Towards a quantum interface between spin waves and paramagnetic spin baths
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2022-02-08 |
| Journal | Physical review. B./Physical review. B |
| Authors | Carlos Gonzalez-Ballestero, Toeno van der Sar, Oriol RomeroāIsart |
| Institutions | UniversitƤt Innsbruck, Austrian Academy of Sciences |
| Citations | 21 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis research presents a comprehensive quantum theory describing the interaction and mutual back-action between spin waves (magnons) in a ferromagnetic insulator (YIG) and an ensemble of paramagnetic spins (Nitrogen-Vacancy, NV, centers in diamond).
- Core Value Proposition: Establishes the theoretical foundation for hybrid quantum systems integrating spin waves and quantum emitters, enabling active control, sensing, and interfacing for next-generation spintronics.
- Spin Wave Control: The paramagnetic spin bath induces strong and tuneable modifications to the spin wave spectrum and propagation properties, including full suppression of propagation and enhancement of propagation length by approximately 50%.
- Back-Action Sensing: Spin wave thermal fluctuations induce a measurable frequency shift in the paramagnetic spins, detectable via state-of-the-art optical fluorescence or nanomechanical force sensing (magnetic thermal Casimir-Polder force).
- Measurable Effects: The predicted frequency shifts (up to 2Ļ x 8 MHz) and forces (down to 10-21 N) are within the sensitivity range of current experimental setups (e.g., NV-YIG hybrid platforms).
- Mechanism: Optimal control is achieved via optical pumping of NV centers, maximizing spin polarization and enhancing the coupling strength by several orders of magnitude compared to thermal equilibrium.
- Applications: The findings pave the way for developing reconfigurable spin wave circuits, including optically-gated spin wave transistors, polarization filters, and magnonic crystals.
Technical Specifications
Section titled āTechnical SpecificationsāThe following parameters were used in the theoretical modeling, focusing on a Yttrium-Iron-Garnet (YIG) thin film coupled to Nitrogen-Vacancy (NV) centers in diamond.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| YIG Film Thickness (d) | 200 | nm | Ferromagnetic insulator geometry. |
| YIG Gyromagnetic Ratio (Ī³) | -1.76 x 1011 | T-1 s-1 | Material constant. |
| YIG Saturation Magnetization (Ms) | 1.39 x 105 | A m-1 | Material constant. |
| YIG Exchange Stiffness (Ī±x) | 2.14 x 10-4 | (Āµm)-2 | Material constant. |
| YIG Gilbert Damping (Ī±G) | 10-4 | Dimensionless | Intrinsic spin wave loss. |
| NV Zero-Field Splitting (D0) | 2Ļ x 2.877 | GHz | Paramagnetic spin energy structure. |
| NV Gyromagnetic Ratio (Ī³s) | -1.76 x 1011 | T-1 s-1 | Material constant. |
| NV Occupation Lifetime (T1) | 3 | ms | Bare relaxation time. |
| NV Coherence Lifetime (T2) | 1 | Āµs | Bare decoherence time. |
| Optimal NV Density (ĻNV) | 104 | (Āµm)-3 | Used for maximum back-action effects. |
| Optimal Optical Pumping Rate (Ī©) | 2Ļ x 10 | kHz | Used for maximum spin polarization. |
| Maximum Linewidth Increase (ĪĪ²,max) | 2Ļ x 20 | MHz | Achieved at optimal pumping (Āµ0H0 ā 10-15 mT). |
| Measurable Frequency Shift (Ī“-) | Up to 2Ļ x 8 | MHz | At room temperature, l = 4d. |
| Force Sensitivity Range | 10-21 - 10-18 | N Hz1/2 | Current ultra-sensitive force detectors. |
| Typical Spin Wave Lifetime (ĻĪ²) | ~300 | ns | Calculated from phenomenological loss theory. |
Key Methodologies
Section titled āKey MethodologiesāThe study is based on a comprehensive quantum theoretical framework, employing open quantum systems techniques to model the coupled dynamics of the spin waves and the paramagnetic spin bath.
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Classical Spin Wave Modeling:
- The dynamics of the YIG magnetization field M(r, t) were governed by the lossless Landau-Lifshitz equation.
- The model included both exchange and dipole-dipole interactions (magnetostatic approximation).
