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arXiv:2505.09428 · Nanoscale Advances

Unraveling spin entanglement using quantum gates with scanning tunneling microscopy-driven electron spin resonance

Eric D. Switzer, José Reina Gálvez, G. Giedke, Talat Shahnaz Rahman, Christoph Wolf, Deung-Jang Choi, Nicolás Lorente

Published Jan 1, 2025• 5 citations
arXivHTMLPDF

Abstract

electron spin resonance combined with scanning tunneling microscopy (ESR-STM). Using two titanium atoms on a MgO/Ag(100) substrate as a model, we construct a two-qubit system whose dynamics are coherently manipulated through tailored microwave pulse sequences. We generate Bell states by implementing a Hadamard gate followed by a controlled-NOT gate, and evaluate its fidelity and concurrence using the quantum-master equation-based code TimeESR. Our results demonstrate that ESR-STM can create entangled states with significant fidelity. This study paves the way for the realization of atom-based quantum circuits and highlights ESR-STM as a powerful tool for probing and engineering entangled states on surfaces.

DOI
10.1039/d5na00421g

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•Jan 1, 2018•41 citations
electron spin resonance combined with scanning tunneling microscopy (ESR-STM). Using two titanium atoms on a MgO/Ag(100) substrate as a model, we construct a two-qubit system whose dynamics are coherently manipulated through tailored microwave pulse sequences. We generate Bell states by implementing a Hadamard gate followed by a controlled-NOT gate, and evaluate its fidelity and concurrence using the quantum-master equation-based code TimeESR. Our results demonstrate that ESR-STM can create entangled states with significant fidelity. This study paves the way for the realization of atom-based quantum circuits and highlights ESR-STM as a powerful tool for probing and engineering entangled states on surfaces.
Electron spin resonance in scanning tunneling microscopy enabled the study of electronic transitions of magnetic impurities on surfaces at the atomic scale. This ESR-STM technique allows to spectroscopically probe and coherently manipulate spins using an all-electrical method without oscillating external magnetic driving fields. Here, we aim to review recent advancements in ESR-STM. We will discuss possible fundamental mechanisms by which the electric field drives spin resonance based on Heisenberg exchange, Kondo scattering, and Anderson impurity models. We validate theoretical predictions against experimental observations, to understand how electronic correlations, spin exchange, and many-body effects manifest in ESR-STM signals. After reviewing coherent spin control in the STM junction, we discuss potential applications of the ESR-STM method for coherent multi-spin control which enables multiple-qubit operations. Finally, we address recent developments in coupled electron-nuclear spin systems, including hyperfine-resolved ESR spectroscopy, and the driving and polarization of nuclear spins in ESR-STM.
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 T2≈T_2\approxT2​≈ 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.
Quantum entanglement permeates the complex ground states of correlated electron materials defying single-particle descriptions. Coupled magnetic atoms have potential as model systems for entanglement in condensed matter giving the opportunity to create artificial many-body states which can be controlled by tuning the underlying interactions. They provide an avenue to unravel the complexities of correlated-electron materials. Here we use low temperature scanning tunnelling microscopy (STM) and atomic manipulation to tune entanglement in chains of magnetic atoms. We find that a Kondo singlet state can emerge from this entanglement. The many electron Kondo state is based on the screening of the entangled spin ground state of the chain by substrate electrons and can be engineered to envelop at least ten magnetic atoms. The concomitant Kondo resonance measured in the differential conductance enables the electric read-out of entanglement. By tuning composition and coupling strength within atomic chains it is possible to create model spin chains with defined entanglement. This lays the foundation for a new class of experiments to construct exotic correlated-electron materials atom by atom.
Manipulation of spin states at the single-atom scale underlies spin-based quantum information processing and spintronic devices. These applications require protection of the spin states against quantum decoherence due to interactions with the environment. While a single spin is easily disrupted, a coupled-spin system can resist decoherence by using a subspace of states that is immune to magnetic field fluctuations. Here, we engineered the magnetic interactions between the electron spins of two spin-1/2 atoms to create a "clock transition" and thus enhance their spin coherence. To construct and electrically access the desired spin structures, we use atom manipulation combined with electron spin resonance (ESR) in a scanning tunneling microscope. We show that a two-level system composed of a singlet state and a triplet state is insensitive to local and global magnetic field noise, resulting in much longer spin coherence times compared with individual atoms. Moreover, the spin decoherence resulting from the interaction with tunneling electrons is markedly reduced by a homodyne readout of ESR. These results demonstrate that atomically precise spin structures can be designed and assembled to yield enhanced quantum coherence.
Individual spin defects in solids are promising building blocks for quantum technologies, but their deterministic creation, individual addressability, and operation near surfaces remain major challenges. Two-dimensional materials provide an attractive alternative, as their single-layer thickness enables direct atomic-scale access to defect states. Here, we demonstrate single-spin control of solid-state defects in a two-dimensional semiconductor by a combination of scanning tunneling microscopy and electron spin resonance. We create and manipulate individual sulfur vacancies and carbon substitution defects in monolayer molybdenum disulfide and characterize their spin dynamics, including coherent control, at the single-defect level. Using atomic manipulation, we further engineer and probe spin-spin interactions between defect pairs. Our results demonstrate deterministic creation, addressability, coherent manipulation, and controlled coupling of individual spin defects within a single experimental platform. This establishes atomically engineered spin defects in two-dimensional semiconductors as a versatile class of controllable solid-state quantum systems and opens a route towards tailored quantum sensing experiments.
Manipulation of spin states at the single-atom scale underlies spin-based quantum information processing and spintronic devices. These applications require protection of the spin states against quantum decoherence due to interactions with the environment. While a single spin is easily disrupted, a coupled-spin system can resist decoherence by using a subspace of states that is immune to magnetic field fluctuations. Here, we engineered the magnetic interactions between the electron spins of two spin-1/2 atoms to create a “clock transition” and thus enhance their spin coherence. To construct and electrically access the desired spin structures, we use atom manipulation combined with electron spin resonance (ESR) in a scanning tunneling microscope. We show that a two-level system composed of a singlet state and a triplet state is insensitive to local and global magnetic field noise, resulting in much longer spin coherence times compared with individual atoms. Moreover, the spin decoherence resulting from the interaction with tunneling electrons is markedly reduced by a homodyne readout of ESR. These results demonstrate that atomically precise spin structures can be designed and assembled to yield enhanced quantum coherence.