Quantum Brownian motion in ratchet potentials: duality relation and its consequences

Quantum Brownian motion in ratchet potentials is investigated by means of an approach based on a duality relation. This relation links the long-time dynamics in a tilted ratchet potential in the presence of dissipation with the one in a driven dissipative tight-binding model. The application to quantum ratchet yields a simple expression for the ratchet current in terms of the transition rates in the tight-binding system.Comment: Chemical Physics (in press

Strong coupling theory for tunneling and vibrational relaxation in driven bistable systems

A study of the dynamics of a tunneling particle in a driven bistable potential which is moderately-to-strongly coupled to a bath is presented. Upon restricting the system dynamics to the Hilbert space spanned by the M lowest energy eigenstates of the bare static potential, a set of coupled non-Markovian master equations for the diagonal elements of the reduced density matrix, within the discrete variale representation, is derived. The resulting dynamics is in good agreement with predictions of ab-initio real-time path integral simulations. Numerous results, analytical as well as numerical, for the quantum relaxation rate and for the asymptotic populations are presented. Our method is particularly convenient to investigate the case of shallow, time-dependent potential barriers and moderate-to-strong damping, where both a semi-classical and a Redfield-type approach are inappropriate.Comment: 37 pages, 23 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

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

Entanglement spectroscopy of a driven solid-state qubit and its detector

We study the asymptotic dynamics of a driven quantum two level system coupled via a quantum detector to the environment. We find multi-photon resonances which are due to the entanglement of the qubit and the detector. Different regimes are studied by employing a perturbative Floquet-Born-Markov approach for the qubit+detector system, as well as non-perturbative real-time path integral schemes for the driven spin-boson system. We find analytical results for the resonances, including the red and the blue sidebands. They agree well with those of exact ab-initio calculations.Comment: 4 pages, 4 figure

Driven Tunneling Dynamics: Bloch-Redfield Theory versus Path Integral Approach

In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-boson dynamics the equivalence between two widely used but seemingly different roads of approximation, namely the path integral approach and the Bloch-Redfield theory. The excellent agreement between these two methods is corroborated by a novel efficient analytical high-frequency approach: it well approximates the decay of quantum coherence via a series of damped coherent oscillations. Moreover, a suitably tuned control field can selectively enhance or suppress quantum coherence.Comment: 4 pages including 3 figures, submitted for publicatio

Decay of correlations in the dissipative two-state system

We study the equilibrium correlation function of the polaron-dressed tunnelling operator in the dissipative two-state system and compare the asymptoptic dynamics with that of the position correlations. For an Ohmic spectral density with the damping strength $K=1/2$, the correlation functions are obtained in analytic form for all times at any $T$ and any bias. For $K<1$, the asymptotic dynamics is found by using a diagrammatic approach within a Coulomb gas representation. At T=0, the tunnelling or coherence correlations drop as $t^{-2K}$, whereas the position correlations show universal decay $\propto t^{-2}$. The former decay law is a signature of unscreened attractive charge-charge interactions, while the latter is due to unscreened dipole-dipole interactions.Comment: 5 pages, 5 figures, to be published in Europhys. Let

Direct observation of band-gap closure for a semiconducting carbon nanotube in a large parallel magnetic field

We have investigated the magnetoconductance of semiconducting carbon nanotubes (CNTs) in pulsed, parallel magnetic fields up to 60 T, and report the direct observation of the predicted band-gap closure and the reopening of the gap under variation of the applied magnetic field. We also highlight the important influence of mechanical strain on the magnetoconductance of the CNTs.Comment: 4 pages, 4 figure

Phase diffusion as a model for coherent suppression of tunneling in the presence of noise

We study the stabilization of coherent suppression of tunneling in a driven double-well system subject to random periodic $\delta-$function ``kicks''. We model dissipation due to this stochastic process as a phase diffusion process for an effective two-level system and derive a corresponding set of Bloch equations with phase damping terms that agree with the periodically kicked system at discrete times. We demonstrate that the ability of noise to localize the system on either side of the double-well potenital arises from overdamping of the phase of oscillation and not from any cooperative effect between the noise and the driving field. The model is investigated with a square wave drive, which has qualitatively similar features to the widely studied cosinusoidal drive, but has the additional advantage of allowing one to derive exact analytic expressions.Comment: 17 pages, 4 figures, submitted to Phys. Rev.