approach. However, these methods are time-consuming and face enormous challenges in characterizing single photons from an ultrafast light source due to the stringent temporal mode matching requirements. Here, we retrieve the spatial wavefunction of indistinguishable single photons from both a continuous wave source and a femtosecond light source using a self-referencing interferometer. Our method only requires nine ensemble-averaged measurements. This technique simplifies the measurement procedure of single-photon wavefunction and automatically mode matches each self-interfering single photon temporally, which enables the measurement of the spatial wavefunction of single photons from an ultrafast light source.

Explanation of Magnetic Destruction of Superconductor Using Schrodinger Equation in the Energy Space

The Wave function of Schrodinger Equation is expressed in terms of time dependent energy eigen function and spatial dependent wave function in the energy space, which gives spatial energy probability. This equation is utilized to find quantum momentum dependent on temperature. This in turn is used to find quantum complex resistance. This expression shows that the superconducting resistance vanishes for temperatures less than a certain critical value. This result conforms to superconductor conventional theory and empirical relations. The application of external magnetic field destroys superconductivity when its strength exceeds a certain critical value. The expression of the relationship between the critical magnetic field and the critical temperature is typical to the conventional one. This is the first time to obtain the conventional relationship for the superconductor’s resistance and critical magnetic field in one model in the energy space.

Complete basis for the pentaquark wave function in a group theory approach

Permutation groups are applied to analyze the symmetries of pentaquark states. All possible quark configurations of the color, flavor, spin and spatial degrees of freedom are worked out in the language of permutation groups, and the corresponding wave functions are constructed systematically in the form of a Yamanouchi basis. The pentaquark spatial wave functions of various symmetries, which are derived in the harmonic-oscillator interaction, are applied as complete bases to evaluate the low-lying light $q^4\overline q$ pentaquark mass of all configurations, where the Cornell-like potential is employed.

The torsional spectrum of the hydrogen trioxide molecule

The energies of the stationary torsional levels of the hydrogen trioxide molecule were calculated at the B3LYP, MP2, and CCSD(T) levels of theory using augmented correlation consistent acc-pVTZ basis set. The molecular symmetry group whose elements are inherent to both equilibrium conformer's symmetry elements (C2 and CS) of the HT molecule was found. Different methods of the molecular parameters calculations were suggested and analyzed. The torsional, spin and total wave functions were classified by irreducible representations of the C2V(M) molecular symmetry group. The 2D dipole moment surface was calculated too. The energies of the stationary torsional states were found using DVR and Fourier methods. With this and acceptable combinations of spatial and spin wave functions, the IR torsional spectrum was calculated at different temperatures. The tunneling frequencies in the ground and some excited torsional states were estimated too.

Multi-Bit SRAMs, Registers, and Logic Using Quantum Well Channel SWS-FETs for Low-Power, High-Speed Computing

This paper presents novel multi-bit static random access memories (SRAMs) using spatial wave-function switched (SWS) FETs. A SWS-FET comprises of two or more vertically stacked quantum well channels while having a single gate and multiple sources and drains. Simulations are presented for 2-bit static random access memories (SRAMs) using cross-coupled 4-states SWS-CMOS inverters. The CMOS inverters are based on 4-state SWS FETs using two Si/SiGe quantum well channels. SWS-structures having 4-quantum well channels processing 8-states/3-bit are described. Logic simulation of multi-bit latches and registers is also presented. Multi-bit CMOS SWS-SRAMs and registers, integrated with logic, and quantum dot nonvolatile random access memories (QD-NVRAMs) presents a new paradigm for low power, high-speed computing.

Simulation of Stacked Quantum Dot Channels SWS-FET Using Multi-FET ABM Modeling

This paper presents simulation of spatial wavefunction switched (SWS) field-effect transistors (FETs) comprising of two vertically stacked quantum dot channels. An analog behavior model (ABM) was used to compare the experimental I-V characteristics of a fabricated QD-SWS-FET. Each channel consists of two quantum dot layers and are connected to the dedicated drains D2 and D1, respectively. The fabricated SWS-FET has one source and one gate. The ABM simulation models SWS-FET comprising of two independent conventional BSIM FETs with their (W/L) ratios, capacitances and other device parameters. The agreement in simulation and experimental data will advance modeling of SWS based adders, logic gates and SRAMs.

Integration of Quantum Dot Gate (QDG) in SWS-FETs for Multi-Bit Logic and QD-NVRAMs for Distributed In-Memory Computing

Compared to multi-valued logic (MVL) with conventional 2-state FETs with a single threshold, MVL computing architectures, based on 4-state SWS (Spatial wavefunction switched) and QDG (quantum dot gate)-FETs having multiple thresholds, results in reduced device count, higher clock (CLK) speed, and lower power consumption. We have experimentally shown multi-state characteristics in SWS-FETs as well as QDG-FETs. This paper presents a novel QDG-SWS-FET that: (1) functions as a multi-bit FET for efficient low-power logic, (2) can be configured as a quantum dot (QD) nonvolatile random access memory (NVRAM), and (3) is suitable for in-memory MVL computing architecture that are compatible with sub-7nm technology nodes. A QDG-SWS-FET with the addition of a control gate dielectric layer functions as a NVRAM cell. Furthermore, it is shown that one single SWS-QD-NVRAM cell gives the functionality of a 1-bit NAND. We have developed circuit/device models and performed quantum simulations for novel multi-layer quantum dot/quantum well FETs and NVRAMs. Our simulations have shown 4-states/2-bit output-input transfer characteristics in SWS-CMOS inverters and NAND gates using two Si/SiGe quantum well channels.

