Antisymmetric States Research Articles

Robust generation of N-partite N-level singlet states by identical particle interferometry

Abstract We propose an interferometric scheme for generating the totally antisymmetric state of N identical bosons with N internal levels (generalized singlet). This state is a resource for various problems with dramatic quantum advantage. The procedure uses a sequence of Fourier multi-ports, combined with coincidence measurements filtering the results. Successful preparation of the generalized singlet is confirmed when the N particles of the input state stay separate (anti-bunch) on each multiport. The scheme is robust to local lossless noise and works even with a totally mixed input state.

Collective model description of parity-doublet bands in odd mass nuclei

The yrast parity doublet rotational bands in odd medium mass and heavy nuclei are described by a quadrupole–octupole axially symmetric collective model within the strong coupling assumption regarding the odd nucleon. Energy levels of the same spin and opposite parity are interpreted as symmetric and antisymmetric quantum states of the quadrupole–octupole shape fluctuation. The energy spectrum and the associated electromagnetic transitions of the parity doublet bands observed in 21 selected nuclei, are reproduced with a very good accuracy. Predictions are performed for energies of unobserved states and electromagnetic properties. The model parameters are used to establish the static or dynamic nature of the octupole correlations in the ground state and their evolution with spin. A general systematization of the octupole effects as a function of nucleon numbers is realized in conjunction with results on even–even nuclei.

Construction of Antisymmetric Variational Quantum States with Real Space Representation.

Electronic state calculations using quantum computers are mostly based on the second quantized formulation, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is based on the first quantized formulation, which is expected to achieve smaller scaling with respect to the number of basis functions than the second quantized formulation. Among basis functions, a real space basis is an attractive option for quantum dynamics simulations in the fault-tolerant quantum computation (FTQC) era. A major difficulty in the first quantized algorithm with a real space basis is state preparation for many-body electronic systems. This difficulty stems from the antisymmetry of electrons, and it is not straightforward to construct antisymmetric quantum states on a quantum circuit. In this study, we provide a design principle for constructing variational quantum circuits to prepare an antisymmetric quantum state. The proposed circuit generates the superposition of exponentially many Slater determinants, that is, multiconfiguration state, which provides a systematic approach to approximating the exact ground state. We performed the variational quantum eigensolver (VQE) to obtain the ground state of a one-dimensional hydrogen molecular system. As a result, the proposed circuit well reproduced the exact antisymmetric ground state and its energy, whereas the conventional variational circuit yielded neither the antisymmetric nor the symmetric state. Furthermore, we analyzed the many-body wave functions based on the quantum information theory, which illustrated the relation between the electron correlation and the quantum entanglement.

Exchange Energy of the Ferromagnetic Electronic Ground State in a Monolayer Semiconductor.

Mobile electrons in the semiconductor monolayer MoS_{2} form a ferromagnetic state at low temperature. The Fermi sea consists of two circles: one at the K point, the other at the K[over ˜] point, both with the same spin. Here, we present an optical experiment on gated MoS_{2} at low electron density in which excitons are injected with known spin and valley quantum numbers. The resulting trions are identified using a model which accounts for the injection process, the formation of antisymmetrized trion states, electron-hole scattering from one valley to the other, and recombination. The results are consistent with a complete spin polarization. From the splittings between different trion states, we measure the exchange energy Σ, the energy required to flip a single spin within the ferromagnetic state, as well as the intervalley Coulomb exchange energy J. We determine Σ=11.2 meV and J=5 meV at n=1.5×10^{12} cm^{-2} and find that J depends strongly on the electron density n.

Bistable Insect-Scale Jumpers with Tunable Energy Barriers for Multimodal Locomotion.

Drawing inspiration from the jumping mechanisms of insects (e.g., click beetles), bistable structures can convert slow deformations of soft actuating material into fast jumping motions (i.e., power amplification). However, bistable jumpers often encounter large energy barriers for energy release/re-storage, posing a challenge in achieving multimodal (i.e., height/distance) and continuous jumps at the insect scale (body length under 20mm). Here, a new offset-buckling bistable design is introduced that features antisymmetric equilibrium states and tunable energy barriers. Leveraging this design, a Boundary Actuation Tunable Energy-barrier (BATE) jumper (body length down to 15mm) is developed, and transform BATE jumper from height-jump mode (up to 12.7 body lengths) to distance-jump mode (up to 20 body lengths). BATE jumpers can perform agile continuous jumping (within 300ms for energy release/re-storage times) and real-time status detection is further demonstrated. This insect-level performance of the proposed BATE jumper showcases its potential toward future applications in exploration, search, and rescue.

