Electron Spin Decoherence Research Articles

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.

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.

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.

Electron Spin Decoherence of Nitrogen-Vacancy Center Coupled to Multiple Spin Baths**Supported by the National Basic Research Program of China under Grant Nos 2014CB921402 and 2015CB921103, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB07010300, and the National Natural Science Foundation of China under Grant No 11574386.

We present the experimental results of nitrogen-vacancy (NV) electron spin decoherence, which are linked to the coexistence of electron spin bath of nitrogen impurity (P1 center) and 13C nuclear spin bath. In previous works, only one dominant decoherence source is studied: P1 electron spin bath for type-Ib diamond; or 13C nuclear spin bath for type-IIa diamond. In general, the thermal fluctuation from both spin baths can be eliminated by the Hahn echo sequence, resulting in a long coherence time (T2) of about 400 μs. However, in a high-purity type-IIa diamond where 13C nuclear spin bath is the dominant decoherence source, dramatic decreases of NV electron spin T2 time caused by P1 electron spin bath are observed under certain magnetic field. We further apply the engineered Hahn echo sequence to confirm the decoherence mechanism of multiple spin baths and quantitatively estimate the contribution of P1 electron spin bath. Our results are helpful to understand the NV decoherence mechanisms, which will benefit quantum computing and quantum metrology.

Spin noise of electrons and holes in (In,Ga)As quantum dots: Experiment and theory

The spin fluctuations of electron and hole doped self-assembled quantum dot ensembles are measured optically in the low-intensity limit of a probe laser in absence and presence of longitudinal or transverse static magnetic fields. The experimental results are modeled by two complementary approaches based either on semiclassical or quantum mechanical descriptions. This allows us to characterize the hyperfine interaction of electron and hole spins with the surrounding bath of nuclei on time scales covering several orders of magnitude. Our results demonstrate (i) the intrinsic precession of the electron spin fluctuations around the effective nuclear Overhauser field caused by the host lattice nuclear spins, (ii) the comparably long time scales for electron and hole spin decoherence, as well as (iii) the dramatic enhancement of the spin lifetimes induced by a longitudinal magnetic field due to the decoupling of nuclear and charge carrier spins.

Quadrupolar and anisotropy effects on dephasing in two-electron spin qubits in GaAs.

Understanding the decoherence of electron spins in semiconductors due to their interaction with nuclear spins is of fundamental interest as they realize the central spin model and of practical importance for using them as qubits. Interesting effects arise from the quadrupolar interaction of nuclear spins with electric field gradients, which have been shown to suppress diffusive nuclear spin dynamics and might thus enhance electron spin coherence. Here we show experimentally that for gate-defined GaAs quantum dots, quadrupolar broadening of the nuclear Larmor precession reduces electron spin coherence by causing faster decorrelation of transverse nuclear fields. However, this effect disappears for appropriate field directions. Furthermore, we observe an additional modulation of coherence attributed to an anisotropic electronic g-tensor. These results complete our understanding of dephasing in gated quantum dots and point to mitigation strategies. They may also help to unravel unexplained behaviour in self-assembled quantum dots and III–V nanowires.

Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Spectral diffusion arising from $^{29}$Si nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on $^{31}$P nuclear spin coherence is measured as a function of $^{29}$Si concentration using X-band pulsed electron nuclear double resonance (ENDOR). The $^{31}$P nuclear spin echo decays show that decoherence is controlled by $^{29}$Si flip-flops resulting in both fast (exponential) and slow (non-exponential) spectral diffusion processes. The decay times span a range from 100 ms in crystals containing 50% $^{29}$Si to 3 s in crystals containing 1% $^{29}$Si. These nuclear spin echo decay times for neutral donors are orders of magnitude longer than those reported for ionized donors in natural silicon. The electron spin of the neutral donors `protects' the donor nuclear spins by suppressing $^{29}$Si flip-flops within a `frozen core', as a result of the detuning of the $^{29}$Si spins caused by their hyperfine coupling to the electron spin.