Generation of four states in MOSFET for future multivalued logic circuit design

Analogue Quaternary logic is very promising logic for multi-valued logic implementation. Four states can be generated in different ways. This paper shows the generation of four states in two different semiconductor MOSFETs by modifying their gate structure as well as channel structure. In three well-spatial wave-function switched FET (SWSFET), the four states are generated by connecting their drain terminals. On the other hand, in the quantum dot gate–spatial wave-function switched FET (QDG-SWSFET), the four states are generated by the combining effects of SWSFET and QDGFET.

Spin-Textures of the Condensates with Two Kinds of Spin-1 Atoms Studied Beyond the Single Spatial Mode Approximation

This paper is based on the coupled Gross–Pitaevskii equations (CGP) for two-species BEC, where both the central and spin-dependent forces are included. Under the Thomas–Fermi approximation (TFA), an approach is proposed to obtain analytical solutions of the CGP. Recall that the spin-textures depend seriously on three factors $$I_A=\int \varphi _A^4\mathrm{d}\mathbf {r}$$, $$I_B=\int \varphi _B^4\mathrm{d}\mathbf {r}$$, and $$I_{AB}=\int \varphi _A^2\varphi _B^2\mathrm{d}\mathbf {r}$$, where $$\varphi _A$$ and $$\varphi _B$$ are the spatial wave functions of the two species. In the single spatial mode approximation (SMA), these three factors remain unknown. However, in this paper, these factors have been obtained and analytically expressed by the input parameters (in which those for the central forces are essential). Besides, a number of formulae have been derived to describe the critical points of spin-transition. Thus, the present theory is a complement of the SMA so that the theoretical result can be compared with the experimental result quantitatively, and the effect of each parameter involved in experiments can be clarified. Finally, the results under the TFA are compared with those from the exact numerical solution of the CGP.

Nonlinear absorption coefficient and refractive index changes of two-dimensional two-electron quantum dot in rigid confinement

The Hamiltonian and wavefunctions describing two-dimensional (2D) two-electron ZnO quantum dot in rigid confinement are developed. Then the Schrödinger equation is solved analytically and numerically for determining the ground and excited state energies. The ground state energy of 2D two-electron ZnO quantum dot (QD) in rigid confinement is studied using perturbation and variational methods. The obtained result show that our trial wavefunction is good enough to describe the 2D two-electron QD in rigid confinement. The wavefunction describing the ground state is the combination of symmetric spatial wavefunction and antisymmetric spin wavefunction which is a para-state. The ground state energy eigenvalue obtained by variational technique is a little above that of a perturbation technique. Based on this; the trial wavefunction for the excited state is developed. The excited state energy of 2D two-electron ZnO QD in rigid confinement is studied computationally using variational method. The wavefunction describing the excited state is the combination of symmetric spatial wavefunction with antisymmetric spin wavefunction (para-state) or vice versa (ortho-state). The para and ortho-state energies of the first excited state are calculated and their difference is twice of the exchange energy. Based on the obtained energy eigenvalues of the ground and the first excited state at the value of the coupling constant [Formula: see text] [Formula: see text] 1, the third-order nonlinear absorption coefficient and refractive index changes are investigated. The optical transition is only considered between the two lowest para states.

Optical simulation of the free Dirac equation

We present a classical optics simulation of the one-dimensional Dirac equation for a free particle. Positive and negative energy components are represented by orthogonal polarizations of a free propagating beam, while the spatial profile represents the spatial wave function of the particle. Using a completely tunable time parameter, we observed the oscillation of the average value of the Dirac position operator - known as zitterbewegung (ZB). We are also able to measure the so called mean-position operator which is a single-particle observable and presents no oscillations. Our work opens the way for optical simulation of interesting phenomenon of relativistic systems, as well as condensed-matter physics, without any requirement for specially engineered medium.