Characteristic features of strong correlation: lessons from a 3-fermion one-dimensional harmonic trap

Abstract Many quantum phenomena responsible for key applications in material science and quantum chemistry arise in the strongly correlated regime. This is at the same time, a costly regime for computer simulations. In the limit of strong correlation analytic solutions exist, but as we move away from this limit numerical simulation are needed, and accurate quantum solutions do not scale well with the number of interacting particles. In this work we propose to use few-particle harmonic traps in combination with twisted light as a quantum emulator to investigate the transition into a strongly-correlated regime. Using both analytic derivations and numerical simulations we generalize previous findings on 2 Coulomb interacting fermions trapped in a one-dimensional harmonic trap to the case of 3 fermions. The 4 signatures of strong correlation we have identified in the one-dimensional harmonic trap are: (i) the ground state density is highly localized around N equilibrium positions, where N is the number of particles, (ii) the symmetric and antisymmetric ground state wavefunctions become degenerate, (iii) the von Neumann entropy grows, (iv) the energy spectrum is fully characterized by N normal modes or less. Our findings describe the low-energy behavior of electrons in quantum wires and ions in Paul traps. Similar features have also been reported for cold atoms in optical lattices.

Demonstrating the Connection between the Nonvalence Correlation-Bound Anions of Polyaromatic Hydrocarbons and the Image Potential States of Graphene Using a One-Electron Model Hamiltonian.

The ground and excited state nonvalence correlation-bound (NVCB) anion states of the hexagonal polycylic aromatic hydrocarbons and of hexagonal graphene nanoflakes are characterized using a one-electron model Hamiltonian which incorporates atomic electrostatic moments up to the quadrupole, coupled inducible charges and dipoles, and atom-centered Gaussians to describe the short-range repulsive interactions. Extrapolation of the calculated electron binding energies of the lowest energy symmetric and antisymmetric (with respect to the molecular plane) NVCB anions of both the polycylic aromatic hydrocarbons and the carbon nanoflakes to the n → ∞ limit yields binding energies that are in good agreement with those of the most stable symmetric and antisymmetric image potential states of freestanding graphene as determined from two-photon photoemission spectroscopy (2PPE) experiments.

JWST/MIRI Detection of Suprathermal OH Rotational Emissions: Probing the Dissociation of the Water by Lyα Photons near the Protostar HOPS 370

Using the MIRI medium-resolution spectrometer on JWST, we have detected pure rotational, suprathermal OH emissions from the vicinity of the intermediate-mass protostar HOPS 370 (OMC2/FIR3). These emissions are observed from shocked knots in a jet/outflow and originate in states of rotational quantum number as high as 46 that possess excitation energies as large as E U /k = 4.65 × 104 K. The relative strengths of the observed OH lines provide a powerful diagnostic of the ultraviolet radiation field in a heavily extinguished region (A V ∼ 10–20) where direct UV observations are impossible. To high precision, the OH line strengths are consistent with a picture in which the suprathermal OH states are populated following the photodissociation of water in its B˜−X band by ultraviolet radiation produced by fast (∼80 km s−1) shocks along the jet. The observed dominance of emission from symmetric ( A′ ) OH states over that from antisymmetric (A″) states provides a distinctive signature of this particular population mechanism. Moreover, the variation of intensity with rotational quantum number suggests specifically that Lyα radiation is responsible for the photodissociation of water, an alternative model with photodissociation by a 104 K blackbody being disfavored at a high level of significance. Using measurements of the Brα flux to estimate the Lyα production rate, we find that ∼4% of the Lyα photons are absorbed by water. Combined with direct measurements of water emissions in the ν 2 = 1 − 0 band, the OH observations promise to provide key constraints on future models for the diffusion of Lyα photons in the vicinity of a shock front.

Bias-Tunable Quantum Well Infrared Photodetector.

