Mechanisms Underlying a Quantum Superposition Microscope Based on THz-Driven Coherent Oscillations in a Two-Level Molecular Sensor

We report pump-probe measurements of a hydrogen molecule (H_{2}) in the tunnel junction of a scanning tunneling microscope coupled to ultrashort terahertz (THz) pulses. The coherent oscillation of the THz-induced dc tunneling current at a frequency of ∼0.5  THz fingerprints the absorption by H_{2} as a two-level system (TLS). Two components of the oscillatory signal are observed and point to both photon and field aspects of the THz pulses. A few loosely bound states with similar energies for the upper state of the TLS are evidenced by the coherent revival of oscillatory signal. Furthermore, the comparison of spectroscopic features of H_{2} with different tips provides an understanding of the TLS for H_{2}.

Stochastic Syncing in Sinusoidally Driven Atomic Orbital Memory

Stochastically fluctuating multiwell systems are a promising route toward physical implementations of energy-based machine learning and neuromorphic hardware. One of the challenges is finding tunable material platforms that exhibit such multiwell behavior and understanding how complex dynamic input signals influence their stochastic response. One such platform is the recently discovered atomic Boltzmann machine, where each stochastic unit is represented by a binary orbital memory state of an individual atom. Here, we investigate the stochastic response of binary orbital memory states to sinusoidal input voltages. Using scanning tunneling microscopy, we investigated orbital memory derived from individual Fe and Co atoms on black phosphorus. We quantify the state residence times as a function of various input parameters such as frequency, amplitude, and offset voltage. The state residence times for both species, when driven by a sinusoidal signal, exhibit synchronization that can be quantitatively modeled by a Poisson process based on the switching rates in the absence of a sinusoidal signal. For individual Fe atoms, we also observe a frequency-dependent response of the state favorability, which can be tuned by the input parameters. In contrast to Fe, there is no significant frequency dependence in the state favorability for individual Co atoms. Based on the Poisson model, the difference in the response of the state favorability can be traced to the difference in the voltage-dependent switching rates of the two different species. This platform provides a tunable way to induce population changes in stochastic systems and provides a foundation toward understanding driven stochastic multiwell systems.

Avoided Level Crossing and Entangled States of Interacting Hydrogen Molecules Detected by the Quantum Superposition Microscope

Pump-probe measurements by ultrashort THz pulses can be used to excite and follow the coherence dynamics in the time domain of single hydrogen molecules (H2) in the junction of a scanning tunneling microscope (STM). By tailoring the resonance frequency through the sample bias, we identified two spectral signatures of the interactions among multiple H2 molecules. First, the avoided level crossing featured by energy gaps ranging from 20 to 80 GHz was observed because of the level repulsion between two H2 molecules. Second, the tip can sense the signal of H2 outside the junction through the projective measurement on the H2 inside the junction, owing to the entangled states created through the interactions. A dipolar-type interaction was integrated into the tunneling two-level system model of H2, enabling accurate reproduction of the observed behaviors. Our results obtained by the quantum superposition microscope reveal the intricate quantum mechanical interplay among H2 molecules and additionally provide a 2D platform to investigate unresolved questions of amorphous materials.

On the origin and elimination of cross coupling between tunneling current and excitation in scanning probe experiments that utilize the qPlus sensor

The qPlus sensor allows for the simultaneous operation of scanning tunneling microscopy (STM) and atomic force microscopy (AFM). When operating a combined qPlus sensor STM/AFM at large tunneling currents, a hitherto unexplained tunneling current-induced cross coupling can occur, which has already been observed decades ago. Here, we study this phenomenon both theoretically and experimentally; its origin is voltage drops on the order of μV that lead to an excitation or a damping of the oscillation, depending on the sign of the current. Ideally, the voltage drops would be phase-shifted by π/2 with respect to a proper phase angle for driving and would, thus, not be a problem. However, intrinsic RC components in the current wiring lead to a phase shift that does enable drive or damping. Our theoretical model fully describes the experimental findings, and we also propose a way to prevent current-induced excitation or damping.

Electrical Manipulation of Quantum Coherence in a Two-Level Molecular System

We report the manipulation of ultrafast quantum coherence of a two-level single hydrogen molecular system by employing static electric field from the sample bias in a femtosecond terahertz scanning tunneling microscope. A H_{2} molecule adsorbed on the polar Cu_{2}N surface develops an electric dipole and exhibits a giant Stark effect. An avoided crossing of the quantum state energy levels is derived from the resonant frequency of the single H_{2} two levels in a double-well potential. The dephasing time of the initial wave packet can also be changed by applying the electric field. The electrical manipulation for different tunneling gaps in three dimensions allows quantification of the surface electrostatic fields at the atomic scale. Our work demonstrated the potential application of molecules as controllable two-level molecular systems.

