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arXiv:2311.01339 · Physical review. B./Physical review. B

Engineering photon-mediated long-range spin interactions in Mott insulators

Paul Fadler, Kai Phillip Schmidt, Jiajun Li, Martin Eckstein

Published Feb 29, 2024• 6 citations
arXivHTMLPDF

Abstract

We investigate the potential to induce long-range spin interactions in a Mott insulator via the quantum electromagnetic field of a cavity. The coupling between light and spins is inherently nonlinear, and occurs via multiphoton processes like Raman scattering and two-photon absorption and emission with electronically excited intermediate states. Based on this, two pathways are elucidated: (i) In the absence of external driving, long-range interactions are mediated by the exchange of at least two virtual cavity photons. We show that these vacuum-mediated interactions can surpass local Heisenberg interactions in mesoscopic setups such as sufficiently small split-ring resonators. (ii) In a laser-driven cavity, interactions can be tailored through a hybrid scheme involving both external laser photons and cavity photons. This offers a versatile pathway for Floquet engineering of long-range interactions in macroscopic systems. In general, the derivation of these interactions requires careful consideration: Notably, we demonstrate that a simple phenomenological approach, based on a spin-photon Hamiltonian that captures Raman and two-photon processes with effective matrix elements, can be used only if the cavity is resonantly driven. Outside of these narrow resonant regimes as well as for the undriven case, a fourth-order series expansion within the underlying electronic model is necessary, which we perform to obtain long-range four-spin interactions in the half-filled Hubbard model.

