Upendra Harbola

Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems

Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Greens functions techniques for computing the energy and particle statistics are presented.

Quantum master equation for electron transport through quantum dots and single molecules

A quantum master equation QME is derived for the many-body density matrix of an open current-carrying system weakly-coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of the number of electrons in the system. We show that coherences between system states with different number of electrons, n Fock space coherences, do not contribute to the transport to second order in system-lead coupling. However, coherences between states with the same n may effect transport properties when the damping rate is of the order of or faster than the system Bohr frequencies. For large bias, when all the system many-body states lie between the chemical potentials of the two leads, we recover previous results. In the rotating wave approximation when the damping is slow compared to the Bohr frequencies, the dynamics of populations and coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.

Superoperator nonequilibrium Green's function theory of many-body systems; applications to charge transfer and transport in open junctions

Abstract Nonequilibrium Green’s functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and introduce superoperator algebra that greatly simplifies the derivation and the physical interpretation of all quantities. Expressions for various observables are derived directly in real time in terms of superoperator nonequilibrium Green’s functions (SNGF), rather than the artificial time-loop required in Schwinger’s Hilbert-space formulation. Applications for computing interaction energies, charge densities, average currents, current induced fluorescence, electroluminescence and current fluctuation (electron counting) statistics are discussed.

Entropy fluctuation theorems in driven open systems: application to electron counting statistics.

The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: Nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: An arbitrary nonequilibrium transformation always produces a change in the total entropy production greater than or equal to the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.

Nonlinear optical spectroscopy of single, few, and many molecules; nonequilibrium Green’s function QED approach

Nonlinear optical signals from an assembly of N noninteracting particles consist of an incoherent and a coherent component, whose magnitudes scale ~ N and ~ N(N - 1), respectively. A unified microscopic description of both types of signals is developed using a quantum electrodynamical (QED) treatment of the optical fields. Closed nonequilibrium Greens function expressions are derived that incorporate both stimulated and spontaneous processes. General (n + 1)-wave mixing experiments are discussed as an example of spontaneously generated signals. When performed on a single particle, such signals cannot be expressed in terms of the nth order polarization, as predicted by the semiclassical theory. Stimulated processes are shown to be purely incoherent in nature. Within the QED framework, heterodyne-detected wave mixing signals are simply viewed as incoherent stimulated emission, whereas homodyne signals are generated by coherent spontaneous emission.

Interference effects in the counting statistics of electron transfers through a double quantum dot

We investigate effects of quantum interferences and Coulomb interaction on the counting statistics of electrons crossing a double quantum dot in a parallel geometry by using a generating function technique based on a quantum master equation approach. The skewness and the average residence time of electrons in the dots are shown to be the quantities most sensitive to interferences and Coulomb coupling. The joint probabilities of consecutive electron transfer processes show characteristic temporal oscillations due to interference. The steady-state fluctuation theorem that predicts a universal relation between the number of forward and backward transfer events is shown to hold even in the presence of the Coulomb coupling and interference.

Fluctuation theorem for counting statistics in electron transport through quantum junctions

(Dated: February 6, 2008)We demonstrate that the probability distribution of the net number of electrons passing througha quantum system in a junction obeys a steady-state fluctuation theorem (FT) which can be testedexperimentally by the full counting statistics (FCS) of electrons crossing the lead-system interface.The FCS is calculated using a many-body quantum master equation (QME) combined with a Li-ouville space generating function (GF) formalism. For a model of two coupled quantum dots, weshow that the FT becomes valid for long binning times and provide an estimate for the finite-timedeviations. We also demonstrate that the Mandel (or Fano) parameter associated with the incomingor outgoing electron transfers show subpoissonian (antibunching) statistics.

Single-Electron Counting Spectroscopy: Simulation Study of Porphyrin in a Molecular Junction

Electron counting of a single porphyrin molecule between two electrodes shows a crossover from sub- to super-Poissonian statistics as the bias voltage is scanned. This is attributed to the simultaneous activation of states with electron transfer rates spanning several orders of magnitude. Time-series analysis of consecutive single-electron transfer events reveals fast and slow transport channels, which are not resolved by the average current alone.

Frequency-domain stimulated and spontaneous light emission signals at molecular junctions.

Using a diagrammatic superoperator formalism we calculate optical signals at molecular junctions where a single molecule is coupled to two metal leads which are held at different chemical potentials. The molecule starts in a nonequilibrium steady state whereby it continuously exchanges electrons with the leads with a constant electron flux. Expressions for frequency domain optical signals measured in response to continuous laser fields are derived by expanding the molecular correlation functions in terms of its many-body states. The nonunitary evolution of molecular states is described by the quantum master equation.

Nonequilibrium superoperator GW equations

Hedins equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Greens function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Greens function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.