Periodic Reporting for period 3 - QFAST (Quantum Fast Spin dynamics addressed by High-Tc superconducting circuits)
Reporting period: 2024-09-01 to 2026-02-28
Summary of the context and overall objectives of the project
QFaST aims to address the quantum properties of quantized spin waves (or magnons) in magnetic textures, which have not been explored so far in the context of quantum and cavity magnonics.
The field of quantum magnonics focuses on leveraging magnonic excitations to achieve challenging tasks relevant for quantum computing, sensing and communication, such as optical-to-microwave transduction or the coherent coupling of spin qubits. This field is relatively new and has benefited from techniques originally developed in the context of quantum optics, such as cavity/circuit quantum electrodynamics. Using these tools, only quasi-homogeneous magnon modes have been studied thus far. In particular, most experimental studies focus on the infinite wavelength Kittel mode that arises in ferromagnets under the influence of external magnetic fields. Also of interest is the study of spin waves in antiferromagnetic materials, where in-phase and out-of-phase magnetization modes emerge. All these sytems essentially behave as magnetic resonators, with mode volume scaling with the physical volume of the magnet. Although very attractive, these approaches always rely on the use of external magnetic fields.
Interestingly, the solid state offers other types of magnetic excitations that arise in magnetic textures confined in nanoscopic regions behaving as quasiparticles such as, e.g. i) domain walls between regions with opposite magnetization, ii) chiral or non-chiral skyrmions in materials where a nanoscopic core with out-of-plane magnetization is surrounded by opposite magnetization, iii) twists of magnetization in materials with Dzyaloshinskii-Moriya interaction under the influence of an external magnetic field, or iv) magnetic vortices, which are the primary focus of QFaST. Vortices are curls of magnetization that naturally occur in thin-film ferromagnets with dimensions too large to maintain a purely homogeneous state but too small to sustain several domains. Vortices are attractive because they are extremely easy to stabilize in all kinds of magnetic materials, as long as they exhibit sufficient saturation magnetization (> 0.1 MA/m). Additionally, the vortex defect can be moved by external magnetic fields or, even more interesting, using dissipation-free spin currents. Finally, vortex excitations in the GHz range can be excited without the need for any externally applied magnetic field. This is highly attractive for the implementation of quantum protocols, which typically require the use of superconducting quantum circuits.
Mastering spin waves at the nanoscale promises many applications for data manipulation and storage. Spin waves exhibit some advantages compared to bosonic fields like phonons or photons. For example, the typical wavelength of magnetization modulations can reach much smaller values than electromagnetic waves of the same frequency. This opens the way for the miniaturization of magnonic devices such as, emitters, waveguides, splitters etc, while also offering spin transport with minimum energy dissipation. Quantum technologies, on the other hand, are rapidly evolving, based on the use of microwave elements and superconducting quantum circuits that could be combined with mangonic components to achieve some difficult tasks. One interesting example, very relevant for this project, is the coherent coupling between distant spin qubits or the detection of individual spin qubits. The challenge is to develop operative magnetic resonators upon no applied external magnetic fields. In this regard, magnetic vortex excitations offer a very attractive possibility. In this way, results obtained from QFaST could benefit the European society in the context of classical magnonics, promoting the development of dissipation-less sustainable data manipulation and, in the context of quantum computing, with the development of qubit gates and sensors.
QFaST is divided into two distinct and complementary research lines:
1. Firstly, QFaST aims to develop useful tools for the study of nanoscopic spin excitations based on superconducting circuits. To achieve this, we will use Superconducting Quantum Interference Devices (nanoSQUIDs) and superconducting resonators. In the case of nanoSQUIDs, we will address quantum spin dynamics from quasistatic up to nanosecond timescales with few Bohr magnetons sensitivity and 100 nm spatial-resolution by implementing a broadband on-chip YBCO-nanoSQUID microscope. For superconducting resonators, we will explore the use of coplanar waveguide or lumped-element resonators.
