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Coherent strong field interactions between a nanomagnet and a photonic cavity

Öney O. Soykal

Published Jul 1, 2010• 0 citations
Publisher

Abstract

Strong coupling of light and matter is an essential element of cavity quantum electrodynamics (cavity-QED) and quantum optics, which may lead to novel mixed states of light and matter and to applications such as quantum computation. In the strong-coupling regime, where the coupling strength exceeds the dissipation, the light-matter interaction produces a characteristic vacuum Rabi splitting. Therefore, strong coupling can be utilized as an effective coherent interface between light and matter (in the form of electron charge, spin or superconducting Cooper pairs) to achieve components of quantum information technology including quantum memory, teleportation, and quantum repeaters. Semiconductor quantum dots, nuclear spins and paramagnetic spin systems are only some of the material systems under investigation for strong coupling in solid-state physics. Mixed states of light and matter coupled via electric dipole transitions often suffer from short coherence times (nanoseconds). Even though magnetic transitions appear to be intrinsically more quantum coherent than orbital transitions, their typical coupling strengths have been estimated to be much smaller. Hence, they have been neglected for the purposes of quantum information technology.\nHowever, we predict that strong coupling is feasible between photons and a ferromagnetic nanomagnet, due to exchange interactions that cause very large numbers of spins to coherently lock together with a significant increase in oscillator strength while still maintaining very long coherence times. In order to examine this new exciting possibility, the interaction of a ferromagnetic nanomagnet with a single photonic mode of a cavity is analyzed in a fully quantum-mechanical treatment. Exceptionally large quantum-coherent magnet-photon coupling with coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of ∼ 1 mm radius with a nanomagnet of ∼ 100 nm radius and ferromagnet resonance frequency of ∼ 200 GHz. This should substantially exceed the coupling observed in solids between orbital transitions and light. Eigenstates of the nanomagnet-photon system correspond to entangled states of spin orientation and photon number over 105 values of each quantum number. Initial coherent state of definite spin and photon number evolve dynamically to produce large coherent oscillations in the microwave power with exceptionally long dephasing times of few seconds. In addition to dephasing, several decoherence mechanisms including elementary excitation of magnons and crystalline magnetic anisotropy are investigated and shown to not substantially affect coherence upto room temperature. For small nanomagnets the crystalline magnetic anisotropy of the magnet strongly localize the eigenstates in photon and spin number, quenching the potential for coherent states and for a sufficiently large nanomagnet the macrospin approximation breaks down and different domains of the nanomagnet may couple separately to the photonic mode. Thus the optimal nanomagnet size is predicted to be just below the threshold for failure of the macrospin approximation. Moreover, it is shown that initially unentangled coherent states of light (cavity field) and spin (nanomagnet spin orientation) can be phase-locked to evolve into a coherent entangled states of the system under the influence of strong coupling.

DOI
10.17077/etd.dt4sliy4

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Coherent strong-field coupling of a ferromagnetic nanomagnet with a photonic cavity

