Wave-packet formalism of full counting statistics

Hassler, Fabian; Suslov, M. V.; Graf, Gian Michele; Лебедев, М. В.; Lesovik, G. B.; Blatter, G.

doi:10.1103/physrevb.78.165330

Cited by 73 publications

(132 citation statements)

References 33 publications

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“…dx |x x| which measures the probability of finding a given particle in the spatial inter- [20,30]. The complementary projector 1 − Q τ similarly measures the probability of not finding the particle.…”

Section: Fig 1 (Color Online) Driven Quantum Point Contactmentioning

confidence: 99%

Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors

2014

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We present a Floquet scattering theory of electron waiting time distributions in periodically driven quantum conductors. We employ a second-quantized formulation that allows us to relate the waiting time distribution to the Floquet scattering matrix of the system. As an application we evaluate the electron waiting times for a quantum point contact, modulating either the applied voltage (external driving) or the transmission probability (internal driving) periodically in time. Lorentzianshaped voltage pulses are of particular interest as they lead to the emission of clean single-particle excitations as recently demonstrated experimentally. The distributions of waiting times provide us with a detailed characterization of the dynamical properties of the quantum-coherent conductor in addition to what can be obtained from the shot noise or the full counting statistics.Introduction.-A surge of interest in dynamic quantum conductors has recently led to a number of groundbreaking experiments [1][2][3][4][5][6]. An on-demand coherent single-electron source based on a submicron capacitor [1,7] has been experimentally realized and successfully operated in the gigahertz regime [2]. Recently, the fermionic analogue of an optical Hong-Ou-Mandel experiment was performed to demonstrate that two such on-demand sources produce indistinguishable electronic quantum states [3]. Additionally, clean single-particle excitations have been created on top of a Fermi sea by applying a periodic sequence of Lorentzian-shaped voltage pulses to an electrical contact [4,5] following a pioneering theoretical proposal by Levitov and co-workers [8][9][10].These experimental breakthroughs hold promises for future gigahertz quantum electronics with precisely synchronized single-particle operations. One may envision circuit architectures with driven single-electron emitters coupled to the edge states of a quantum Hall conductor (or to the helical edge states in a topological insulator [11,12]) serving as rail tracks for charge and information carriers by guiding them to beam splitters (quantum point contacts) and particle interferometers for further processing. To facilitate progress towards this goal, a detailed understanding of the single-particle emitters and their statistical properties is required.In one approach, the full counting statistics of emitted charge is analyzed [13][14][15][16][17]. The charge fluctuations are typically integrated over many periods of the driving and important short-time physics may be lost. In a complementary approach, one considers the distribution of waiting times between charge carriers [18][19][20][21][22][23][24][25]. This view on quantum transport seems promising as picosecond single-electron detection is now becoming feasible [6]. A quantum theory of electron waiting times has recently been developed for voltage-biased mesoscopic conductors [20], however, so far without an explicit driving. To describe the statistical properties of coherent single-electron emitters, a theory of waiting time distributions (WTD)...

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Section: Fig 1 (Color Online) Driven Quantum Point Contactmentioning

confidence: 99%

Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors

2014

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“…Before presenting a derivation of (4.1) among others [4,22], let us make a digression on second quantization. In vague terms, the second quantization A of a single-particle operator A is the sum of its contributions from all particles i, A = i (A i − A i ρ ), though with expectation value subtracted.…”

Section: Second Quantization 41 Binomial Statisticsmentioning

confidence: 99%

Time Ordering and Counting Statistics

2009

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The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a tunnel junction.

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“…[2][3][4] The theory of GF for current was generalized to a general quantum mechanical variable by Nazarov and Kindermann, 23 and was extended to study short time behavior of dc and ac current using the wavepacket formalism. 19,21,24 In this paper, we develop a theoretical formalism for WTD for coherent conductors. Using the non-equilibrium Green's function 25,26 and path integral method in the two-time quantum measurement scheme 27 , we obtain GF for the electron transport system which allows us to study FCS and WTD in dc, ac, and transient regimes.…”

Section: Introductionmentioning

confidence: 99%

Waiting time distribution of quantum electronic transport in the transient regime

Tang

Wang

2014

Phys. Rev. B

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Waiting time is an important transport quantity that is complementary to average current and its fluctuation. So far all the studies of waiting time distribution (WTD) are limited to steady state transport (either dc or ac). The existing theory can not deal with WTD in the transient regime. In this regard, we develop a theoretical formalism based on Keldysh non-equilibrium Green's functions formalism to study WTD. This theory is suitable for dc, ac, and transient transport and can be used for first principles calculation on realistic systems. We apply this theory to a quantum dot system with a upward bias pulse and calculate cumulants of transferred charge as well as WTD in the transient regime. The oscillatory behavior of WTD is found in the transient regime. We give a general relation between WTD and experimental measured quantity and demonstrate its feasibility for a quantum dot system in the transient regime.

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Wave-packet formalism of full counting statistics

Cited by 73 publications

References 33 publications

Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors

Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors

Time Ordering and Counting Statistics

Waiting time distribution of quantum electronic transport in the transient regime

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