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Physics Letters A

Electron spin resonance as a probe to measure the possible discrete nature of time as a dynamical variable

C. Wolf

Published Aug 1, 1987• 18 citations
Publisher
DOI
10.1016/0375-9601(87)90061-2

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Time as a dynamical variable in quantum decay

Rafael de la Madrid

Nuclear Physics A•Jun 17, 2013•7 citations

On the interpretation of Hahn echo measurements in electron spin resonance scanning tunneling microscopy

Paul Greule, Wantong Huang, Máté Stark +5 more

Electron spin resonance scanning tunneling microscopy (ESR-STM) has become a powerful tool for probing spin dynamics and coherence of individual atoms and molecules on surfaces. In this work, we perform Rabi oscillation and Hahn echo pulse protocols on individual iron phthalocyanine (FePc) molecules on MgO/Ag(001) using ESR-STM. While Hahn echo protocols are widely used to extract spin coherence times, we show that in ESR-STM they are particularly susceptible to misinterpretation due to tunneling electrons generated by the applied radio-frequency (RF) voltage. The RF voltage not only drives the spin, but simultaneously probes and relaxes it, which consequently leads to an exponential decay that reflects spin relaxation rather than intrinsic phase coherence. We moreover show that varying both delay times in the refocusing pulse sequence is a reliable way to ensure a coherent nature of the echo signal. The extracted decay for the latter protocol suggests that T2 is approximately 30 ns and is thus closer to the decoherence time observed in Rabi oscillation measurements. This is significantly shorter than values reported in previous echo measurements. Our findings underscore the need for caution in interpreting T2 times from Hahn echo and Carr-Purcell protocols in ESR-STM and provide practical criteria for distinguishing true spin echoes from tunneling-induced relaxometry signals.

cond-mat.mes-hallCross-listedarXiv:2603.26255•Mar 30, 2026

Designing a quantum computer based on pulsed electron spin resonance

Gavin W. Morley

Electron spin resonance (ESR) experiments are used to assess the possibilities for processing quantum information in the electronic and nuclear spins of endohedral fullerenes. It is shown that ¹⁵N@C₆₀ can be used for universal two-qubit quantum computing. The first step in this scheme is to initialize the nuclear and electron spins that each store one qubit. This was achieved with a magnetic field of 8.6 T at 3 K, by applying resonant RF and microwave radiation. This dynamic nuclear polarization technique made it possible to show that the nuclear T₁ time of ¹⁵N@C����� is on the order of twelve hours at 4.2 K. The electronic T₂ is the limiting decoherence time for the system. At 3.7 K, this can be extended to 215 μs by using amorphous sulphur as the solvent. Pulse sequences are described that could perform all single-qubit gates to the two qubits independently, as well as CNOT gates. After these manipulations, the value of the qubits should be measured. Two techniques are demonstrated for this, by measuring the nuclear spin. Sc@C₈₂ could also be useful for quantum computation. By comparing ESR measurements with density functional theory calculations, it is shown how the orientation of a Sc@C₈₂ molecule in an applied magnetic field affects the molecule's Zeeman and hyperfine coupling. Hence the g- and A-tensors are written in the coordinate frame of the molecule. Pulsed ESR measurements show that the decoherence time at 20 K is 13 μs, which is 20 times longer than had been previously reported. Carbon nanotubes have been filled with endohedral fullerenes, forming 1D arrays that could lead to a scalable quantum computer. N@C₆₀ and Sc@C₈₂ have been used for this filling in various concentrations. ESR measurements of these samples are consistent with simulations of the dipolar coupling.

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Quantum Dynamics in the Proper Time

Zbigniew Haba

Springer eBooks•Jul 4, 2007•0 citations

Spin-orbit and angle-resolved resonant attosecond photoionization delays

Dhruba J. Biswas, J. K. Wood, Nisnat Chakraborty +2 more

Understanding how spin-orbit coupling shapes ultrafast electron dynamics remains a central challenge across atomic, molecular, and condensed-matter systems. Here, we demonstrate that spin-orbit splitting in krypton naturally separates two distinct regimes of attosecond interferometry: a conventional above-threshold process involving interference between continuum pathways and an under-threshold regime in which discrete and continuum intermediate states coexist and interfere. Using spin-orbit and angle-resolved measurements with attosecond precision, supported by time-dependent simulations, we reveal that the under-threshold channel exhibits dramatic phase and delay variations—up to several hundred attoseconds—highly sensitive to photon energy and emission direction. In contrast, the conventional above-threshold channel shows smooth, featureless behavior. This duality exposes the strong influence of metastable resonances, establishing spin-orbit splitting as a built-in control knob for accessing structured continua. Beyond krypton, our results provide a broadly applicable framework for probing and controlling coupled spin, orbital, and many-body correlation dynamics at the attosecond timescale.