With the rapid advancement of Artificial Intelligence-driven object recognition, the development of cognitive tunable imaging sensors has become a critically important field. In this paper, we demonstrate an infrared (IR) sensor with spectral tunability controlled by the applied bias between the long-wave and mid-wave IR spectral regions. The sensor is a Quantum Well Infrared Photodetector (QWIP) containing asymmetrically doped double QWs where the external electric field alters the electron population in the wells and hence spectral responsivity. The design rules are obtained by calculating the electronic transition energies for symmetric and antisymmetric double-QW states using a Schrödinger-Poisson solver. The sensor is grown and characterized aiming detection in mid-wave (~5 µm) to long-wave IR (~8 µm) spectral ranges. The structure is grown using molecular beam epitaxy (MBE) and contains 25 periods of coupled double GaAs QWs and Al0.38Ga0.62As barriers. One of the QWs in the pair is modulation-doped to provide asymmetry in potential. The QWIPs are tested with blackbody radiation and FTIR down to 77 K. As a result, the ratio of the responsivities of the two bands at about 5.5 and 8 µm is controlled over an order of magnitude demonstrating tunability between MWIR and LWIR spectral regions. Separate experiments using parameterized image transformations of wideband LWIR imagery are performed to lay the framework for utilizing tunable QWIP sensors in object recognition applications.

Identifying families of multipartite states with non-trivial local entanglement transformations

The study of state transformations by spatially separated parties with local operations assisted by classical communication (LOCC) plays a crucial role in entanglement theory and its applications in quantum information processing. Transformations of this type among pure bipartite states were characterized long ago and have a revealing theoretical structure. However, it turns out that generic fully entangled pure multipartite states cannot be obtained from nor transformed to any inequivalent fully entangled state under LOCC. States with this property are referred to as isolated. Nevertheless, multipartite states are classified into families, the so-called SLOCC classes, which possess very different properties. Thus, the above result does not forbid the existence of particular SLOCC classes that are free of isolation, and therefore, display a rich structure regarding LOCC convertibility. In fact, it is known that the celebrated n-qubit GHZ and W states give particular examples of such classes and in this work, we investigate this question in general. One of our main results is to show that the SLOCC class of the 3-qutrit totally antisymmetric state is isolation-free as well. Actually, all states in this class can be converted to inequivalent states by LOCC protocols with just one round of classical communication (as in the GHZ and W cases). Thus, we consider next whether there are other classes with this property and we find a large set of negative answers. Indeed, we prove weak isolation (i.e., states that cannot be obtained with finite-round LOCC nor transformed by one-round LOCC) for very general classes, including all SLOCC families with compact stabilizers and many with non-compact stabilizers, such as the classes corresponding to the n-qunit totally antisymmetric states for n≥4. Finally, given the pleasant feature found in the family corresponding to the 3-qutrit totally antisymmetric state, we explore in more detail the structure induced by LOCC and the entanglement properties within this class.

Chaos-Assisted Tunneling.

The ability of particles to "tunnel" through potential energy barriers is a purely quantum phenomenon. A classical particle in a symmetric double-well potential, with energy below the potential barrier, will be trapped on one side of the potential well. A quantum particle, however, can sit on both sides, in either a symmetric state or an antisymmetric state. An analogous phenomenon occurs in conservative classical systems with two degrees of freedom and no potential barriers. If only the energy is conserved, the phase space will be a mixture of regular "islands" embedded in a sea of chaos. Classically, a particle sitting in one regular island cannot reach another symmetrically located regular island when the islands are separated by chaos. However, a quantum particle can sit on both regular islands, in symmetric and antisymmetric states, due to chaos-assisted tunneling. Here, we give an overview of the theory and recent experimental observations of this phenomenon.

Exciton interactions of chlorophyll tetramer in water-soluble chlorophyll-binding protein BoWSCP