Electron g-factor and spin decoherence in GaAs quantum nanodisks fabricated by fully top-down lithography

GaAs nanodisks (NDs), with a thickness of 8nm and a diameter of 15nm, were directly fabricated from GaAs quantum wells (QW) by damage-free neutral-beam etching using bio-nanotemplates. We observed the electron g-factor and spin dephasing in NDs with different barrier heights in the lateral direction by means of time-resolved Kerr rotation. The magnitude of the g-factor depends on the degree of lateral confinement originating from enhanced penetration of the electron wavefunction from an ND into the surrounding AlGaAs barriers. The spin-dephasing time is also observed to be altered by ND formation.

A comparative study of electron spin decoherence at X- and W-band frequencies as a function of local disorder

The impact of geometrical frustration on electron spin decoherence pathways is studied by electron paramagnetic resonance spectroscopy (EPR) at X- and W-band frequencies. The glassy and crystalline state of solid ethanol served as a simple model of two extreme realizations of host molecular packing probed by relaxation behavior of incorporated paramagnetic nitroxyl radical TEMPO. The specific molecular dynamics is revealed as arising from the local disorder of the environment, suggesting the importance of nuclear spin bath coupling with the electron spin. It is proposed that spectral diffusion might be useful indicator of the extent of frustration in disordered/glassy matrices.

Electron spin decoherence in silicon carbide nuclear spin bath

In this Rapid Communication, we study the electron spin decoherence of single defects in silicon carbide (SiC) nuclear spin bath. We find that, although the natural abundance of $^{29}\mathrm{Si}$ (${p}_{\mathrm{Si}}=4.7%$) is about four times larger than that of ${}^{13}\mathrm{C}$ (${p}_{\mathrm{C}}=1.1%$), the electron spin coherence time of defect centers in SiC nuclear spin bath in a strong magnetic field ($B>300\phantom{\rule{0.28em}{0ex}}\mathrm{G}$) is longer than that of nitrogen-vacancy (NV) centers in ${}^{13}\mathrm{C}$ nuclear spin bath in diamond. In addition to the smaller gyromagnetic ratio of $^{29}\mathrm{Si}$, and the larger bond length in SiC lattice, a crucial reason for this counterintuitive result is the suppression of the heteronuclear-spin flip-flop process in a finite magnetic field. Our results show that electron spin of defect centers in SiC are excellent candidates for solid state spin qubit in quantum information processing.

Hybrid paramagnetic-ferromagnetic quantum computer design based on electron spin arrays and a ferromagnetic nanostripe

Electron spins placed in a magnetic field gradient, interacting by dipolar magnetic couplings and manipulated by microwave pulses represent a possible architecture for a quantum computer. Here, a general design for the practical implementation of such nanodevice is presented on the example of electron spins in silicon carbide placed nearby a permalloy ferromagnetic nanostripe. Firstly, the confined spin wave resonance spectrum of the nanostripe and the properties of its magnetic field gradient are calculated. Then, I show how to avoid microwave driven electron spin decoherence. Then, I show that at temperatures requiring only nitrogen gaz cooling, the silicon vacancy decoherence process due to ferromagnetic fluctuations is negligible compared to the one due to a two phonons Raman process, as long as the silicon vacancies spins are placed far enough from the ferromagnetic nanostripe. I then show that a nitrogen cooled hybrid quantum processor with 32 silicon vacancies spins qubits in SiC is theoretically possible. NV centers in diamond, N@C60 molecules, and radical molecules are three other good spin qubits candidates for implementing this hybrid quantum processor.

Influence of electronic spin and spin-orbit coupling on decoherence in mononuclear transition metal complexes.

