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Research in Optical Sciences

Weak measurement of an interacting virtual state: the case of cotunneling time

Alessandro Romito, Yuval Gefen

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We propose a weak measurement protocol to access the electron tunneling time through an interacting quantum dot. Surprisingly, this many-body cotunneling time may deviate from the prediction of the time-energy uncertainty relation.
DOI
10.1364/hilas.2014.jw2a.56

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Quantum mechanics allows the existence of ``virtual states'' that have no classical analog. Such virtual states defy direct observation through strong measurement, which would destroy the volatile virtual state. Here, we show how a virtual state of an interacting many-body system can be detected employing a weak measurement protocol with post-selection. We employ this protocol for the measurement of the time it takes an electron to tunnel through a virtual state of a quantum dot (cotunneling). Contrary to classical intuition, this cotunneling time is independent of the strength of the dot-lead coupling and may deviate from that predicted by time-energy uncertainty relation. Our approach, amenable to experimental verification, may elucidate an important facet of quantum mechanics which hitherto was not accessible by direct measurements.
We introduce a rate formalism to treat classically forbidden electron transport through a quantum dot (cotunneling) in the presence of a coupled measurement device. We demonstrate this formalism for a toy model case of cotunneling through a single-level dot while being coupled to a strongly pinched-off quantum point contact (QPC). We find that the detector generates three types of back-action: the measurement collapses the coherent transport through the virtual state, but at the same time allows for QPC-assisted incoherent transport, and widens the dot level. Last, we obtain the measured cotunneling time from the cross correlation between dot and QPC currents.
We investigate nonequilibrium transport through superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite-gap effects, and to account for both quasiparticle and Cooper-pair tunneling. With focus on the weak-tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. For the particular case of a strongly interacting quantum dot sandwiched between two superconductors, we identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current, and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of $0\ensuremath{-}\ensuremath{\pi}$ transitions. The latter signal the interplay between strong interactions and tunneling at finite bias.
Electron cotunneling in semiconductor quantum dots is a higher-order tunneling mechanism that connects initial and final charge states through energetically inaccessible virtual intermediate configurations. In quantum-dot arrays, such processes can produce simultaneous charge motion across multiple tunnel junctions and enable transitions that would otherwise be suppressed by Coulomb blockade. Here, building on an earlier proof-of-principle demonstration, we investigate radio-frequency (rf)-driven correlated cotunneling and its application to dispersive quantum-dot readout. Using both theoretical modeling and experimental measurements in two different foundry-fabricated silicon devices, we show that an external rf drive can induce correlated cyclic single-electron transitions, resulting in enhanced charge-polarization of the system. We develop a general theoretical framework for rf electron-cascade readout, which exploits cotunneling events in quantum-dot systems with three or more dots to produce a relative signal enhancement, and extend its experimental demonstration to a gate-sensed device architecture. Our results establish the operating principles of rf electron-cascade readout and provide a route to increased dispersive readout fidelity in semiconductor quantum computing architectures.