Strong electromechanical coupling of an atomic force microscope cantilever to a quantum dot

Remote-Controllable Interfacial Electron Tunneling at Heterogeneous Molecular Junctions via Tip-Induced Optoelectrical Engineering

Molecular electronics enables functional electronic behavior via single molecules or molecular self-assembled monolayers, providing versatile opportunities for hybrid molecular-scale electronic devices. Although various molecular junction structures are constructed to investigate charge transfer dynamics, significant challenges remain in terms of interfacial charging effects and far-field background signals, which dominantly block the optoelectrical observation of interfacial charge transfer dynamics. Here, tip-induced optoelectrical engineering is presented that synergistically correlates photo-induced force microscopy and Kelvin probe force microscopy to remotely control and probe the interfacial charge transfer dynamics with sub-10 nm spatial resolution. Based on this approach, the optoelectrical origin of metal-molecule interfaces is clearly revealed by the nanoscale heterogeneity of the tip-sample interaction and optoelectrical reactivity, which theoretically aligned with density functional theory calculations. For a practical device-scale demonstration of tip-induced optoelectrical engineering, interfacial tunneling is remotely controlled at a 4-inch wafer-scale metal-insulator-metal capacitor, facilitating a 5.211-fold current amplification with the tip-induced electrical field. In conclusion, tip-induced optoelectrical engineering provides a novel strategy to comprehensively understand interfacial charge transfer dynamics and a non-destructive tunneling control platform that enables real-time and real-space investigation of ultrathin hybrid molecular systems.

Fully Quantized Electron Transfer Observed in a Single Redox Molecule at a Metal Interface

Long-range electron transfer is a ubiquitous process that plays an important role in electrochemistry, biochemistry, organic electronics, and single molecule electronics. Fundamentally, quantum mechanical processes, at their core, manifest through both electron tunneling and the associated transition between quantized nuclear vibronic states (intramolecular vibrational relaxation) mediated by electron-nuclear coupling. Here, we report on measurements of long-range electron transfer at the interface between a single ferrocene molecule and a gold substrate separated by a hexadecanethiol quantum tunneling barrier. These redox measurements exhibit quantized nuclear transitions mediated by electron-nuclear coupling at 4.7 K in vacuum. By detecting the electric force associated with redox events by atomic force microscopy (AFM), with increasing AFM oscillation amplitude, the intensity of the observed  cantilever resonance frequency shift peak increases and then exhibits a series of discrete steps that are indicative of quantized nuclear transitions. The observed peak shapes agree well with a single-electron tunneling model with quantized nuclear state transitions associated with the conversion of the molecule between oxidized and reduced electronic states. This technique opens the door to simultaneously investigating quantized electron and nuclear dynamics in a diverse range of systems.

Nanomechanical pump-probe measurements of insulating electronic states in a carbon nanotube

Transport measurements have been an indispensable tool in studying conducting states of matter. However, there exists a large set of interesting states that are insulating, often due to electronic interactions or topology, and are difficult to probe via transport. Here, through an experiment on carbon nanotubes, we present a new approach capable of measuring insulating electronic states through their back action on nanomechanical motion. We use a mechanical pump-probe scheme, allowing the detection of shifts in both frequency and dissipation rate of mechanical vibrational modes, in an overall insulating system. As an example, we use this method to probe the non-conducting configurations of a double quantum dot, allowing us to observe the theoretically predicted signature of nanomechanical back action resulting from a coherently tunnelling electron. The technique opens a new way for measuring the internal electronic structure of a growing variety of insulating states in one- and two-dimensional systems.