Enabling the rational synthesis of molecular candidates for quantum information processing requires design principles that minimize electron spin decoherence. Here we report a systematic investigation of decoherence via the synthesis of two series of paramagnetic coordination complexes. These complexes, [M(C2O4)3](3-) (M = Ru, Cr, Fe) and [M(CN)6](3-) (M = Fe, Ru, Os), were prepared and interrogated by pulsed electron paramagnetic resonance (EPR) spectroscopy to assess quantitatively the influence of the magnitude of spin (S = (1)/2, (3)/2, (5)/2) and spin-orbit coupling (ζ = 464, 880, 3100 cm(-1)) on quantum decoherence. Coherence times (T2) were collected via Hahn echo experiments and revealed a small dependence on the two variables studied, demonstrating that the magnitudes of spin and spin-orbit coupling are not the primary drivers of electron spin decoherence. On the basis of these conclusions, a proof-of-concept molecule, [Ru(C2O4)3](3-), was selected for further study. The two parameters establishing the viability of a qubit are a long coherence time, T2, and the presence of Rabi oscillations. The complex [Ru(C2O4)3](3-) exhibits both a coherence time of T2 = 3.4 μs and the rarely observed Rabi oscillations. These two features establish [Ru(C2O4)3](3-) as a molecular qubit candidate and mark the viability of coordination complexes as qubit platforms. Our results illustrate that the design of qubit candidates can be achieved with a wide range of paramagnetic ions and spin states while preserving a long-lived coherence.

Magnetic properties and hyperfine interactions in Cr₈, Cr₇Cd, and Cr₇Ni molecular rings from ¹⁹F-NMR.

A detailed experimental investigation of the (19)F nuclear magnetic resonance is made on single crystals of the homometallic Cr8 antiferromagnetic molecular ring and heterometallic Cr7Cd and Cr7Ni rings in the low temperature ground state. Since the F(-) ion is located midway between neighboring magnetic metal ions in the ring, the (19)F-NMR spectra yield information about the local electronic spin density and (19)F hyperfine interactions. In Cr8, where the ground state is a singlet with total spin S(T) = 0, the (19)F-NMR spectra at 1.7 K and low external magnetic field display a single narrow line, while when the magnetic field is increased towards the first level crossing field, satellite lines appear in the (19)F-NMR spectrum, indicating a progressive increase in the Boltzmann population of the first excited state S(T) = 1. In the heterometallic rings, Cr7Cd and Cr7Ni, whose ground state is magnetic with S(T) = 3/2 and S(T) = 1/2, respectively, the (19)F-NMR spectrum has a complicated structure which depends on the strength and orientation of the magnetic field, due to both isotropic and anisotropic transferred hyperfine interactions and classical dipolar interactions. From the (19)F-NMR spectra in single crystals we estimated the transferred hyperfine constants for both the F(-)-Ni(2+) and the F(-)-Cd(2+) bonds. The values of the hyperfine constants compare well to the ones known for F(-)-Ni(2+) in KNiF3 and NiF2 and for F(-)-Cr(3+) in K2NaCrF6. The results are discussed in terms of hybridization of the 2s, 2p orbitals of the F(-) ion and the d orbitals of the magnetic ion. Finally, we discuss the implications of our results for the electron-spin decoherence.

Extending the electron spin coherence time of atomic hydrogen by dynamical decoupling

We study the electron spin decoherence of encapsulated atomic hydrogen in octasilsesquioxane cages induced by the 1H and 29Si nuclear spin bath. By applying the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence we significantly suppress the low-frequency noise due to nuclear spin flip-flops up to the point where a maximum T2 = 56 us is observed. Moreover, dynamical decoupling with the CPMG sequence reveals the existence of two sources of high-frequency noise: first, a fluctuating magnetic field with the proton Larmor frequency, equivalent to classical magnetic field noise imposed by the 1H nuclear spins of the cage organic substituents, and second, decoherence due to entanglement between the electron and the inner 29Si nuclear spin of the cage.

Suppression of electron spin decoherence of the diamond NV center by a transverse magnetic field

We demonstrate that the spin decoherence of nitrogen vacancy (NV) centers in diamond can be suppressed by a transverse magnetic field if the electron spin bath is the primary decoherence source. The NV spin coherence, created in ``a decoherence-free subspace,'' is protected by the transverse component of the zero-field splitting, increasing the spin-coherence time about twofold. The decoherence due to the electron spin bath is also suppressed at magnetic fields stronger than \ensuremath{\sim}25 G when applied parallel to the NV symmetry axis. Our method can be used to extend the spin-coherence time of similar spin systems for applications in quantum computing, field sensing, and other metrologies.