DOI
10.1103/physrevb.109.085149

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We investigate the potential to induce long-range spin interactions in a Mott insulator via the quantum electromagnetic field of a cavity. The coupling between light and spins is inherently nonlinear, and occurs via multiphoton processes like Raman scattering and two-photon absorption and emission with electronically excited intermediate states. Based on this, two pathways are elucidated: (i) In the absence of external driving, long-range interactions are mediated by the exchange of at least two virtual cavity photons. We show that these vacuum-mediated interactions can surpass local Heisenberg interactions in mesoscopic setups such as sufficiently small split-ring resonators. (ii) In a laser-driven cavity, interactions can be tailored through a hybrid scheme involving both external laser photons and cavity photons. This offers a versatile pathway for Floquet engineering of long-range interactions in macroscopic systems. In general, the derivation of these interactions requires careful consideration: Notably, we demonstrate that a simple phenomenological approach, based on a spin-photon Hamiltonian that captures Raman and two-photon processes with effective matrix elements, can be used only if the cavity is resonantly driven. Outside of these narrow resonant regimes as well as for the undriven case, a fourth-order series expansion within the underlying electronic model is necessary, which we perform to obtain long-range four-spin interactions in the half-filled Hubbard model.
Engineering long-range interacting spin systems with ultra cold atoms offers the possibility to explore exotic magnetically ordered phases in strongly-correlated scenarios. Quantum gases in optical cavities provide a versatile experimental platform to further engineer photon-mediated interactions and access the underlying microscopic processes by probing the cavity field. Here, we study a two-component spin Bose-Hubbard system with cavity-mediated interactions. We provide a comprehensive overview of its phase diagram and transitions in experimentally relevant regimes. The interplay of different energy scales yields a rich phase diagram with superfluid and insulating phases exhibiting density modulation or spin ordering. In particular, the combined effect of contact and global-range interactions gives rise to an antiferromagnetically ordered phase for arbitrarily small spin-dependent light-matter coupling, while long-range and inter-spin contact interactions introduce regions of instability and phase separation in the phase diagram. We further study the low energy excitations above the antiferrogmagnetic phase. Besides particle-hole branches, it hosts spin-exchange excitations with a tunable energy gap. The studied lattice model can be readily realized in cold-atom experiments with optical cavities.
Controlling the states of quantum systems is a subject of major interest for both fundamental science and technological development. In this thesis, we carry out theoretical studies on how this can be achieved using light, both of classical and of quantum mechanical nature. We study a driven cavity system, where the driving field is classical and the cavity field is quantum mechanical. We demonstrate how virtual scattering of driving photons inside the cavity via two-photon processes can induce controllable long-range electron interactions in two-dimensional materials. We show that both the strength and the sign of the interactions can be tuned by the driving parameters and that the interactions are not screened effectively except at very low frequencies. For realistic cavity parameters, driving-induced heating of the electrons by inelastic photon scattering is suppressed and coherent electron interactions dominate. When the interactions are attractive, they cause an instability in the Cooper channel at a temperature proportional to the square root of the driving intensity. Our results open up a new avenue for engineering quantum materials on-demand and the possibility of studying the effect of long-range interactions in condensed matter systems. Following that, we take a more general approach to investigate the effect of long-range density-density electron attractive interactions on a superconductor. We show that the low-lying excitations of a 2D conventional superconductor can be significantly altered by these long-range interactions. Using BCS theory, we find that these interactions combine non-linearly with the intrinsic local attractions of the superconductor to increase the Bogoliubov quasiparticle excitation energies, thus enlarging the superconducting gap. Moreover, we show how the long-range nature of the driven-cavity-induced attractions qualitatively changes the collective excitations of the superconductor. Specifically, they lead to the appearance of additional collective excitations of the excitonic modes. They further push the Higgs mode "in gap": it lies below the Bogoliubov quasiparticle continuum such that it cannot decay through the quasiparticle excitations.
We consider a pair of quantum dot-based spin qubits that interact via microwave photons in a superconducting cavity and that are also parametrically driven by separate external electric fields. For this system, we formulate a model for spin qubit entanglement in the presence of mutually off-resonant qubit and cavity frequencies. We show that the sidebands generated via the driving fields enable highly tunable qubit-qubit entanglement using only ac control and without requiring the qubit and cavity frequencies to be tuned into simultaneous resonance. The model we derive can be mapped to a variety of qubit types, including detuning-driven one-electron spin qubits in double quantum dots and three-electron resonant exchange qubits in triple quantum dots. The high degree of nonlinearity inherent in spin qubits renders these systems particularly favorable for parametric drive-activated entanglement. We determine multiple common resonance conditions for the two driven qubits and the cavity and identify experimentally relevant parameter regimes that enable the implementation of entangling gates with suppressed sensitivity to cavity photon occupation and decay. The parametrically driven sideband resonance approach that we describe provides a promising route toward scalability and modularity in spin-based quantum information processing through drive-enabled tunability that can also be implemented in micromagnet-free electron and hole systems for spin-photon coupling. Published by the American Physical Society 2024
Abstract Nonlocal qubit interactions are a hallmark of advanced quantum information technologies1–5. The ability to transfer quantum states and generate entanglement over distances much larger than qubit length scales greatly increases connectivity and is an important step towards maximal parallelism and the implementation of two-qubit gates on arbitrary pairs of qubits6. Qubit-coupling schemes based on cavity quantum electrodynamics2, 7, 8 also offer the possibility of using high-quality-factor resonators as quantum memories3, 9. Extending qubit interactions beyond the nearest neighbour is particularly beneficial for spin-based quantum computing architectures, which are limited by short-range exchange interactions10. Despite the rapidly maturing device technology for silicon spin qubits11–16, experimental progress towards achieving long-range spin–spin coupling has so far been restricted to interactions between individual spins and microwave photons17–20. Here we demonstrate resonant microwave-mediated coupling between two electron spins that are physically separated by more than four millimetres. An enhanced vacuum Rabi splitting is observed when both spins are tuned into resonance with the cavity, indicating a coherent interaction between the two spins and a cavity photon. Our results imply that microwave-frequency photons may be used to generate long-range two-qubit gates between spatially separated spins.
The ultrastrong coupling regime has emerged as a fascinating and distinctive phenomenon in cavity-QED and light-matter interactions, where the occupation of virtual excitations (e.g., photons) is possible in vacuum, which is a consequence of counter-rotating wave effects and breaking U(1) symmetry. However, an ongoing challenge is how to convert these virtual photons into real photons. We will first discuss how to “Floquet engineer” the quantum Rabi model for a two-level system coupled to a quantized cavity mode, under periodic modulation of the cavity-dipole coupling rate, leading to rich Floquet states. Exploiting the quantum vacuum, in the ultrastrong coupling regime, we show how purely mechanical driving can produce real photons. These periodic driving schemes are promising for the coherent manipulation of hybrid quantum systems and quantum vacuum effects, with applications for quantum state engineering and the study of nonequilibrium quantum phenomena.
The electronic spin degrees of freedom in semiconductors typically have decoherence times that are several orders of magnitude longer than other relevant time scales. A solid-state quantum computer based on localized electron spins as qubits is therefore of potential interest. Here, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed. The effective long-range interaction is mediated by the vacuum field of a high finesse microcavity. By using conduction-band-hole Raman transitions induced by classical laser fields and the cavity-mode, parallel controlled-not operations, and arbitrary single qubit rotations can be realized.