Initiating and Monitoring the Evolution of Single Electrons Within Atom-Defined Structures

Using a noncontact atomic force microscope, we track and manipulate the position of single electrons confined to atomic structures engineered from silicon dangling bonds on the hydrogen terminated silicon surface. An attractive tip surface interaction mechanically manipulates the equilibrium position of a surface silicon atom, causing rehybridization that stabilizes a negative charge at the dangling bond. This is applied to controllably switch the charge state of individual dangling bonds. Because this mechanism is based on short range interactions and can be performed without applied bias voltage, we maintain both site-specific selectivity and single-electron control. We extract the short range forces involved with this mechanism by subtracting the long range forces acquired on a dimer vacancy site. As a result of relaxation of the silicon lattice to accommodate negatively charged dangling bonds, we observe charge configurations of dangling bond structures that remain stable for many seconds at 4.5 K. Subsequently, we use charge manipulation to directly prepare the ground state and metastable charge configurations of dangling bond structures composed of up to six atoms.

An atomistic model for the charge distribution in layered MoS2

We present an atomistic model for predicting the distribution of doping electric charges in layered molybdenum disulfide (MoS₂). This model mimics the charge around each ion as a net Gaussian-spatially distributed charge plus an induced dipole, and is able to predict the distribution of doping charges in layered MoS₂ in a self-consistent scheme. The profiles of doping charges in monolayer MoS₂ flakes computed by this charge-dipole model are in good agreement with those obtained by density-functional-theory calculations. Using this model, we quantitatively predict the charge enhancement in MoS₂ monolayer nanoribbons, with which strong ionic charge-localization effects are shown.

Enhancing Cavity Quantum Electrodynamics via Antisqueezing: Synthetic Ultrastrong Coupling

We present and analyze a method where parametric (two-photon) driving of a cavity is used to exponentially enhance the light-matter coupling in a generic cavity QED setup, with time-dependent control. Our method allows one to enhance weak-coupling systems, such that they enter the strong coupling regime (where the coupling exceeds dissipative rates) and even the ultrastrong coupling regime (where the coupling is comparable to the cavity frequency). As an example, we show how the scheme allows one to use a weak-coupling system to adiabatically prepare the highly entangled ground state of the ultrastrong coupling system. The resulting state could be used for remote entanglement applications.

Coupling graphene nanomechanical motion to a single-electron transistor

Graphene-based electromechanical resonators have attracted great interest recently because of the outstanding mechanical and electrical properties of graphene and their various applications. However, the coupling between mechanical motion and charge transport has not been explored in graphene. Herein, we studied the mechanical properties of a suspended 50 nm wide graphene nanoribbon, which also acts as a single-electron transistor (SET) at low temperatures. Using the SET as a sensitive detector, we found that the resonance frequency could be tuned from 82 MHz to 100 MHz and the quality factor exceeded 30 000. The strong charge-mechanical coupling was demonstrated by observing the SET induced ∼140 kHz resonance frequency shifts and mechanical damping. We also found that the SET can enhance the nonlinearity of the resonator. Our SET-coupled graphene mechanical resonator could approach an ultra-sensitive mass resolution of ∼0.55 × 10^-21 g and a force sensitivity of ∼1.9 × 10^-19 N (Hz)^-1/2, and can be further improved. These properties indicate that our device is a good platform for both fundamental physical studies and potential applications.

Quantum state readout of individual quantum dots by electrostatic force detection

Electric charge detection by atomic force microscopy (AFM) with single-electron resolution (e-EFM) is a promising way to investigate the electronic level structure of individual quantum dots (QDs). The oscillating AFM tip modulates the energy of the QDs, causing single electrons to tunnel between QDs and an electrode. The resulting oscillating electrostatic force changes the resonant frequency and damping of the AFM cantilever, enabling electrometry with a single-electron sensitivity. Quantitative electronic level spectroscopy is possible by sweeping the bias voltage. Charge stability diagram can be obtained by scanning the AFM tip around the QD. e-EFM technique enables to investigate individual colloidal nanoparticles and self-assembled QDs without nanoscale electrodes. e-EFM is a quantum electromechanical system where the back-action of a tunneling electron is detected by AFM; it can also be considered as a mechanical analog of admittance spectroscopy with a radio frequency resonator, which is emerging as a promising tool for quantum state readout for quantum computing. In combination with the topography imaging capability of the AFM, e-EFM is a powerful tool for investigating new nanoscale material systems which can be used as quantum bits.

