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Christoph Wolf

Publications and source records attributed to Christoph Wolf.

28 records · Page 2Linked to original sources

All-electrical driving and probing of dressed states in a single spin

The sub-nanometer distance between tip and sample in a scanning tunneling microscope (STM) enables the application of very large electric fields with a strength as high as ~ 1 GV/m. This has allowed for efficient electrical driving of Rabi oscillations of a single spin on a surface at a moderate radio-frequency (RF) voltage of the order of tens of millivolts. Here, we demonstrate the creation of dressed states of a single electron spin localized in the STM tunnel junction by using resonant RF driving voltages. The read-out of these dressed states was achieved all-electrical by a weakly coupled probe spin. Our work highlights the strength of the atomic-scale geometry inherent to the STM that facilitates creation and control of dressed states, which are promising for a design of atomically well-defined single spin quantum devices on surfaces.

cond-mat.mes-hall↗

Protocol for certifying entanglement in surface spin systems using a scanning tunneling microscope

Certifying quantum entanglement is a critical step towards realizing quantum-coherent applications of surface spin systems. In this work, we show that entanglement can be unambiguously shown in a scanning tunneling microscope (STM) with electron spin resonance by exploiting the fact that entangled states undergo a free time evolution with a distinct characteristic time constant that clearly distinguishes it from any other time evolution in the system. By implementing a suitable phase control scheme, the phase of this time evolution can be mapped back onto the population of one entangled spin in a pair, which can then be read out reliably using a weakly coupled sensor spin in the junction of the scanning tunneling microscope. We demonstrate through open quantum system simulations with realistic spin systems, which are currently available with spin coherence times of $T_2\approx$ 300 ns, that a signal directly correlated with the degree of entanglement can be measured at a temperature range of 100$-$400 mK accessible in sub-Kelvin cryogenic STM systems.

cond-mat.mes-hall↗

Electric-field-driven spin resonance by on-surface exchange coupling to a single-atom magnet

Coherent control of individual atomic and molecular spins on surfaces has recently been demonstrated by using electron spin resonance (ESR) in a scanning tunneling microscope (STM). Here we present a combined experimental and modeling study of the ESR of a single hydrogenated Ti atom that is exchange-coupled to a Fe adatom located in 0.6-0.8 nm away. Continuous wave and pulsed ESR of the Ti spin showed a Rabi rate with two contributions, one from the tip and the other from the Fe, whose spin interactions with Ti were modulated by the radio-frequency electric field. The Fe contribution is comparable to the tip, as revealed from its dominance when the tip was retracted, and tunable using a vector magnetic field. Our new ESR scheme allows on-surface individual spins to be addressed and coherently controlled without the need for magnetic interaction with a tip. This study establishes a feasible implementation of spin-based multi-qubit systems on surfaces.

cond-mat.mes-hall↗

Many-body non-equilibrium effects in all-electric electron spin resonance

Motivated by recent developments in measurements of electron spin resonances of individual atoms and molecules with the scanning tunneling microscope (ESR-STM), we study electron transport through an impurity under periodic driving as a function of the transport parameters in a model junction. The model consists of a single-orbital quantum impurity connected to two electrodes via time-dependent hopping terms. The hopping terms are treated at the lowest order in perturbation theory to recover a Lindblad-like quantum master equation with electron transport. As in the experiment, the ESR-STM signal is given by the variation of the long-time DC current with the driving frequency. The density-matrix coherences play an important role in the evaluation of the ESR-STM signal. Electron correlation is included in our impurity mode. The charging energy $U$ has significant influence on the spin dynamics depending on the sign and magnitude of the applied DC bias. Our model allows direct insight into the origin of the ESR signal from the many-body dynamics of the impurity.

cond-mat.mes-hall↗

An electron-spin qubit platform assembled atom-by-atom on a surface

Creating a quantum-coherent architecture at the atomic scale has long been an ambition in quantum science and nanotechnology. This ultimate length scale requires the use of fundamental quantum properties of atoms, such as the spin of electrons, which naturally occurs in many solid-state environments and allows high-fidelity operations and readout by electromagnetic means. Despite decades of effort, however, it remains a formidable task to realize an atomic-scale quantum architecture where multiple electron spin qubits can be precisely assembled, controllably coupled, and coherently operated. Electron spin qubits created in dopants in semiconductors and color centers in insulators, for example, can be well controlled individually6-8 but are difficult to couple together into a circuit. On the other hand, multiple magnetic atoms and molecules on surfaces can be coupled to each other by building sophisticated atomic structures using a scanning tunneling microscope (STM), but coherent operation has so far been limited to a single qubit in the tunnel junction. Here we demonstrate an atomic-scale qubit platform by showing atom-by-atom construction, coherent operations, and readout of multiple electron-spin qubits on a surface. To enable the coherent control of remote qubits that are outside the tunnel junction, we complement each electron spin with a local magnetic field gradient from a nearby single-atom magnet. To enable readout of remote qubits, we employ a sensor qubit in the tunnel junction and implement pulsed double electron spin resonance. Using these methods, we demonstrate fast single-, two-, and three-qubit operations in an all-electrical fashion. Our work marks the creation of an Angstrom-scale qubit platform, where quantum functionalities using electron spin arrays, built atom-by-atom on a surface, are now within reach.

