Coherent Particle Transfer in an On-Demand Single-Electron Source

Keeling, Jonathan; Shytov, A. V.; Levitov, L. S.

doi:10.1103/physrevlett.101.196404

Cited by 111 publications

(157 citation statements)

References 27 publications

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“…[8][9][10] and recently demonstrated experimentally by Dubois et al [4,5] and hereafter named levitons. The same outgoing state can be created by a mesoscopic capacitor with a slow linear driving protocol [11,12,[34][35][36][37].We treat the adiabatic regime, where the time scale over which the voltage is modulated is much longer than the time it takes an electron to pass through the scattering region. The Floquet scattering matrix S can then be related to the "frozen" scattering matrix S f (t) at time 26,32].…”

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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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confidence: 99%

Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors

2014

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“…Remarkably, our approach requires neither multiple spatial paths [9,10] nor noise measurements [8,22,23], relying instead on quantum beats in spontaneous emission of electrons back to the source lead. Using a generic [22,24] effective single-particle model we predict an interference pattern in the charge capture probability that reflects the dynamical quantum phase accumulated between the isolation of the localized quantum state and the onset of backtunelling. …”

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Quantum Fluctuations and Coherence in High-Precision Single-Electron Capture

Kashcheyevs

Timoshenko

2012

Phys. Rev. Lett.

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The phase of a single quantum state is undefined unless the history of its creation provides a reference point. Thus quantum interference may seem hardly relevant for the design of deterministic single-electron sources which strive to isolate individual charge carriers quickly and completely. We provide a counterexample by analyzing the non-adiabatic separation of a localized quantum state from a Fermi sea due to a closing tunnel barrier. We identify the relevant energy scales and suggest ways to separate the contributions of quantum non-adiabatic excitation and backtunneling to the rare non-capture events. In the optimal regime of balanced decay and non-adiabaticity, our simple electron trap turns into a single-lead Landau-Zener-backtunneling interferometer, revealing the dynamical phase accumulated between the particle capture and leakage. The predicted "quantum beats in backtunneling" may turn the error of a single-electron source into a valuable signal revealing essentially non-adiabatic energy scales of a dynamic quantum dot.PACS numbers: 73.63. Kv, 73.23.Hk, 73.21.La Successful demonstration of electron-on-demand sources based on electrostatic modulation of nanoelectronic circuit elements such as dynamic quantum dots [1][2][3] or mesoscopic capacitors [4,5] has offered a prospect of building an electronic analog of few-photon quantum optics [6] that exploits the particle-wave duality and entanglement of individual elementary excitations in a Fermi sea [7][8][9][10]. This ambitious goal is complemented by a long-standing challenge in quantum metrology [11] to untie the definition of ampere from the mechanical units of SI [12] and implement a current standard based on direct counting of discrete charge carriers. So far the overlap between these research directions [13,14] has been rather limited arguably because metrological applications strive to maximize the particle nature of on-demand excitations.Optimizing the trade-off between speed and accuracy of single-electron isolation [2] does require consideration of quantum error mechanisms such as non-adiabatic excitation [15][16][17] or backtunneling [18][19][20][21]. However, these effects have been hard to differentiate experimentally owing to complexity of non-equilibrium many-particle quantum dynamics [22] and experimental challenges in exercising high-speed control of the electrostatic landscape. The quantum phase of the captured particle has been considered thus far as inconsequential for accuracy and inaccessible for measurement unless the particle is ejected into a separate interferometer [10].In this work, we propose a new type of interferometry to measure and thus control the non-equilibrium energy scales governing the decoupling of a dynamic quantum dot from a Fermi sea. Remarkably, our approach requires neither multiple spatial paths [9,10] nor noise measurements [8,22,23], relying instead on quantum beats in spontaneous emission of electrons back to the source lead. Using a generic [22,24] effective single-particle model we predict an interfer...

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“…A Floquet scattering matrix approach 7,8,9 , used to deal with quantum pumping 24,25,26,27,28,29 , enables us to investigate the dynamics of the system beyond the linearresponse regime and adiabatic approximations. The full time-dependent current response to a periodic modulation with frequency Ω is…”

Section: Model and Formalismmentioning

confidence: 99%

“…7,8,9. We develop the conditions for nullifying the total current and investigate the measuring precision.…”

Section: Introductionmentioning

confidence: 99%

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Electron counting with a two-particle emitter

et al. 2008

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We consider two driven cavities (capacitors) connected in series via an edge state. The cavities are driven such that they emit an electron and a hole in each cycle. Depending on the phase lag the second cavity can effectively absorb the carriers emitted by the first cavity and nullify the total current or the set-up can be made to work as a two-particle emitter. We examine the precision with which the current can be nullified and with which the second cavity effectively counts the particles emitted by the first one. To achieve single-particle detection we examine pulsed cavities.

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Coherent Particle Transfer in an On-Demand Single-Electron Source

Cited by 111 publications

References 27 publications

Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors

Floquet Theory of Electron Waiting Times in Quantum-Coherent Conductors

Quantum Fluctuations and Coherence in High-Precision Single-Electron Capture

Electron counting with a two-particle emitter

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