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A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. However, accurately measuring these rates poses a significant challenge, especially when they span a wide range of time scales. Here we introduce a broadband measurement method, called stochastic resonance spectroscopy (SRS), that operates in the frequency domain and quantifies the stochastic dynamics of atomic-scale quantum systems. We apply this method to determine spin switching rates in a scanning tunneling microscope over an extremely wide frequency range, from 199 ms^-1 for few-atom structures to 1.73 ns^-1 for individual atoms. SRS relies on the universal phenomenon of stochastic resonance which synchronizes stochastic dynamics to an oscillating perturbation. We develop an analytical theory that extracts quantitative transition rates from scanning tunneling microscopy measurements of the frequency-dependent tunnel current and show that the signal is dominated by homodyne detection. Our theory indicates that SRS is not limited to spin dynamics and we corroborate this by measuring transport dynamics through a bound state in a superconductor. We anticipate that the ability to characterize broadband stochastic dynamics at the atomic scale will enable insights into excited-state dynamics of quantum systems and even non-Markovian processes emerging from correlations with the environment., Comment: 12 pages, 5 figures

The nuclear spin, being much more isolated from the environment than its electronic counterpart, enables quantum experiments with prolonged coherence times and presents a gateway towards uncovering the intricate dynamics within an atom. These qualities have been demonstrated in a variety of nuclear spin qubit architectures, albeit with limited control over the direct environment of the nuclei. As a contrasting approach, the combination of electron spin resonance (ESR) and scanning tunnelling microscopy (STM) provides a bottom-up platform to study the fundamental properties of nuclear spins of single atoms on a surface. However, access to the time evolution of these nuclear spins, as was recently demonstrated for electron spins, remained a challenge. Here, we present an experiment resolving the nanosecond coherent dynamics of a hyperfine-driven flip-flop interaction between the spin of an individual nucleus and that of an orbiting electron. We use the unique local controllability of the magnetic field emanating from the STM probe tip to bring the electron and nuclear spins in tune, as evidenced by a set of avoided level crossings in ESR-STM. Subsequently, we polarize both spins through scattering of tunnelling electrons and measure the resulting free evolution of the coupled spin system using a DC pump-probe scheme. The latter reveals a complex pattern of multiple interfering coherent oscillations, providing unique insight into the atom's hyperfine physics. The ability to trace the coherent hyperfine dynamics with atomic-scale structural control adds a new dimension to the study of on-surface spins, offering a pathway towards dynamic quantum simulation of low-dimensional magnonics.

Historically, electron spin resonance (ESR) has provided excellent insight into the electronic, magnetic, and chemical structure of samples hosting spin centers. In particular, the hyperfine interaction between the electron and the nuclear spins yields valuable structural information of these centers. In recent years, the combination of ESR and scanning tunneling microscopy (ESR-STM) has allowed to acquire such information on individual spin centers of magnetic atoms bound atop a surface, while additionally providing spatial information about the binding site. Here, we conduct a full angle-dependent investigation of the hyperfine splitting for individual titanium atoms on MgO/Ag(001) by measurements in a vector magnetic field. We observe strong anisotropy in both the g-factor and the hyperfine tensor. Combining the results of the hyperfine splitting with the symmetry properties of the binding site obtained from STM images and a basic point charge model allows us to predict the shape of the electronic ground state configuration of the titanium atom. Relying on experimental values only, this method paves the way for a new protocol for electronic structure analysis for spin centers on surfaces.

Atomically engineered artificial lattices are a useful tool for simulating complex quantum phenomena, but have so far been limited to the study of Hamiltonians where electron-electron interactions do not play a role -- but it's precisely the regime in which these interactions do matter where computational times lend simulations a critical advantage over numerical methods. Here, we propose a new platform for constructing artificial matter that relies on the confinement of field-emission resonances, a class of vacuum-localized discretized electronic states. We use atom manipulation of surface vacancies in a chlorine-terminated Cu(100) surface to reveal square patches of the underlying metal, thereby creating atomically-precise potential wells that host particle-in-a-box modes. By adjusting the shape and size of the confining potential, we can access states with different quantum numbers, making these patches attractive candidates as quantum dots or artificial atoms. We demonstrate that the lifetime of electrons in these engineered states can be extended and tuned through modification of the confining potential, either via atomic assembly or by changing the tip-sample distance. We also demonstrate control over a finite range of state-filling, a parameter which plays a key role in the evolution of quantum many-body states. We model the transport through the localized state to disentangle and quantify the lifetime-limiting processes, illustrating the critical dependency of the electron lifetime on the properties of the underlying bulk band structure. The interplay with the bulk bands also gives rise to negative differential resistance, opening possible avenues for engineering custom atomic-scale resonant tunnelling diodes, which exhibit similar current-voltage characteristics.

Differential conductance spectroscopy performed in the high bias regime -- in which the applied voltage exceeds the sample work function -- is a poor measure of the local density of states due to the effects of the changing tunnel barrier. Additionally, the large applied voltage oftentimes makes constant-height measurement experimentally impractical, lending constant-current spectroscopy an advantageous edge; but the differential conductance in that case is even further removed from the local density of states due to the changing tip height. Here, we present a normalization scheme for extracting the local density of states from high bias scanning tunneling spectroscopy, obtained in either constant-current or constant-height mode. We extend this model to account for the effects of the in-plane momentum of the probed states to the overall current. We demonstrate the validity of the proposed scheme by applying it to laterally confined field-emission resonances, which appear as peak-shaped spectroscopic features with a well-defined in-plane momentum.

Full insight into the dynamics of a coupled quantum system depends on the ability to follow the effect of a local excitation in real-time. Here, we trace the coherent evolution of a pair of coupled atomic spins by means of scanning tunneling microscopy. We use a pump-probe scheme to detect the local magnetization following a current-induced excitation performed on one of the spins. Making use of magnetic interaction with the probe tip, we are able to tune the relative precession of the spins. We show that only if their Larmor frequencies match, the two spins can entangle, causing the excitation to be swapped back and forth. These results provide insight into the locality of electron-spin scattering, and set the stage for controlled migration of a quantum state through an extended spin lattice.

Magnetic adsorbates on superconductors induce a Kondo resonance outside and Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. When probed by scanning tunneling spectroscopy, the associated differential-conductance spectra frequently exhibit characteristic bias-voltage asymmetries. Here, we observe correlated variations of Kondo and YSR asymmetries across an Fe-porphyrin molecule adsorbed on Pb(111). We show that both asymmetries originate in interfering tunneling paths via a spin-carrying orbital and the highest occupied molecular orbital (HOMO). Strong evidence for this model comes from nodal planes of the HOMO, where tunneling reveals symmetric Kondo and YSR resonances. Our results establish an important mechanism for the asymmetries of Kondo and YSR lineshapes.

The exchange scattering at magnetic adsorbates on superconductors gives rise to Yu-Shiba-Rusinov (YSR) bound states. Depending on the strength of the exchange coupling, the magnetic moment perturbs the Cooper pair condensate only weakly, resulting in a free-spin ground state, or binds a quasiparticle in its vicinity, leading to a (partially) screened spin state. Here, we use the flexibility of Fe-porphin molecules adsorbed on a Pb(111) surface to reversibly and continuously tune between these distinct ground states. We find that the FeP moment is screened in the pristine adsorption state. Approaching the tip of a scanning tunneling microscope, we exert a sufficiently strong attractive force to tune the molecule through the quantum phase transition into the free-spin state. We ascertain and characterize the transition by investigating the transport processes as function of tip-molecule distance, exciting the YSR states by single-electron tunneling as well as (multiple) Andreev reflections.