2. Secondly, QFaST aims to access interesting quantum properties of vortex excitations, such as the characterization of zero-point magnetization fluctuations in vortices or their coherent coupling to photons in superconducting resonators. Achieving this entails the exchange of vortex and photon populations in the form of Rabi oscillations. Based on this, we will explore strong coupling of high-order vortex modes and cavity photons, emphasizing the possibility of transducing single photons into coherent spin-waves
The field of quantum magnonics focuses on leveraging magnonic excitations to achieve challenging tasks relevant for quantum computing, sensing and communication, such as optical-to-microwave transduction or the coherent coupling of spin qubits. This field is relatively new and has benefited from techniques originally developed in the context of quantum optics, such as cavity/circuit quantum electrodynamics. Using these tools, only quasi-homogeneous magnon modes have been studied thus far. In particular, most experimental studies focus on the infinite wavelength Kittel mode that arises in ferromagnets under the influence of external magnetic fields. Also of interest is the study of spin waves in antiferromagnetic materials, where in-phase and out-of-phase magnetization modes emerge. All these sytems essentially behave as magnetic resonators, with mode volume scaling with the physical volume of the magnet. Although very attractive, these approaches always rely on the use of external magnetic fields.
Interestingly, the solid state offers other types of magnetic excitations that arise in magnetic textures confined in nanoscopic regions behaving as quasiparticles such as, e.g. i) domain walls between regions with opposite magnetization, ii) chiral or non-chiral skyrmions in materials where a nanoscopic core with out-of-plane magnetization is surrounded by opposite magnetization, iii) twists of magnetization in materials with Dzyaloshinskii-Moriya interaction under the influence of an external magnetic field, or iv) magnetic vortices, which are the primary focus of QFaST. Vortices are curls of magnetization that naturally occur in thin-film ferromagnets with dimensions too large to maintain a purely homogeneous state but too small to sustain several domains. Vortices are attractive because they are extremely easy to stabilize in all kinds of magnetic materials, as long as they exhibit sufficient saturation magnetization (> 0.1 MA/m). Additionally, the vortex defect can be moved by external magnetic fields or, even more interesting, using dissipation-free spin currents. Finally, vortex excitations in the GHz range can be excited without the need for any externally applied magnetic field. This is highly attractive for the implementation of quantum protocols, which typically require the use of superconducting quantum circuits.
Mastering spin waves at the nanoscale promises many applications for data manipulation and storage. Spin waves exhibit some advantages compared to bosonic fields like phonons or photons. For example, the typical wavelength of magnetization modulations can reach much smaller values than electromagnetic waves of the same frequency. This opens the way for the miniaturization of magnonic devices such as, emitters, waveguides, splitters etc, while also offering spin transport with minimum energy dissipation. Quantum technologies, on the other hand, are rapidly evolving, based on the use of microwave elements and superconducting quantum circuits that could be combined with mangonic components to achieve some difficult tasks. One interesting example, very relevant for this project, is the coherent coupling between distant spin qubits or the detection of individual spin qubits. The challenge is to develop operative magnetic resonators upon no applied external magnetic fields. In this regard, magnetic vortex excitations offer a very attractive possibility. In this way, results obtained from QFaST could benefit the European society in the context of classical magnonics, promoting the development of dissipation-less sustainable data manipulation and, in the context of quantum computing, with the development of qubit gates and sensors.
QFaST is divided into two distinct and complementary research lines:
1. Firstly, QFaST aims to develop useful tools for the study of nanoscopic spin excitations based on superconducting circuits. To achieve this, we will use Superconducting Quantum Interference Devices (nanoSQUIDs) and superconducting resonators. In the case of nanoSQUIDs, we will address quantum spin dynamics from quasistatic up to nanosecond timescales with few Bohr magnetons sensitivity and 100 nm spatial-resolution by implementing a broadband on-chip YBCO-nanoSQUID microscope. For superconducting resonators, we will explore the use of coplanar waveguide or lumped-element resonators.
