Two-phonon Processes Research Articles

The Limit of Spin Lifetime in Solid-State Electronic Spins.

The development of spin qubits for quantum technologies requires their protection from the main source of finite-temperature decoherence: atomic vibrations. Here we eliminate one of the main barriers to the progress in this field by providing a complete first-principles picture of spin relaxation that includes up to two-phonon processes. Our method is based on machine learning and electronic structure theory and makes the prediction of spin lifetime in realistic systems feasible. We study a prototypical vanadium-based molecular qubit and reveal that the spin lifetime at high temperature is limited by Raman processes due to a small number of THz intramolecular vibrations. These findings effectively change the conventional understanding of spin relaxation in this class of materials and open new avenues for the rational design of long-living spin systems.

Effect of phonons on the electron spin resonance absorption spectrum

The unavoidable presence of vibrations in solid-state devices can drastically modify the expected electron spin resonance (ESR) absorption spectrum in magnetically active systems. In this work, we model the effect of phonons and temperature on the ESR signal in molecular systems with strong E ⊗ e Jahn–Teller (JT) effect and an electronic spin-1/2. Our microscopic model considers the linear JT interaction with a continuum of phonon modes, the spin–orbit coupling, the Zeeman effect, and the response of the system under a weak oscillating magnetic field. We derive a Lindblad master equation for the orbital and spin degrees of freedom, where one- and two-phonon processes are considered for the phonon-induced relaxation, and the thermal dependence of Ham reduction factors is calculated. We find that the suppression of ESR signals is due to phonon broadening but not based on the common assumption of orbital quenching. Our results can be applied to explain the experimentally observed absence of the ESR signal in color centers in diamond, such as the neutral nitrogen-vacancy and negatively charged silicon-vacancy color centers in diamond.

Quadratic optomechanical coupling in an active-passive-cavity system

We investigate an active-passive-cavity system where a membrane is quadratically coupled to the passive cavity. When the passive cavity is strong coherently driven to enhance the optomechanical coupling, the optical field interacts with the mechanical oscillator through the two-phonon process. By calculating the eigenfrequencies of system in Keldysh framework, we show the significant splitting of exceptional point in the presence of the optomechanical coupling. We also calculate the transmission rate to show how this system responds to an additional weak probe field. We find the gain effect will induce the two-phonon process amplification window. However, the gain effect becomes weak when the photon-tunneling strength increases. Then the transmission rate of the probe field changes from amplification to absorption. These results have potential applications in quantum metrology, quantum information processing, and quantum optical devices.

Unconventional Spin Relaxation Involving Localized Vibrational Modes in Ho Single-Atom Magnets.

We investigate the spin relaxation of Ho single atom magnets on MgO/Ag(100) as a function of temperature and magnetic field. We find that the spin relaxation is thermally activated at low field, while it remains larger than 1000s up to 30K and 8T. This behavior contrasts with that of single molecule magnets and bulk paramagnetic impurities, which relax faster at high field. Combining our results with density functional theory, we rationalize this unconventional behavior by showing that local vibrations activate a two-phonon Raman process with a relaxation rate that peaks near zero field and is suppressed at high field. Our work shows the importance of these excitations in the relaxation of axially coordinated magnetic atoms.

Nitrogen and group-IV (Si, Ge) vacancy color centres in nano-diamonds: photoluminescence study at high temperature (25 °C–600 °C)

Raman scattering and photoluminescence measurements have been carried out on nano-diamonds containing Nitrogen-vacancy (NV−), Silicon-Vacancy (SiV−) and Germanium-vacancy (GeV−) synthesized by high pressure and high temperature method. Optical zero-phonon-line transition of these negatively charged centres were measured from room temperature up to 600 °C under air. The results show that all nano-diamonds are stable at this temperature range and spectra are reproducible for heating and cooling cycles. Thermal behaviors of linewidth and zero phonon line, for SiV− and GeV− centres, are well described by the second-order electron-phonon interactions involving two-phonon and elastic processes.

