Generalized constraints on quantum amplification

We derive quantum constraints on the minimal amount of noise added in linear amplification involving input or output signals whose component operators do not necessarily have c-number commutators, as is the case for fermion currents. This is a generalization of constraints derived for the amplification of bosonic fields whose components posses c-number commutators.Comment: 4 pages, 1 figure, submitted to Physical Review Letter

Shot-noise in transport and beam experiments

Consider two Fermi gases with the same {\it average} currents: a transport gas, as in solid-state experiments where the chemical potentials of terminal 1 is $\mu+eV$ and of terminal 2 and 3 is $\mu$, and a beam, i.e., electrons entering only from terminal 1 having energies between $\mu$ and $\mu+eV$. By expressing the current noise as a sum over single-particle transitions we show that the temporal current fluctuations are very different: The beam is noisier due to allowed single-particle transitions into empty states below $\mu$. Surprisingly, the correlations between terminals 2 and 3 are the same.Comment: 4 pages, 2 figure

Applications of nonequilibrium Kubo formula to the detection of quantum noise

The Kubo fluctuation-dissipation theorem relates the current fluctuations of a system in an equilibrium state with the linear AC-conductance. This theorem holds also out of equilibrium provided that the system is in a stationary state and that the linear conductance is replaced by the (dynamic) conductance with respect to the non equilibrium state. We provide a simple proof for that statement and then apply it in two cases. We first show that in an excess noise measurement at zero temperature, in which the impedance matching is maintained while driving a mesoscopic sample out of equilibrium, it is the nonsymmetrized noise power spectrum which is measured, even if the bare measurement, i.e. without extracting the excess part of the noise, obtains the symmetrized noise. As a second application we derive a commutation relation for the two components of fermionic or bosonic currents which holds in every stationary state and which is a generalization of the one valid only for bosonic currents. As is usually the case, such a commutation relation can be used e.g. to derive Heisenberg uncertainty relationships among these current components.Comment: 10 pages, Invited talk to be given by Y. I. at the SPIE Noise Conference, Grand Canary, June 2004. Added reference and 2 footnotes, corrected typo in Eq.

AC-Conductance through an Interacting Quantum Dot

We investigate the linear ac-conductance for tunneling through an arbitrary interacting quantum dot in the presence of a finite dc-bias. In analogy to the well-known Meir-Wingreen formula for the dc case, we are able to derive a general formula for the ac-conductance. It can be expressed entirely in terms of local correlations on the quantum dot, in the form of a Keldysh block diagram with four external legs. We illustrate the use of this formula as a starting point for diagrammatic calculations by considering the ac-conductance of the noninteracting resonant level model and deriving the result for the lowest order of electron-phonon coupling. We show how known results are recovered in the appropriate limits.Comment: 4+ pages, 4 figure

Emission and absorption noise in the fractional quantum Hall effect

We compute the high-frequency emission and absorption noise in a fractional quantum Hall effect (FQHE) sample at arbitrary temperature. We model the edges of the FQHE as chiral Luttinger liquids (LL) and we use the non-equilibrium perturbative Keldysh formalism. We find that the non-symmetrized high frequency noise contains important signatures of the electron-electron interactions that can be used to test the Luttinger liquid physics, not only in FQHE edge states, but possibly also in other one-dimensional systems such as carbon nanotubes. In particular we find that the emission and absorption components of the excess noise (defined as the difference between the noise at finite voltage and at zero voltage) are different in an interacting system, as opposed to the non-interacting case when they are identical. We study the resonance features which appear in the noise at the Josephson frequency (proportional to the applied voltage), and we also analyze the effect of the distance between the measurement point and the backscattering site. Most of our analysis is performed in the weak backscattering limit, but we also compute and discuss briefly the high-frequency noise in the tunneling regime.Comment: 26 pages, 11 figure