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Charge and Orbital Order in Transition Metal Oxides

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issue 2
212-231
EN
A short introduction to the complex phenomena encountered in transition metal oxides with either charge or orbital or joint charge-and-orbital order, usually accompanied by magnetic order, is presented. It is argued that all the types of above ordered phases in these oxides follow from strong Coulomb interactions as a result of certain compromise between competing instabilities towards various types of magnetic order and optimize the gain of kinetic energy in doped systems. This competition provides a natural explanation of the stripe order observed in doped cuprates, nickelates and manganites. In the undoped correlated insulators with orbital degrees of freedom the orbital order stabilizes particular types of anisotropic magnetic phases, and we contrast the case of decoupled (disentangled) spin and orbital degrees of freedom in the manganites with entangled spin-orbital states which decide about certain rather exotic phenomena observed in the perovskite vanadates at finite temperature. Examples of successful concepts in the theoretical approaches to these complex systems are given and some open problems of current interest are indicated.
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Spin-Orbital Physics in Transition Metal Oxides

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EN
We present the main features of the spin-orbital superexchange which describes the magnetic and optical properties of the Mott insulators with orbital degrees of freedom. In contrast to the SU(2) symmetry of spin superexchange, the orbital part of the superexchange obeys the lower cubic symmetry of the lattice and is intrinsically frustrated. This intrinsic frustration and spin-orbital entanglement induce enhanced quantum fluctuations, and we point out a few situations where this leads to disordered states. Strong coupling between the spin and orbital degrees of freedom is discussed on the example of the RVO_3 perovskites, with R standing for rare-earth ion, La,...,Lu. We explain the observed evolution of the orbital T_{OO} and Néel T_{N1} transition temperature in the RVO_3 series with decreasing ionic radius r_R. A few open problems and the current directions of research in the field of spin-orbital physics are pointed out.
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We study the tests of the Bell-CHSH & CH inequalities by superposition of two coherent states (ı/2 out of phase), a class of non-Gaussian state, using photon parity and on/off measurements. Large violations of the Bell-type inequalities have been observed theoretically confirming the interpretation and validity of quantum mechanics against the local-realistic theories.
Acta Physica Polonica A
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2011
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vol. 120
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issue 3
390-396
EN
The influence of nonlinear Kerr-like medium on the phenomenon of entanglement sudden death and birth in a double Jaynes-Cummings model is investigated. It is shown that the entanglement sudden death and birth phenomenon may appear in this system and the duration of entanglement sudden death and birth can be controlled by the nonlinear Kerr-like medium. Particularly, the phenomenon of entanglement sudden death and birth disappears one after another if we increase the value of the Kerr coefficient χ continuously, and all disappears if the value of the Kerr coefficient χ is large enough.
EN
The universal frustration measure and its extension to anisotropic systems is calculated for a family of spin Hamiltonians modeling a hypothetical ring-shaped chromium-based molecular magnets. The proposed extension takes into account the impact of single-ion anisotropy on the magnetic centers and behaves more consistently with respect to the isotropic counterpart. The influence of anisotropy on both measures is assessed, which leads to a conclusion that frustration decreases with increasing absolute value of single ion anisotropy.
Acta Physica Polonica A
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2011
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vol. 120
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issue 6A
A-95-A-99
EN
We demonstrate the dependence of the entanglement dynamics on the global classical regime of regular, mixed and chaotic dynamics with initial squeezed coherent states. By squeezing the initial states, we are able to enhance or suppress the entanglement entropy of the dynamically generated quantum states relative to those produced via initial coherent states. This suggests the possibility of exploiting a judicious selection of initial squeezed states to create quantum states with enhanced entanglement entropy dynamically for the purpose of robust quantum information processing.
EN
Quantum dots have been identified as potential sources of entangled photon pairs, essential for many applications in quantum information. However, in practice structural properties of the dots result in polarisation splitting of the emission lines, which has prevented the realisation of such a source. Here, we present two techniques developed to control the polarisation splitting in a quantum dot both irreversibly and reversibly. We find that the splitting is strongly dependent upon the emission energy, or lateral confinement, of the quantum dot. Thus by precise control of the InAs deposition thickness, it is possible to produce ensembles from which dots with zero polarisation splitting can be easily selected. Additionally, we demonstrate that by using modest in-plane magnetic fields to partially mix the bright and dark exciton states, the polarisation splitting can be reversibly tuned to zero for most dots of a certain type. Finally, we demonstrate the emission of triggered entangled photon pairs from a quantum dot with approximately zero splitting with fidelity >70%.
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Stripes and Pairing in High Temperature Superconductors

