Electron-nuclear Spin System Research Articles

Discrimination of quantum dots using an optically created nuclear field

We investigated an optically created nuclear field in a single InAlAs quantum dot and demonstrated that the nuclear field can be used to discriminate whether photoluminescence lines originate from the same dot or a different dot. Since the nonlinear response of the nuclear field is sensitive to the electron g factor and correlation time of a coupled electron-nuclear spin system, the resultant Overhauser shift is their good measure for individual quantum dots. This method provides a simple and convenient alternative to the standard photon cross-correlation method.

Switched control of electron nuclear spin systems

We study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static ${B}_{0}$ field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.

Subsecond Spin Relaxation Times in Quantum Dots at Zero Applied Magnetic Field Due to a Strong Electron-Nuclear Interaction

A key to ultralong electron spin memory in quantum dots (QDs) at zero magnetic field is the polarization of the nuclei, such that the electron spin is stabilized along the average nuclear magnetic field. We demonstrate that spin-polarized electrons in n-doped (In,Ga)As/GaAs QDs align the nuclear field via the hyperfine interaction. A feedback onto the electrons occurs, leading to stabilization of their polarization due to formation of a nuclear spin polaron [I. A. Merkulov, Phys. Solid State 40, 930 (1998)]. Spin depolarization of both systems is consequently greatly reduced, and spin memory of the coupled electron-nuclear spin system is retained over 0.3 sec at temperature of 2 K.

Hysteretic dynamic nuclear polarization inGaAs/AlxGa1−xAs(110) quantum wells

We investigated the dynamics of a coupled electron-nuclear spin system in a GaAs/AlGaAs (110) quantum well by time-resolved Faraday rotation measurements. Photoexcited electron spins with long coherence time ${(T}_{2}^{*}=6\mathrm{ns})$ are strongly subject to a nuclear field as well as polarizing the nuclei. A hysteretic behavior was observed in the magnetic-field dependence of the nuclear polarization under optical orientation. Our quantitative analysis based on self-consistent calculations reproduced the experimental observation of the bistable configurations of dynamic nuclear polarization.

Dynamics of intrinsic optical bistability in two weakly interacting quantum systems

The dynamics of the intrinsic optical bistability (IOB) in an elementary quantum system is investigated in the situation where this system is composed of two weakly interacting subsystems. Numerical calculations have been performed for two 'real' systems where IOB has been experimentally observed. The first situation corresponds to the electron-nuclear spin system of {beta}-Ga{sub 2}O{sub 3}, where the transition between electron spin states exhibit a strong bistability. The other situation corresponds to optical transitions in Yb{sup 3+} pairs in CsCdBr{sub 3}:Yb compound, where IOB has been experimentally observed. It is shown that, in addition to the classical hysteresis of the response of the system upon variation of the power of the external field, the observation of the so-called critical slowing down is a clear signature of IOB.

Radio-frequency-driven electron spin echo envelope modulation spectroscopy on spin systems with isotropic hyperfine interactions

Three-pulse radio-frequency (rf) driven electron spin echo envelope modulation (ESEEM) is introduced as a method to measure hyperfine couplings of electron–nuclear spin systems in liquids. It is distinguished from the corresponding two-pulse experiment by narrower lines. Numerical simulations of rf-driven ESEEM based on Floquet theory are given and compared with average Hamiltonian theory. Artifacts which appear in rf-driven ESEEM spectra are discussed, and approaches for the removal of these artifacts such as time-proportional phase incrementation (TPPI) of the rf phase and an rf phase cycle (0, π) are presented. The validity of the analytical description of the rf-driven ESEEM experiment is shown by comparison with experimental results.