- Eigenmodes (magnons) were computed using a perturbative approach (Kalinikos method) for the thin film geometry (Damon-Eshbach and parallel propagation).
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System Quantization:
- The spin waves were quantized using bosonic ladder operators (magnons), yielding the free Hamiltonian Hsw.
- The paramagnetic NV centers (S=1 triplet ground state) were modeled with their free Hamiltonian Hps, including zero-field splitting (D0) and Zeeman splitting (H0).
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Interaction and Dissipation:
- The interaction potential (V) was derived from the magnetic dipole interaction, calculated up to second order in magnon operators.
- Intrinsic spin wave dissipation (Gilbert damping, Dsw) and NV center dissipation (decay/dephasing, Dps) were included using Lindblad superoperators.
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Effective Dynamics Derivation (Tracing Out):
- The effective dynamics for the spin waves (Section III) were obtained by tracing out the NV center bath using the Born-Markov master equation formalism.
- The effective dynamics for the paramagnetic spins (Section IV) were obtained by tracing out the spin wave bath, also using the Born-Markov approximation (justified by the timescale separation, Ī³Ī²T2 >> 1).
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Modeling of NV Pumping:
- Optical pumping of the NV centers was modeled using an extended six-level system master equation, allowing calculation of steady-state occupations and correlation times (Tnv) under incoherent driving (Ī©).
- The āfrozen bathā model was used to incorporate the slow occupation dynamics of the NV centers into the spin wave master equation.
Commercial Applications
Section titled āCommercial ApplicationsāThe theoretical results provide pathways for developing novel components and architectures in spintronics and quantum technologies.
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Magnon Spintronics and Logic:
- Reconfigurable Circuits: The ability to suppress or enhance spin wave propagation allows for the dynamic creation of spin wave mirrors, waveguides, and filters without physical microstructuring.
- Optically-Gated Transistors: Using controlled optical pumping to tune the NV bath coupling, the flow of spin currents can be actively modulated, leading to optically-gated magnonic transistors.
- Magnonic Crystals: The induced narrow-band modifications to the dispersion relation can be exploited to create tuneable magnonic crystals.
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Quantum Sensing and Metrology:
- Spin Wave Detection: The back-action of spin waves on the NV center frequency shift provides a highly sensitive, localized method for probing spin wave fields and their thermal fluctuations.
- Distance Metrology: The strong dependence of the NV center lifetime (T1) and coherence (T2) on the NV-film separation (l) can be used to optically measure the distance between the quantum emitter and the magnetic film with high precision.
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Hybrid Quantum Systems:
- Magneto-Mechanical Transduction: The predicted spin wave-induced force (magnetic thermal Casimir-Polder force) on the NV centers, detectable by nanomechanical resonators (e.g., diamond cantilevers), enables a new platform for magneto-mechanical coupling and transduction between magnonic, mechanical, and optical degrees of freedom.
- Unconventional Physics: The directional and non-reciprocal coupling mechanisms identified (chirality) can be leveraged to study complex many-body physics and directional quantum information processing.
View Original Abstract
<p>Spin waves have risen as promising candidate information carriers for the next generation of information technologies. Recent experimental demonstrations of their detection using electron spins in diamond pave the way towards studying the back-action of a controllable paramagnetic spin bath on the spin waves. Here, we present a macroscopic quantum theory describing the interaction between spin waves and paramagnetic spins. As a case study, we consider an ensemble of nitrogen-vacancy spins in diamond in the vicinity of an yttrium-iron-garnet thin film. We show how the back-action of the ensemble results in strong and tuneable modifications of the spin wave spectrum and propagation properties. These modifications include the full suppression of spin wave propagation and, in a different parameter regime, the enhancement of their propagation length by Formula Presented for modes near resonance with the NV transition frequency. Furthermore, we show how the spin wave thermal fluctuationsāeven down to the quantum magnonic ground stateāinduce a measurable frequency shift of the paramagnetic spins in the bath. This shift results in a thermal dispersion force that can be measured optically and/or mechanically with a diamond mechanical resonator. In addition, we use our theory to compute the spin wave-mediated interaction between the spins in the bath. We show that all the above effects are measurable by state-of-the-art experiments. Our results provide the theoretical foundation for describing hybrid quantum systems of spin waves and spin baths and establish the potential of quantum spins as active control, sensing, and interfacing tools for spintronics.</p>