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EN
We review briefly several approaches used to investigate the stability of stripe phases in high temperature superconductors, where charge inhomogeneities arise from competing kinetic and magnetic energies. The mechanism of stripe formation, their consequences for the normal state and enhancement of pairing interaction triggered by charge inhomogeneities are briefly summarized. Finally, we demonstrate that orbital degeneracy (i) leads to a more subtle mechanism of stripe formation, and (ii) plays an important role and determines the symmetry of the superconducting state in pnictides.
EN
Normalized quantum Stokes operators introduced in Phys. Rev. A 95, 042113 (2017) enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers. For a given run of an experiment the new quantum Stokes operators are defined by the differences of the measured intensities (or photon numbers) at the exits of a polarizer divided by their sum. It is this ratio that is to be averaged, and not the numerator and the denominator separately, as it is in the conventional approach. The new approach allows to construct more robust entanglement indicators against photon-loss noise, which can detect entangled optical states in situations in which witnesses using standard Stokes operators fail. Here we show an extension of this approach beyond phenomena linked with polarization. We discuss EPR-like experiments involving correlations produced by optical beams in a multi-mode bright squeezed vacuum state. EPR-inspired entanglement conditions for all prime numbers of modes are presented. The conditions are much more resistant to noise due to photon loss than similar ones which employ standard Glauber-like intensity, correlations.
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Entangled states are essential in basics quantum communication protocols and quantum cryptography. Ferromagnetic contacts can work as a spin detector, giving possibility of converting information about electron spin to the electric charge, and therefore, detection of entangled states with the electric current measurements is possible. Method of confirming entanglement with non-ideal detectors is presented, the impact of decoherence and noise on states and quality of entanglement is discussed. Entanglement witness (EW) operator method is compared with the CHSH inequalities approach. Required spin polarization for the EW is lower than for the CHSH inequalities. System with asymmetric spin polarizations of detectors was analyzed, including the CHSH inequalities and the EW method.
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vol. 126
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issue 3
652-656
EN
We show the special dynamic characteristic of Gaussian quantum discord, exhibited by two-mode Gaussian symmetric squeezed thermal states (STS) in continuous-variable (CV) systems with a common non-Markovian environment, is definitely different from Markov processes. We demonstrate that Gaussian quantum discord can be created whenever the information flow from environment back to the system. We also show that the rate of decrease for Gaussian quantum discord is related to the coupling constant. We discover that the initial value of Gaussian quantum discord is determined by the average number of thermal photons of the system.
EN
The development of quantum computing in quantum dots systems requires highly efficient and continuous solid-state source of spatially separated spin-entangled electrons. One of the approaches is a use of double quantum dot system connected to superconducting lead, where Cooper pairs provide a source of naturally entangled electrons. Apart from the source, an useful tool for detection of quantum entanglement is needed. We present entanglement detection by the ferromagnetic electrodes using entanglement witness operator method and direct measurement of spin polarized current in the system. We investigate requirements that have to be fulfilled by ferromagnetic detectors.
13
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Entanglement in Open Quantum Systems

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EN
We give a compact review of some of our recent results on the quantification, the measurement, and the time evolution of entanglement in open quantum systems of variable structure and dimension. Also a first experimental implementation is briefly discussed.
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Random Unitary Matrices Associated to a Graph

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We analyze composed quantum systems consisting of k subsystems, each described by states in the n-}dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order n^2. The global evolution operator is represented by a unitary matrix of size N = n^{k}. We investigate statistical properties of such matrices and show that they display spectral properties characteristic to the Haar random unitary matrices provided the corresponding graph is connected. Thus basing on random unitary matrices of a small size n^2 one can construct a fair approximation of large random unitary matrices of size n^{k}. Graph-structured random unitary matrices investigated here allow one to define the corresponding structured ensembles of random pure states.
EN
The effect of a position measurement on one component of a two-particle wave packet in a regularized space-momentum entangled state is analyzed. The wave packet interacts in the physical space with a potential barrier. When a position or momentum measurement is performed on one particle, a consequent strong modification of the dynamics of the other particle occurs.
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