The dissipative two-level system under strong ac-driving: a combination of Floquet and Van Vleck perturbation theory

We study the dissipative dynamics of a two-level system (TLS) exposed to strong ac driving. By combing Floquet theory with Van Vleck perturbation theory in the TLS tunneling matrix element, we diagonalize the time-dependent Hamiltonian and provide corrections to the renormalized Rabi frequency of the TLS, which are valid for both a biased and unbiased TLS and go beyond the known high-frequency and rotating-wave results. In order to mimic environmental influences on the TLS, we couple the system weakly to a thermal bath and solve analytically the corresponding Floquet-Bloch-Redfield master equation. We give a closed expression for the relaxation and dephasing rates of the TLS and discuss their behavior under variation of the driving amplitude. Further, we examine the robustness of coherent destruction of tunneling (CDT) and driving-induced tunneling oscillations (DITO). We show that also for a moderate driving frequency an almost complete suppression of tunneling can be achieved for short times and demonstrate the sensitiveness of DITO to a change of the external parameters.Comment: 21 pages, 18 figures; published versio

Non-Fermi liquid behavior in transport across carbon nanotube quantum dots

A low energy-theory for non-linear transport in finite-size single-wall carbon nanotubes, based on a microscopic model for the interacting pz electrons and successive bosonization, is presented. Due to the multiple degeneracy of the energy spectrum diagonal as well as off-diagonal (coherences) elements of the reduced density matrix contribute to the nonlinear transport. A four-electron periodicity with a characteristic ratio between adjacent peaks, as well as nonlinear transport features, in quantitative agreement with recent experiments, are predicted.Comment: 5 pages, 3 figure

Dynamics of the spin-boson model with a structured environment

We investigate the dynamics of the spin-boson model when the spectral density of the boson bath shows a resonance at a characteristic frequency $\Omega$ but behaves Ohmically at small frequencies. The time evolution of an initial state is determined by making use of the mapping onto a system composed of a quantum mechanical two-state system (TSS) which is coupled to a harmonic oscillator (HO) with frequency $\Omega$. The HO itself is coupled to an Ohmic environment. The dynamics is calculated by employing the numerically exact quasiadiabatic path-integral propagator technique. We find significant new properties compared to the Ohmic spin-boson model. By reducing the TSS-HO system in the dressed states picture to a three-level system for the special case at resonance, we calculate the dephasing rates for the TSS analytically. Finally, we apply our model to experimentally realized superconducting flux qubits coupled to an underdamped dc-SQUID detector.Comment: 26 pages, 11 figures, Chemical Physics Special Issue on the Spin-Boson Problem, ed. by H. Grabert and A. Nitzan, in pres

Interference effects in the Coulomb blockade regime: current blocking and spin preparation in symmetric nanojunctions

We consider nanojunctions in the single-electron tunnelling regime which, due to a high degree of spatial symmetry, have a degenerate many body spectrum. As a consequence, interference phenomena which cause a current blocking can occur at specific values of the bias and gate voltage. We present here a general formalism to give necessary and sufficient conditions for interference blockade also in the presence of spin polarized leads. As an example we analyze a triple quantum dot single electron transistor (SET). For a set-up with parallel polarized leads, we show how to selectively prepare the system in each of the three states of an excited spin triplet without application of any external magnetic field.Comment: 10 pages, 9 figures. Corrected typos and updated reference

Kondo effect in interacting nanoscopic systems: Keldysh field integral theory

Kondo physics in nonequilibrium interacting nanoscale devices is an attractive fundamental many-particle phenomenon with a rich potential for applications. Due to enormous complexity its clear and flexible theory is still highly desirable. We develop a physically transparent analytical theory capable to correctly describe the Kondo effect in strongly interacting systems at temperatures close to and above the Kondo temperature. We derive a nonequilibrium Keldysh field theory valid for a system with any finite electron-electron interaction which is much stronger than the coupling of the system to contacts. Finite electron-electron interactions are treated involving as many slave-boson degrees of freedom as one needs for a concrete many-body system. In a small vicinity of the zero slave-bosonic field configuration weak slave-bosonic oscillations, induced by the dot-contacts tunneling, are described by an effective Keldysh action quadratic in the slave-bosonic fields. For clarity the theory is presented for the single impurity Anderson model but the construction of the Keldysh field integral is universal and applicable to systems with more complex many-body spectra.Comment: 5 pages, 2 figure