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Strong coupling of light and matter is an essential element of cavity quantum electrodynamics (cavity-QED) and quantum optics, which may lead to novel mixed states of light and matter and to applications such as quantum computation. In the strong-coupling regime, where the coupling strength exceeds the dissipation, the light-matter interaction produces a characteristic vacuum Rabi splitting. Therefore, strong coupling can be utilized as an effective coherent interface between light and matter (in the form of electron charge, spin or superconducting Cooper pairs) to achieve components of quantum information technology including quantum memory, teleportation, and quantum repeaters. Semiconductor quantum dots, nuclear spins and paramagnetic spin systems are only some of the material systems under investigation for strong coupling in solid-state physics. Mixed states of light and matter coupled via electric dipole transitions often suffer from short coherence times (nanoseconds). Even though magnetic transitions appear to be intrinsically more quantum coherent than orbital transitions, their typical coupling strengths have been estimated to be much smaller. Hence, they have been neglected for the purposes of quantum information technology.\nHowever, we predict that strong coupling is feasible between photons and a ferromagnetic nanomagnet, due to exchange interactions that cause very large numbers of spins to coherently lock together with a significant increase in oscillator strength while still maintaining very long coherence times. In order to examine this new exciting possibility, the interaction of a ferromagnetic nanomagnet with a single photonic mode of a cavity is analyzed in a fully quantum-mechanical treatment. Exceptionally large quantum-coherent magnet-photon coupling with coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of ∼ 1 mm radius with a nanomagnet of ∼ 100 nm radius and ferromagnet resonance frequency of ∼ 200 GHz. This should substantially exceed the coupling observed in solids between orbital transitions and light. Eigenstates of the nanomagnet-photon system correspond to entangled states of spin orientation and photon number over 105 values of each quantum number. Initial coherent state of definite spin and photon number evolve dynamically to produce large coherent oscillations in the microwave power with exceptionally long dephasing times of few seconds. In addition to dephasing, several decoherence mechanisms including elementary excitation of magnons and crystalline magnetic anisotropy are investigated and shown to not substantially affect coherence upto room temperature. For small nanomagnets the crystalline magnetic anisotropy of the magnet strongly localize the eigenstates in photon and spin number, quenching the potential for coherent states and for a sufficiently large nanomagnet the macrospin approximation breaks down and different domains of the nanomagnet may couple separately to the photonic mode. Thus the optimal nanomagnet size is predicted to be just below the threshold for failure of the macrospin approximation. Moreover, it is shown that initially unentangled coherent states of light (cavity field) and spin (nanomagnet spin orientation) can be phase-locked to evolve into a coherent entangled states of the system under the influence of strong coupling.
We predict that strong coupling is feasible between photons and a ferromagnetic nanomagnet, due to exchange interactions that cause very large numbers of spins to coherently lock together with a significant increase in oscillator strength while still maintaining very long coherence times. The interaction of a ferromagnetic nanomagnet with a single photonic mode of a cavity is analyzed in a fully quantum-mechanical treatment. Exceptionally large quantum-coherent magnet-photon coupling with coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of ~ 1 mm radius with a nanomagnet of ~ 100 nm radius and ferromagnet resonance frequency of ~ 200 GHz. This should substantially exceed the coupling observed in solids between orbital transitions and light. Eigenstates of the nanomagnet-photon system correspond to entangled states of spin orientation and photon number over 105 values of each quantum number. Initial coherent state of definite spin and photon number evolve dynamically to produce large coherent oscillations in the microwave power with exceptionally long dephasing times of few seconds. In addition to dephasing, several decoherence mechanisms including elementary excitation of magnons and crystalline magnetic anisotropy are investigated and shown to not substantially affect coherence upto room temperature. The optimal nanomagnet size is predicted to be just below the threshold for failure of the macrospin approximation.
We analyze the interaction of a nanomagnet (ferromagnetic) with a single photonic mode of a cavity in a fully quantum-mechanical treatment and find that exceptionally large quantum-coherent magnet-photon coupling can be achieved. Coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of approximately 1 mm radius with a nanomagnet of approximately 100 nm radius and ferromagnetic resonance frequency of approximately 200 GHz. Eigenstates of the magnet-photon system correspond to entangled states of spin orientation and photon number, in which over 10{5} values of each quantum number are represented; conversely, initial (coherent) states of definite spin and photon number evolve dynamically to produce large oscillations in the microwave power (and nanomagnet spin orientation), and are characterized by exceptionally long dephasing times.
The coherent dynamics of a coupled photonic cavity and a nanomagnet is explored as a function of nanomagnet size. For sufficiently strong coupling eigenstates involving highly entangled photon and spin states are found, which can be combined to create coherent states. As the size of the nanomagnet increases its coupling to the photonic mode also monotonically increases, as well as the number of photon and spin states involved in the system's eigenstates. For small nanomagnets the crystalline anisotropy of the magnet strongly localizes the eigenstates in photon and spin number, quenching the potential for coherent states. For a sufficiently large nanomagnet the macrospin approximation breaks down and different domains of the nanomagnet may couple separately to the photonic mode. Thus the optimal nanomagnet size is just below the threshold for failure of the macrospin approximation.