The exciton interaction of four chlorophyll a (Chl a) molecules in a symmetrical tetrameric complex of the water-soluble chlorophyll-binding protein BoWSCP was analyzed in the pH range of 3–11. Exciton splitting ΔE = 232 ± 2 cm−1 of the Qy band of Chl a into two subcomponents with relative intensities of 78.1 ± 0.7 % and 21.9 ± 0.7 % was determined by a joint decomposition of the absorption and circular dichroism spectra into Gaussian functions. The exciton coupling parameters were calculated based on the BoWSCP atomic structure in three approximations: the point dipole model, the distributed atomic monopoles, and direct ab initio calculations in the TDDFT/PCM approximation. The Coulomb interactions of monomers were calculated within the continuum model using three values of optical permittivity. The models based on the properties of free Chl a in solution suffer from significant errors both in estimating the absolute value of the exciton interaction and in the relative intensity of exciton transitions. Calculations within the TDDFT/PCM approximation reproduce the experimentally determined parameters of the exciton splitting and the relative intensities of the exciton bands. The following factors of pigment-protein and pigment–pigment interactions were examined: deviation of the macrocycle geometry from the planar conformation of free Chl; the formation of hydrogen bonds between the macrocycle and water molecules; the overlap of wave functions of monomers at close distances. The most significant factor is the geometrical deformation of the porphyrin macrocycle, which leads to an increase in the dipole moment of Chl monomer from 5.5 to 6.9 D and to a rotation of the dipole moment by 15° towards the cyclopentane ring. The contributions of resonant charge-transfer states to the wave functions of the Chl dimer were determined and the transition dipole moments of the symmetric and antisymmetric charge-transfer states were estimated.

Single-Photon Superradiance and Subradiance as Collective Emission from Symmetric and Anti-Symmetric States

Single-Photon Superradiance and Subradiance as Collective Emission from Symmetric and Anti-Symmetric States

Cluster model of C12 in the density functional theory framework

We employ the constrained density functional theory to investigate cluster phenomena for the $^{12}\mathrm{C}$ nucleus. The proton and neutron densities are generated from the placement of three $^{4}\mathrm{He}$ nuclei ($\ensuremath{\alpha}$ particles) geometrically. These densities are then used in a density constrained Hartree-Fock calculation that produces an antisymmetrized state with the same densities through energy minimization. In the calculations no a priori analytic form for the single-particle states is assumed and the full energy density functional is utilized. The geometrical scan of the energy landscape provides the ground state of $^{12}\mathrm{C}$ as an equilateral triangular configuration of three $\ensuremath{\alpha}\mathrm{s}$ with molecular bond like structures. The use of the nucleon localization function provides further insight to these configurations. One can conclude that these configurations are a hybrid between a pure mean-field and a pure $\ensuremath{\alpha}$ particle condensate. This development could facilitate density functional theory based fusion calculations with a more realistic $^{12}\mathrm{C}$ ground state.

Dynamics of an excitation-transfer trimer: Interference, coherence, Berry's phase development, and vibrational control of non-adiabaticity.

We detail several interesting features in the dynamics of an equilaterally shaped electronic excitation-transfer (EET) trimer with distance-dependent intermonomer excitation-transfer couplings. In the absence of electronic-vibrational coupling, symmetric and antisymmetric superpositions of two single-monomer excitations are shown to exhibit purely constructive, oscillatory, and purely destructive interference in the EET to the third monomer, respectively. In the former case, the transfer is modulated by motion in the symmetrical framework-expansion vibration induced by the Franck-Condon excitation. Distortions in the shape of the triangular framework degrade that coherent EET while activating excitation transfer in the latter case of an antisymmetric initial state. In its symmetrical configuration, two of the three single-exciton states of the trimer are degenerate. This degeneracy is broken by the Jahn-Teller-active framework distortions. The calculations illustrate closed, approximately circular pseudo-rotational wave-packet dynamics on both the lower and the upper adiabatic potential energy surfaces of the degenerate manifold, which lead to the acquisition after one cycle of physically meaningful geometric (Berry) phases of π. Another manifestation of Berry-phase development is seen in the evolution of the vibrational probability density of a wave packet on the lower Jahn-Teller adiabatic potential comprising a superposition of clockwise and counterclockwise circular motions. The circular pseudo-rotation on the upper cone is shown to stabilize the adiabatic electronic state against non-adiabatic internal conversion via the conical intersection, a dynamical process analogous to Slonczewski resonance. Strategies for initiating and monitoring these various dynamical processes experimentally using pre-resonant impulsive Raman excitation, short-pulse absorption, and multi-dimensional wave-packet interferometry are outlined in brief.

Degenerate normal-mode states above the cutoff frequency as analogs of the thickness-shear mode for finite Timoshenko–Ehrenfest beams with free ends

In this work, we demonstrate, analytically and numerically, that degenerate states of a beam with free ends, with anti-symmetrical transverse mode shape and occurring in the first-degeneracy points above the cutoff frequency, tend asymptotically to the thickness-shear mode in the infinitely long beam limit, which has not been previously reported. We compare our numerical results, obtained using a Timoshenko–Ehrenfest beam theory of second order, with those obtained with the Finite Element method and plane stress elastodynamics theory, obtaining an excellent agreement. We show that anti-symmetric states within the vicinity of these first-degeneracy states are very similar and closely resemble the so-called thickness-shear mode but for a finite beam with free ends under flexural vibrations.