2. Secondly, QFaST aims to access interesting quantum properties of vortex excitations, such as the characterization of zero-point magnetization fluctuations in vortices or their coherent coupling to photons in superconducting resonators. Achieving this entails the exchange of vortex and photon populations in the form of Rabi oscillations. Based on this, we will explore strong coupling of high-order vortex modes and cavity photons, emphasizing the possibility of transducing single photons into coherent spin-waves
Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far
On the instrumentation side (research line 1), QFaST has so far advanced the development of the broadband on-chip YBCO-nanoSQUID microscope. This entails two parallel developments: a) Sensor optimization of broad-band operation and b) Development of an on-chip nanopositioner for sample scanning. Regarding a), we have successfully fabricated YBCO nanoSQUID sensors on MgO substrates. Compared to traditionally used STO substrates, MgO will provide much better behaviour at large frequencies. New SQUID design includes the coupling to a transmission line and a high frequency flux line to allow for broadband excitation and readout. For DC biasing the devices we have used external bias tees. First sensors have been characterized down to very low temperatures and sweeping magnetic fields. Regarding b), we have designed and fabricated two kinds of nanopositioners. The first one is based on micro electromechanics actuators consisting of comb capacitors that hold a suspended central mesa that can be scanned in plane. The second one is based on a CMOS compatible piezoelectric material (AlN) that can be actuated by means of comb or plate capacitors. The advantage of this approach is that it should allow also for out-of-plane scanning in perpendicular direction. Preliminary devices have been fabricated and tested showing very promising results.
Regarding research line 2, first preliminary experiments have been performed to grasp the experimental conditions to achieve vortex-photon strong coupling with superconducting resonators. First, we have realized numerous experiments on magnon-photon coupling using homogeneous Kittel modes in shaped ferromagnets. For this purpose, we have explored the tuning of the resonance frequency of magnonics resonators based on their aspect ratio. By doing so we can excite Kittel modes (with k=0) at very high frequencies (for low applied magnetic fields) and also high order k modes by exploiting non-homogeneities in the radiofrequency excitation field. These experiments result particularly useful as they have proven the validity of the theory we have developed to quantify the coupling between arbitrary non-uniform magnetic excitations and superconducting circuits. On the other hand, we have also developed a theory that allow us to numerically normalize any magnon mode in ferromagnets of arbitrary size and shape. This can be used to calculate the zero-point magnetization fluctuations in confined nanomagnets including homogeneous magnon modes but also spin textures like domain walls, vortices, or skyrmions. Using these results, we have theoretically demonstrated that vortex excitations are potentially very interesting for performing on-chip scanning electron paramagnetic resonance. The vortex magnetization profile serves, on the one hand, to generate static field gradients to distinguish between magnetic color centers. On the other, the vortex core can be scanned using low external fields of a few mT or, alternatively, spin-currents. Finally, the circularly polarized radiofrequency magnetic field produced by the vortex excitation can be used to induce spin transitions. Such process yields a measurable splitting or broadening of the vortex resonance frequency. Theoretically, our simulations suggest that it should be possible to detect single spins or to increase their coupling to superconducting circuits so to implement qubit readout protocols.
Regarding research line 2, first preliminary experiments have been performed to grasp the experimental conditions to achieve vortex-photon strong coupling with superconducting resonators. First, we have realized numerous experiments on magnon-photon coupling using homogeneous Kittel modes in shaped ferromagnets. For this purpose, we have explored the tuning of the resonance frequency of magnonics resonators based on their aspect ratio. By doing so we can excite Kittel modes (with k=0) at very high frequencies (for low applied magnetic fields) and also high order k modes by exploiting non-homogeneities in the radiofrequency excitation field. These experiments result particularly useful as they have proven the validity of the theory we have developed to quantify the coupling between arbitrary non-uniform magnetic excitations and superconducting circuits. On the other hand, we have also developed a theory that allow us to numerically normalize any magnon mode in ferromagnets of arbitrary size and shape. This can be used to calculate the zero-point magnetization fluctuations in confined nanomagnets including homogeneous magnon modes but also spin textures like domain walls, vortices, or skyrmions. Using these results, we have theoretically demonstrated that vortex excitations are potentially very interesting for performing on-chip scanning electron paramagnetic resonance. The vortex magnetization profile serves, on the one hand, to generate static field gradients to distinguish between magnetic color centers. On the other, the vortex core can be scanned using low external fields of a few mT or, alternatively, spin-currents. Finally, the circularly polarized radiofrequency magnetic field produced by the vortex excitation can be used to induce spin transitions. Such process yields a measurable splitting or broadening of the vortex resonance frequency. Theoretically, our simulations suggest that it should be possible to detect single spins or to increase their coupling to superconducting circuits so to implement qubit readout protocols.
