arXiv subjects

Yao-Zhong Zhang

Publications and source records attributed to Yao-Zhong Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2018

Influence of a dark-soliton on the reflection of a Bose-Einstein condensate by a square barrier

We study the quantum reflection of a two-dimensional disk-shaped Bose-Einstein condensate with a dark-soliton excitation by a square potential barrier. For the giving geometry, the dark-soliton initially located at the centre of the condensate cloud survive long enough for investigating the reflection process. We show the time evolution of the reflection probability with respect to various width of the barrier. The asymptotic value of the reflection probability is decreased by the existence of a dark-soliton, and is highly sensitive to the initial orientation of the dark-soliton which also affects the excitation properties during the process of condensate and barrier interaction.

cond-mat.quant-gas↗

arXiv2018

Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator

We construct ladder operators, $\tilde{C}$ and $\tilde{C^\dagger}$, for a multi-step rational extension of the harmonic oscillator on the half plane, $x\ge0$. These ladder operators connect all states of the spectrum in only infinite-dimensional representations of their polynomial Heisenberg algebra. For comparison, we also construct two different classes of ladder operator acting on this system that form finite-dimensional as well as infinite-dimensional representations of their respective polynomial Heisenberg algebras. For the rational extension, we construct the position wavefunctions in terms of exceptional orthogonal polynomials. For a particular choice of parameters, we construct the coherent states, eigenvectors of $\tilde{C}$ with generally complex eigenvalues, $z$, as superpositions of a subset of the energy eigenvectors. Then we calculate the properties of these coherent states, looking for classical or non-classical behaviour. We calculate the energy expectation as a function of $|z|$. We plot position probability densities for the coherent states and for the even and odd cat states formed from these coherent states. We plot the Wigner function for a particular choice of $z$. For these coherent states on one arm of a beamsplitter, we calculate the two excitation number distribution and the linear entropy of the output state. We plot the standard deviations in $x$ and $p$ and find no squeezing in the regime considered. By plotting the Mandel $Q$ parameter for the coherent states as a function of $|z|$, we find that the number statistics is sub-Poissonian.

math-ph↗

arXiv2018

Bell inequalities violation within non-Bunch-Davies states

We study the quantum nature of non-Bunch-Davies states in de Sitter space by evaluating CHSH inequality on a localized two-atom system. We show that quantum nonlocality can be generated through the Markovian evolution of two-atom, witnessed by a violation of CHSH inequality on its final equilibrium state. We find that the upper bound of inequality violation is determined by different choices of de Sitter-invariant vacua sectors. In particular, with growing Gibbons-Hawking temperature, the CHSH bound degrades monotonously for Bunch-Davies vacuum sector. Due to the intrinsic correlation of non-Bunch-Davies vacua, we find that the related violation of inequality can however drastically increase after certain turning point, and may persist for arbitrarily large environment decoherence. This implies that the CHSH inequality is useful to classify the initial quantum state of the Universe. Finally, we clarify that the witnessed intrinsic correlation of non-Bunch-Davies vacua can be utilized for quantum information applications, e.g., surpassing the Heisenberg uncertainty bound of quantum measurement in de Sitter space.

hep-th↗

arXiv2018

Extended Laplace-Runge-Lentz vectors, new family of superintegrable systems and quadratic algebras

We present a useful proposition for discovering extended Laplace-Runge-Lentz vectors of certain quantum mechanical systems. We propose a new family of superintegrable systems and construct their integrals of motion. We solve these systems via separation of variables in spherical coordinates and obtain their exact energy eigenvalues and the corresponding eigenfunctions. We give the quadratic algebra relations satisfied by the integrals of motion. Remarkably these algebra relations involve the Casimir operators of certain higher rank Lie algebras in the structure constants.

math-ph↗

arXiv2018

Quantum estimation in an expanding spacetime

We investigate the quantum estimation on the Hubble parameter of an expanding de Sitter space by quantum metrological techniques. By exploring the dynamics of a freely falling Unruh-DeWitt detector, which interacts with a scalar field coupling to curvature, we calculate the Fisher information (FI) and quantum Fisher information (QFI) for the detector, which bound the highest precision of the estimation on Hubble parameter. In standard Bunch-Davies vacuum, we show that the maxima of FI/QFI are located for particular initial state of probe. Beside its dependence on the evolving time of detector and the energy spacing of atom $ω$, we show that the maxima of FI/QFI can be significantly enhanced once a proper coupling of scalar field to curvature is chosen. For instance, we show numerically that the estimation in the scenario with minimally/nearly minimally coupling scalar field can always outperform that with conformally coupling scalar field, corresponding to a higher FI/QFI in estimation. Moreover, we find that for general $α-$vacua of de Sitter space, a further improvement of estimation can be achieved, attributed to the squeezed nature of $α-$vacua that heavily constrains the measurement uncertainty. Some implications of our results are also discussed.