cond-mat.mes-hall↗

Anisotropic hyperfine interaction of surface-adsorbed single atoms

Hyperfine interactions between electron and nuclear spins have been widely used in material science, organic chemistry, and structural biology as a sensitive probe to the local chemical environment through spatial identification of nuclear spins. With the nuclear spins identified, the isotropic and anisotropic components of the hyperfine interactions in turn offer unique insight into the electronic ground-state properties of the paramagnetic centers. However, traditional ensemble measurements of hyperfine interactions average over a macroscopic number of spins with different geometrical locations and nuclear isotopes. Here, we use a scanning tunneling microscope (STM) combined with electron spin resonance (ESR) to measure hyperfine spectra of hydrogenated-titanium (Ti) atoms on MgO/Ag(100) and thereby determine the isotropic and anisotropic hyperfine interactions at the single-atom level. By combining vector-field ESR spectroscopy with STM-based atom manipulation, we characterize the full hyperfine tensor of individual Ti-47 and Ti-49 atoms and identify significant spatial anisotropy of hyperfine interaction for both isotopes when they are adsorbed at low-symmetry binding sites. Density functional theory calculations reveal that the large hyperfine anisotropy arises from a highly anisotropic distribution of the ground-state electron spin density. Our work highlights the power of ESR-STM-enabled single-atom hyperfine spectroscopy as a powerful tool in revealing ground-state electronic structures and atomic-scale chemical environments with nano-electronvolt resolution.

cond-mat.mes-hall↗

Spin Resonance Amplitude and Frequency of a Single Atom on a Surface in a Vector Magnetic Field

We used electron spin resonance (ESR) combined with scanning tunneling microscopy (STM) to measure hydrogenated Ti (spin-1/2) atoms at low-symmetry binding sites on MgO in vector magnetic fields. We found strongly anisotropic g-values in all three spatial directions. Interestingly, the amplitude and lineshape of the ESR signals are also strongly dependent on the angle of the field. We conclude that the Ti spin is aligned along the magnetic field, while the tip spin follows its strong magnetic anisotropy. Our results show the interplay between the tip and surface spins in determining the ESR signals and highlight the precision of ESR-STM to identify the single atom's spin states.

cond-mat.mes-hall↗

Epidemics with Behavior

We study equilibrium distancing during epidemics. Distancing reduces the individual's probability of getting infected but comes at a cost. It creates a single-peaked epidemic, flattens the curve and decreases the size of the epidemic. We examine more closely the effects of distancing on the outset, the peak and the final size of the epidemic. First, we define a behavioral basic reproduction number and show that it is concave in the transmission rate. The infection, therefore, spreads only if the transmission rate is in the intermediate region. Second, the peak of the epidemic is non-monotonic in the transmission rate. A reduction in the transmission rate can lead to an increase of the peak. On the other hand, a decrease in the cost of distancing always flattens the curve. Third, both an increase in the infection rate as well as an increase in the cost of distancing increase the size of the epidemic. Our results have important implications on the modeling of interventions. Imposing restrictions on the infection rate has qualitatively different effects on the trajectory of the epidemics than imposing assumptions on the cost of distancing. The interventions that affect interactions rather than the transmission rate should, therefore, be modeled as changes in the cost of distancing.

econ.GN↗

Orbital-resolved single atom magnetism measured with X-ray absorption spectroscopy

Lanthanide atoms and molecules are promising candidates for atomic data storage and quantum logic due to the long magnetic lifetime of their electron quantum states. Accessing these states through electrical transport requires the engineering of their electronic configuration down to the level of individual atomic orbitals. Here, we address the magnetism of surface-supported lanthanide atoms, clusters, and films with orbital selectivity using X-ray absorption spectroscopy and magnetic circular dichroism. We exploit the selection rules of electric dipole transitions to reveal the occupation and magnetism of the valence electrons of Gd and Ho deposited on MgO/Ag(100). Comparing our results with multiplet calculations and density functional theory, we identify a charge transfer mechanism that leaves the lanthanide species in an unconventional singly ionized configuration. Our approach allows determining the role of valence electrons on the quantum level structure of lanthanide-based nanostructures.

cond-mat.mes-hall↗

Compressive Time-of-Flight 3D Imaging Using Block-Structured Sensing Matrices

Spatially and temporally highly resolved depth information enables numerous applications including human-machine interaction in gaming or safety functions in the automotive industry. In this paper, we address this issue using Time-of-flight (ToF) 3D cameras which are compact devices providing highly resolved depth information. Practical restrictions often require to reduce the amount of data to be read-out and transmitted. Using standard ToF cameras, this can only be achieved by lowering the spatial or temporal resolution. To overcome such a limitation, we propose a compressive ToF camera design using block-structured sensing matrices that allows to reduce the amount of data while keeping high spatial and temporal resolution. We propose the use of efficient reconstruction algorithms based on l^1-minimization and TV-regularization. The reconstruction methods are applied to data captured by a real ToF camera system and evaluated in terms of reconstruction quality and computational effort. For both, l^1-minimization and TV-regularization, we use a local as well as a global reconstruction strategy. For all considered instances, global TV-regularization turns out to clearly perform best in terms of evaluation metrics including the PSNR.

math.NA↗