Using multiparticle distribution functions, we calculate the correlations produced by a periodically driven scatterer in a system of noninteracting electrons at zero temperature. The multiparticle correlations due to a quantum exchange effect are expressed in terms of photon-assisted scattering amplitudes. The results we obtain are valid for slow but arbitrary in strength driving. We show that even for large amplitude pumps the zero-frequency noise power is related to two-particle correlations. In addition to two-particle correlations a large amplitude pump can generate multiparticle correlations.
Using multiparticle distribution functions, we calculate the correlations produced by a periodically driven scatterer in a system of noninteracting electrons at zero temperature. The multiparticle correlations due to a quantum exchange effect are expressed in terms of photon-assisted scattering amplitudes. The results we obtain are valid for slow but arbitrary in strength driving. We show that even for large amplitude pumps the zero-frequency noise power is related to two-particle correlations. In addition to two-particle correlations a large amplitude pump can generate multiparticle correlations.
Theory predicts that electrons emitted from independent electron sources (metallic contacts) can nevertheless interfere. This interference is manifest in an exchange contribution to the shot noise correlation of currents at different contacts of a mesoscopic conductor. A geometry has been proposed in which second order (single particle) interference due to superposition of amplitudes is absent but fourth order (two-particle) interference exhibits Aharonov-Bohm oscillations. Recently such a geometry has been realized in an experiment and the theoretically predicted two-particle Aharonov-Bohm effect has been detected. We discuss Bell measurements and quantum state tomography using shot noise correlations. We discuss in addition structures in which two-particle interference effects are generated dynamically by varying electrostatic potentials with the help of gates or by generating electron-hole pairs by irradiating contacts of a mesoscopic conductor. These examples emphasize that two-particle processes are not related to a particular geometry but are a general feature of multiparticle observables like shot noise correlations.
Abstract The sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices, whose signals are linear in the number N of active atoms, have practically arrived at their theoretical limit. Further enhancement of the sensitivities of such devices requires the introduction of new physical processes to improve on their present achievements. Many-body collective correlation among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As such correlations introduce interference terms in the intensity of the scattering amplitudes they may enhance the signal as N ( N − 1) for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of N 2 and contribute to better sensitivity in quantum metrology. Moreover, atomic correlation may provide a quantum noise limit, the Heisenberg limit. In the present letter a novel operator is introduced that expresses photon-induced excitation exchange that takes into account energy conservation, V i j = a ˆ † σ i σ j † a ˆ , where σ i = g i e i is the lowering operator of the i - th atom, and a ˆ † , a ˆ are photon creation and annihilation operators. Here i and j stand for two different atoms. This operator describes real or virtual photon-assisted excitation exchange between two atoms. Moreover, it conserves the total number of excitations in the joint electromagnetic field and the quantum system. A photon-induced excitation exchange between two atoms is calculated and clearly exhibits correlation and collective effects.