Fabrication and upconversion luminescence of novel transparent Er2O3 ceramics

Transparent Er2O3 ceramics were successfully fabricated via vacuum sintering for the first time, using low-temperature synthetic layered rare-earth hydroxide (LRH) as the precursor. The LRH exhibits single crystal structure and characteristic two-dimensional nanosheet morphology with a thickness of only ∼10 nm. Calcining the LRH precursor at optimum temperature of 1000 °C yields a rounded fine oxide powder with an average particle size of ∼35 nm and relatively uniform size distribution. With the sinterable oxide particle, the vacuum sintered Er2O3 ceramic has a relatively high transparency of ∼80 % at around 5.4 μm (∼99 % of the theoretical value) and an average grain size of ∼55 μm. Under 980 nm laser excitation, the Er2O3 ceramic displays strong red emission at ∼654‒685 nm and weak green emission at ∼553‒565 nm arising from 4F9/2→4I15/2 and 4S3/2/2H11/2→4I15/2 transitions, respectively. The intensities of red and green emissions rise along with increasing laser output powers, the upconversion mechanisms of which are both attributable to two-phonon processes. The CIE chromaticity diagrams move towards cooler tone from yellow to greenish-yellow colours with enhanced output powers. The lifetimes of the Er2O3 ceramic were determined to be ∼13.0 and 8.4 μs for the 684 and 565 nm emissions, respectively.

Generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions.

We investigate theoretically the generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions. It is shown that the generation of frequency components at the sum sideband stems from the nonlinear optomechanical interactions via two-phonon processes in the quadratically coupled optomechanical system, while an optical parametric amplifier (OPA) inside the system can considerably improve the sum sideband generation (SSG). The dependence of SSG on the system parameters, including the power of the control field, the frequency detuning of the probe fields and the nonlinear gain of OPA are analyzed in detail. Our analytic calculation indicates that the SSG can be obtained even under weak driven fields and greatly enhanced via meeting the matching conditions. The effect of SSG may have potential applications for achieving measurement of electric charge (or other weak forces) with higher precision and on-chip manipulation of light propagation.

Broadband electron paramagnetic resonance spectroscopy in diverse field conditions using optically detected nitrogen-vacancy centers in diamond

Paramagnetic magnetic resonance, a powerful technique for characterizing and identifying chemical targets, is increasingly used for imaging; however, low spin polarization at room temperature and moderate magnetic fields poses challenges for detecting small numbers of spins. In this work, we use fluorescence from nitrogen-vacancy (NV) centers in diamond to detect the electron paramagnetic resonance (EPR) spectrum of optically inactive target spins under various conditions of field magnitude and orientation. The protocol requires neither direct microwave manipulation of the NV spins nor spectral overlap between NV and target spin resonances, thus enabling broadband detection. This unexpected non-resonant coupling is attributable to a two-phonon process that relaxes NV spins proximate to the fluctuating dipole moment of the target spin, suggesting that the sensitivity is determined by the dipole–dipole coupling strength. This approach holds promise for sensitive EPR detection, particularly in settings where control over the diamond-crystal orientation is difficult. This is notably the case for biological sensing applications, where nanodiamonds are being pursued for their bright, stable fluorescence and biocompatibility.

