Multipartite quantum correlations among atoms in QED cavities

We study the nonlocality dynamics for two models of atoms in cavity quantum electrodynamics (QED); the first model contains atoms in a single cavity undergoing nearest-neighbor interactions with no initial correlation, and the second contains atoms confined in n different and noninteracting cavities, all of which were initially prepared in a maximally correlated state of n qubits corresponding to the atomic degrees of freedom. The nonlocality evolution of the states in the second model shows that the corresponding maximal violation of a multipartite Bell inequality exhibits revivals at precise times, defining, nonlocality sudden deaths and nonlocality sudden rebirths, in analogy with entanglement. These quantum correlations are provided analytically for the second model to make the study more thorough. Differences in the first model regarding whether the array of atoms inside the cavity is arranged in a periodic or open fashion are crucial to the generation or redistribution of quantum correlations. This contribution paves the way to using the nonlocality multipartite correlation measure for describing the collective complex behavior displayed by slightly interacting cavity QED arrays.     

Two-way quantum communication: Generalization of secure quantum information exchange to quantum network

The idea of secure quantum information exchange (SQIE) [J. Phys. B: At. Mol. Opt. Phys.44, 115504 (2011)] is introduced for the secure exchange of single qubit information states between two legitimate users, Alice and Bob. In the present paper, we extend this original SQIE protocol by presenting a scheme, which enables the secure exchange of n-single qubit information states among the n nodes of a quantum network, with the aid of a special kind of 4n-qubit entangled state and the classical assistance of an extra participant Charlie. For experimental realization of our extended SQIE protocol, we suggest an efficient scheme for the generation of a special kind of 4n-qubit entangled state using the interaction between highly detuned Λ-type three-level atoms and optical coherent field. Further, by discussing the various experimental parameters, we show that the special kind 4n-qubit entangled state can be generated with the presently available technology.     

On the structure of strips exhibiting the integral quantum Hall effect in an inhomogeneous 2D electron system

A formalism is developed to generalize the results obtained for “incompressible” strips exhibiting the integral quantum Hall effect in a spatially inhomogeneous 2D electron system to the cases of finite temperatures, significant electron density gradients, etc. Specifically, the concept of the “quality” of a given integer quantum Hall effect strip (channel) is introduced; the quality is proportional to the derivative dn(x)/dx in the central part of the channel [n(x) is the electron density distribution over the channel]. For a well-defined channel, this derivative tends to zero. If a noticeable gradient arises in the n(x) distribution, the channel does not exhibit the quantum Hall effect and ceases to exist. The conditions are determined under which a channel exhibiting the integral quantum Hall effect breaks down. The results of calculations are used to interpret the available experimental data.     

The real solution to scalar field equation in 5D black string space

After the nontrivial quantum parameters Ω _n and quantum potentials V _n obtained in our previous research, the circumstance of a real scalar wave in the bulk is studied with the similar method of Brevik and Simonsen (Gen. Rel. Grav. 33:1839, 2001). The equation of a massless scalar field is solved numerically under the boundary conditions near the inner horizon r _e and the outer horizon r _c . Unlike the usual wave function Ψ_ωl in 4D, quantum number n introduces a new functions Ψ_{ωl n} , whose potentials are higher and wider with bigger n. Using the tangent approximation, a full boundary value problem about the Schrödinger-like equation is solved. With a convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients are obtained. If extra dimension does exist and is visible at the neighborhood of black holes, the unique wave function Ψ_{ωl n} may say something to it.     

Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Coulomb deexcitation of muonic hydrogen within the quantum close-coupling method

The Coulomb deexcitation of muonic hydrogen in collisions with the hydrogen atom has been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The calculations of the l-averaged cross sections of the Coulomb deexcitation are performed for (μp)_n and (μd)_n atoms in the initial states with the principal quantum number n = 3–9 and at relative energies E = 0.1–100 eV. The obtained results for the n and E dependences of the Coulomb deexcitation cross sections drastically differ from the semiclassical results. An important contribution of the transitions with Δn > 1 to the total Coulomb deexcitation cross sections (up to ～37%) is predicted.     

Multiple multicontrol unitary operations: Implementation and applications

The efficient implementation of computational tasks is critical to quantum computations. In quantum circuits, multicontrol unitary operations are important components. Here, we present an extremely efficient and direct approach to multiple multicontrol unitary operations without decomposition to CNOT and single-photon gates. With the proposed approach, the necessary two-photon operations could be reduced from O(n³) with the traditional decomposition approach to O(n), which will greatly relax the requirements and make large-scale quantum computation feasible. Moreover, we propose the potential application to the (n-k)-uniform hypergraph state.     

