New Class Of States Research Articles

Size Isomers at Threshold States

An overview is provided for a new class of states, which we have named as the size isomers. Such states are weakly bound and have an exotic structure (cluster states, halo/‘‘skin’’). The development of methods for measuring the radii of nuclei in their short-lived excited states led to the discovery of new classes of states. The size of a nucleus defined by the radius of its nucleon (proton and neutron) density distribution and the proton charge distribution is one of the most fundamental and important nuclear characteristics. Nuclear radius determines the basic properties of nuclei and is a consequence of the fundamental features of the strong interaction. Up to now two groups of the size isomers were identified: the excited states with halos (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{9}$$\\end{document}Be, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{11}$$\\end{document}Be, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}N) and some specific alpha-cluster states (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{11}$$\\end{document}B, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{12}$$\\end{document}C, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C). All the observed states are dilute, however, some indication to possible existence of more compact than the ground states was obtained as well (in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C). The phenomenon of size isomerism occurred to be not a rare one especially if we take into account rotational bands based on some of such states. The structure of size isomers is related with some new features, e.g., rotating halos, halos in continuum, different types of quasimolecular configurations. Some rudimentary signs of alpha-particle condensation (a ‘‘ghost’’ of condensate) were observed in the Hoyle state of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{12}$$\\end{document}C, however, we cannot speak about confirmation of this ambitious theory. Analogs to the Hoyle state, expected in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{11}$$\\end{document}B, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{13}$$\\end{document}C, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{16}$$\\end{document}O, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{20}$$\\end{document}Ne near the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-emission thresholds, are considered.

Constructing squeezed states of light with associated Hermite polynomials

A new class of states of light is introduced that is complementary to the well-known squeezed states. The construction is based on the general solution of the three-term recurrence relation that arises from the saturation of the Schr\"odinger inequality for the quadratures of a single-mode quantized electromagnetic field. The new squeezed states are found to be linear superpositions of the photon-number states whose coefficients are determined by the associated Hermite polynomials. These results do not seem to have been noticed before in the literature. As an example, the new class of squeezed states includes superpositions characterized by odd-photon number states only, so they represent the counterpart of the prototypical squeezed-vacuum state which consists entirely of even-photon number states.

Composite particles with minimum uncertainty in spacetime

Composite particles---atoms, molecules, or microspheres---are unique tools for testing joint quantum and general relativistic effects, macroscopic limits of quantum mechanics, and searching for new physics. However, all studies of the free propagation of these particles find that they delocalise into separate internal energy components, destroying their spatial coherence. This renders them unsuitable for experimental applications, as well as theoretical studies where they are used as idealised test masses or clocks. Here we solve this problem by introducing a new class of states with minimal uncertainty in space-time that fully overcome the delocalisation. The relevant physics comes from minimising the uncertainty between position and velocity, rather than position and momentum, while directly accounting for mass as an operator. Our results clarify the nature of composite particles, providing a currently missing theoretical tool with direct relevance for studies of joint foundations of quantum and relativistic phenomena, which removes a roadblock that could limit near-future quantum tests using composite particles.

Towards Gaussian states for loop quantum gravity

An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a vacuum in which geometry is highly degenerate. Additionally, fluctuations are distributed very unevenly between configuration and momentum variables. Coherent states that have been proposed to balance the uncertainties more evenly can, up to now, only do this for finitely many degrees of freedom. Our work is motivated by the desire to obtain Gaussian states that encompass all degrees of freedom. To obtain a toy-model we reformulate the U(1) holonomy-flux algebra in any dimension as a Weyl algebra, and discuss generalisations to SU(2). We then define and investigate a new class of states on these algebras which behave like quasifree states on the momentum variables.