The nuclear magnetic resonance spectrum of 31Pdonors in a silicon quantum computer

The influence of an electric field created by a gatepotential of the silicon quantum computer on the hyperfine interactionconstant (HIC) is obtained. The errors due to the technological inaccuracy ofthe location of donor atoms under a gate are evaluated. The energy spectra ofan electron-nuclear spin system of two interacting donor atoms with variousvalues of HIC are calculated. The presence of two pairs of anticrossinglevels in the ground electronic state is shown. The parameters of the structureat which the error rate can be greatly minimized are found.

Solid effect in the electron spin dressed state: A new approach for dynamic nuclear polarization

We describe a new type of solid effect for dynamic nuclear polarization (DNP) that is based on simultaneous, near resonant microwave (mw) and radio frequency (rf) irradiation of a coupled electron nuclear spin system. The interaction of the electron spin with the mw field is treated as an electron spin dressed state. In contrast to the customary laboratory frame solid effect, it is possible to obtain nuclear polarization with the dressed state solid effect (DSSE) even in the absence of nonsecular hyperfine coupling. Efficient, selective excitation of dressed state transitions generates nuclear polarization in the nuclear laboratory frame on a time scale of tens of μs, depending on the strength of the electron–nuclear coupling, the mw and rf offset and field strength. The experiment employs both pulsed mw and rf irradiation at a repetition rate comparable to T1e−1, where T1e is the electronic spin lattice relaxation time. The DSSE is demonstrated on a perdeuterated BDPA radical in a protonated matrix of polystyrene.

The hyperfine energy spectrum of31P donors in a silicon NMR quantum computer

The effect of an electric field on the hyperfine interaction constant (HIC) of a donor atom is considered within the silicon quantum computer model. The field is produced by the potential of a circular (disk-shaped) or strip gate. A spread in the HIC values because of inaccurately placing donor atoms under the gate is estimated. The energy spectrum of the electron-nuclear spin system for two interacting donor atoms with different HICs is evaluated. Two pairs of levels anticrossing in the ground state are shown to exist.

Investigations of dielectric Van Vleck paramagnets at high magnetic fields and low temperatures

The influence of high magnetic fields on the magnetic properties of dielectric Van Vleck paramagnets is discussed. The dynamics of coupled electron–nuclear spin system is investigated at high magnetic fields and low temperatures.

Dark magnetic resonance in an electron-nuclear spin system

Dark magnetic resonance in the solid state is observed and is shown to be analogous to electromagnetically induced transparency in coherent optics. The basis of the two effects is coherent population trapping, which can conveniently be described by the product operator formalism. It is demonstrated that pulse electron paramagnetic resonance experiments on electron-nuclear spin systems provide a simple means for studying the physics of these types of coherence phenomena.

Matched two-pulse electron spin echo envelope modulation spectroscopy

The theory of nonideal microwave pulses acting on electron–nuclear spin systems is extended and applied to optimize the two-pulse electron spin echo envelope modulation (ESEEM) experiment. A superoperator approach for a computationally efficient simulation of experiments involving non-ideal pulses is introduced and the corresponding unitary transformation superoperator is given analytically for a system consisting of one electron spin S=1/2 and one nuclear spin I=1/2. Density operator single-element transfers are divided into allowed and forbidden ones and are classified according to their functioning in pulse ESR. By increasing the efficiency of forbidden transfers by Hartmann–Hahn matching during prolonged pulses, the sensitivity of the conventional two-pulse ESEEM experiment may drastically be improved and discrimination between basic, hyperfine, and combination frequencies becomes possible. The implications of the theory for spin systems with an arbitrary number of nuclear spins 1/2 are investigated by deriving and discussing a general condition for Hartmann–Hahn matching of forbidden transitions. It is shown that the product rule valid for two-pulse echo modulations caused by more than one nucleus does not hold for nonideal pulses. A method is developed that allows one to reduce the thus arising large dimensionality of the diagonalization problem in numerical simulations. The theoretical conclusions are verified by experiments on two transition metal complexes in single crystals and on a spin-label-doped polymer sample.