Suppression of Ferromagnetic Order by Uniaxial Anisotropy and Its Influence on Nuclear Magnetic Relaxation for Li9V3(P2O7)3(PO4)2

The spin dynamics of the Li9V3(P2O7)3(PO4)2 insertion electrode system is explored with the results of magnetization and nuclear magnetic resonance for Li ions. The magnetic susceptibility at high temperatures exhibits a Curie–Weiss law with a ferromagnetic Weiss temperature of about 3 K, while at low temperatures, the enhancement and suppression of susceptibility appear in the absence of long-range order. This aspect is understood on the basis of the XXZ model with the single-ion uniaxial anisotropy. Thus, the slowing down of ferromagnetic spin fluctuations without the long-range order occurs at temperatures below 10 K. In the vicinity of the virtual transition temperature, the spin–lattice relaxation rate \(T_{1}^{ - 1}\) can be expressed by the theoretical asymptotic form with the spin susceptibility χs, \(T_{1}^{ - 1} \propto \chi _{\text{s}}^{1/2}\). At temperatures above 150 K, on the other hand, a quadrupole relaxation by spin–phonon coupling through the two-phonon Raman process may become dominant, which is likely caused by the significantly oscillated Li ions in the large tunnel of the characteristic crystal structure.

Evolution of the infrared emissivity of Ni during thermal oxidation until oxide layer opacity

The mid-infrared (3–22 μm) emissivity of high-purity Ni has been studied in its pure state, during an isothermal oxidation in air at 730 °C and in the fully oxidized state. Measurements in pure Ni were performed in Ar between 200 and 800 °C and a change of slope in the temperature dependence of the total normal emissivity around its Curie temperature (354 °C) was observed. An oxidation process was carried out at 730 °C for 33 days, when the emissivity stopped evolving and the results were representative of NiO. During the first stages, the emissivity evolved forming the usual interference patterns of semi-transparent films. A mixture of oscillatory and monotonic behaviours of the emissivity as a function of wavelength and oxide layer thickness was found, which manifests as a non-trivial evolution of the total normal emissivity, different than that reported in previous studies. Finally, the emissivity of NiO was measured from below its Néel temperature (252 °C) to 850 °C. It showed the typical shape of a ceramic material with an extra vibrational mode due to two-phonon processes and an additional absorption band around 5 μm in the antiferromagnetic phase produced by magnons. The temperature dependence of its total normal emissivity differs significantly from that of a lightly oxidized nickel sample from the literature. Overall, the influence of the surface characteristics on the thermal radiative properties of oxidized Ni is thoroughly discussed and highlights the importance of accounting for all possible sources of infrared emissivity evolution in order to make accurate radiative heat transfer calculations.

Atomistic S -matrix method for numerical simulation of phonon reflection, transmission, and boundary scattering

The control of phonon scattering by interfaces is critical to the manipulation of heat conduction in composite materials and semiconducting nanostructures. However, one of the factors limiting our understanding of elastic phonon scattering is the lack of a computationally efficient approach for describing the phenomenon in a manner that accounts for the atomistic configuration of the interface and the exact bulk phonon dispersion. Building on the atomistic Green's function (AGF) technique for ballistic phonon transport, we formulate an atomistic S-matrix method that treats bulk phonon modes as the scattering channels and can determine the numerically exact scattering amplitudes for individual two-phonon processes, enabling a highly detailed analysis of the phonon transmission and reflection spectrum as well as the directional dependence of the phonon scattering specularity. Explicit formulas for the individual phonon reflection, absorption and transmission coefficients are given in our formulation. This AGF-based S-matrix approach is illustrated through the investigation of: (1) phonon scattering at the junction between two isotopically different but structurally identical carbon nanotubes, and (2) phonon boundary scattering at the zigzag and armchair edges in graphene. In particular, we uncover the role of edge chirality on phonon scattering specularity and explain why specularity is reduced for the ideal armchair edge. The application of the method can shed new light on the relationship between phonon scattering and the atomistic structure of interfaces.

Spin–Flip Relaxation Between the Landau Levels in Gapped Graphene

Within the frame of the Huang–Rhys’s lattice relaxation model, we theoretically investigate the spin–flip relaxation assisted by two-phonon processes between the zeroth and first-excited Landau level in gapped graphene on different polar substrates. We give the comparisons between the spin-conserving and the spin–flip of two-phonon processes, which are composed of the surface-optical phonons and longitudinal acoustic phonons. The dependences of two-phonon processes on the energy separation, temperature and polarizability of substrates are discussed. Moreover, we find that the relaxation time of spin–flip can be tuned on a large scale by adjusting the Rashba spin–orbital coupling and internal distance between the graphene and the polar substrate.

