Spin Decoherence Research Articles

Magnetic edge states and coherent manipulation of graphene nanoribbons.

Graphene, a single-layer network of carbon atoms, has outstanding electrical and mechanical properties 1 . Graphene ribbons with nanometre-scale widths2,3 (nanoribbons) should exhibit half-metallicity 4 and quantum confinement. Magnetic edges in graphene nanoribbons5,6 have been studied extensively from a theoretical standpoint because their coherent manipulation would be a milestone for spintronic 7 and quantum computing devices 8 . However, experimental investigations have been hampered because nanoribbon edges cannot be produced with atomic precision and the graphene terminations that have been proposed are chemically unstable 9 . Here we address both of these problems, by using molecular graphene nanoribbons functionalized with stable spin-bearing radical groups. We observe the predicted delocalized magnetic edge states and test theoretical models of the spin dynamics and spin-environment interactions. Comparison with a non-graphitized reference material enables us to clearly identify the characteristic behaviour of the radical-functionalized graphene nanoribbons. We quantify the parameters of spin-orbit coupling, define the interaction patterns and determine the spin decoherence channels. Even without any optimization, the spin coherence time is in the range of microseconds at room temperature, and we perform quantum inversion operations between edge and radical spins. Our approach provides a way of testing the theory of magnetism in graphene nanoribbons experimentally. The coherence times that we observe open up encouraging prospects for the use of magnetic nanoribbons in quantum spintronic devices.

Spin decoherence of InAs surface electrons by transition metal ions

Spin interactions between a two-dimensional electron system at the InAs surface and transition metal ions, ${\mathrm{Fe}}^{3+}$, ${\mathrm{Co}}^{2+}$, and ${\mathrm{Ni}}^{2+}$, deposited on the InAs surface, are probed by antilocalization measurements. The spin-dependent quantum interference phenomena underlying the quantum transport phenomenon of antilocalization render the technique sensitive to the spin states of the transition metal ions on the surface. The experiments yield data on the magnitude and temperature dependence of the electrons' inelastic scattering rates, spin-orbit scattering rates, and magnetic spin-flip rates as influenced by ${\mathrm{Fe}}^{3+}$, ${\mathrm{Co}}^{2+}$, and ${\mathrm{Ni}}^{2+}$. A high magnetic spin-flip rate is shown to mask the effects of spin-orbit interaction, while the spin-flip rate is shown to scale with the effective magnetic moment of the surface species. The spin-flip rates and their dependence on temperature yield information about the spin states of the transition metal ions at the surface, and in the case of ${\mathrm{Co}}^{2+}$ suggest either a spin transition or formation of a spin-glass system.

Probing Conformal Invariant of Non-unitary Two-Dimensional Systems by Central Spin Decoherence

Universality classes of non-unitary critical theories in two-dimensions are characterized by the central charge. However, experimental determination of the central charge of a non-unitary critical theory has not been done before because of the intrinsic difficulty that complex parameters usually occur in non-unitary theory, which is not physical. Here we propose to extract the effective central charge of the non-unitary critical point of a two-dimensional lattice model from the quantum coherence measurement of a probe spin which is coupled to the lattice model. A recent discovery shows that quantum coherence of a probe spin which is coupled to a bath is proportional to the partition function of the bath with a complex parameter. Thus the effective central charge of a non-unitary conformal field theory may be extracted from quantum coherence measurement of a probe spin which is coupled to a bath. We have applied the method to the Yang-Lee edge singularity of the two-dimensional Ising model and extracted the effective central charge of the Yang-Lee edge singularity with good precision and tested other predictions of non-unitary conformal field theory. This work paves the way for the first experimental observation of the effective central charge of non-unitary conformal field theory.

Suppression of electron spin decoherence in Rabi oscillations induced by an inhomogeneous microwave field

The decay of Rabi oscillations provides direct information about coherence of electron spins. When observed in EPR experiments, it is often shortened by spatial inhomogeneity of the microwave field amplitude in a bulk sample. In order to suppress this undesired loss of coherence, we propose an additional dressing of spin states by a weak longitudinal continuous radiofrequency field. The Gaussian, cosine and linear distributions of the microwave amplitude is analyzed. Our calculations of the Rabi oscillations between the doubly dressed spin states show that for all these distributions the maximum suppression of the inhomogeneity-induced decoherence is achieved at the so-called Rabi resonance when the radio-field frequency is in resonance with the Rabi frequency of spins in the microwave field. The manifestations of such suppression in the published EPR experiments with the bichromatic driving are discussed. The realization of the Rabi resonance using the radiofrequency field could open new possibilities for separating the contributions of relaxation mechanisms from those due to the inhomogeneous driving in spin decoherence.