Heralded Control of Mechanical Motion by Single Spins

We propose a method to achieve a high degree of control of nanomechanical oscillators by coupling their mechanical motion to single spins. Manipulating the spin alone and measuring its quantum state heralds the cooling or squeezing of the oscillator even for weak spin-oscillator couplings. We analytically show that the asymptotic behavior of the oscillator is determined by a spin-induced thermal filter function whose overlap with the initial thermal distribution of the oscillator determines its cooling, heating, or squeezing. Counterintuitively, the rate of cooling dependence on the instantaneous thermal occupancy of the oscillator renders robust cooling or squeezing even for high initial temperatures and damping rates. We further estimate how the proposed scheme can be used to control the motion of a thin diamond cantilever by coupling it to its defect centers at low temperature.

Charge-state dynamics in electrostatic force spectroscopy

We present a numerical model that allows us to study the response of an oscillating probe in electrostatic force spectroscopy to charge switching in quantum dots at various time scales. The model provides more insight into the behavior of frequency shift and dissipated energy under different scanning conditions when measuring a temporarily charged quantum dot on a surface. Namely, we analyze the dependence of the frequency shift, the dissipated energy, and their fluctuations on the resonance frequency of the tip and on the electron tunneling rates across the tip-quantum dot and quantum dot-sample junctions. We discuss two complementary approaches to simulating the charge dynamics, a stochastic and a deterministic one. In addition, we derive analytic formulas valid for small amplitudes, describing relations between the frequency shift, dissipated energy, and the characteristic rates driving the charging and discharging processes.

Observation of a phononic Mollow triplet in a multimode hybrid spin-nanomechanical system

Reminiscent of the bound character of a qubit's dynamics confined on the Bloch sphere, the observation of a Mollow triplet in the resonantly driven qubit fluorescence spectrum represents one of the founding signatures of quantum electrodynamics. Here we report on its observation in a hybrid spin-nanomechanical system, where a nitrogen-vacancy spin qubit is magnetically coupled to the vibrations of a silicon carbide nanowire. A resonant microwave field turns the originally parametric hybrid interaction into a resonant process, where acoustic phonons are now able to induce transitions between the dressed qubit states, leading to synchronized spin-oscillator dynamics. We further explore the vectorial character of the hybrid coupling to the bidimensional deformations of the nanowire. The demonstrated microwave assisted synchronization of the spin-oscillator dynamics opens novel perspectives for the exploration of spin-dependent forces, the key ingredient for quantum state transfer.

The Mollow triplet, originally observed in the fluorescence spectrum of an optically excited two level system, is a signature of quantum electrodynamics. Here, the authors observe its phononic equivalent by magnetically coupling a single nitrogen-vacancy qubit to the vibrations of a silicon carbide nanowire.

Periodic Charging of Individual Molecules Coupled to the Motion of an Atomic Force Microscopy Tip

Individual molecules at the edges of self-assembled islands grown on Ag(111) can be deliberately switched in their charge state with the electric field from a scanning-probe tip. Close to the threshold voltage for a charge state transition, periodic switching of the charge is directly driven by the cantilever motion in frequency-modulated atomic force microscopy (AFM), as can be deduced from the signature in the measured frequency shift. In this regime, the integrated frequency shift yields the tip-sample force that is due to a single additional electron. Further, the signature of the dynamic charging response provides information on the electronic coupling of the molecule to the substrate. In analogy to previous experiments on quantum dots, this may also be used in the future to access excited state properties of single molecules from AFM experiments.