Heat-Bath Algorithmic Cooling with optimal thermalization strategies

Heat-Bath Algorithmic Cooling is a set of techniques for producing highly pure quantum systems by utilizing a surrounding heat-bath and unitary interactions. These techniques originally used the thermal environment only to fully thermalize ancillas at the environment temperature. Here we extend HBAC protocols by optimizing over the thermalization strategy. We find, for any d-dimensional system in an arbitrary initial state, provably optimal cooling protocols with surprisingly simple structure and exponential convergence to the ground state. Compared to the standard ones, these schemes can use fewer or no ancillas and exploit memory effects to enhance cooling. We verify that the optimal protocols are robusts to various deviations from the ideal scenario. For a single target qubit, the optimal protocol can be well approximated with a Jaynes-Cummings interaction between the system and a single thermal bosonic mode for a wide range of environmental temperatures. This admits an experimental implementation close to the setup of a micromaser, with a performance competitive with leading proposals in the literature. The proposed protocol provides an experimental setup that illustrates how non-Markovianity can be harnessed to improve cooling. On the technical side we 1. introduce a new class of states called maximallyactivestates and discuss their thermodynamic significance in terms of optimal unitary control, 2. introduce a new set of thermodynamic processes, called β-permutations, whose access is sufficient to simulate a generic thermalization process, 3. show how to use abstract toolbox developed within the resource theory approach to thermodynamics to perform challenging optimizations, while combining it with open quantum system dynamics tools to approximate optimal solutions within physically realistic setups.

Excitation and depression of coherent state of the simple harmonic oscillator

Othman and Yevick [Int. J. Theor. Phys. 57, 2293 (2018)] introduced a new class of states defined as “near” coherent states attached to the simple harmonic oscillator. Such states can be expressed as superposition of a standard coherent state and a derivative state, which are neither completely quantum nor completely classical. Here, we introduce photon-added (-depleted) near coherent states [PA(D)NCS] through “m” times application of creation (annihilation) operators â†(â) to the near coherent state. A general analysis of nonclassical properties of the PA(D)NCS, such as sub-Poissonian statistics and squeezing effect, is given analytically and numerically in the context of the conventional quantum optics. We also derive the Wigner distribution function of the PA(D)NCS over phase space which may bear negative values, which is a good indication of their nonclassical properties. Finally, an experimental procedure for generating the PA(D)NCSs is established.

Continuous Tensor Network States for Quantum Fields

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean invariant, and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending Projected Entangled Pair States (PEPS), we propose a generalization bearing similarities with the continuum Multi-scale Entanglement Renormalization Ansatz (cMERA).

Some Numerical Cases of Entanglement Concentration Using Entanglement Swapping

The quantum information network is important in establishing next-generation technology. In particular, maximal and long-distance entangled states are important in realizing a number of quantum information technologies, such as teleportation, key distribution and so forth. Entanglement swapping is a scheme that creates a long-distance network by using multiple short ones. Entanglement swapping protocols applied to non-maximal correlations have been thoroughly investigated by various people. Rather than providing any new analytic results, some examples of a numerical approach will be provided in this paper. In particular, the paper reveals the existence of different classes of coefficients that approximate the optimal outcome (i.e., the weaker average maximal entanglement between the two initial states). The new class of states is non-trivial in the sense that their coefficients are just as widely distributed as the coefficients of states satisfying optimality conditions are. Moreover, we will numerically examine entanglement swapping methods and show the distribution of optimal and general coefficients for three and four 2-level correlations.

A new class of states of reversible entanglement manipulation under positive partial transpose operations**Project supported by the National Natural Science Foundation of China (Grant No. 11671244).

We first study the reversibility for a class of states under the operations which completely preserve the positivity of partial transpose (PPT) and show that the entanglement cost is equal to the distillable entanglement for a rank-two mixed state on the 4⊗4 antisymmetric subspace under PPT operations. By using a similar method in finding the irreversibility, we also find that the value of a new efficiently computable additive lower bound Eη(ρ) for the asymptotic PPT-relative entropy of entanglement presented in [Phys. Rev. Lett.119, 180506 (2017)] is equal to the regularized Rains’ bound and an upper bound EN(ρ) for distillable entanglement for these states. Furthermore, we find states on the symmetric subspace satisfying the relation mentioned above, generalize the antisymmetric states and symmetric states in higher dimensions, and give a specific value for distillable entanglement and entanglement cost for these states under the PPT operations.

Beyond Gisin's Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering.

We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin’s theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications.

Nonclassicality of New Class of States Produced by Superposition of Two Nonlinear Squeezed States with Respective Phase φ

In this paper, we consider two classes of nonlinear squeezed states: squeezed vacuum and squeezed one-photon states, which according to their generation processes, essentially include respectively even and odd bases of Fock space. Then, we produce their general superposition with respective phase φ which consists of all bases of Fock space. As a physical realization of the presented approach, we will use the q -deformation nonlinearity function to produce the corresponding nonlinear squeezed states and their superposition. In the continuation, due to extensive interest in nonclassicality features, we discuss about their main nonclassical properties such as sub-Poissonian statistics, normal and amplitude squared squeezing, number and phase squeezing and Husimi quasi-probability function of the obtained states and compare with those of the original constituent components. Meanwhile, we also pay attention to linear squeezed states (vacuum and one-photon) and particularly their superposition, too. Accordingly, the nonclassicality features of the introduced states are evidently established. At last, simple schemes for the generation of such states are presented.