Quantum control of nitrogen-vacancy center in diamond

Quantum computing and quantum sensing have received much attention in recent years. As an atomic quantum system with super-long coherence time and spin-dependent optical transitions at room temperature, nitrogen-vacancy (NV) center in diamond is one of the well-studied physical systems in quantum information science. In this review, we brief the working principles and quantum control techniques of this single spin system, and also several experimental demonstrations. We focus on the following points:1) coherent manipulation of single spins with optically detected magnetic resonance; 2) main mechanism of NV election spin decoherence and schemes of coherence protection; 3) quantum sensing and quantum computing applications of spin quantum control techniques. Some open questions are discussed at the end of this review.

Spin-orbit coupling fluctuations as a mechanism of spin decoherence

We discuss a general framework to address spin decoherence resulting from fluctuations in a spin Hamiltonian. We performed a systematic study on spin decoherence in the compound K$_6$[V$_{15}$As$_6$O$_{42}$(D$_2$O)] $\cdot$ 8D$_2$O, using high-field Electron Spin Resonance (ESR). By analyzing the anisotropy of resonance linewidths as a function of orientation, temperature and field, we find that the spin-orbit term is a major decoherence source. The demonstrated mechanism can alter the lifetime of any spin qubit and we discuss how to mitigate it by sample design and field orientation.

Room-temperature cavity quantum electrodynamics with strongly coupled Dicke states

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 sqrt 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 T_2^*sim 3 μs. When coupled to a 1.45 GHz TE01δ mode supported by a high Purcell factor strontium titanate dielectric cavity (V_{mathrm{m}}sim 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.

Noninvasive detection of nanoparticle clustering by water proton NMR

It is shown that water proton NMR can detect uncontrolled clustering of inert nanoparticles (NPs) formulated as aqueous suspensions. The clustering of NPs causes the compartmentalization of water molecules, leading to accelerated proton spin de-coherence, and hence, much faster water transverse relaxation rates. The results suggest that water proton NMR can be used to noninvasively inspect NP products by commercial end users and researchers.

Probing Yang–Lee edge singularity by central spin decoherence

Yang–Lee edge singularities are the branch point of free energy on the complex plane of physical parameters and have been shown to be the simplest universality class of phase transitions. However, Yang–Lee edge singularities have not been regarded as experimentally observable since they occur at complex physical parameters which are unphysical. A recent discovery regarding the relation between partition functions and probe spin coherence makes it experimentally feasible to access the complex plane of physical parameters. However, how to extract the critical point and the critical exponent of Yang–Lee edge singularities in many-body systems, which occurs only at the thermodynamic limit, has still been elusive. Here we show that the quantum coherence of a probe spin coupled to finite-size Ising-type spin systems presents universal scaling behavior near the Yang–Lee edge singularity. The finite-size scaling behavior of the quantum coherence of the probe spin predicts that one can extract the critical point and the critical exponent of the Yang–Lee edge singularity of an Ising-type spin system in the thermodynamic limit from the spin coherence measurement of the probe spin coupled to finite-size Ising-type spin systems. This finding provides a practical approach to studying the nature of Yang–Lee edge singularities of many-body systems.

Electron spin decoherence as a measure of nuclear spin bath frustration

Two realisations of solid-state environment, which differ in molecular packing, glassy and crystalline solid ethanol, are used as a model systems to study disorder in terms of nuclear spin bath frustration. It is probed by the hyperfine interaction of the electron spin from the incorporated paramagnetic nitroxyl radical TEMPO. Nuclear spectral diffusion from ethanol protons is presented as the dominant mechanism of electron spin decoherence and proposed as a descriptor of the extent of disorder present in the system. It is shown that the dynamical decoupling control of the electron spin is affected by the extent of disorder in terms of the heterospin dephasing and can be numerically evaluated for the specific model system. The effect of odd/even number of decoupling pulses was not observed suggesting that for the description of proton spin bath frustration in solid ethanol higher terms than fourth-order proton spin correlations might be considered in modelling spectral diffusion mechanism.