Physical Review Research•Mar 22, 2026•1 citation

Deriving Spin within a Discrete-Time Theory

Erasmo Recami, Giovanni Salesi

arXiv:quant-ph/0512113•Foundations of Physics•Jan 18, 2007•0 citations
Electron spin resonance scanning tunneling microscopy (ESR-STM) has become a powerful tool for probing spin dynamics and coherence of individual atoms and molecules on surfaces. In this work, we perform Rabi oscillation and Hahn echo pulse protocols on individual iron phthalocyanine (FePc) molecules on MgO/Ag(001) using ESR-STM. While Hahn echo protocols are widely used to extract spin coherence times, we show that in ESR-STM they are particularly susceptible to misinterpretation due to tunneling electrons generated by the applied radio-frequency (RF) voltage. The RF voltage not only drives the spin, but simultaneously probes and relaxes it, which consequently leads to an exponential decay that reflects spin relaxation rather than intrinsic phase coherence. We moreover show that varying both delay times in the refocusing pulse sequence is a reliable way to ensure a coherent nature of the echo signal. The extracted decay for the latter protocol suggests that T2 is approximately 30 ns and is thus closer to the decoherence time observed in Rabi oscillation measurements. This is significantly shorter than values reported in previous echo measurements. Our findings underscore the need for caution in interpreting T2 times from Hahn echo and Carr-Purcell protocols in ESR-STM and provide practical criteria for distinguishing true spin echoes from tunneling-induced relaxometry signals.
Electron spin resonance (ESR) experiments are used to assess the possibilities for processing quantum information in the electronic and nuclear spins of endohedral fullerenes. It is shown that ¹⁵N@C₆₀ can be used for universal two-qubit quantum computing. The first step in this scheme is to initialize the nuclear and electron spins that each store one qubit. This was achieved with a magnetic field of 8.6 T at 3 K, by applying resonant RF and microwave radiation. This dynamic nuclear polarization technique made it possible to show that the nuclear T₁ time of ¹⁵N@C����� is on the order of twelve hours at 4.2 K. The electronic T₂ is the limiting decoherence time for the system. At 3.7 K, this can be extended to 215 μs by using amorphous sulphur as the solvent. Pulse sequences are described that could perform all single-qubit gates to the two qubits independently, as well as CNOT gates. After these manipulations, the value of the qubits should be measured. Two techniques are demonstrated for this, by measuring the nuclear spin. Sc@C₈₂ could also be useful for quantum computation. By comparing ESR measurements with density functional theory calculations, it is shown how the orientation of a Sc@C₈₂ molecule in an applied magnetic field affects the molecule's Zeeman and hyperfine coupling. Hence the g- and A-tensors are written in the coordinate frame of the molecule. Pulsed ESR measurements show that the decoherence time at 20 K is 13 μs, which is 20 times longer than had been previously reported. Carbon nanotubes have been filled with endohedral fullerenes, forming 1D arrays that could lead to a scalable quantum computer. N@C₆₀ and Sc@C₈₂ have been used for this filling in various concentrations. ESR measurements of these samples are consistent with simulations of the dipolar coupling.
Understanding how spin-orbit coupling shapes ultrafast electron dynamics remains a central challenge across atomic, molecular, and condensed-matter systems. Here, we demonstrate that spin-orbit splitting in krypton naturally separates two distinct regimes of attosecond interferometry: a conventional above-threshold process involving interference between continuum pathways and an under-threshold regime in which discrete and continuum intermediate states coexist and interfere. Using spin-orbit and angle-resolved measurements with attosecond precision, supported by time-dependent simulations, we reveal that the under-threshold channel exhibits dramatic phase and delay variations—up to several hundred attoseconds—highly sensitive to photon energy and emission direction. In contrast, the conventional above-threshold channel shows smooth, featureless behavior. This duality exposes the strong influence of metastable resonances, establishing spin-orbit splitting as a built-in control knob for accessing structured continua. Beyond krypton, our results provide a broadly applicable framework for probing and controlling coupled spin, orbital, and many-body correlation dynamics at the attosecond timescale.