All possible Cayley-Klein contractions of quantum orthogonal groups

Spaces of constant curvature and their motion groups are described most naturally in the Cartesian basis. All these motion groups, also known as CK groups, are obtained from an orthogonal group by contractions and analytical continuations. On the other hand, quantum deformation of orthogonal group SO(N) is most easily performed in the so-called symplectic basis. We reformulate its standard quantum deformation to the Cartesian basis and obtain all possible contractions of quantum orthogonal group SO _q (N) for both untouched and transformed deformation parameters. It turned out that, similar to the undeformed case, all CK contractions of SO _q (N) are realized. An algorithm for obtaining nonequivalent (as Hopf algebra) contracted quantum groups is suggested. Contractions of SO _q (N), N = 3, 4, 5, are regarded as examples.     

Superfield generating equation of field–antifield formalism as a hyper-gauge theory

Within a superfield approach, we formulate a simple quantum generating equation of the field–antifield formalism. Then we derive the Schroedinger equation with the Hamiltonian whose \(\Delta \)-exact part serves as a generator to the quantum master transformations. We show that these generators do satisfy a nice composition law in terms of the quantum antibrackets. We also present an Sp(2) symmetric extension to the main construction, with specific features caused by the principal fact that all basic equations become Sp(2) vector-valued ones.     

Infinitive Operator-Sum Representation for Damping in a Squeezed Heat Reservoir via the Thermo Entangled State Approach

Using the thermo entangled state approach, we successfully solve the master equation of a damped harmonic oscillator affected by a linear resonance force in a squeezed heat reservoir, and obtain the analytical evolution formula for the density operator in the infinitive Kraus operator-sum representation. Interestingly, the Kraus operators M_l,m,n,r and \(\mathfrak {M}_{l,m,n,r}^{\dag }\) are not Hermite conjugate, but they are still trace-preserving quantum operations because of the normalization condition. We also investigate the evolution for an initial coherent state for damping in a squeezed heat reservoir, which shows that the initial coherent state decays to a complex mixed state as a result of damping and thermal noise.     

Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model

This is the second part of a paper dealing with the “internal” (gauge) symmetry of the Wess–Zumino–Novikov–Witten (WZNW) model on a compact Lie group G. It contains a systematic exposition, for G = SU(n), of the canonical quantization based on the study of the classical model (performed in the first part) following the quantum group symmetric approach first advocated by L.D. Faddeev and collaborators. The internal symmetry of the quantized model is carried by the chiral WZNW zero modes satisfying quadratic exchange relations and an n-linear determinant condition. For generic values of the deformation parameter the Fock representation of the zero modes’ algebra gives rise to a model space of U _q (sl(n)). The relevant root of unity case is studied in detail for n = 2 when a “restricted” (finite dimensional) quotient quantum group is shown to appear in a natural way. The module structure of the zero modes’ Fock space provides a specific duality with the solutions of the Knizhnik–Zamolodchikov equation for the four point functions of primary fields suggesting the existence of an extended state space of logarithmic CFT type. Combining left and right zero modes (i.e., returning to the 2D model), the rational CFT structure shows up in a setting reminiscent to covariant quantization of gauge theories in which the restricted quantum group plays the role of a generalized gauge symmetry.     

Second-order superintegrable quantum systems

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n ? 1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, then the system is second-order superintegrable, the most tractable case and the one we study here. Such systems have remarkable properties: multi-integrability and separability, a quadratic algebra of symmetries whose representation theory yields spectral information about the Schrödinger operator, and deep connections with expansion formulas relating classes of special functions. For n = 2 and for conformally flat spaces when n = 3, we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here, we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension.     

On the derivation of the Boltzmann-Landau equation from the quantum mechanical hierarchy

The general solution of the equation of motion for the quantum mechanical distribu tion functionf ₂(r ₁ P ₁,r ₂ p ₂;t)in the two particle space is given by means of the Schrödinger scattering functions. A special initial condition leads to the usual Boltzmann equation plus density correction terms, which depend on the scattering matrixt(p′,p). In the long wavelength limit and in lowest order oft(p′,p) the Landau corrections to the simple Boltzmann streaming part are obtained.     