Amplitude Sensing below the Zero-Point Fluctuations with a Two-Dimensional Trapped-Ion Mechanical Oscillator.

We present a technique to measure the amplitude of a center-of-mass (c.m.) motion of a two-dimensional ion crystal of ∼100 ions. By sensing motion at frequencies far from the c.m. resonance frequency, we experimentally determine the technique's measurement imprecision. We resolve amplitudes as small as 50pm, 40 times smaller than the c.m. mode zero-point fluctuations. The technique employs a spin-dependent, optical-dipole force to couple the mechanical oscillation to the electron spins of the trapped ions, enabling a measurement of one quadrature of the c.m. motion through a readout of the spin state. We demonstrate sensitivity limits set by spin projection noise and spin decoherence due to off-resonant light scattering. When performed on resonance with the c.m. mode frequency, the technique demonstrated here can enable the detection of extremely weak forces (<1 yN) and electric fields (<1 nV/m), providing an opportunity to probe quantum sensing limits and search for physics beyond the standard model.

Multiple-Quantum Transitions and Charge-Induced Decoherence of Donor Nuclear Spins in Silicon.

We study single- and multiquantum transitions of the nuclear spins of an ensemble of ionized arsenic donors in silicon and find quadrupolar effects on the coherence times, which we link to fluctuating electrical field gradients present after the application of light and bias voltage pulses. To determine the coherence times of superpositions of all orders in the 4-dimensional Hilbert space, we use a phase-cycling technique and find that, when electrical effects were allowed to decay, these times scale as expected for a fieldlike decoherence mechanism such as the interaction with surrounding ^{29}Si nuclear spins.

Decoherence and fluctuation dynamics of the quantum dot nuclear spin bath probed by nuclear magnetic resonance

Dynamics of nuclear spin decoherence and nuclear spin flip-flops in self-assembled InGaAs/GaAs quantum dots are studied experimentally using optically detected nuclear magnetic resonance (NMR). Nuclear spin-echo decay times are found to be in the range 1-4 ms. This is a factor of ~3 longer than in strain-free GaAs/AlGaAs structures and is shown to result from strain-induced quadrupolar effects that suppress nuclear spin flip-flops. The correlation times of the flip-flops are examined using a novel frequency-comb NMR technique and are found to exceed 1 s, a factor of ~1000 longer than in strain-free structures. These findings complement recent studies of electron spin coherence and reveal the paradoxical dual role of the quadrupolar effects in self-assembled quantum dots: large increase of the nuclear spin bath coherence and at the same time significant reduction of the electron spin-qubit coherence. Approaches to increasing electron spin coherence are discussed. In particular the nanohole filled GaAs/AlGaAs quantum dots are an attractive option: while their optical quality matches the self-assembled dots the quadrupolar effects measured in NMR spectra are a factor of 1000 smaller.

Tuning the spin coherence time of Cu(II)-(bis)oxamato and Cu(II)-(bis)oxamidato complexes by advanced ESR pulse protocols.

We have investigated with the pulsed ESR technique at X- and Q-band frequencies the coherence and relaxation of Cu spins S = 1/2 in single crystals of diamagnetically diluted mononuclear [n-Bu4N]2[Cu(opba)] (1%) in the host lattice of [n-Bu4N]2[Ni(opba)] (99%, opba = o-phenylenebis(oxamato)) and of diamagnetically diluted mononuclear [n-Bu4N]2[Cu(opbon-Pr2)] (1%) in the host lattice of [n-Bu4N]2[Ni(opbon-Pr2)] (99%, opbon-Pr2 = o-phenylenebis(N(propyl)oxamidato)). For that we have measured the electron spin dephasing time Tm at different temperatures with the two-pulse primary echo and with the special Carr–Purcell–Meiboom–Gill (CPMG) multiple microwave pulse sequence. Application of the CPMG protocol has led to a substantial increase of the spin coherence lifetime in both complexes as compared to the primary echo results. It shows the efficiency of the suppression of the electron spin decoherence channel in the studied complexes arising due to spectral diffusion induced by a random modulation of the hyperfine interaction with the nuclear spins. We argue that this method can be used as a test for the relevance of the spectral diffusion for the electron spin decoherence. Our results have revealed a prominent role of the opba4– and opbon-Pr24– ligands for the dephasing of the Cu spins. The presence of additional 14N nuclei and protons in [Cu(opbon-Pr2)]2– as compared to [Cu(opba)]2– yields significantly shorter Tm times. Such a detrimental effect of the opbon-Pr24− ligands has to be considered when discussing a potential application of the Cu(II)−(bis)oxamato and Cu(II)−(bis)oxamidato complexes as building blocks of more complex molecular structures in prototype spintronic devices. Furthermore, in our work we propose an improved CPMG pulse protocol that enables elimination of unwanted echoes that inevitably appear in the case of inhomogeneously broadened ESR spectra due to the selective excitation of electron spins.