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)
NanoSQUID readout at frequencies up to 100 MHz or even GHz has not been previously achieved, as nanoSQUIDs are typically amplified using feedback loops limited to 20 MHz or SQUID arrays with similar frequency constraints. Consequently, devices fabricated within the scope of QFaST represent advancements beyond the state of the art. To date, we have successfully fabricated three operational MgO nanoSQUIDs and characterized their field response and noise. In the upcoming months, we plan to conduct initial tests on measuring magnetization dynamics. These tests will involve characterizing both the DC response to static magnetic fields and the excitation spectrum of magnetic vortices.
Additionally, while the development of MEMs nanopositioners has been reported previously, the use of AlN piezoelectric actuators in such a geometry is novel. Over the next few months, we anticipate demonstrating nanometric control over the mesa position in all three spatial directions within a range of a few micrometers. Furthermore, initial tests will be conducted at low temperatures. In parallel, efforts will be made to integrate the nanopositioner with the nanoSQUID sensor using a mask alignment setup.
Regarding research line 2, we have developed for the first time a protocol to numerically calculate the magnon-photon coupling between magnetic excitations and superconducting circuits and we have implemented a modification of Mumax3 to include the coupling to resonant photons as an effective field entering the Landau Lifshitz Gilbert equation. This method provides excellent agreement with experiments as demonstrated comparing numerical results with measurements performed on transmission line and on cavity. On the other hand, we have also shown how to numerically calculate the coupling between magnetic excitations and individual spins qubits. The latter still needs experimental validation. These two protocols are very relevant for the purposes of QFaST since they are applicable to nanomagnets with arbitrary shape and non-homogeneous magnetization profile such as domain walls, skyrmions or vortices. Additionally, this method also allows us to consider non-homogeneous distribution or radiofrequency fields within the cavity. Using these tools, we can now design the optimal experimental conditions to demonstrate vortex photon strong coupling. For this purpose, in the following months we need to develop new protocols to characterize the vortex resonances in individual discs using superconducting resonators. This might require us to investigate the regime of non-linear response and to work in a dispersive regime. In parallel, we expect to develop the full theory of the zero-point magnetization fluctuations in magnetic textures.
Additionally, while the development of MEMs nanopositioners has been reported previously, the use of AlN piezoelectric actuators in such a geometry is novel. Over the next few months, we anticipate demonstrating nanometric control over the mesa position in all three spatial directions within a range of a few micrometers. Furthermore, initial tests will be conducted at low temperatures. In parallel, efforts will be made to integrate the nanopositioner with the nanoSQUID sensor using a mask alignment setup.
Regarding research line 2, we have developed for the first time a protocol to numerically calculate the magnon-photon coupling between magnetic excitations and superconducting circuits and we have implemented a modification of Mumax3 to include the coupling to resonant photons as an effective field entering the Landau Lifshitz Gilbert equation. This method provides excellent agreement with experiments as demonstrated comparing numerical results with measurements performed on transmission line and on cavity. On the other hand, we have also shown how to numerically calculate the coupling between magnetic excitations and individual spins qubits. The latter still needs experimental validation. These two protocols are very relevant for the purposes of QFaST since they are applicable to nanomagnets with arbitrary shape and non-homogeneous magnetization profile such as domain walls, skyrmions or vortices. Additionally, this method also allows us to consider non-homogeneous distribution or radiofrequency fields within the cavity. Using these tools, we can now design the optimal experimental conditions to demonstrate vortex photon strong coupling. For this purpose, in the following months we need to develop new protocols to characterize the vortex resonances in individual discs using superconducting resonators. This might require us to investigate the regime of non-linear response and to work in a dispersive regime. In parallel, we expect to develop the full theory of the zero-point magnetization fluctuations in magnetic textures.