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arXiv:2607.24350

Electron Shuttle Waiting Times for Electric Field Sensing

Alberto Mayorgas, Alberto López-García, Enamul Haque, Javier Cerrillo

quant-phSubmitted Jul 27, 2026• Announced Jul 28, 2026
arXivHTMLPDF

Abstract

We explore the use of waiting-time statistics in a quantum electron shuttle for electric-field sensing. Electron shuttles convert nanomechanical motion into charge transport, showing a noise-broadened crossover between stochastic tunneling and mechanically assisted charge transfer. This allows investigation of how transport fluctuations encode electromechanical parameters. Using a single-level quantum shuttle in strong-Coulomb-blockade and high-bias regimes with a Markovian quantum master equation, we analyze stationary dynamics in phase space and waiting time distributions. By estimating the electromechanical coupling, proportional to the electric field, we evaluate the classical Fisher information in waiting times and compare it with the quantum Fisher information of the stationary state. We relate the metrological response to mean waiting time, variance, and Fano factor. Our results show that the crossover from tunneling to shuttling is characterized by enhanced fluctuations and increased parameter sensitivity, leading to a pronounced enhancement of the Fisher information.

Comments
11 pages, 6 figures

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We explore the use of waiting-time statistics in a quantum electron shuttle for electric-field sensing. Electron shuttles convert nanomechanical motion into charge transport, showing a noise-broadened crossover between stochastic tunneling and mechanically assisted charge transfer. This allows investigation of how transport fluctuations encode electromechanical parameters. Using a single-level quantum shuttle in strong-Coulomb-blockade and high-bias regimes with a Markovian quantum master equation, we analyze stationary dynamics in phase space and waiting time distributions. By estimating the electromechanical coupling, proportional to the electric field, we evaluate the classical Fisher information in waiting times and compare it with the quantum Fisher information of the stationary state. We relate the metrological response to mean waiting time, variance, and Fano factor. Our results show that the crossover from tunneling to shuttling is characterized by enhanced fluctuations and increased parameter sensitivity, leading to a pronounced enhancement of the Fisher information.
We formulate a quantum theory of electron waiting time distributions for charge transport in nanostructures described by non-Markovian generalized master equations. We illustrate our method by calculating the waiting time distribution of electron transport through a dissipative double quantum dot, where memory effects are present due to a strongly coupled heat bath. We consider the influence of non-Markovian dephasing on the distribution of electron waiting times and discuss how spectral properties of the heat bath may be detected through measurements of the electron waiting time.
Quantum systems used for metrology can offer enhanced precision over their classical counterparts. The design of quantum sensors can be optimized by maximizing the quantum Fisher information (QFI), which characterizes the precision of parameter estimation for an ideal measurement. Here we consider the response of a quantum system as a means to estimate the strength of a weak external perturbation. General expressions for the QFI in the nonequilibrium steady-state are derived, which hold for arbitrary interacting many-body systems at finite or zero temperature, and can be related to susceptibilities or linear-response transport coefficients. For quantum dot nanoelectronics devices, we show that electron interactions can lead to *exponential* scaling of the QFI with system size, highlighting that quantum resources can be utilized in the full Fock space. The precision estimation of voltages and fields can also be achieved by practical measurements. In particular, we show that current-based metrology in quantum circuits can leverage many-body effects for enhanced sensing.
This thesis is concerned with employing the statistics of charge transfer in a conductor as a tool for quantum measurement. The physical systems studied are electronic devices made by nanoscale manufacturing techniques. In this context quantum measurement appears not as a postulate, but as physical process. In this thesis I am considering a quantum system, in particular a qubit or a nanomechanical resonator, interacting with a tunnel junction. The effect of coupling a quantum system to a tunnel junction is twofold: The state of the quantum system will be changed and there will be information about the quantum system in the statistics of charge transfer of the tunnel junction. As the first example a quantum measurement process of a qubit is considered. A common description of the system and charge dynamics is found by introducing a new quantity, the charge specific density matrix. By deriving and solving a Markovian master equation for this quantity the measurement process is analyzed. The measurement is shown to be a dynamical process, where correlations between the initial state of the qubit and the number of charges transferred in the tunnel junction arise on a typical timescale, the measurement time. As another example of a quantum system a nanomechanical oscillator is considered. It is found, that