Hyperfine coupled spins with time evolution readout

Project Information

HYPSTER

Grant agreement ID: 101095574

DOI

10.3030/101095574

EC signature date 8 August 2023

Start date 1 January 2024

End date 31 December 2028

Funded under

• European Research Council (ERC)

Total cost

€ 2 498 741,00

EU contribution

€ 2 498 741,00

Coordinated by

TECHNISCHE UNIVERSITEIT DELFT
Netherlands

Periodic Reporting for period 1 - HYPSTER (Hyperfine coupled spins with time evolution readout)

Reporting period: 2024-01-01 to 2026-06-30

Summary of the context and overall objectives of the project

The counterintuitive laws of quantum mechanics manifest themselves prominently on the scale of individual atoms. In particular, the magnetism of the atom shows fascinating quantum behavior, where spins can be in superposition states and entangle with each other.

Scanning tunneling microscopy (STM) allows for addressing individual magnetic atoms and accessing this intriguing quantum world. The STM approach comes with one downside, however, which is that it requires electric (tunneling) contacts to the outside world. These contacts cause the spin states of the electrons on the atom to decohere (i.e. lose their quantum information) within a short period of time.

In HYPSTER, we strive to gain access to the nuclear spins of individual atoms. Nuclear spins are much better isolated from their environments than electron spins and are also much less sensitive to local magnetic field fluctuations. Gaining insight into their behavior contributes to our level of control of nuclear spin for quantum information purposes as well as to our understanding of the emergence of magnetism on macroscopic length scales.

The general idea of all experiments performed as part of this project is to initialize a nuclear spin in a specific state, then leave it untouched as much as possible as its quantum state evolves over time, until after a set time we readout its final state. During the free evolution time, we allow the nuclear spin to engage with other spins in a controllable fashion. These can be other nuclear spins, but more generally electron spins that themselves may be connected to other nuclear spins.

These experiments are highly challenging, as they not only require exquisite control over the positions of individual atoms with sub-nanometer precision, but also control over the voltage signals that are sent to and received from the atoms on sub-nanosecond time scales.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Before the start of this project, our group had recently demonstrated the ability to observe the free coherent oscillation of an electron spin coupled to a second electron spin on an adjacent atom. For this purpose, we had developed a measurement scheme that combines electron spin resonance (ESR) and pump-probe spectroscopy.

Our first objective as part of HYPSTER was to modify that methodology in such a way that it could be used to observe the coherent motion of and electron spin coupled to a nuclear spin on the same atom. As a result of the hyperfine interaction, the spins are then expected to perform flip-flop oscillations, where a spin excitation is exchanged back and forth between the two spins.

This idea came with two major challenges. First, due to the small hyperfine splitting, all nuclear spin states (we typically work with 47Ti and 49Ti isotopes, carrying nuclear spins of 5/2 and 7/2 respectively) have equal thermal population even at our cryogenic measurement temperature of 1 K. In order to initiate a flip-flop interaction, we needed to ‘pump’ the nuclear spin into one particular magnetization state. We demonstrated empirically that it was possible to do so by applying an extended voltage pulse generating a spin-polarized current. While we have a general understanding of how this mechanism works, an in-depth analysis of what is at play in the framework of spin torque is basis for follow-up research.

Second, again resulting from the weak hyperfine interaction, the avoided level crossings the give rise to coherent dynamics occur at very low field values. This implied that we not only needed to reduce the external magnetic field strength to just 15 mT (thus limiting our spin-polarized contrast), but also had to pull back the tip in order to minimize the tip-induced magnetic field (thus limiting our signal-to-noise ratio).

Despite these major challenges, we managed to perform the experiment, which yielded a very rich oscillatory pattern of the electron spin. By performing Lindblad calculations, we were able to identify each observed frequency and associate it with a specific hybridization between two quantum states of the combined electron-nuclear spin system. This work was published in Nature Communications in 2024.

In a second experiment, we focused on the energy relaxation time of a nuclear spin. While STM measurements are typically slow compared to the switching time of spins, ideally at any given moment, there should be only one ESR peak at a single frequency corresponding to the nuclear spin state that is occupied at that moment. We therefore optimized our noise levels and managed to bring down the integration time of our current measurement to 20 ms. This turned out to be sufficiently short to observe stochastic switching (telegraph noise) of the nuclear resonance frequency.

We subsequently devised a pulsed measurement scheme, where in two consecutive pulses we ‘interrogated’ the nuclear spin as to whether it occupied the probed state or not. For measurements where the outcome for pulses was positive, we performed statistics. This eventually allowed us to determine the relaxation time T1 of the nuclear to be as long as 5 seconds.

By offering various voltage signals (both DC and AC, varying both amplitude and frequency) in the wait time between the two probe pulses, we were able to gain additional insight into what mechanisms affect the lifetime. This work was published in Nature Communications in 2025.

A third experiment revolved around the ability to perform electron-nuclear double resonance (ENDOR) on a single atom. In an ENDOR experiment, two frequencies are offered to simultaneously drive both the electron and nuclear spins. In particular, this concept allows for using the electronic (ESR) signal to independently verify the effect of the nuclear (NMR) driving.

We implemented this concept and were able confirm independent NMR driving up to magnetic fields of 1.5 T, corresponding to an electric Zeeman energy that is two orders of magnitude stronger than the hyperfine interaction. At this field, the system is detuned very far away from any hyperfine-induced avoided crossing, in a regime where it is fully justified to treat the electron and nuclear spins as separate entities. In the ensuing manuscript, which is currently under review, we discuss a number of driving mechanisms that could explain these observations.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

All results described above to beyond the state of the art. Yet, there is a specific aspect to this work that is worth mentioning as an achievement of its own, which is the ability to perform sub-nanosecond pulsed experiments in an STM configuration. In particular the combination of DC and AC pulses, which are offered within a single pulse train as part of a measurement protocol, poses a significant challenge to STM researchers.

In the early stages of HYPSTER, we decided that, rather than making use of a combination of a pulse generator and an RF generator, our best strategy to approach this challenge was by programming all signals directly using an arbitrary waveform generator (AWG). Using this equipment, we have performed various tests to characterize the transmission lines of our STM systems and to optimize the temporal resolution of our measurements. These findings, which are reported in the Methods sections of our publications, can be readily used and adopted by other groups in our research field.