Tracking the Interaction between a CO-Functionalized Probe and Two Ag-Phthalocyanine Conformers by Local Vertical Force Spectroscopy

Intentionally terminating scanning probes with a single atom or molecule belongs to a rapidly growing field in the quantum chemistry and physics at surfaces. However, the detailed understanding of the coupling between the probe and adsorbate is in its infancy. Here, an atomic force microscopy probe functionalized with a single CO molecule is approached with picometer control to two conformational isomers of Ag-phthalocyanine adsorbed on Ag(111). The isomer with the central Ag atom pointing to CO exhibits a complex evolution of the distance-dependent interaction, while the conformer with Ag bonded to the metal surface gives rise to a Lennard-Jones behavior. By virtue of spatially resolved force spectroscopy and the comparison with results obtained from microscope probes terminated with a single Ag atom, the mutual coupling of the protruding O atom of the tip and the Ag atom of the phthalocyanine molecule is identified as the cause for the unconventional variation of the force. Simulations of the entire junction within density functional theory unveil the presence of ample relaxations in the case of one conformer, which represents a rationale for the peculiar vertical-distance evolution of the interaction. The simulations highlight the role of physisorption, chemisorption, and unexpected junction distortions at the verge of bond formation in the interpretation of the distance-dependent force between two molecules.

Atomic-scale intermolecular interaction of hydrogen with a single VOPc molecule on the Au(111) surface

Molecular dynamics of hydrogen molecules (H2) on surfaces and their interactions with other molecules have been studied with the goal of improvement of hydrogen storage devices for energy applications. Recently, the dynamic behavior of a H2 at low temperature has been utilized in scanning tunnelling microscopy (STM) for sub-atomic resolution imaging within a single molecule. In this work, we have investigated the intermolecular interaction between H2 and individual vanadyl phthalocyanine (VOPc) molecules on Au(111) substrates by using STM and non-contact atomic force microscopy (NC-AFM). We measured tunnelling spectra and random telegraphic noise (RTN) on VOPc molecules to reveal the origin of the dynamic behavior of the H2. The tunnelling spectra show switching between two states with different tunnelling conductance as a function of sample bias voltage and RTN is measured near transition voltage between the two states. The spatial variation of the RTN indicates that the two-state fluctuation is dependent on the atomic-scale interaction of H2 with the VOPc molecule. Density functional theory calculations show that a H2 molecule can be trapped by a combination of a tip-induced electrostatic potential well and the potential formed by a VOPc underneath. We suggest the origin of the two-state noise as transition of H2 between minima in these potentials with barrier height of 20-30 meV. In addition, the bias dependent AFM images verify that H2 can be trapped and released at the tip-sample junction.

Hypothetical Efficiency of Electrical to Mechanical Energy Transfer during Individual Stochastic Molecular Switching Events

There are now many examples of single molecule rotors, motors, and switches in the literature that, when driven by photons, electrons, or chemical reactions, exhibit well-defined motions. As a step toward using these single molecule devices to perform useful functions, one must understand how they interact with their environment and quantify their ability to perform work on it. Using a single molecule rotary switch, we examine the transfer of electrical energy, delivered via electron tunneling, to mechanical motion and measure the forces the switch experiences with a noncontact q-plus atomic force microscope. Action spectra reveal that the molecular switch has two stable states and can be excited resonantly between them at a bias of 100 mV via a one-electron inelastic tunneling process which corresponds to an energy input of 16 zJ. While the electrically induced switching events are stochastic and no net work is done on the cantilever, by measuring the forces between the molecular switch and the AFM cantilever, we can derive the maximum hypothetical work the switch could perform during a single switching event, which is ∼55 meV, equal to 8.9 zJ, which translates to a hypothetical efficiency of ∼55% per individual inelastic tunneling electron-induced switching event. When considering the total electrical energy input, this drops to 1 × 10^-7% due to elastic tunneling events that dominate the tunneling current. However, this approach constitutes a general method for quantifying and comparing the energy input and output of molecular-mechanical devices.

Quantum Otto engine working with interacting spin systems: Finite power performance in stochastic thermodynamics

A quantum Otto engine using two-interacting spins as its working medium is analyzed within framework of stochastic thermodynamics. The time-dependent power fluctuations and average power are explicitly derived for a complete cycle of engine operation. We find that the efficiency and power fluctuations are affected significantly by interparticle interactions, but both of them become interaction-independent under maximal power via optimizing the external control parameter. The behavior of the efficiency at maximum power is further explained by analyzing the optimal protocol of the engine.

Quantum dissipation driven by electron transfer within a single molecule investigated with atomic force microscopy

Intramolecular charge transfer processes play an important role in many biological, chemical and physical processes including photosynthesis, redox chemical reactions and electron transfer in molecular electronics. These charge transfer processes are frequently influenced by the dynamics of their molecular or atomic environments, and they are accompanied with energy dissipation into this environment. The detailed understanding of such processes is fundamental for their control and possible exploitation in future technological applications. Most of the experimental studies of the intramolecular charge transfer processes so far have been carried out using time-resolved optical spectroscopies on large molecular ensembles. This hampers detailed understanding of the charge transfer on the single molecular level. Here we build upon the recent progress in scanning probe microscopy, and demonstrate the control of mixed valence state. We report observation of single electron transfer between two ferrocene redox centers within a single molecule and the detection of energy dissipation associated with the single electron transfer.