hep-th↗

arXiv2018

Fine-grained uncertainty relation under the relativistic motion

Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this Letter, we explore this uncertainty relation in relativistic regime. For observer undergoes an uniform acceleration who is immersed in an Unruh thermal bath, we show that the uncertainty bound is dependent on the acceleration parameter and choice of Unruh modes. We find that the measurements in mutually unbiased bases, sharing same uncertainty bound in inertial frame, could be distinguished from each other for a noninertial observer. In an alternative scenario, for the observer restricted in a single rigid cavity, we show that the uncertainty bound exhibits a periodic evolution w.r.t. the duration of acceleration. With properly chosen cavity parameters, the uncertainty bounds could be protected. Moreover, we find that uncertainty bound can be degraded for specific quantum measurements to violate the bound exhibited in nonrelativistic limit, which can be attributed to the entanglement generation between cavity modes during particular epoch. Several implications of our results are discussed.

quant-ph↗

arXiv2018

Quantum superintegrable system with a novel chain structure of quadratic algebras

We analyse the $n$-dimensional superintegrable Kepler-Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

math-ph↗

arXiv2018

Coherent states for ladder operators of general order related to exceptional orthogonal polynomials

We construct the coherent states of general order, $m$ for the ladder operators, $c(m)$ and $c^\dagger(m)$, which act on rational deformations of the harmonic oscillator. The position wavefunctions of the eigenvectors involve type III Hermite exceptional orthogonal polynomials. We plot energy expectations, time-dependent position probability densities for the coherent states and for the even and odd cat states, Wigner functions, and Heisenberg uncertainty relations. We find generally non-classical behaviour, with one exception: there is a regime of large magnitude of the coherent state parameter, $z$, where the otherwise indistinct position probability density separates into $m+1$ distinct wavepackets oscillating and colliding in the potential, forming interference fringes when they collide. The Mandel $Q$ parameter is calculated to find sub-Poissonian statistics, another indicator of non-classical behaviour. We plot the position standard deviation and find squeezing in many of the cases. We calculate the two-photon-number probability density for the output state when the $m=4$, $μ=-5$ coherent states (where $μ$ labels the lowest weight in the superposition) are placed on one arm of a beamsplitter. We find that it does not factorize, again indicating non-classical behaviour. Calculation of the linear entropy for this beamsplitter output state shows significant entanglement, another non-classical feature. We also construct linearized versions, $\tilde c(m)$, of the annihilation operators and their coherent states and calculate the same properties that we investigate for the coherent states. For these we find similar behaviour to the $c(m)$ coherent states, at much smaller magnitudes of $z$, but comparable average energies.

math-ph↗

arXiv2018

On superintegrable monopole systems

Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to admit the Kepler-type symmetries and provide non-trivial generalizations of the usual Kepler problems. In this paper, we overview new families of superintegrable Kepler, MIC-harmonic oscillator and deformed Kepler systems interacting with Yang-Coulomb monopoles in the flat and curved Taub-NUT spaces. We present their higher-order, algebraically independent integrals of motion via the direct and constructive approaches which prove the superintegrability of the models. The integrals form symmetry polynomial algebras of the systems with structure constants involving Casimir operators of certain Lie algebras. Such algebraic approaches provide a deeper understanding to the degeneracies of the energy spectra and connection between wave functions and differential equations and geometry.

math-ph↗

arXiv2017

Structures of Nichols (braided) Lie algebras of diagonal type

Let $V$ be a braided vector space of diagonal type. Let $\mathfrak B(V)$, $\mathfrak L^-(V)$ and $\mathfrak L(V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Lie algebra over $V$, respectively. We show that a monomial belongs to $\mathfrak L(V)$ if and only if that this monomial is connected. We obtain the basis for $\mathfrak L(V)$ of arithmetic root systems and the dimension for $\mathfrak L(V)$ of finite Cartan type. We give the sufficient and necessary conditions for $\mathfrak B(V) = F\oplus \mathfrak L^-(V)$ and $\mathfrak L^-(V)= \mathfrak L(V)$. We obtain an explicit basis of $\mathfrak L^ - (V)$ over quantum linear space $V$ with $\dim V=2$.

math.QA↗

arXiv2017

Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.

math-ph↗

arXiv2017

Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials

We construct the coherent states and Schrödinger cat states associated with new types of ladder operators for a particular case of a rationally extended harmonic oscillator involving type III Hermite exceptional orthogonal polynomials. In addition to the coherent states of the annihilation operator, $c$, we form the linearised version, \tilde{c}, and obtain its coherent states. We find that while the coherent states defined as eigenvectors of the annihilation operator $c$ display only quantum behaviour, those of the linearised version, \tilde{c}, have position probability densities displaying distinct wavepackets oscillating and colliding in the potential. The collisions are certainly quantum, as interference fringes are produced, but the remaining evolution indicates a classical analogue.