the biased tunnel junction, acting as a non-equilibrium environment to the oscillator, increases the temperature of the oscillator from its thermal equilibrium value. The current in the junction is modulated by the interaction with the oscillator, but the influence vanishes for bias voltages smaller than the oscillator frequency. For an asymmetric junction and non-vanishing oscillator momentum a current is shown to flow through the junction even at zero bias. The current noise spectrum induced by the oscillator in the tunnel junction consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency and double the oscillator frequency. The peak heights are dependent on the coupling strength between oscillator and junction, the occupation number of the oscillator, the bias voltage and the junction temperature. I show how the peak height can be used as a measure of the oscillator temperature, demonstrating that the noise of a tunnel junction can be used for electronic thermometry of a nanomechanical oscillator.
We analyze charge fluctuations in a parasitic state strongly coupled to a superconducting Josephson-junction-based charge detector. The charge dynamics of the state resembles that of electron transport in a quantum dot with two charge states, and hence we refer to it as a two-level fluctuator. By constructing the distribution of waiting times from the measured detector signal and comparing it with a waiting time theory, we extract the electron in- and out-tunneling rates for the two-level fluctuator, which are severely asymmetric.
Transport-induced self-sustained oscillations in electromechanical systems convert a static electrochemical bias into robust, autonomous oscillatory motion in the absence of any external periodic drive. However, an exact description of such self-oscillations remains challenging in nanoscale electromechanical devices featuring a simultaneously large bosonic Hilbert space, strong interactions, and structured fermionic leads. We formulate a tensor-network framework that combines a binary representation of the vibrational mode with mesoscopic reservoir embeddings that enable controlled access to the self-oscillatory steady states and relevant transport observables without explicit real-time propagation. We demonstrate the emergence of mechanical self-oscillations across a broad set of operating conditions, in which strong electromechanical backaction, nonadiabatic oscillator dynamics, and energy-dependent electronic tunneling processes compete. Furthermore, we observe that for both slow and fast vibrating mechanical modes, suppressed vibrational occupation fluctuations in the self-oscillation window along the electromechanical coupling strength sweep are preceded by a peak in the occupation fluctuations. Collectively, we explore how both intrinsic system properties and environmental parameters govern such autonomous oscillations over a broad range of operating conditions. The broad applicability of our framework will facilitate further extension of the method to more complex and experimentally relevant scenarios to study the thermodynamics of quantum autonomous devices with potential applications in quantum sensing, timekeeping, information processing, and energy conversion.
Long-distance transfer of quantum information in architectures based on quantum dot spin qubits will be necessary for their scalability. One way of achieving this goal is to simply move the electron between two quantum registers. Precise control over the process of shuttling such a single electron through a chain of tunnel-coupled quantum dots is possible when interdot energy detunings are changed adiabatically. The deterministic character of shuttling is, however, endangered by the open nature of the system, as the transferred electron is coupled to thermal reservoirs: sources of fluctuations of electric fields and lattice vibrations. We present a comprehensive analysis showing how the electron transfer between two voltage-controlled quantum dots is affected by electron-phonon scattering and interaction with sources of 1/f1/f1/f and Johnson charge noise in both detuning and tunnel coupling. The electron-phonon scattering turns out to be irrelevant in Si quantum dots, with charge noise dominating the dynamics of the system at slow detuning sweep, when the electron spends more time delocalized between the dots (i.e., near the anticrossing of the tunnel-coupled states). Competition between the effects of charge noise and the Landau-Zener effect leads to an existence of an optimal detuning sweep rate, leading to minimal probability of leaving the electron behind. In GaAs quantum dots, on the other hand, piezoelectric coupling to phonons is strong enough to make the processes of interdot transfer assisted by phonon emission and absorption dominate over transitions caused by charge noise. The probability of leaving the electron behind then depends monotonically on detuning the sweep rate over a broad range of rates, and values much smaller than in silicon can be obtained for slow sweeps. However, after taking into account limitations on transfer time imposed by the need for preservation of a shuttled electron's spin coherence, the minimal probabilities of leaving the electron behind in both GaAs- and Si-based double quantum dots turn out to be of the same order of magnitude. Bringing them down below ${10}^{\ensuremath{-}3}$ requires temperatures $\ensuremath{\le}100$ mK and tunnel couplings above $20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{eV}$.