(Invited) Tuning Molecular Singlet Fission – Strong Versus Weak Electronic Coupling

Innovative strategies are necessary to overcome the Shockley-Queisser limit, which places the maximum solar conversion efficiency for a single p-n junction to slightly more than 30%. One such strategy, singlet fission (SF), allows high energy, singlet excited state photons (S1) to be down-converted into up to twice as many low-energy, triplet excited state photons (T1). As such, SF is a fascinating many-electron problem from a physical chemistry perspective. In an optimal SF scenario, a chromophore in a singlet excited state (S1) interacts with a nearby ground state (S0) chromophore to yield up to two, non-interacting T1s. Doubling the number of excited states, thus, goes hand in hand with sacrificing half or more of the overall energy per excited state. The energetic requirement for SF is E(S1) ≥ 2(E(T1)), and the free reaction enthalpy for the S1 ® 2(T1) conversion governs the energy loss in SF. The SF rate depends on the free reaction energy and the electronic coupling matrix element between one chromophore in its S1 and another in its S0 ground state. A strict definition of the SF rate implies the formation rate of the two individual triplets (T1 + T1), not that of the correlated triplet pair, 1(T1T1). In (T1 + T1), the two triplets should have lost electronic coherence owing to interactions with the environment, but can retain spin coherence on much longer timescales. In a nutshell, electronic coupling between the chromophores should be sufficient to drive SF, while at the same time keeping the coupling sufficiently weak to allow spin decoherence leading to two independent triplet states. The systematic variation / comprehensive understanding of electronic coupling between the individual pentacenes constitutes one of the grand challenges in the field of molecular SF, especially when experiments are conducted in solution. By means of tailoring the synthesis of pentacene dimers, trimers, and tetramers we will span our investigations from a weakly coupled, charge transfer to a strongly coupled, charge separated regime. In turn, we are confident to gain control over the rates and yields of intramolecular SF and, subsequent, inter- and intramolecular charge extraction. In particular, we plan to investigate pentacene materials, in which the energy of the charge transfer state and that of the charge separated state is tuned in the range around twice of the triplet excited state, and to explore the impact on the formation of pairs of independent triplets (T1 + T1).

Atomic structure study of the pyrochloreYb2Ti2O7and its relationship with low-temperature magnetic order

Exchange interactions with itinerant electrons are known to act as a relaxation mechanism for individual local spins. The same exchange interactions are also known to induce the so called RKKY indirect exchange interaction between two otherwise decoupled local spins. Here we show that both the spin relaxation and the RKKY coupling can be seen as the dissipative and reactive response to the coupling of the local spins with the itinerant electrons. We thereby predict that the spin relaxation rates of magnetic nanostructures of exchanged coupled local spins, such as as nanoengineered spin chains, have an oscillatory dependence on $k_F d$ , where $k_F$ is the Fermi wave length and $d$ is the inter-spin distance, very much like the celebrated oscillations in the RKKY interaction. We demonstrate that both $T_1$ and $T_2$ can be enhanced or suppressed, compared to the single spin limit, depending on the interplay between the Fermi surface and the nanostructure geometrical arrangement. Our results open a route to engineer spin relaxation and decoherence in atomically designed spin structures.