Disordered elastic systems are studied in the quantum, classical, and dynamic regime in the present thesis. The thesis consists of two main parts: In the first part we study the low temperature phase diagram of one-dimensional weakly disordered quantum systems like charge or spin density waves and Luttinger liquids by a full finite temperature renormalization group (RG) calculation. In the classical region, for vanishing quantum fluctuations those results are supplemented by an exact solution of the model in the case of strong disorder, described by the ground state and the correlation function. Furthermore, by a mapping of the problem onto a Burgers equation with noise, in the case of weak disorder, we can derive an expression for the correlation length. At zero temperature we reproduce the (quantum) phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At finite temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wave length of the phason excitations. The existence of a zero temperature transition is reflected in a rich cross-over phase diagram determined by the correlation functions. In particular we find four different scaling regions: a classical disordered, a quantum disordered, a quantum critical, and a thermal region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential, and for the case of density waves we discuss the influence of quantum phase-slips, which might lead to a new scenario for the unpinning (delocalization) transition at zero temperature. Additionally, we analyze the current noise in a classical one-dimensional charge density wave system in the weak pinning regime by solving the overdamped equation of motion numerically. At low temperatures and just above the zero temperature depinning threshold, the power spectrum of the current noise reveals the existence of 1/f or flicker noise. Our results are in agreement with experimental measurements in quasi-one-dimensional charge density wave systems. In part two, we examine the viscous motion of an interface driven by a periodically oscillating external field in a random medium. The velocity exhibits a smeared depinning transition showing a pronounced hysteresis, which is absent in the adiabatic case. Its width is determined by a new length scale, introduced by the frequency of the external drive and - in the low frequency regime - by the critical exponents of the zero frequency depinning transition. Scaling arguments and an approximate renormalization group treatment predict a power law behavior of the velocity as a function of frequency and field amplitude at the dc depinning threshold, which is confirmed numerically. Thermal fluctuations lead to an additional smearing of the transition. If the amplitude of the external driving force is smaller than the depinning field, the motion of the interface by avalanches has to be taken into account in order to describe the velocity hysteresis. To check the validity of our model with respect to experimental results, we calculate the complex susceptibilities using an adiabatic and non-adiabatic approach numerically for finite systems and compare it to measurements of a superferromagnetic granular multilayer system and find that the model of an ac driven interface in a disordered environment can describe the main features of the experimental results. Additionally, the influence of a strong surface potential on the critical depinning of an elastic system, driven in a random medium is considered. If the surface potential prevents depinning completely, the curvature of the displacement profile at zero temperature exhibits a pronounced rhombic hysteresis curve with width of two times the (bulk) depinning field. The hysteresis disappears at non-zero temperatures if the driving force is changed adiabatically. If the surface depinns by the applied force or thermal creep, the curvature is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, flux-line lattices, and charge-density waves. As addendum we examine low dimensional interacting, but clean Bose systems at low temperatures. The interaction leads to scattering events of the over-condensate particles for which we calculate the scattering times using Fermi's golden rule. With that we derive the thermal conductivity and the related weak localization corrections. This is done for short and long-range interactions.
We have obtained an exact analytical solution for a system of two particles moving under the action of a central harmonic-oscillator potential and the mutual Coulomb interaction augmented by a potential linear in the interparticle coordinate. The expressions for the single-particle density, the exchange-correlation energy quantities, and the correlation functions are thereby derived. Numerical results on the exchange-correlation contributions are presented using plots of various local energy densities as well as the corresponding global energy quantities for varying strengths of the oscillator potential.
For a number of noninteracting identical particles entering a multichannel scatterer in various wave-packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean numbers of particles, nm, scattered into a given (mth) channel, single-channel statistics, and interchannel correlations. We show that for initially uncorrelated particles, indistinguishability changes single-channel statistics without altering the value of nm. For uncorrelated bosons and fermions, bunching and antibunching behavior can be detected in the extreme-case probabilities, to have all particles scattered into the same channel, or none of particles scattered into a channel, or channels. As an example, we consider a cavity with a single long-lived resonance accessible to the particles, which allows them to ``pile up'' inside the scatterer.
We consider a two-dimensional electron or hole system at zero temperature and low carrier densities, where the long-range Coulomb interactions dominate over the kinetic energy. In this limit the clean system will form a Wigner crystal. Nontrivial quantum-mechanical corrections to the classical ground state lead to multiparticle exchange processes that can be expressed as an effective spin Hamiltonian involving competing interactions. Disorder will destroy the Wigner crystal on large length scales, and the resulting state is called a Wigner glass. The notion of multiparticle-exchange processes is still applicable in the Wigner glass, but the exchange frequencies now follow a random distribution. We compute the exchange frequencies for a large number of relevant exchange processes in the Wigner crystal, and the frequency distributions for some important processes in the Wigner glass. The resulting effective low-energy spin Hamiltonian should be the starting point of an analysis of the possible ground-state phases and quantum phase transitions between them. We find that disorder plays a crucial role and speculate on a possible zero-temperature phase diagram.