Dynamical Coulomb blockade of tunnel junctions driven by alternating voltages

The theory of dynamical Coulomb blockade is extended to tunneling elements driven by a time-dependent voltage. It is shown that for standard set-ups where an external voltage is applied to a tunnel junction via an impedance, time-dependent driving entails an excitation of the modes of the electromagnetic environment by the applied voltage. Previous approaches for ac driven circuits need to be extended to account for the driven bath modes. A unitary transformation involving also the variables of the electromagnetic environment is introduced which allows to split-off the time-dependence from the Hamiltonian in the absence of tunneling. This greatly simplifies perturbation-theoretical calculations based on treating the tunneling Hamiltonian as a perturbation. In particular, the average current flowing in the leads of the tunnel junction is studied. Explicit results are given for the case of an applied voltage with a constant dc part and a sinusoidal ac part. The connection with standard dynamical Coulomb blockade theory for constant applied voltage is established. It is shown that an alternating voltage source reveals significant additional effects caused by the electromagnetic environment. The hallmark of dynamical Coulomb blockade in ac driven devices is a suppression of higher harmonics of the current by the electromagnetic environment. The theory presented basically applies to all tunneling devices driven by alternating voltages.Comment: 13 pages, 2 figur

Quantum Effects in Barrier Dynamics

The dynamics near the top of a potential barrier is studied in the temperature region where quantum effects become important. The time evolution of the density matrix of a system that deviates initially from equilibrium in the vicinity of the barrier top but is in local equilibrium away from the barrier top is determined. Explicit results are given for a range of parameters where the nonequilibrium state is not affected by anharmonicities of the barrier potential except for the barrier height. In particular, for a system confined initially to one side of the barrier the relaxation to a quasi--stationary flux state is determined. The associated rate constant is evaluated and the relation to other rate formulas is discussed in detail.Comment: 22 pages, 2 Postscript figures; in press (Chem. Phys.

Tuning Excess Noise by Aharonov-Bohm Interferometry

A voltage bias applied to a conductor induces a change of the current noise with respect to the equilibrium noise known as excess noise. We analyze the excess noise of the electronic current flowing through a mesoscopic Aharonov-Bohm ring threaded by a magnetic flux, coupled to a side gate, and contacted by two metallic electrodes. It is shown that the excess noise can be controlled both magnetically and electrostatically, demonstrating the full tunability of the system. At zero frequency, the ratio of the noise strength to the current (Fano factor) can thereby be minimized. Remarkably, at finite frequency, regions of negative excess noise emerge.Comment: 6 pages, 5 figures, final version, corrected typos and updated reference

Semiclassical theory of vibrational energy relaxation

A theory of vibrational energy relaxation based on a semiclassical treatment of the quantum master equation is presented. Using new results on the semiclassical expansion of dipole matrix elements, we show that in the classical limit the master equation reduces to the Zwanzig energy diffusion equation. The leading quantum corrections are determined and discussed for the harmonic and Morse potentials.Comment: See also at http://vesta.physik.uni-freiburg.de/www/dqs/sfb.htm

Coulomb Charging at Large Conduction

We discuss the suppression of Coulomb charging effects on a small metallic island coupled to an electrode by a tunnel junction. At high temperatures the quantum corrections to the classical charging energy $E_c=e^2/2C$, where $C$ is the island capacitance, are evaluated. At low temperatures the large quantum fluctuations of the island charge cause a strong reduction of the effective $E_c$ which is determined explicitly in the limit of a large tunneling conductance.Comment: 4 page

Effect of zero point phase fluctuations on Josephson tunneling

In the presence of phase fluctuations the dc Josephson effect is modified and the supercurrent at zero voltage is replaced by a peak at small but finite voltages. It is shown that at zero temperature this peak is determined by two complementary expansions of finite radius of convergence. The leading order expressions are related to results known from the regimes of Coulomb blockade and of macroscopic quantum tunneling. The peak positions and the suppression of the critical current by quantum fluctuations are discussed.Comment: 4 pages, 4 figures, RevTe

Interplay of Rayleigh and Peierls Instabilities in Metallic Nanowires

A quantum-mechanical stability analysis of metallic nanowires within the free-electron model is presented. The stability is determined by an interplay of electron-shell effects, the Rayleigh instability due to surface tension, and the Peierls instability. Although the latter effect limits the maximum length also for wires with "magic radii", it is found that nanowires in the micrometer range can be stable at room temperature.Comment: 4 pages, 4 figure