Comparative study of the pressure dependence of optical-phonon transverse-effective charges and linewidths in wurtzite InN

We investigate the hydrostatic pressure dependence of the zone center optical phonons of $c$-plane and $a$-plane wurtzite InN epilayers grown on GaN substrates. The longitudinal to transverse mode splitting for the ${A}_{1}$ and ${E}_{1}$ modes was found to increase with increasing pressure, whereas the associated transverse effective charge decreases for both modes as ${e}_{T}^{*}({A}_{1})=2.93--9.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}P$ and ${e}_{T}^{*}({E}_{1})=2.80--10.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}P$ (in units of elementary charge and $P$ in GPa). These observations are well in line with results for other II--VI, III--V, and group-IV semiconductor compounds as far as the relation between the magnitude and sign of the pressure derivative of ${e}_{T}^{*}$ and the bond ionicity is concerned. As the latter increases so does $|\ensuremath{\partial}{e}_{T}^{*}/\ensuremath{\partial}P|$ with a sign change from positive to negative for bond ionicities around ${f}_{i}=0.46$ for compounds with anions belonging to the first row of the Periodic Table. A comparison of the results for InN and other nine tetrahedrally bonded compounds indicate that the pressure behavior of the transverse effective charge is mainly determined by the strength of the Pauli repulsion between cation valence electrons and those of the anion core. We also perform ab initio calculations in order to address the origin of the observed increase in linewidth of the ${E}_{2}^{\text{high}}$ mode which is found to arise from a pressure-induced increase in the rate of two-phonon decay processes. This broadening is associated with tuning into resonance of a steep edge in the two-phonon density of states around 460 ${\mathrm{cm}}^{\ensuremath{-}1}$ with the frequency of the ${E}_{2}^{\text{high}}$ mode.

Analytical study of static beyond-Fröhlich Bose polarons in one dimension

Grusdt et al. [New J. Phys. 19, 103035 (2017)] recently made a renormalization group study of a one-dimensional Bose polaron in cold atoms. Their study went beyond the usual Frohlich description, which includes only single-phonon processes, by including two-phonon processes in which two phonons are simultaneously absorbed or emitted during impurity scattering [Shchadilova et al. Phys. Rev. Lett. 117, 113002 (2016)]. We study this same beyond-Frohlich model, but in the static impurity limit where the ground state is described by a multimode squeezed state instead of the multimode coherent state in the static Frohlich model. We solve the system exactly by applying the generalized Bogoliubov transformation, an approach that can be straightforwardly adapted to higher dimensions. Using our exact solution, we obtain a polaron energy free of infrared divergences and construct analytically the polaron phase diagram. We find that the repulsive polaron is stable on the positive side of the impurity-boson interaction but is always thermodynamically unstable on the negative side of the impurity-boson interaction, featuring a bound state, whose binding energy we obtain analytically. We find that the attractive polaron is always dynamically unstable, featuring a pair of imaginary energies which we obtain analytically. We expect the multimode squeezed state to help with studies that go not only beyond the Frohlich paradigm but also beyond Bogoliubov theory, just as the multimode coherent state has helped with the study of Frohlich polarons.

Spin Lifetime and Charge Noise in Hot Silicon Quantum Dot Qubits.

We investigate the magnetic field and temperature dependence of the single-electron spin lifetime in silicon quantum dots and find a lifetime of 2.8ms at a temperature of 1.1K. We develop a model based on spin-valley mixing and find that Johnson noise and two-phonon processes limit relaxation at low and high temperature, respectively. We also investigate the effect of temperature on charge noise and find a linear dependence up to 4K. These results contribute to the understanding of relaxation in silicon quantum dots and are promising for qubit operation at elevated temperatures.

