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

Abstract

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...

Non-adiabatic quantized charge pumping with tunable-barrier quantum dots: a review of current progress

“…Due to barrier-plunger crosstalk, the electrochemical potentials on the dot drift during closing at a certain rate dµ n (t)/dt. Whether this drift is important enough to dominate the capture error mechanism, depends on the value of the plunger-to-barrier ratio, ∆ ptb = τ |dµ n (t)/dt|, as first discussed by Kashcheyevs and Timoshenko in [150]. If ∆ ptb kT then the Fermi functions in (3.1) do not change appreciably during the decoupling process, and a sudden approximation is appropriate.…”

Counting Statistics for Electron Capture in a Dynamic Quantum Dot

“…Fluctuations in the capture probability (i.e. P n ) will be strongest for n that have t c n and t b n close to each other [28].…”

The Tunnelling Current through Oscillating Resonance and the Sisyphus Effect

“…As a consequence, the particle can be activated to much higher energies (close to the barrier's height) and penetrates through the well with much higher probability. This dynamic resonant tunnelling was investigated in a variety of fields: from the foundations of quantum mechanics [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] via nano-and microelectronics [14,[31][32][33] to biochemistry and biology [34][35][36][37][38][39][40].…”