Generation and transfer of coherence in electron—nuclear spin systems by non-ideal microwave pulses

Generation and transfer of coherence in electron—nuclear spin systems by non-ideal microwave pulses

Generation and transfer of coherence in electron-nuclear spin systems by non-ideal microwave pulses

A quantum mechanical treatment based on a suitably truncated Hamiltonian is developed for the evolution during microwave (MW) irradiation of an S = 1/2, I = 1/2 electron–nuclear spin system with anisotropic hyperfine coupling. It is shown that there is a close analogy between this problem and the well understood phenomena in heteronuclear spin systems with resolved J couplings during double irradiation (L. Müller and R. R. Ernst, 1979, Molec. Phys., 38, 963). A general expression is derived for the MW field strength necessary to establish the modified Hartmann–Hahn condition where electron and nuclear spin states mix completely and maximum nuclear coherence can be generated. The theory is then applied to the discussion of hyperfine decoupling and coherence generation from Boltzmann equilibrium by a MW pulse of arbitrary field strength and duration. It is demonstrated that the build-up of nuclear coherence during such a pulse is slow and oscillatory, and that maximum nuclear coherence is achieved at nominal flip angles considerably larger than 2 π. The creation of both nuclear coherence and coherence on forbidden electron transitions is found to be optimum at the modified Hartmann–Hahn condition, and not to be limited by the modulation depth parameter known from electron spin echo envelope modulation (ESEEM) theory. The theoretical results are used to interpret a number of recent experimental observations that could not be understood by existing theories, and to propose an alternative explanation for nuclear modulations observed in experiments on bacterial photosystems. Effects in systems with a nuclear spin I = 1 are discussed taking into account nuclear quadrupole interactions. It is demonstrated both by numerical simulations and experiments that the well established two-pulse ESEEM experiment can be optimized by using pulses with matched microwave field strength and nominal flip angles larger than 2 π.

Analytical description of selective excitation in pulsed EPR and application to the two-pulse coherent Raman beat experiment

An analytical expression describing the evolution of an electron-nuclear spin system with anisotropic hyperfine coupling during selective microwave excitation is derived. The approach is applied to the two-pulse coherent Raman beat (CRB) EPR experiment, and is shown to be valid far beyond the linear regime approximation. The accuracy of the analytical formula is verified by model calculations, and the delay of the CRB signal observed in the linear regime is demonstrated to be a general characteristic of two-pulse CRB experiments independent of the strength of the probe pulse.

Primary Nuclear Spin Echoes in EPR Induced by Microwave Pulses

Primary nuclear spin echoes in electron-nuclear spin systems, created and detected by exciting electron-spin transitions only, are presented. Two pulse sequences for the generation of this new type of echo in magnetic resonance are proposed. The first sequence consists of twosemi-selectivemicrowave pulses with flip angles π and 2π followed by a weak microwave probe pulse for detection. It is noteworthy that the flip angles are doubled compared to that used in the usual primary spin-echo experiment. In the second sequence, the nuclear spin echo is created by nonselective microwave pulses and observed as a modulation on top of the electron spin echo. Both experiments are analyzed theoretically by using the product-operator formalism. The predicted features are verified experimentally, in particular, the separation of the primary echoes from the coherence-transfer echoes by using two-dimensional representations of the data in the frequency domain. As an example of application, the determination of the phase-memory time of nuclei coupled to the electron spin is discussed.