Strong negative nonlinear friction from induced two-phonon processes in vibrational systems

Self-sustained vibrations in systems ranging from lasers to clocks to biological systems are often associated with the coefficient of linear friction, which relates the friction force to the velocity, becoming negative. The runaway of the vibration amplitude is prevented by positive nonlinear friction that increases rapidly with the amplitude. Here we use a modulated electromechanical resonator to show that nonlinear friction can be made negative and sufficiently strong to overcome positive linear friction at large vibration amplitudes. The experiment involves applying a drive that simultaneously excites two phonons of the studied mode and a phonon of a faster decaying high-frequency mode. We study generic features of the oscillator dynamics with negative nonlinear friction. Remarkably, self-sustained vibrations of the oscillator require activation in this case. When, in addition, a resonant force is applied, a branch of large-amplitude forced vibrations can emerge, isolated from the branch of the ordinary small-amplitude response.

Phonon-assisted relaxation and decoherence of singlet-triplet qubits in Si/SiGe quantum dots

We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.

Suggested design of gold-nanoobjects-based terahertz radiation source for biomedical research

Gold nanoparticles (GNPs) may serve as devices to emit electromagnetic radiation in the terahertz (THz) range, whereby the energy is delivered by radio frequency or microwave photons which will not by themselves induce transitions between sparse confinement-shaped electron levels of a GNP, but may borrow the energy from longitudinal acoustic (LA) phonons to overcome the confinement gap. Upon excitation, the Fermi electron cannot relax otherwise than via emitting a THz photon, the other relaxation channels being blocked by force of shape and size considerations. Within this general scope that has already been outlined earlier, the present work specifically discusses two-phonon processes, namely (i) a combined absorption–emission of two phonons from the top of the LA branch, and (ii) an absorption of two such phonons with nearly identical wavevectors. The case (i) may serve as a source of soft THz radiation (at ≃0.54 THz), the case (ii) the hard THz radiation at 8.7 THz. Numerical estimates are done for crystalline particles in the shape of rhombicuboctahedra, of 5–7 nm size. A technical realisation of this idea is briefly discussed, assuming the deposition of GNPs onto/within the substrate of Teflon®, the material sustaining high temperatures and transparent in the THz range.

Role of thermal two-phonon scattering for impurity dynamics in a low-dimensional Bose-Einstein condensate

We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one- or two-dimensional, ultracold Bose-gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergencies in the corresponding scattering rates in the thermodynamic limit, which are a manifestation of the Mermin-Wagner-Hohenberg theorem. It makes it necessary to include second-order phonon scattering in one-dimensional systems even at $T=0$ and above a crossover temperature $T_\textrm{2ph}$ in two spatial dimensions. $T_\textrm{2ph}$ scales inversely with the system size and is much smaller than currently experimentally accessible.

Exchange narrowing of the one- and two-phonon contributions to the electron spin resonance linewidth in Co3O4

We investigate the temperature dependence of the electron spin resonance (ESR) linewidth above the critical region in Co3O4. The focus is on the temperature dependence of the one and two-phonon processes. We express the linewidth as a sum of three terms, a constant, associated with spin-spin interactions, a one-phonon term, and a two-phonon term, and use a least-squares fit over the temperature range 50 K ≤ T ≤ 500 K in analyzing the data. It is found that the spin-spin mechanism is dominant below 100 K, while the two-phonon mechanism is most important above 250 K. In the intermediate region, all three mechanisms make significant contributions. The success of the high temperature approximation for the phonon terms, which occurs well below the Debye temperature of 525 K, is attributed to the exchange narrowing of the bandwidth of the phonons contributing to the linewidth. The phonon mechanisms for the ESR linewidth in magnetic insulators are compared with the phonon linewidth mechanisms for magnetic impurities in non-magnetic crystals.