Ferromagnetism in graphene traced to antisymmetric orbital combination of involved electronic states

Based on first principles calculations, we reveal that the origin of ferromagnetism caused by electrons in graphene with vacancies can be traced to electrons partially filling -antibonding and -nonbonding states, which are induced by the vacancies and appear near the Fermi level. Because the spatial wavefunctions of both states are composed of atomic orbitals in an antisymmetric configuration, their spin wavefunctions should be symmetric according to the electron exchange antisymmetric principle, leading to electrons partially filling these states in spin polarization. Since this state originates not from interactions between the atoms but from the unpaired orbitals due to the removal of orbitals on the minority sublattice, the state is constrained, distributed on the atoms of the majority sublattice, and decays gradually from the vacancy as ∼. According to these characteristics, we concluded that the state plays a critical role in magnetic ordering in graphene with vacancies. If the vacancy concentration in graphene is large enough to cause the decay-length regions to overlap, constraining the orbital components as little as possible on the minority sublattice atoms in the overlap regions results in the vacancy-induced states being coherent. The coherent process in the overlap region leads to the wavefunctions in all the involved regions antisymmetrized, consequently causing ferromagnetism according to the electron exchange antisymmetric principle. This unusual mechanism concerned with the origin of -electron magnetism and magnetic ordering has never before been reported and is distinctly different from conventional mechanisms. Consequently, we can explain how such a weak magnetization with such a high critical temperature can be experimentally observed in proton-irradiated graphene.

Prediction of a topological p + ip excitonic insulator with parity anomaly

Excitonic insulators are insulating states formed by the coherent condensation of electron and hole pairs into BCS-like states. Isotropic spatial wave functions are commonly considered for excitonic condensates since the attractive interaction among the electrons and the holes in semiconductors usually leads to s-wave excitons. Here, we propose a new type of excitonic insulator that exhibits order parameter with p + ip symmetry and is characterized by a chiral Chern number Cc = 1/2. This state displays the parity anomaly, which results in two novel topological properties: fractionalized excitations with e/2 charge at defects and a spontaneous in-plane magnetization. The topological insulator surface state is a promising platform to realize the topological excitonic insulator. With the spin-momentum locking, the interband optical pumping can renormalize the surface electrons and drive the system towards the proposed p + ip instability.

Electron Correlation in the Singlet and Triplet States of the Atomic 2px12py1 Configuration

The angular correlation in the xy-plane for the singlet and triplet states of the atomic 2px12py1 configuration as discussed by McMillin (J. Chem. Educ. 2018, 95, 1587–1591) is explored without reference to radial coordinates and expanded to outside of the xy-plane. The triplet state (with antisymmetric spatial wave function) is shown to prefer electrons with azimuths that project onto any pair of perpendicular axes in the plane but avoid projections onto any collinear axes. In contrast, the singlet state (with symmetric spatial wave function) does not show any overall bias for projected collinear or perpendicular axes in the xy-plane. However, relative to each other, there is a striking difference between the probability densities of the singlet and triplet states along the axes that have maximal orbital overlap: the singlet (triplet) state shows elevated (reduced) density at collinear projected arrangements, but reduced (elevated) density at perpendicular projected arrangements.

Interface Roughness, Carrier Localization, and Wave Function Overlap in c -Plane (In,Ga)N/GaN Quantum Wells: Interplay of Well Width, Alloy Microstructure, Structural Inhomogeneities, and Coulomb Effects

In this work we present a detailed analysis of the interplay of Coulomb effects and different mechanisms that can lead to carrier localization effects in c-plane InGaN/GaN quantum wells. As mechanisms for carrier localization we consider here effects introduced by random alloy fluctuations as well as structural inhomogeneities such as well width fluctuations. Special attention is paid to the impact of the well width on the results. All calculations have been carried out in the framework of atomistic tight-binding theory. Our theoretical investigations show that independent of the here studied well widths, carrier localization effects due to built-in fields, well width fluctuations and random alloy fluctuations dominate over Coulomb effects in terms of charge density redistributions. However, the situation is less clear cut when the well width fluctuations are absent. For large well width (approx. > 2.5 nm) charge density redistributions are possible but the electronic and optical properties are basically dominated by the spatial out-of plane carrier separation originating from the electrostatic built-in field. The situation changes for lower well width (< 2.5 nm) where the Coulomb effect can lead to significant charge density redistributions and thus might compensate a large fraction of the spatial in-plane wave function separation observed in a single-particle picture. Given that this in-plane separation has been regarded as one of the main drivers behind the green gap problem, our calculations indicate that radiative recombination rates might significantly benefit from a reduced quantum well barrier interface roughness.

A Novel One SWS-FET Transistor for AND/OR Logic Gate

This paper presents the design and modeling of AND/OR logic gate using one high-mobility n-channel spatial wave-function switched field-effect transistor (n-SWS-FET), which provide a significant reduction of cell area and power dissipation. In SWSFET, the channel between source and drain has two or more quantum well (QW) layers separated by a high band gap material between them. The gate voltage controls the charge carrier concentration in the two quantum well layers and it causes the switching of charge carriers from one channel to other channel of the SWS device. This switching property promises to build AND/OR logic gate with one n-SWS-FET transistor, where Complementary Metal Oxide Semiconductor (CMOS) AND/OR gate is built by 6 transistors. The proposed gate configures as AND/OR by change sources signal. The SWS-FET device with two well Si/Si0.5Ge0.5 has been modeled using Berkeley Short-channel IGFET Model (BSIM4.6.0) and Analog Behavioral Model (ABM), the model is suitable for transient analysis at circuit level. This model is optimized for AND/OR logic and used to replace a conventional CMOS logic.