Quantum decoherence of the central spin in a sparse system of dipolar coupled spins

The central spin decoherence problem has been researched for over 50 years in the context of both nuclear magnetic resonance and electron spin resonance. Until recently, theoretical models have employed phenomenological stochastic descriptions of the bath-induced noise. During the last few years, cluster expansion methods have provided a microscopic, quantum theory to study the spectral diffusion of a central spin. These methods have proven to be very accurate and efficient for problems of nuclear-induced electron spin decoherence in which hyperfine interactions with the central electron spin are much stronger than dipolar interactions among the nuclei. We provide an in-depth study of central spin decoherence for a canonical scale-invariant all-dipolar spin system. We show how cluster methods may be adapted to treat this problem in which central and bath spin interactions are of comparable strength. Our extensive numerical work shows that a properly modified cluster theory is convergent for this problem even as simple perturbative arguments begin to break down. By treating clusters in the presence of energy detunings due to the long-range (diagonal) dipolar interactions of the surrounding environment and carefully averaging the effects over different spin states, we find that the nontrivial flip-flop dynamics among the spins becomes effectively localized by disorder in the energy splittings of the spins. This localization effect allows for a robust calculation of the spin echo signal in a dipolarly coupled bath of spins of the same kind, while considering clusters of no more than 6 spins. We connect these microscopic calculation results to the existing stochastic models. We, furthermore, present calculations for a series of related problems of interest for candidate solid state quantum bits including donors and quantum dots in silicon as well as nitrogen-vacancy centers in diamond.

Magneto-optical analysis of the effectivegtensor and electron spin decoherence in the multivalley conduction band of bulk germanium

We present a comprehensive study of electron spin decoherence in bulk germanium. As a first cornerstone, the effective $g$ tensor of $L$-valley electrons in germanium is deduced from time-domain magneto-optical experiments. The decay of the ensemble spin polarization is then found to be closely related to intervalley scattering. In particular, the angular and temperature dependences of the experiment are well described in a model including Elliott-Yafet-type spin-flip processes as well as dephasing due to scattering between valleys exhibiting different effective $g$ factors.

Electron spin coherence in antiferromagnetically coupled binuclear Mn complexes

We report a pulse electron spin resonance study of binuclear Mn molecular complexes whose magnetic properties are controlled by the ligand substitution. An electron spin echo in these complexes in the solid phase and also diluted in a frozen solution matrix was detected, and the spin decoherence time ${T}_{2}$ of Mn spins at different temperatures was determined. We observe a simple exponential ${T}_{2}$ relaxation in the latter samples and a nonexponential relaxation process in the former ones. The data analysis establishes the hyperfine coupling to the protons as an important source of the electron spin decoherence. Furthermore, the data clearly suggest an important role of the intermolecular spin-spin coupling for the ${T}_{2}$ relaxation. The influence of both mechanisms should be considered as limiting factors for coherent spin manipulation in molecular magnets with regard to their possible application for quantum computing.

Semiclassical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath

We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semi-classical model for the interaction between the electron and nuclear spins, in which the time-dependent Overhauser fields induced by the nuclear spins are treated as classical vector variables. Comparison of the model with experimentally-obtained echo signals allows us to quantify the contributions of various processes such as coherent Larmor precession and spin diffusion to the nuclear spin evolution.

The effect of surface conductance on lateral gated quantum devices in Si/SiGe heterostructures

Quantum dots in Si/SiGe heterostructures are expected to have relatively long electron spin decoherence times, because of the low density of nuclear spins and the weak coupling between nuclear and electron spins. We provide experimental evidence suggesting that electron motion in a conductive layer parallel to the two-dimensional electron gas, possibly resulting from the donors used to dope the Si quantum well, is responsible for the well-known difficulty in achieving well-controlled dots in this system. Charge motion in the conductive layer can cause depletion on large length scales, making electron confinement in the dot impossible, and can give rise to noise that can overwhelm the single-electron charging signal. Results of capacitance versus gate bias measurements to characterize this conductive layer are presented.