math-ph↗

arXiv2017

One loop amplitude from null string

We generalize the CHY formalism to one-loop level, based on the framework of the null string theory. The null string, a tensionless string theory, produces the same results as the ones from the chiral ambitwistor string theory, with the latter believed to give a string interpretation of the CHY formalism. A key feature of our formalism is the interpretation of the modular parameters. We find that the $S$ modular transformation invariance of the ordinary string theory does not survive in the case of the null string theory. Treating the integration over the modular parameters this way enable us to derive the n-gons scattering amplitude in field theory, thus proving the n-gons conjecture.

hep-th↗

arXiv2017

On the 2-mode and $k$-photon quantum Rabi models

By mapping the Hamiltonians of the two-mode and 2-photon Rabi models to differential operators in suitable Hilbert spaces of entire functions, we prove that the two models possess entire and normalizable wavefunctions in the Bargmann-Hilbert spaces only if the frequency $ω$ and coupling strength $g$ satisfy certain constraints. This is in sharp contrast to the quantum Rabi model for which entire wavefunctions always exist. For model parameters fulfilling the aforesaid constraints we determine transcendental equations whose roots give the regular energy eigenvalues of the models. Furthermore, we show that for $k\geq 3$ the $k$-photon Rabi model does not possess wavefunctions which are elements of the Bargmann-Hilbert space for all non-trivial model parameters. This implies that the $k\geq 3$ case is not diagonalizable, unlike its RWA cousin, the $k$-photon Jaynes-Cummings model which can be completely diagonalized for all $k$.

quant-ph↗

arXiv2017

Nichols algebras over classical Weyl groups, Fomin-Kirillov algebras and Lyndon basis

We show that except in several cases conjugacy classes of classical Weyl groups $W(B_n)$ and $W(D_n)$ are of type {\rm D}. We prove that except in three cases Nichols algebras of irreducible Yetter-Drinfeld ({\rm YD} in short )modules over the classical Weyl groups are infinite dimensional. We establish the relationship between Fomin-Kirillov algebra $\mathcal E_n$ and Nichols algebra $\mathfrak{B} ({\mathcal O}_{(1, 2)} , ε\otimes {\rm sgn})$ of transposition over symmetry group by means of quiver Hopf algebras. We generalize {\rm FK } algebra. The characteristic of finiteness of Nichols algebras in thirteen ways and of {\rm FK } algebras ${\mathcal E}_n$ in nine ways is given. All irreducible representations of finite dimensional Nichols algebras %({\rm FK } algebras ${\mathcal E}_n$) and a complete set of hard super- letters of Nichols algebras of finite Cartan types are found. The sufficient and necessary condition for Nichols algebra $\mathfrak B(M)$ of reducible {\rm YD} module $M$ over $A \rtimes \mathbb{S}_n$ with ${\rm supp } (M) \subseteq A$ to be finite dimensional is given. % Some conditions for a braided vector space to become a {\rm YD} module over finite commutative group are obtained. It is shown that hard braided Lie Lyndon word, standard Lyndon word, Lyndon basis path, hard Lie Lyndon word and standard Lie Lyndon word are the same with respect to $ \mathfrak B(V)$, Cartan matrix $A_c$ and $U(L^+)$, respectively, where $V$ and $L$ correspond to the same finite Cartan matrix $A_c$.

math.QA↗

arXiv2016

Exact solution of the two-axis countertwisting Hamiltonian for the half-integer $J$ case

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Properties of the zeros of the related extended Heine-Stieltjes polynomials for half-integer $J$ cases are discussed. It is clearly shown that double degenerate level energies for half-integer $J$ are symmetric with respect to the $E=0$ axis. It is also shown that the excitation energies of the `yrast' and other `yrare' bands can all be asymptotically given by quadratic functions of $J$, especially when $J$ is large.

quant-ph↗

arXiv2016

Exact solution of the two-axis countertwisting Hamiltonian

It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz equations of the problem is derived. It is shown that solutions of the Bethe ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials. The total number of the four sets of the zeros equals exactly to $2J+1$ for a given integer angular momentum quantum number $J$, which proves the completeness of the solutions. It is also shown that double degeneracy in level energies may also occur in the $J\rightarrow\infty$ limit for integer $J$ case except a unique non-degenerate level with zero excitation energy.

quant-ph↗

arXiv2016

Quadratic algebra for superintegrable monopole system in a Taub-NUT space

We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrodinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables.

math-ph↗