Effect of ionized impurity screening on spin decoherence at low and intermediate temperatures in GaAs

AbstractWe study the effect of charged impurity screening on spin decoherence in bulk n‐type GaAs, and analyze in details the effect of the use of different Born approximations applied to a linearized Thomas–Fermi screening theory. The spin relaxation times are calculated by ensemble Monte Carlo techniques, including electron–electron, electron–impurities, and electron–phonons scattering. We carefully choose a parameter region so that all the physical approximations hold, and, in particular, a Yukawa‐type potential can be used to describe the screened Coulomb interaction and the Born series converges. Our results show that including the second order Born approximation yields much shorter spin relaxation times compared to the commonly implemented first Born approximation: spin relaxation times may be reduced by hundreds of picoseconds, with the first Born approximation overestimating results by 30% or more for a large region of parameters. Though our ensemble Monte Carlo simulations include electron–electron and electron‐phonon interactions, when considering low to intermediate carrier densities and T &gt; 50 K, but T smaller than the Fermi temperature, our results are in good agreement with Dyakonov–Perel theory when this includes electron‐impurity interactions only, which supports this to be the most relevant scattering mechanism for bulk GaAs in this low‐intermediate temperature regime.

Synthetic Approach To Determine the Effect of Nuclear Spin Distance on Electronic Spin Decoherence.

Nuclear-electronic interactions are a fundamental phenomenon which impacts fields from magnetic resonance imaging to quantum information processing (QIP). The realization of QIP would transform diverse areas of research including accurate simulation of quantum dynamics and cryptography. One promising candidate for the smallest unit of QIP, a qubit, is electronic spin. Electronic spins in molecules offer significant advantages with regard to QIP, and for the emerging field of quantum sensing. Yet relative to other qubit candidates, they possess shorter superposition lifetimes, known as coherence times or T2, due to interactions with nuclear spins in the local environment. Designing complexes with sufficiently long values of T2 requires an understanding of precisely how the position of nuclear spins relative to the electronic spin center affects decoherence. Herein, we report the first synthetic study of the relationship between nuclear spin-electron spin distance and decoherence. Through the synthesis of four vanadyl complexes, (Ph4P)2[VO(C3H6S2)2] (1), (Ph4P)2[VO(C5H6S4)2] (2), (Ph4P)2[VO(C7H6S6)2] (3), and (Ph4P)2[VO(C9H6S8)2] (4), we are able to synthetically place a spin-laden propyl moiety at well-defined distances from an electronic spin center by employing a spin-free carbon-sulfur scaffold. We interrogate this series of molecules with pulsed electron paramagnetic resonance (EPR) spectroscopy to determine their coherence times. Our studies demonstrate a sharp jump in T2 when the average V-H distance is decreased from 6.6(6) to 4.0(4) Å, indicating that spin-active nuclei sufficiently close to the electronic spin center do not contribute to decoherence. These results illustrate the power of synthetic chemistry in elucidating the fundamental mechanisms underlying electronic polarization transfer and provide vital principles for the rational design of long-coherence electronic qubits.

RKKY oscillations in the spin relaxation rates of atomic-scale nanomagnets

Exchange interactions with itinerant electrons are known to act as a relaxation mechanism for individual local spins. The same exchange interactions induce the so-called RKKY indirect exchange interaction between two otherwise decoupled local spins. Here, we show that both the spin relaxation and the RKKY coupling can be seen as the dissipative and reactive response to the coupling of the local spins with the itinerant electrons. We thereby predict that the spin relaxation rates of magnetic nanostructures of exchanged coupled local spins, such as nanoengineered spin chains, have an oscillatory dependence on ${k}_{F}d$, where ${k}_{F}$ is the Fermi wave number and $d$ is the interspin distance, very much like the celebrated oscillations in the RKKY interaction. We demonstrate that both ${T}_{1}$ and ${T}_{2}$ can be enhanced or suppressed, compared to the single-spin limit, depending on the interplay between the Fermi surface and the nanostructure geometrical arrangement. Our results open a route to engineer spin relaxation and decoherence in atomically designed spin structures.

Anisotropic decoherence in quantum wells with arbitrary magnetic fields: Interplay of the spin-orbit coupling terms

We present a theoretical study of the anisotropy of the spin relaxation and decoherence in typical quantum wells with an arbitrary magnetic field. In such systems, the orientation of the magnetic field relative to the main crystallographic directions is crucial, owing to the lack of spin-rotation symmetry. For typical high mobility samples, relaxation anisotropies owing to the interplay of Rashba and Dresselhaus spin-orbit coupling are calculated. We also include the effect of the cubic-in-momentum terms. Although commonly ignored in literature, the latter were experimentally evidenced by the observation of strong anisotropy in spin decoherence measurements by different experimental groups and has long remained unexplained. This work suggests a method to determine the relative strength of spin-orbit coupling terms by angular resolution of decoherence in electron spin resonance experiments.