Here, the authors use atomic force microscopy under ultra-high vacuum conditions to study intramolecular single electron transfer within a single molecule. This allows them to investigate energy dissipation process related to the electron transfer as a function of temperature.

A Single Hydrogen Molecule as an Intensity Chopper in an Electrically Driven Plasmonic Nanocavity

Photon statistics is a powerful tool for characterizing the emission dynamics of nanoscopic systems and their photophysics. Recent advances that combine correlation spectroscopy with scanning tunneling microscopy induced luminescence (STML) have allowed the measurement of the emission dynamics from individual molecules and defects, demonstrating their nature as single-photon emitters. The application of correlation spectroscopy to the analysis of the dynamics of a well-characterized adsorbate system in an ultrahigh vacuum remained to be demonstrated. Here, we combine single-photon time correlations with STML to measure the dynamics of individual H₂ molecules between a gold tip and an Au(111) surface. An adsorbed H₂ molecule performs recurrent excursions below the tip apex. We use the fact that the presence of the H₂ molecule in the junction modifies plasmon emission to study the adsorbate dynamics. Using the H₂ molecule as a chopper for STM-induced optical emission intensity, we demonstrate bunching in the plasmonic photon train in a single measurement over 6 orders of magnitude in the time domain (from microseconds to seconds) that takes only a few seconds. Our findings illustrate the power of using photon statistics to measure the diffusion dynamics of adsorbates with STML.

Single-Atom Heat Machines Enabled by Energy Quantization

Quantization of energy is a quintessential characteristic of quantum systems. Here we analyze its effects on the operation of Otto cycle heat machines and show that energy quantization alone may alter and increase machine performance in terms of output work, efficiency, and even operation mode. We show that this difference in performance occurs in machines with inhomogeneous energy level scaling, while quantum machines with homogeneous level scaling behave like classical machines. Our results demonstrate that quantum thermodynamics enables the realization of classically inconceivable Otto machines, such as those with an incompressible working substance. We propose to measure these effects experimentally using a laser-cooled trapped ion as a microscopic heat machine.

Toward Low-Frequency Mechanical Energy Harvesting Using Energy-Dense Piezoelectrochemical Materials

The piezoelectrochemical coupling between mechanical stress and electrochemical potential is explored in the context of mechanical energy harvesting and shown to have promise in developing high-energy-density harvesters for low-frequency applications (e.g., human locomotion). This novel concept is demonstrated experimentally by cyclically compressing an off-the-shelf lithium-ion battery and measuring the generated electric power output.

Trapping and Characterization of a Single Hydrogen Molecule in a Continuously Tunable Nanocavity

Using inelastic electron tunneling spectroscopy with the scanning tunneling microscope (STM-IETS) and density functional theory calculations (DFT), we investigated properties of a single H2 molecule trapped in nanocavities with controlled shape and separation between the STM tip and the Au (110) surface. The STM tip not only serves for the purpose of characterization, but also is directly involved in modification of chemical environment of molecule. The bond length of H2 expands in the atop cavity, with a tendency of dissociation when the gap closes, whereas it remains unchanged in the trough cavity. The availability of two substantially different cavities in the same setup allows understanding of H2 adsorption on noble metal surfaces and sets a path for manipulating a single chemical bond by design.

Two-level spatial modulation of vibronic conductance in conjugated oligophenylenes on boron nitride

Intramolecular current-induced vibronic excitations are reported in highly ordered monolayers of quaterphenylene dicarbonitriles at an electronically patterned boron nitride on copper platform (BN/Cu(111)). A first level of spatially modulated conductance at the nanometer-scale is induced by the substrate. Moreover, a second level of conductance variations at the molecular level is found. Low temperature scanning tunneling microscopy studies in conjunction with molecular dynamics calculations reveal collective amplification of the molecule's interphenylene torsion angles in the monolayer. Librational modes influencing these torsion angles are identified as initial excitations during vibronic conductance. Density functional theory is used to map phenylene breathing modes and other vibrational excitations that are suggested to be at the origin of the submolecular features during vibronic conductance.

Molecular actuators driven by cooperative spin-state switching

Molecular switches have great potential to convert different forms of energy into mechanical motion; however, their use is often limited by the narrow range of operating conditions. Here we report on the development of bilayer actuator devices using molecular spin crossover materials. Motion of the bilayer cantilever architecture results from the huge spontaneous strain accompanying the spin-state switching. The advantages of using spin crossover complexes here are substantial. The operating conditions used to switch the device can be manipulated through chemical modification, and there are many existing compounds to choose from. Spin crossover materials may be switched by diverse stimuli including light, temperature, pressure, guest molecules and magnetic field, allowing complex input combinations or highly specific operation. We demonstrate the versatility of this approach by fabricating actuators from four different spin crossover materials and by using both thermal variation and light to induce motion in a controlled direction.

Chemistry. A single-molecule engine

A single hydrogen molecule can be used to drive the tip motion of a scanning tunneling microscope.