Symmetry-resolved entanglement of C2 -symmetric topological insulators

For a many-body system of arbitrary dimension, we consider fermionic ground states of noninteracting Hamiltonians invariant under a ${C}_{2}$ cyclic group. The absolute difference $\mathrm{\ensuremath{\Delta}}$ between the number of occupied symmetric and antisymmetric single-particle states is a topological invariant in this case. We prove lower bounds on the configurational and the number entropy based on this invariant. Entanglement entropies are particularly important for identifying topological phases protected by spatial symmetries because they lack gapless boundary modes in general. In topological crystalline insulators, the topological invariant $\mathrm{\ensuremath{\Delta}}$ and the entropy bounds can be directly determined from high-symmetry points in the Brillouin zone.

Identical damped harmonic oscillators described by coherent states

Some aspects of quantum damped harmonic oscillator (DHO) obeying a Markovian master equation are considered in the absence of thermal noise. The continuity equation is derived and Bohmian trajectories are constructed. As a solution of the master equation, we take a single coherent state and compute analytically the relative entropy of coherence, [Formula: see text], in the energy, position and momentum bases. Although [Formula: see text] is constant in both the position and the momentum bases, it is a decreasing function of time in the energy basis becoming zero at long times, revealing its role as the preferred basis. Then, quantum coherence is computed for a superposition of two coherent states, a cat state, and also a superposition of two cat states in the energy basis as a function of separation, in the complex plane, between the two superposed states. It is seen that the quantum coherence increases with this separation. Furthermore, quantum coherence of superposition is compared to that of decomposed states in the superposition. Finally, by considering a system of two noninteracting DHOs, the effect of quantum statistics is studied on the coherence of reduced single-particle states, the joint detection probability and the mean square separation of particles. Our computations show that the single-particle coherence for antisymmetric states is always less than that of symmetric ones. Furthermore, boson anti-bunching and fermion bunching is seen in this open system. This behavior of bosons is the matter-wave analogue of photon anti-bunching seen in a modified Hanbury Brown–Twiss (HBT) interferometer.

Topological Fano resonance of symmetric Lamb wave induced by antisymmetric trapped mode

The rapid development of topological physics in recent years has greatly enriched the methods for manipulating classic waves. Fano resonance is a widespread phenomenon featured with asymmetric and ultrasharp transmission line shape, which is induced by the constructive and destructive interference of two resonance modes with different quality factors. The temporal coupling mode theory is introduced to theoretically describe the physical process of Fano phenomena with two topological resonance states. The mechanism of the pass band led by the coupling between local resonance and Bragg scattering is introduced to design the antisymmetric topological resonance state and suppress the interference of the antisymmetric propagation mode. The complex eigenvalue analysis shows that the antisymmetric topological resonance state can be treated as the bound state in continuum (BIC). The periods of the phononic crystal (PnC) can be largely reduced by this scheme. The mechanism of coupling between two topological resonance modes attributed to geometric parameter variation is explained by the perturbing perspective and the temporal coupled mode theory. By theoretical analysis, the antisymmetric topological resonance state can be simultaneously treated as symmetric protected BIC and Friedrich–Wintgen BIC. Then, the design method for PnC with Fano resonance is proposed. The numerical results are in good agreement with the theoretical outcomes. The research results may find potential applications and offer the theoretical directive guideline for design in the fields of non-destructive testing, radio-frequency filters, resonators, and sensors.

Collective transitions of two entangled atoms near a Schwarzschild black hole

We study the collective transitions of a pair of static atoms near a Schwarzschild black hole. The two atoms are assumed to be placed along the radial direction of the black hole and be coupled with fluctuating massless scalar fields in the Hartle-Hawking and Unruh vacua. When the two-atom system is prepared in the symmetric or antisymmetric entangled state, the average rate of change of energy of the two-atom system is oblivious of the vacuum fluctuations and solely a result of the radiation reaction. Consequently, the average rate, contrary to the existing results in the literature, is finite near the event horizon and is not affected by the Hawking radiation of the black hole.