Quantum phase transitions of the Dirac oscillator in a minimal length scenario

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within a minimal length ($\Delta x_0=\hbar \sqrt{\beta}$), or generalised uncertainty principle (GUP) scenario. This system in ordinary quantum mechanics has a single left-right chiral quantum phase transition (QPT). We show that a non zero minimal length turns on a infinite number of quantum phase transitions which accumulate towards the known QPT when $\beta \to 0$. It is also shown that the presence of the minimal length modifies the degeneracy of the states and that in this case there exist a new class of states which do not survive in the ordinary quantum mechanics limit $\beta \to 0$.

Preface to the special topic on topological insulators

The most important aspect of condensed matter physics in the last century has been the classification of quantum states in terms of spontaneous symmetry breaking. In 1980, the quantum Hall state—which is independent of material details and topologically different from the previously known states of matter— was discovered in the two-dimensional electron gas under an external magnetic field. Two years later, the fractional quantum Hall state was discovered in a similar two-dimensional system. The quantum Hall states belong to a topological class that has no spontaneously broken symmetry. The physical behaviors of the system depend only on its topology and not on its particular geometry. Very recently, a completely new class of states, called topological insulators, has emerged. Topological insulators have a bulk energy gap and gapless edge/surface states that are protected by the time-reversal symmetry and immune to impurities and geometric perturbations. To form such new states, the coupling between the spin and the orbital motion must be strong. Therefore, topological insulator states usually occur in a compound material that is composed of heavy elements. Because of the many exotic phenomena—including the quantum spin Hall effect, the quantum anomalous Hall effect, a magnetic monopole and Majorana fermions—that can exist in topological insulators, this new class of topological states has attracted increasing attention over the last seven years and has largely revolutionized modern condensed matter physics. We selected this particularly interesting area of topological insulators for our first issue ofNational Science Review.The issue contains a general review on topological phases in condensed matter physics by Shunqing Shen, and a review on the newly discovered quantized anomalous Hall effect by Ke He. The interesting story behind this discovery is presented in an interview to Xucun Ma. In a perspective article by Canhua Liu and Jinfeng Jia, they discuss methods to createMajorana fermions with topological insulators. Peizhe Tang and Wenhui Duan report their recent work on the quantum anomalous Hall effect in materials with in-plane magnetization, while Feng Liu and JianWu discuss new organic topological materials in two research highlight articles, respectively. In a perspective article, Kai Chang discusses topological insulating phases in commonly used semiconductors. As the guest editor of this special topic in the inaugural issue, I would like to take this opportunity to thank these authors for their generous contributions. The research of topological insulators is just at its very beginning. I believe further progress will be made in the near future and hope that the special topic can provide some useful information and promote research in this rapidly developing field. Last but not least, I would like to thank the editorial staff ofNational Natural Science for their sustained support during the preparation of this special issue.

Truncated Coherent States and Photon-Addition

A class of states of the electromagnetic field involving superpositions of all the excited states above a specified low energy eigenstate of the electromagnetic field is introduced. These states and the photon-added coherent states are shown to be the limiting cases of a generalized photon-added coherent state. This new class of states is nonclassical, non-Gaussian and has equal uncertainties in the field quadratures. For suitable choices of parameters, these uncertainties are very close to those of the coherent states. Nevertheless, these states exhibit sub-Poissonian photon number distribution, which is a nonclassical feature. Under suitable approximations, these states become the generalized Bernoulli states of the field. Nonclassicality of these states is quantified using their entanglement potential.