Duality Relation for Quantum Ratchets

A duality relation between the long-time dynamics of a quantum Brownian particle in a tilted ratchet potential and a driven dissipative tight-binding model is reported. It relates a situation of weak dissipation in one model to strong dissipation in the other one, and vice versa. We apply this duality relation to investigate transport and rectification in ratchet potentials: From the linear mobility we infer ground-state delocalization for weak dissipation. We report reversals induced by adiabatic driving and temperature in the ratchet current and its dependence on the potential shape.Comment: Modified content, corrected typo

Electronic spectra of commensurate and incommensurate DWNTs in parallel magnectic field

We study the electronic spectra of commensurate and incommensurate double-wall carbon nanotubes (DWNTs) of finite length. The coupling between nanotube shells is taken into account as an inter-shell electron tunneling. Selection rules for the inter-shell coupling are derived. Due to the finite size of the system, these rules do not represent exact conservation of the crystal momentum, but only an approximate one; therefore the coupling between longitudinal momentum states in incommensurate DWNTs becomes possible. The use of the selection rules allows a fast and efficient calculation of the electronic spectrum. In the presence of a magnetic field parallel to the DWNT axis, we find spectrum modulations that depend on the chiralities of the shells

Effects of spin-orbit coupling and many-body correlations in STM transport through copper phthalocyanine

The interplay of exchange correlations and spin-orbit interaction (SOI) on the many-body spectrum of a copper phtalocyanine (CuPc) molecule and their signatures in transport are investigated. We first derive a minimal model Hamiltonian in a basis of frontier orbitals which is able to reproduce experimentally observed singlet-triplet splittings; in a second step SOI effects are included perturbatively. Major consequences of the SOI are the splitting of former degenerate levels and a magnetic anisotropy, which can be captured by an effective low-energy spin Hamiltonian. We show that STM-based magnetoconductance measurements can yield clear signatures of both these SOI induced effects.Comment: 12 pages, 6 figure

The two classes of low energy spectra in finite carbon nanotubes

Electrons in carbon nanotubes (CNTs) possess spin and orbital degrees of freedom. The latter is inherited from the bipartite graphene lattice with two inequivalent Dirac points. The electronic spectra obtained in several transport experiments on CNT quantum dots in parallel magnetic field often show an anticrossing of spectral lines assigned to the opposite Dirac valleys. So far this valley mixing has been attributed to the disorder, with impurity induced scattering. We show that this effect can arise also in ultraclean CNTs of the armchair class and it can be caused solely by the presence of the boundaries. In contrast, in CNTs of the zigzag class it does not occur. These two fundamentally different classes of spectra arise because of different symmetries of the low energy eigenstates of the two types of CNTs. The magnitude of the level splitting depends in a nonmonotonous way on the distance of the involved energy levels from the charge neutrality point.Comment: 5 pages, 4 figures, available Supplementary Materia

Helicity and electron correlation effects on transport properties of double-walled carbon nanotubes

We analytically demonstrate helicity determined selection rules for intershell tunneling in double-walled nanotubes with commensurate (c-DWNTs) and incommensurate (i-DWNTs) shells. For i-DWNTs the coupling is negligible between lowest energy subbands, but it becomes important as the higher subbands become populated. In turn the elastic mean free path of i-DWNTs is reduced for increasing energy, with additional suppression at subband onsets. At low energies, a Luttinger liquid theory for DWNTs with metallic shells is derived. Interaction effects are more pronounced in i-DWNTs.Comment: 4 pages, 3 figure