We consider strongly correlated quantum circuits where a dc drive is added on top of an initial out-of-equilibrium (OE) stationary state. Within a perturbative approach, we derive unifying OE fluctuation relations for high-frequency current noise, shown to be completely determined by zero-frequency noise and dc current. We apply them to the fractional quantum Hall effect at arbitrary incompressible filling factors, driven by OE sources, without knowledge of the underlying model. We show that such OE relations provide robust methods for an unambiguous determination of the fractional charge or of key interaction parameters entering in the exploration of anyonic statistics within an anyon collider.
We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in Ref.[23]. The nonequilibrium current noise at zero-temperature and finite frequencies shows a singular dip in the de-localized phase for the magnitude of frequencies equal to the bias voltage; while the dip is smeared out as the system moves to the localized phase. The corresponding peak-to-dip crossover is found in the AC conductance for the magnitude of frequencies equal to the bias voltage. The relevance and applications of our results for the experiments and for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral Luttinger liquids are discussed.
We consider a one-channel coherent conductor with a good transmission embedded into an Ohmic environment, the impedance of which is equal to the quantum of resistance
Rq=h/e2 below the
RC frequency. This choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid with one impurity, the interaction parameter of which corresponds to the specific value
K=1/2, allowing for a refermionization procedure. The ``new'' fermions have an energy-dependent transmission amplitude, which incorporates the strong correlation effects and yields the exact dc current and zero-frequency noise through expressions similar to those of the scattering approach. We recall and discuss these results for our present purpose. Then, we compute the finite-frequency differential conductance and the finite-frequency nonsymmetrized noise. Contrary to intuitive expectation, both can not be expressed within the scattering approach for the new fermions, even though they are still determined by the transmission amplitude. Even more, the finite-frequency conductance obeys an exact relation in terms of the dc current, which is similar to that derived perturbatively with respect to weak tunneling within the Tien-Gordon theory, and extended recently to arbitrary strongly interacting systems coupled eventually to an environment and/or with a fractional charge. We also show that the emission excess noise vanishes exactly above
eV, even though the underlying Tomonaga-Luttinger liquid model corresponds to a many-body correlated system. Our results apply for all ranges of temperature, voltages, and frequencies below the
RC frequency, and they allow us to explore fully the quantum regime.
Current quantum noise can be pictured as a sum over transitions through which the electronic system exchanges energy with its environment. We formulate this picture and use it to show which type of current correlators are measurable, and in what measurement the zero point fluctuations will play a role (the answer to the latter is as expected: only if the detector excites the system.) Using the above picture, we calculate and give physical interpretation of the finite-frequency finite-temperature current noise in a noninteracting Landauer-type system, where the chemical potentials of terminals 1 and 2 are
μ+eV/2 and
μ−eV/2 respectively, and derive a detailed-balance condition for this nonequilibrium system. Finally, we derive a generalized form of the Kubo formula for a wide class of interacting nonequilibrium systems, relating the differential conductivity to the current noise.
The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature, and often in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a nonequilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Instead of being proportional, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations vanish at zero temperature. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, in both its microscopic origins and its influence upon systems. Moreover, it is shown that there is a coupling-dependent nonequilibrium fluctuation-dissipation relation that determines the nonequilibrium uncertainty relation of linear systems in the weak-damping limit.
We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is nonperturbative with respect to strong coupling to an electromagnetic environment or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage
Vdc, and the out-of-equilibrium dc current which encodes the effects of interactions. We extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge
q free from unknown parameters through the robustness of the Josephson-like frequency. We have derived similar relations for noise (I. Safi, arXiv:1401.5950) which have been exploited, recently, to determine the fractional charge in the fractional quantum Hall effect (FQHE) within the Jain series [M. Kapfer et al., Science (to be published)]. The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates rectification exploited here to propose methods to measure the charge
q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-Gaussian source of noise. We also apply the theory to the Tomonaga-Luttinger liquid (TLL), showing a counterintuitive feature: A Lorentzian pulse superimposed on
Vdc can reduce the current compared to its dc value, at the same
Vdc, questioning the terminology ``photoassisted.'' Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect or voltage drop across a phase-slip Josephson junction.