Nuclear coherence-transfer echoes in pulsed EPR

Nuclear coherence-transfer echoes created in disordered electron–nuclear spin systems by microwave pulses are described. Once nuclear coherence is generated, a nonselective microwave π pulse inverts the electron spins thereby interchanging nuclear coherence between the two electron spin manifolds. This exchange refocuses the inhomogeneity of the secular part of the hyperfine interaction. The mechanisms of echo formation for weak and strong hyperfine couplings are explained by using simple vector diagrams. Various methods to create and detect nuclear coherence by microwave pulses are discussed with special attention directed to the sequence π/2–τ–π/2–t1–π–t2–π/2–τ. In this four-pulse experiment the nuclear coherence-transfer echo is observed as an amplitude modulation of the electron spin echo intensity. The nuclear coherence-transfer echo can be shifted to a time interval fully separated from the one covered by the instrumental deadtime. The time evolution of an S=1/2, I=1/2 model spin system during the four-pulse sequence is described using the density operator formalism. Several one- and two-dimensional four-pulse experiments are discussed on this basis and their spectra are analyzed in terms of nuclear coherence-transfer pathways. A new one-dimensional experiment based on nuclear coherence-transfer echoes, deadtime free ESEEM by nuclear coherence-transfer echoes (DEFENCE) is proposed to exploit undistorted electron spin echo envelope modulation (ESEEM) spectra. DEFENCE is a fast pulsed EPR technique that is unpretentious with respect to the required microwave equipment. The predicted features of the nuclear coherence-transfer echoes and of the DEFENCE approach are verified experimentally.

Continuous wave multiquantum electron paramagnetic resonance spectroscopy. IV. Multiquantum electron–nuclear double resonance

We report a theoretical and experimental investigation of the interaction of a coupled electron–nuclear spin system with three electromagnetic fields: two equally intense microwave fields resonant with the electron spin, and one radio-frequency field resonant with the nuclear spin. This is an electron–nuclear double-resonance experiment where the effect of the nuclear transition is detected via changes of the electron multiple photon transitions (MQ-EPR) rather than steady-state saturation and, therefore, is called multiquantum electron–nuclear double resonance (MQ-ENDOR). The theoretical framework previously developed for the description of multiple photon phenomena in a two level system is extended to the case of a four level system. The equation of motion of the density matrix is solved in the presence of three fields, which results in five master equations relating various populations and coherences. A ten photon approximation is used to study the functional dependence on spectral parameters and determine the sensitivity of this technique to spin relaxation rates. The experimental investigation is carried out on a sample of tri-t-butyl phenoxyl radical dissolved in mineral oil. At low values of the electron saturation factor Se, the rf-swept MQ-ENDOR is a de-enhancement of the 3Q-EPR signal (i.e., the first intermodulation sidebands). As the microwave field strength increases, the MQ-ENDOR signal changes phase by 180° due to dominance of generalized saturation. Higher order MQ-EPR signals (i.e., higher order sidebands) have larger negative enhancement and tend to display smaller positive enhancement. Line splitting results if the microwave frequency difference or field strength is increased. The dependence of MQ-ENDOR displays on various spectral parameters was found to be consistent with the general trends predicted by the theory. These displays provide a convenient way to estimate electron and nuclear relaxation rates.

Magnetic coupling contributions to the thermal boundary resistance between3He and metals

In a recent experiment, Perry, DeConde, Sauls, and Stein found a thermal boundary resistance between3He and platinum that was inversely proportional to temperature and decreased with application of a magnetic field. These authors suggested an explanation of the experimental observations in terms of a hyperfine contact interaction between the helium nuclear spins in the first surface monolayer and the conduction electrons of the metal. In the present work the magnetic coupling between the electron-nuclear spin systems is investigated for the contact interaction using a realistic representation of the metallic spin susceptibility at the helium site. The longer range dipole interaction is also considered and results for copper, silver, gold, and platinum indicate that both magnetic coupling mechanisms are orders of magnitude too weak to account for experimentally observed heat transfer rates. The much larger heat transfer rate obtained by Perryet al. is traced to their overestimation of the conduction electron local density of states at the helium site.

On the theory of acoustic self-induced transparency

The effect of coherent interaction of a sound pulse of longitudinal polarization with an electron-nuclear spin system in an external constant magnetic field under the conditions of a “forbidden” transition is investigated. The parameters of the stationary electron-nuclear sound pulse are determined.