Quantum computing is a powerful way of improving computing efficiency. For some specific problems, quantum processor can exponentially reduce computation time compared to the classical computer. Cavity quantum electrodynamics, which studies the coherent interaction between photons in an optical cavity and atoms or other two-level systems, is of enormous significance to quantum computing and quantum information processing. The strong coupling regime where a cavity photon mode and an atom exchange a single quantum energy coherently has attracted extensive interest in varied experimental platforms and systems such as alkali atoms, Rydberg atoms, large spin ensembles, magnons, etc. The semiconductor gate-defined double quantum dot (DQD) system is one of the most promising platforms that possesses advantages of advanced micro-nano processing technology and outstanding scalability. Introducing the concept of cavity QED into superconducting circuits (circuit QED, cQED), provides an opportunity to study interaction between electrons confined in semiconductor DQD and photons trapped in a superconducting resonator. Reaching strong coupling regime in this hybrid system paves the way to large-scale network of quantum computing. Electrons confined in DQD have large electrical dipoles, thus are able to couple to photons with relatively large coupling rate. Whereas, due to the charge noise and other dissipation channels in the hybrid system, the decoherence rate of the system is larger than the coupling rate, leaving the strong coupling a great challenge. In recent years, different methods have been proposed to access the strong coupling regime. Taking advantage of a high-quality heterojunction structure, an overlapping gate architecture and a low-pass LC filter on the DC bias line, the decoherence of the charge qubit and microwave leakage of the resonator can be effectively suppressed. The coupling strength of the hybrid system can be improved utilizing a high impedance resonator which is comprised of high kinetic inductance materials. Spin, which does not interact directly with the electric field, is insensitive to charge noise and has much longer decoherence time than charge qubit. However, the weak interaction results in a small coupling rate between the spin and the photon. To solve this problem, the method of coherent hybridization between the spin and the charge state is proposed to improve the coupling strength. This hybridization can be achieved by applying a non-uniform magnetic field, utilizing spin-orbit interaction or spin exchange interaction. At present, both charge qubits and spin qubits have achieved strong coupling with the cavity and the coupling distance between long-range qubits is greatly expanded as long as millimeters. This review introduces basic ideas about cQED and fundamental elements in semiconductor cQED systems. Recent progress in strong coupling hybrid system and methods for improving coupling structures are discussed. In future research, more efforts will be devoted into long-range transfer of qubit states and photon-mediated two or multi-qubit gates.
Abstract The strong coupling regime is essential for efficient transfer of excitations between states in different quantum systems on timescales shorter than their lifetimes. The coupling of single spins to microwave photons is very weak but can be enhanced by increasing the local density of states by reducing the magnetic mode volume of the cavity. In practice, it is difficult to achieve both small cavity mode volume and low cavity decay rate, so superconducting metals are often employed at cryogenic temperatures. For an ensembles of N spins, the spin–photon coupling can be enhanced by N\sqrt NN​ N through collective spin excitations known as Dicke states. For sufficiently large N the collective spin–photon coupling can exceed both the spin decoherence and cavity decay rates, making the strong-coupling regime accessible. Here we demonstrate strong coupling and cavity quantum electrodynamics in a solid-state system at room-temperature. We generate an inverted spin-ensemble with N ~ 1015 by photo-exciting pentacene molecules into spin-triplet states with spin dephasing time T2∗∼3T_2^*\sim 3T2∗​∼3 T 2 * ~ 3 μs. When coupled to a 1.45 GHz TE01δ mode supported by a high Purcell factor strontium titanate dielectric cavity ( Vm∼0.25V_{\mathrm{m}}\sim 0.25Vm​∼0.25 V m ~ 0.25 cm3, Q ~ 8,500), we observe Rabi oscillations in the microwave emission from collective Dicke states and a 1.8 MHz normal-mode splitting of the resultant collective spin–photon polariton. We also observe a cavity protection effect at the onset of the strong-coupling regime which decreases the polariton decay rate as the collective coupling increases.
The strong-coupling regime of cavity-quantum-electrodynamics (cQED) represents the light-matter interaction at the fully quantum level. Adding a single photon shifts the resonance frequencies, a profound nonlinearity. cQED is a test-bed of quantum optics and the basis of photon-photon and atom-atom entangling gates. At microwave frequencies, success in cQED has had a transformative effect. At optical frequencies, the gates are potentially much faster; the photons can propagate over long distances; and the photons can be detected easily, ideal features for quantum networks. Following pioneering work on single atoms, solid-state implementations using semiconductor quantum dots are emerging, an important prospect for quantum technology. We present here a gated, ultralow-loss microcavity-device which forms a highly coherent photon−-−quantum-dot interface with a cooperativity of C=150C=150C=150. The gates allow both the quantum dot charge state and resonance frequency to be controlled electrically; crucially, they eliminate the noise-source which has complicated quantum dot cQED in the past −-− scattering from the bare microcavity mode even at the quantum dot-microcavity resonance. Even in the microcavity, the quantum dot has a linewidth close to the radiative limit. In addition to a very pronounced avoided-crossing in the spectral domain, we observe a clear coherent exchange of a single energy-quantum between the ``atom" and cavity in the time domain (vacuum Rabi-oscillations). Decoherence arises predominantly via the atom and photon loss-channels. The coherence is exploited to probe the transitions between the singly- and doubly-excited photon-atom system via photon-statistics spectroscopy. We propose this system as a platform for quantum technology, for instance a photon-photon entangling gate.