Bitwise bell-inequality violations for an entangled state involving 2N ions

Following on from previous work [J.-A. Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving 2N trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of N particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations.

Duality of weak and strong scatterer in a Luttinger liquid coupled to massless bosons

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ?WS?WL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

Duality in multi-channel Luttinger Liquid with local scatterer

We have devised a general scheme that reveals multiple duality relations valid for all multi-channel Luttinger Liquids. The relations are universal and should be used for establishing phase diagrams and searching for new non-trivial phases in low-dimensional strongly correlated systems. The technique developed provides universal correspondence between scaling dimensions of local perturbations in different phases. These multiple relations between scaling dimensions lead to a connection between different inter-phase boundaries on the phase diagram. The dualities, in particular, constrain phase diagram and allow predictions of emergence and observation of new phases without explicit model-dependent calculations. As an example, we demonstrate the impossibility of non-trivial phase existence for fermions coupled to phonons in one dimension. © 2013 EPLA.

A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05

Resonance vector mode locking

A mode locked fibre laser as a source of ultra-stable pulse train has revolutionised a wide range of fundamental and applied research areas by offering high peak powers, high repetition rates, femtosecond range pulse widths and a narrow linewidth. However, further progress in linewidth narrowing seems to be limited by the complexity of the carrier-envelope phase control. Here for the first time we demonstrate experimentally and theoretically a new mechanism of resonance vector self-mode locking where tuning in-cavity birefringence leads to excitation of the longitudinal modes sidebands accompanied by the resonance phase locking of sidebands with the adjacent longitudinal modes. An additional resonance with acoustic phonons provides the repetition rate tunability and linewidth narrowing down to Hz range that drastically reduces the complexity of the carrier-envelope phase control and so will open the way to advance lasers in the context of applications in metrology, spectroscopy, microwave photonics, astronomy, and telecommunications.

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

Vanadate conformation variations in vanadium pentoxide nanostructures

We report the comparative structural-vibrational study of nanostructures of nanourchins, nanotubes, and nanorods of vanadium oxide. The tube walls comprise layers of vanadium oxide with the organic surfactant intercalated between atomic layers. Both Raman scattering and infrared spectroscopies showed that the structure of nanourchins, nanotubes, and nanorods of vanadium oxide nanocomposite are strongly dependent on the valency of the vanadium, its associated interactions with the organic surfactant template, and on the packing mechanism and arrangement of the surfactant between vanadate layers. Accurate assignment of the vibrational modes to the V-O coordinations has allowed their comparative classification and relation to atomic layer structure. Although all structures are formed from the same precursor, differences in vanadate conformations due to the hydrothermal treatment and surfactant type result in variable degrees of crystalline order in the final nanostructure. The nanotube-containing nanourchins contain vanadate layers in the nanotubes that are in a distorted γ- V5+ conformation, whereas the the nanorods, by comparison, show evidence for V5+ and V4+ species-containing ordered VOx lamina.

Giant enhancement of n-type carrier mobility in highly strained germanium nanostructures

First-principles electronic structure methods are used to predict the rate of n-type carrier scattering due to phonons in highly-strained Ge. We show that strains achievable in nanoscale structures, where Ge becomes a direct bandgap semiconductor, cause the phonon-limited mobility to be enhanced by hundreds of times that of unstrained Ge, and over a thousand times that of Si. This makes highly tensile strained Ge a most promising material for the construction of channels in CMOS devices, as well as for Si-based photonic applications. Biaxial (001) strain achieves mobility enhancements of 100 to 1000 with strains over 2%. Low temperature mobility can be increased by even larger factors. Second order terms in the deformation potential of the Gamma valley are found to be important in this mobility enhancement. Although they are modified by shifts in the conduction band valleys, which are caused by carrier quantum confinement, these mobility enhancements persist in strained nanostructures down to sizes of 20 nm.

Electronic Instability and Anharmonicity in SnSe

The binary compound SnSe exhibits record high thermoelectric performance, largely because of its very low thermal conductivity. The origin of the strong phonon anharmonicity leading to the low thermal conductivity of SnSe is investigated through first-principles calculations of the electronic structure and phonons. It is shown that a Jahn-Teller instability of the electronic structure is responsible for the high-temperature lattice distortion between the Cmcm and Pnma phases. The coupling of phonon modes and the phase transition mechanism are elucidated, emphasizing the connection with hybrid improper ferroelectrics. This coupled instability of electronic orbitals and lattice dynamics is the origin of the strong anharmonicity causing the ultralow thermal conductivity in SnSe. Exploiting such bonding instabilities to generate strong anharmonicity may provide a new rational to design efficient thermoelectric materials.

Manifestation of Colossal Thermoelectric Power by Charge Ordered Small and Intermediate Bandwidth Manganites

Thermoelectric materials are revisited for various applications including power generation. The direct conversion of temperature differences into electric voltage and vice versa is known as thermoelectric effect. Possible applications of thermoelectric materials are in eco-friendly refrigeration, electric power generation from waste heat, infrared sensors, temperature controlled-seats and portable picnic coolers. Thermoelectric materials are also extensively researched upon as an alternative to compression based refrigeration. This utilizes the principle of Peltier cooling. The performance characteristic of a thermoelectric material, termed as figure of merit (ZT) is a function of several transport coefficients such as electrical conductivity (σ), thermal conductivity (κ) and Seebeck coefficient of the material (S). ZT is expressed asκσTZTS2=, where T is the temperature in degree absolute. A large value of Seebeck coefficient, high electrical conductivity and low thermal conductivity are necessary to realize a high performance thermoelectric material. The best known thermoelectric materials are phonon-glass electron – crystal (PGEC) system where the phonons are scattered within the unit cell by the rattling structure and electrons are scattered less as in crystals to obtain a high electrical conductivity. A survey of literature reveals that correlated semiconductors and Kondo insulators containing rare earth or transition metal ions are found to be potential thermoelectric materials. The structural magnetic and charge transport properties in manganese oxides having the general formula of RE1−xAExMnO3 (RE = rare earth, AE= Ca, Sr, Ba) are solely determined by the mixed valence (3+/4+) state of Mn ions. In strongly correlated electron systems, magnetism and charge transport properties are strongly correlated. Within the area of strongly correlated electron systems the study of manganese oxides, widely known as manganites exhibit unique magneto electric transport properties, is an active area of research.Strongly correlated systems like perovskite manganites, characterized by their narrow localized band and hoping conduction, were found to be good candidates for thermoelectric applications. Manganites represent a highly correlated electron system and exhibit a variety of phenomena such as charge, orbital and magnetic ordering, colossal magneto resistance and Jahn-Teller effect. The strong inter-dependence between the magnetic order parameters and the transport coefficients in manganites has generated much research interest in the thermoelectric properties of manganites. Here, large thermal motion or rattling of rare earth atoms with localized magnetic moments is believed to be responsible for low thermal conductivity of these compounds. The 4f levels in these compounds, lying near the Fermi energy, create large density of states at the Fermi level and hence they are likely to exhibit a fairly large value of Seebeck coefficient.

Thermodynamics and Heat Transport of doped Spin-Ice Materials

In this thesis the low-temperature magnetism of the spin-ice systems Dy2Ti2O7 and Ho2Ti2O7 is investigated. In general, a clear experimental evidence for a sizable magnetic contribution kappa_{mag} to the low-temperature, zero-field heat transport of both spin-ice materials is observed. This kappa_{mag} can be attributed to the magnetic monopole excitations, which are highly mobile in zero field and are suppressed by a rather small external field resulting in a drop of kappa(H). Towards higher magnetic fields, significant field dependencies of the phononic heat conductivities kappa_{ph}(H) of Ho2Ti2O7 and Dy2Ti2O7 are found, which are, however, of opposite signs, as it is also found for the highly dilute reference materials (Ho0.5Y0.5)2Ti2O7 and (Dy0.5Y0.5)2Ti2O7. The dominant effect in the Ho-based materials is the scattering of phonons by spin flips which appears to be significantly stronger than in the Dy-based materials. Here, the thermal conductivity is suppressed due to enhanced lattice distortions observed in the magnetostriction. Furthermore, the thermal conductivity of Dy2Ti2O7 has been investigated concerning strong hysteresis effects and slow-relaxation processes towards equilibrium states in the low-temperature and low-field regime. The thermal conductivity in the hysteretic regions slowly relaxes towards larger values suggesting that there is an additional suppression of the heat transport by disorder in the non-equilibrium states. The equilibration can even be governed by the heat current for particular configurations. A special focus was put on the dilution series Dy2Ti2O7x. From specific heat measurements, it was found that the ultra-slow thermal equilibration in pure spin ice Dy2Ti2O7 is rapidly suppressed upon dilution with non-magnetic yttrium and vanishes completely for x>=0.2 down to the lowest accessible temperatures. In general, the low-temperature entropy of (Dy1-xYx)2Ti2O7, considerably decreases with increasing x, whereas its temperature-dependence drastically increases. Thus, it could be clarified that there is no experimental evidence for a finite zero-temperature entropy in (Dy1-xYx)2Ti2O7 above x>=0.2, in clear contrast to the finite residual entropy S_{P}(x) expected from a generalized Pauling approximation. A similar discrepancy is also present between S_{P}(x) and the low-temperature entropy obtained by Monte Carlo simulations, which reproduce the experimental data from 25 K down to 0.7 K, whereas the data at 0.4 K are overestimated. A straightforward description of the field-dependence kappa(H) of the dilution series with qualitative models justifies the extraction of kappa_{mag}. It was observed that kappa_{mag} systematically scales with the degree of dilution and its low-field decrease is related to the monopole excitation energy. The diffusion coefficient D_{mag} for the monopole excitations was calculated by means of c_{mag} and kappa_{mag}. It exhibits a broad maximum around 1.6 K and is suppressed for T<=0.5 K, indicating a non-degenerate ground state in the long-time limit, and in the high-temperature range for T>=4 K where spin-ice physics is eliminated. A mean-free path of 0.3 mum is obtained for Dy2Ti2O7 at about 1 K within the kinetic gas theory.

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Carrier momentum relaxation in highly doped polar semiconductors and semiconductor heterostructures

Highly doped polar semiconductors are essential components of today’s semiconductor industry. Most strikingly, transistors in modern electronic devices are polar semiconductor heterostructures. It is important to thoroughly understand carrier transport in such structures. In doped polar semiconductors, collective excitations of the carriers (plasmons) and the atoms (polar phonons) couple. These coupled collective excitations affect the electrical conductivity, here quantified through the carrier mobility. In scattering events, the carriers and the coupled collective modes transfer momentum between each other. Carrier momentum transferred to polar phonons can be lost to other phonons through anharmonic decay, resulting in a finite carrier mobility. The plasmons do not have a decay mechanism which transfers carrier momentum irretrievably. Hence, carrier-plasmon scattering results in infinite carrier mobility. Momentum relaxation due to either carrier–plasmon scattering or carrier–polar-phonon scattering alone are well understood. However, only this thesis manages to treat momentum relaxation due to both scattering mechanisms on an equal footing, enabling us to properly calculate the mobility limited by carrier–coupled plasmon–polar phonon scattering. We achieved this by solving the coupled Boltzmann equations for the carriers and the collective excitations, focusing on the “drag” term and on the anharmonic decay process of the collective modes. Our approach uses dielectric functions to describe both the carrier-collective mode scattering and the decay of the collective modes. We applied our method to bulk polar semiconductors and heterostructures where various polar dielectrics surround a semiconducting monolayer of MoS2, where taking plasmons into account can increase the mobility by up to a factor 15 for certain parameters. This screening effect is up to 85% higher than if calculated with previous methods. To conclude, our approach provides insight into the momentum relaxation mechanism for carrier–coupled collective mode scattering, and better tools for calculating the screened polar phonon and interface polar phonon limited mobility.