Revealing energy level structure of individual quantum dots by tunneling rate measured by single-electron sensitive electrostatic force spectroscopy

We present theoretical and experimental studies of the effect of the density of states of a quantum dot (QD) on the rate of single-electron tunneling that can be directly measured by electrostatic force microscopy (e-EFM) experiments. In e-EFM, the motion of a biased atomic force microscope cantilever tip modulates the charge state of a QD in the Coulomb blockade regime. The charge dynamics of the dot, which is detected through its back-action on the capacitavely coupled cantilever, depends on the tunneling rate of the QD to a back-electrode. The density of states of the QD can therefore be measured through its effect on the energy dependence of tunneling rate. We present experimental data on individual 5 nm colloidal gold nanoparticles that exhibit a near continuous density of state at 77 K. In contrast, our analysis of already published data on self-assembled InAs QDs at 4 K clearly reveals discrete degenerate energy levels.

Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator

We report on single electronic spins coupled to the motion of mechanical resonators by a novel mechanism based on crystal strain. Our device consists of single-crystal diamond cantilevers with embedded nitrogen-vacancy center spins. Using optically detected electron spin resonance, we determine the unknown spin-strain coupling constants and demonstrate that our system resides well within the resolved sideband regime. We realize coupling strengths exceeding 10 MHz under mechanical driving and show that our system has the potential to reach strong coupling. Our novel hybrid system forms a resource for future experiments on spin-based cantilever cooling and coherent spin-oscillator coupling.

Nonlinear optomechanical detection for Majorana fermions via a hybrid nanomechanical system

: The pursuit for detecting the existence of Majorana fermions is a challenging task in condensed matter physics at present. In this work, we theoretically propose a novel nonlinear optical method for probing Majorana fermions in the hybrid semiconductor/superconductor heterostructure. Our proposal is based on a hybrid system constituted by a quantum dot embedded in a nanomechanical resonator. With this method, the nonlinear optical Kerr effect presents a distinct signature for the existence of Majorana fermions. Further, the vibration of the nanomechanical resonator will enhance the nonlinear optical effect, which makes the Majorana fermions more sensitive to be detected. This proposed method may provide a potential supplement for the detection of Majorana fermions.

Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system

Recent progress in nanotechnology has allowed the fabrication of new hybrid systems in which a single two-level system is coupled to a mechanical nanoresonator. In such systems the quantum nature of a macroscopic degree of freedom can be revealed and manipulated. This opens up appealing perspectives for quantum information technologies, and for the exploration of the quantum-classical boundary. Here we present the experimental realization of a monolithic solid-state hybrid system governed by material strain: a quantum dot is embedded within a nanowire that features discrete mechanical resonances corresponding to flexural vibration modes. Mechanical vibrations result in a time-varying strain field that modulates the quantum dot transition energy. This approach simultaneously offers a large light-extraction efficiency and a large exciton-phonon coupling strength g0. By means of optical and mechanical spectroscopy, we find that g0/2 π is nearly as large as the mechanical frequency, a criterion that defines the ultrastrong coupling regime.

Synchronizing the dynamics of a single nitrogen vacancy spin qubit on a parametrically coupled radio-frequency field through microwave dressing

A hybrid spin-oscillator system in parametric interaction is experimentally emulated using a single nitrogen vacancy (NV) spin qubit immersed in a radio frequency (rf) field and probed with a quasiresonant microwave (MW) field. We report on the MW-mediated locking of the NV spin dynamics onto the rf field, appearing when the MW-driven Rabi precession frequency approaches the rf frequency and for sufficiently large rf amplitudes. These signatures are analogous to a phononic Mollow triplet in the MW rotating frame for the parametric interaction and promise to have impact in spin-dependent force detection strategies.

Room-temperature single-electron charging detected by electrostatic force microscopy

We use atomic force microscopy to measure electron addition spectra of individual Au nanoparticles that exhibit Coulomb blockade at room temperature. The cantilever tip charges individual nanoparticles supported on an ultra-thin NaCl film via single-electron tunneling from the metal back electrode. The tunneling is detected by measuring frequency shift and damping of the oscillating cantilever. Finite element electrostatic calculations indicate that the total nanoparticle capacitance is dominated by mutual capacitance to the back electrode.