On phase-space representations of quantum mechanics using Glauber coherent states

A phase-space formulation of quantum mechanics is proposed by constructing two representations (identified as pq and qp) in terms of the Glauber coherent states, in which phase-space wave functions (probability amplitudes) play the central role, and position q and momentum p are treated on equal footing. After finding some basic properties of the pq and qp wave functions, the quantum operators in phase-space are represented by differential operators, and the Schrödinger equation is formulated in both pictures. Afterwards, the method is generalized to work with the density operator by converting the quantum Liouville equation into pq and qp equations of motion for two-point functions in phase-space. A coordinate transformation between those points allows one to construct a cell in phase-space, whose central point can be treated as a parameter. In this way, one gets equations of motion describing the evolution of one-point functions in phase-space. Finally, it is shown that some quantities obtained in this paper are related in a natural way with cross-Wigner functions, which are constructed with either the position or the momentum wave functions.     

Limiting rate of secret-key generation in quantum cryptography in spacetime

The fundamental restrictions on the maximum admissible rate of secret-key commitment in quantum cryptography in real time are discussed. It is shown that the maximum rate in a quantum channel with limited transmission band is achieved in a cryptosystem on orthogonal states. The dimensionless rate (the number of bits per unit time frequency band through unit of the channel) is determined by the universal function C(λ₀(ΔkT))/ΔkT [where C(λ₀(ΔkT)) is the transmission capacity of a classical binary channel, Δk is the transmission band width, 1/T is the transmission frequency of quantum states, and λ₀ is the maximum eigenvalue of a certain integral equation].     

Solution of scaling quantum networks

We show that all scaling quantum graphs are explicitly solvable, i.e., that any one of their spectral eigenvalues E_n is computable analytically, explicitly, and individually for any given n. This is surprising, since quantum graphs are excellent models of quantum chaos (see, e.g., T. Kottos and H. Schanz, Physica E 9, 523 (2001)).     

Edge electroluminescence of silicon: An amorphous-silicon-crystalline-silicon heterostructure

Silicon edge electroluminescence (EL) was observed on an amorphous-silicon-crystalline-silicon heterostructure (a-Si: H(n)/c-Si(p)) in the temperature range from 77 to 300 K. The room-temperature EL internal quantum efficiency of the heterostructure under study was found to be about 0.1%. A theoretical analysis of the emissive properties of the a-Si: H(n)/c-Si(p) heterostructure was made in terms of the model of an abrupt planar p-n junction and showed that, for optimal doping, the internal quantum efficiency of the EL may be as high as a few percent at a modulation frequency of about 50 kHz.     

Role of qubit-cavity entanglement for switching dynamics of quantum interfaces in superconductor metamaterials

We study quantum effects of strong driving field applied to dissipative hybrid qubit-cavity system which are relevant for a realization of quantum gates in superconducting quantum metamaterials. We demonstrate that effects of strong and non-stationary drivings have significantly quantum nature and cannot be treated by means of mean-field approximation. This is shown from a comparison of steady state solution of the standard Maxwell–Bloch equations and numerical solution of Lindblad equation on a density matrix. We show that mean-field approach provides very good agreement with the density matrix solution at not very strong drivings f < f* but at f > f* a growing value of quantum correlations between fluctuations in qubit and photon sectors changes a behavior of the system. We show that in regime of non-adiabatic switching on of the driving such a quantum correlations influence a dynamics of qubit and photons even at weak f.     

Intuitionistic Quantum Logic of an <Emphasis Type="Italic">n</Emphasis>-level System

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the concrete example of the C*-algebra M _n (?) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ _n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ?(M _n (?)) of projections in M _n (?) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice \(\mathcal{O}(\Sigma_{n})\) of functions from the poset \(\mathcal{C}(M_{n}(\mathbb{C}))\) of all unital commutative C*-subalgebras C of M _n (?) to ?(M _n (?)). The lattice \(\mathcal{O}(\Sigma_{n})\) is essentially the (pointfree) topology of the quantum phase space Σ _n , and as such defines a Heyting algebra. Each element of \(\mathcal{O}(\Sigma_{n})\) corresponds to a “Bohrified” proposition, in the sense that to each classical context \(C\in\mathcal{C}(M_{n}(\mathbb{C}))\) it associates a yes-no question (i.e. an element of the Boolean lattice ?(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann.