Spin-spin correlations of entangled qubit pairs in the Bohm interpretation of quantum mechanics

A general entangled qubit pair is analyzed in the de Broglie-Bohm formalism corresponding to two spin-1/2 quantum rotors. Several spin-spin correlators of Bohm's hidden variables are analyzed numerically and a detailed comparison with results obtained by standard quantum mechanics is outlined. In addition to various expectation values the Bohm interpretation allows also a study of the corresponding probability distributions, which enables a novel understanding of entangled qubit dynamics. In particular, it is shown how the angular momenta of two qubits in this formalism can be viewed geometrically and characterized by their relative angles. For perfectly entangled pairs, for example, a compelling picture is given, where the qubits exhibit a unison precession making a constant angle between their angular momenta. It is also demonstrated that the properties of standard quantum mechanical spin-spin correlators responsible for the violation of Bell's inequalities are identical to their counterparts emerging from the probability distributions obtained by the Bohmian approach.Comment: Extended version of talk presented at the International Workshop 21st-century directions in de Broglie-Bohm theory and beyond, Vallico Sotto 201

Exact unitary transformation for Rashba rings in magnetic and electric fields

An exact solution for single electron states on mezoscopic rings with the Rashba coupling and in the presence of external magnetic and electric fields is derived by means of a unitary transformation. The transformation maps the model to a bare ring, which gives the possibility of a very simple formulation of single or many electron problems. As an example some exact results for spin and energy levels are presented.Comment: International conference ECN-2015, Odessa, 3-6 September 2015; v2: added reference

Effects of noise on fidelity in spin-orbit qubit transformations

We analyse non-adiabatic non-Abelian holonomic transformations of spin-qubits confined to a linear time dependent harmonic trap with time dependent Rashba interaction. For this system exact results can be derived for spin rotation angle which also enables exact treatment of white gate-noise effects. We concentrate in particular on the reliability of cyclic transformations quantified by fidelity defined by the probability that the qubit after one full cycle remains in the ground-state energy manifold. The formalism allows exact analysis of spin transformations that optimise final fidelity. Various examples of time dependent fidelity probability distributions are presented and discussed.Comment: Int. Conf. ECSN-2017, Odessa, 17-20 Augus

Pseudogap and the Fermi surface in the t-J model

We calculate spectral functions within the t-J model as relevant to cuprates in the regime from low to optimum doping. On the basis of equations of motion for projected operators an effective spin-fermion coupling is derived. The self energy due to short-wavelength transverse spin fluctuations is shown to lead to a modified selfconsistent Born approximation, which can explain strong asymmetry between hole and electron quasiparticles. The coupling to long-wavelength longitudinal spin fluctuations governs the low-frequency behavior and results in a pseudogap behavior, which at low doping effectively truncates the Fermi surface.Comment: Proc. of SNS 2001 (Chicago); submitted to J. of Phys. and Chem. of Solids, 6 RevTex pages, 4 figures (3 color

Spectral Functions and Pseudogap in Models of Strongly Correlated Electrons

The theoretical investigation of spectral functions and pseudogap in systems with strongly correlated electrons is discussed, with the emphasis on the single-band t-J model as relevant for superconducting cuprates. The evidence for the pseudogap features from numerical studies of the model is presented. One of the promising methods to study spectral functions is the method of equations of motion. The latter can deal systematically with the local constraints and projected fermion operators inherent for strongly correlated electrons. In the evaluation of the self energy the decoupling of spin and single-particle fluctuations is performed. In an undoped antiferromagnet the method reproduces the selfconsistent Born approximation (SCBA). For finite doping the approximation evolves into a paramagnon contribution which retains large incoherent contribution in the hole part. On the other hand, the contribution of longer-range spin fluctuations is essential for the emergence of the pseudogap. The latter shows up at low doping in the effective truncation of the large Fermi surface, reduced electron density of states and at the same time reduced quasiparticle density of states at the Fermi level.Comment: Proc. of conference 'Strongly Correlated Electron Systems', Krakow 200

Vibrational effects on low-temperature properties of molecular conductors

We calculate characteristic correlation functions for the Anderson model with additional phonon-assisted coupling to the odd conduction channel. This model describes, for example, the behavior of a molecule embedded between two electrodes in linear transport experiments where the position of the molecule with respect to the leads affects the tunneling amplitudes. We use variational projection-operator method and numerical renormalization group (NRG) method. The spin is Kondo screened either by even or odd conduction channel depending on the gate voltage and electron-phonon coupling. However, in all regimes the gate-voltage dependence of the zero temperature conductance is found to be qualitatively the same as in the model with no coupling to the vibrational mode.Comment: 2 pages, 3 figures, to be presented on "The International Conference on Strongly Correlated Electron Systems" SCES'07, May 13-18, Houston, US

SU(2) and SU(4) Kondo effect in double quantum dots

We investigate serial double quantum dot systems with on-site and inter-site interaction by means of Sch\"onhammer-Gunnarsson projection-operator method. The ground state is established by the competition between extended Kondo phases and localized singlet phases in spi$ degrees of freedom. We present and discuss different phases, as discerned by characteristic correlation functions. We discuss also how different phases would be seen in linear transport measurements.Comment: 5 pages, 2 figures, presented on "XI Training Course in the Physics of Strongly Correlated Systems", Vietri sul Mare, Salerno, Ital

Kondo effect in double quantum dots with inter-dot repulsion

We investigate a symmetrical double quantum dot system serially attached to the leads. The emphasis is on the numerical analysis of finite inter-dot tunneling in the presence of inter-dot repulsive capacitive coupling. The results reveal the competition between extended Kondo phases and local singlet phases in spin and charge degrees of freedom. The corresponding phase diagram is determined quantitatively.Comment: 4 pages, 4 figure

Exact spin-orbit qubit manipulation

We consider exactly solvable manipulation of spin-qubits confined in a moving harmonic trap and in the presence of the time dependent Rashba interaction. Non-adiabatic Anandan phase for cyclic time evolution is compared to the Wilczek-Zee adiabatic counterpart. It is shown that the ratio of these two phases can for a chosen system be any real number. Next we demonstrate the possibility of arbitrary qubit transformation in a ring with spin-orbit interaction. Finally, we present an example of exact analysis of spin-orbit dynamics influenced by the Ornstein-Uhlenbeck coloured noise.Comment: 14th Granada Seminar 2017, Granada, 19-24 Jun 201

Exact Nonadiabatic Holonomic Transformations of Spin-Orbit Qubits

An exact analytical solution is derived for the wavefunction of an electron in a one-dimensional moving quantum dot in a nanowire, in the presence of time-dependent spin-orbit coupling. For cyclic evolutions we show that the spin of the electron is rotated by an angle proportional to the area of a closed loop in the parameter space of the time-dependent quantum dot position and the amplitude of a fictitious classical oscillator driven by the time-dependent spin-orbit coupling. By appropriate choice of parameters, we show that arbitrary spin rotations may be performed on the Bloch sphere. Exact expressions for dynamical and geometrical phases are also derived.Comment: 5+4 pages, 1+6 figure