Detecting non-Abelian anyons by charging spectroscopy

Observation of non-Abelian statistics for the e/4 quasiparticles in the ν = 5/2 fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states in a system with localized quasiparticles, and, hence, an additional low temperature entropy. Recent experiments, which detect changes in the number of quasiparticles trapped in a local potential well as a function of an applied gate voltage, V(G), provide a possibility for measuring this entropy, if carried out over a suitable range of temperatures, T. We present a microscopic model for quasiparticles in a potential well and study the effects of non-Abelian statistics on the charge stability diagram in the V(G)-T plane, including broadening at finite temperature. We predict a measurable slope for the first quasiparticle charging line and an even-odd effect in the diagram, which is a signature of non-Abelian statistics.

Stochastic noise in atomic force microscopy

Having reached the quantum and thermodynamic limits of detection, atomic force microscopy (AFM) experiments are routinely being performed at the fundamental limit of signal to noise. A critical understanding of the statistical properties of noise leads to more accurate interpretation of data, optimization of experimental protocols, advancements in instrumentation, and new measurement techniques. Furthermore, accurate simulation of cantilever dynamics requires knowledge of stochastic behavior of the system, as stochastic noise may exceed the deterministic signals of interest, and even dominate the outcome of an experiment. In this article, the power spectral density (PSD), used to quantify stationary stochastic processes, is introduced in the context of a thorough noise analysis of the light source used to detect cantilever deflections. The statistical properties of PSDs are then outlined for various stationary, nonstationary, and deterministic noise sources in the context of AFM experiments. Following these developments, a method for integrating PSDs to provide an accurate standard deviation of linear measurements is described. Lastly, a method for simulating stochastic Gaussian noise from any arbitrary power spectral density is presented. The result demonstrates that mechanical vibrations of the AFM can cause a logarithmic velocity dependence of friction and induce multiple slip events in the atomic stick-slip process, as well as predicts an artifactual temperature dependence of friction measured by AFM.

Electron fluctuation induced resonance broadening in nano electromechanical systems: the origin of shear force in vacuum

This article presents a study of the poorly understood "shear-force" used in an important class of near-field instruments that use mechanical resonance feedback detection. In the case of a metallic probe near a metallic surface in vacuum, we show that in the 10-60 nm range there is no such a thing as a shear-force in the sense of the nonconservative friction force. Fluctuations of the oscillator resonance frequency, likely induced by local charge variations, could account for the reported effects in the literature without introducing a dissipative force.

Excited-state spectroscopy on an individual quantum dot using atomic force microscopy

We present a new charge sensing technique for the excited-state spectroscopy of individual quantum dots, which requires no patterned electrodes. An oscillating atomic force microscope cantilever is used as a movable charge sensor as well as gate to measure the single-electron tunneling between an individual self-assembled InAs quantum dot and back electrode. A set of cantilever dissipation versus bias voltage curves measured at different cantilever oscillation amplitudes forms a diagram analogous to the Coulomb diamond usually measured with transport measurements. The excited-state levels as well as the electron addition spectrum can be obtained from the diagram. In addition, a signature which can result from inelastic tunneling by phonon emission or a peak in the density of states of the electrode is also observed, which demonstrates the versatility of the technique.

Energy levels of few-electron quantum dots imaged and characterized by atomic force microscopy

Strong confinement of charges in few-electron systems such as in atoms, molecules, and quantum dots leads to a spectrum of discrete energy levels often shared by several degenerate states. Because the electronic structure is key to understanding their chemical properties, methods that probe these energy levels in situ are important. We show how electrostatic force detection using atomic force microscopy reveals the electronic structure of individual and coupled self-assembled quantum dots. An electron addition spectrum results from a change in cantilever resonance frequency and dissipation when an electron tunnels on/off a dot. The spectra show clear level degeneracies in isolated quantum dots, supported by the quantitative measurement of predicted temperature-dependent shifts of Coulomb blockade peaks. Scanning the surface shows that several quantum dots may reside on what topographically appears to be just one. Relative coupling strengths can be estimated from these images of grouped coupled dots.