Computing reaction paths of a bifurcation reaction: an action wave-front-based perspective

Application of Hamilton–Jacobi (HJ) equation to reaction systems which involve energy barrier(s) leading to the product is relatively new. Such problems are described by a new class of HJ equation, called the generalised HJ equation. This new HJ equation renders an anisotropic propagation for the wave front. In this paper, we describe the adaptation of the fast marching method (FMM) and the generalised HJ equation to understand a new class of reaction process where the energy barrier does not lead to the product; instead, a new class of states are detected along the reaction path of such reactions. These states are valley-ridge inflection point, branching point and potential energy ridge. Such reactions are characterised as bifurcation reactions. We have identified a new classical wave front, called the reaction action front (RAF) which distinctly separates the reaction system into a reactant zone and a product zone connected by a third zone, called ‘neck’. The RAF is an important tool to understand the bifurcation reaction and the associated reaction paths. We have also introduced a convenient way to compute the reaction path force (RPF) using the FMM. The RPF for a bifurcation reaction significantly differs from the reactions with energy barrier, and so, the RPF provides vital information about the occurrence of branching of a path. The method has been tested for the isomerisation reaction of methoxy radical (H3C) to hydroxymethylene radical (H2ĊOH).

Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

We prove lower bounds for the entanglement of formation and the squashed entanglement for any a bipartite density matrix in terms of the conditional entropy of the bipartite state with respect to either of its partial traces, and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.

Spatial fluctuations of helical Dirac fermions on the surface of topological insulators

Surfaces of topological insulators host a new class of states with Dirac dispersion and helical spin texture. Potential quantum computing and spintronic applications using these states require manipulation of their electronic properties at the Dirac energy of their band structure by inducing magnetism or superconductivity through doping and proximity effect. Yet, the response of these states near the Dirac energy in their band structure to various perturbations has remained unexplored. Here we use spectroscopic mapping with the scanning tunneling microscope to study their response to magnetic and non-magnetic bulk dopants in Bi2Te3 and Bi2Se3. Far from the Dirac energy helicity provides remarkable resilience to backscattering even in the presence of ferromagnetism. However, approaching the Dirac point, where the surface states' wavelength diverges bulk doping results in pronounced nanoscale spatial fluctuations of energy, momentum, and helicity. Our results and their connection with similar studies of Dirac electrons in graphene demonstrate that while backscattering and localization are absent for Dirac topological surface states, reducing charge defects is required for both tuning the chemical potential to Dirac energy and achieving high electrical mobility for these novel states.

Detecting multipartite classical states and their resemblances

We study various types of multipartite states lying near the quantum-classical boundary. The class of so-called classical states are precisely those in which each party can perform a projective measurement to identify a locally held state without disturbing the global state, a task known as non-disruptive local state identification (NDLID). We introduce a new class of states called generalized-classical states which allow for NDLID when the most general quantum measurements are permitted. A simple analytic method as well as a physical criterion are presented for detecting whether a multipartite state is classical. To decide whether a state is generalized-classical, we provide a semi-definite programming algorithm which can be adapted for use in other unrelated contexts such as signal processing.

Modes of random lasers

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, emission pattern, directivity, and polarization. In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. The sharp peaks in the emission spectra of semiconductor powders, first observed in 1999, has therefore lead to an intense debate about the nature of the lasing modes in these so-called lasers with resonant feedback. We review numerical and theoretical studies aimed at clarifying the nature of the lasing modes in disordered scattering systems with gain. The past decade has witnessed the emergence of the idea that even the low-Q resonances of such open systems could play a role similar to the cavity modes of a conventional laser and produce sharp lasing peaks. We focus here on the near-threshold single-mode lasing regime where nonlinear effects associated with gain saturation and mode competition can be neglected. We discuss in particular the link between random laser modes near threshold and the resonances or quasi-bound (QB) states of the passive system without gain. For random lasers in the localized (strong scattering) regime, QB states and threshold lasing modes were found to be nearly identical within the scattering medium. These studies were later extended to the case of more lossy systems such as random systems in the diffusive regime, where it was observed that increasing the openness of such systems eventually resulted in measurable and increasing differences between quasi-bound states and lasing modes. Very recently, a theory able to treat lasers with arbitrarily complex and open cavities such as random lasers established that the threshold lasing modes are in fact distinct from QB states of the passive system and are better described in terms of a new class of states, the so-called constant-flux states. The correspondence between QB states and lasing modes is found to improve in the strong scattering limit, confirming the validity of initial work in the strong scattering limit.

A Class of Bound Entangled States of Two Qutrits

We provide a new class of states of two qutrits displaying the so-called bound entanglement. We investigate the states using various versions of computable cross-norm and realignment criteria recently introduced in [7].