Storage of multiple coherent microwave excitations in an electron spin ensemble

Strong coupling between a microwave photon and electron spins, which could enable a long-lived quantum memory element for superconducting qubits, is possible using a large ensemble of spins. This represents an inefficient use of resources unless multiple photons, or qubits, can be orthogonally stored and retrieved. Here we employ holographic techniques to realize a coherent memory using a pulsed magnetic field gradient and demonstrate the storage and retrieval of up to 100 weak 10?GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds.     

Enhancement of electron spin coherence by optical preparation of nuclear spins

We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.     

Spin polarization of two-dimensional electron system in different Laughlin states and around filling factor

The spin configuration of the ground state of a two-dimensional electron system is investigated for different FQHE states from an analysis of circular polarization of time-resolved luminescence. The method clearly distinguishes between fully spin polarized, partially spin polarized and spin unpolarized FQHE ground states. We demonstrate that FQHE states which are spin unpolarized or partially polarized at low magnetic fields become fully spin polarized at high fields. Temperature dependence of the spin polarization reveals a nonmonotonic behavior at . At and the electron system is found to be fully spin polarized. This result does not indicate the existence of any skyrmionic excitations in high magnetic field limit. However, at the observed spin depolarization of electron system at and becomes broader for lower magnetic fields, so that full spin polarization remains only in a small vicinity of . Such a behavior could be considered as a precursor of skirmionic depolarization, which would dominate for smaller ratios between Zeeman and Coulomb energies.We demonstrate that the spin polarization of 2D-electron system at and can be strongly affected by hyperfine interaction between electrons and optically spin-oriented nuclears. This result is due to the fact that hyperfine interaction can both enhance and suppress effective Zeeman splitting in fixed external magnetic field.     

Voltage-selective bidirectional polarization and coherent rotation of nuclear spins in quantum dots

We propose and demonstrate that the nuclear spins of the host lattice in GaAs double quantum dots can be polarized in either of two opposite directions, parallel or antiparallel to an external magnetic field. The direction is selected by adjusting the dc voltage. This nuclear polarization manifests itself by repeated controlled electron-nuclear spin scattering in the Pauli spin-blockade state. Polarized nuclei are also controlled by means of nuclear magnetic resonance. This Letter confirms that the nuclear spins in quantum dots are long-lived quantum states with a coherence time of up to 1 ms, and may be a promising resource for quantum-information processing such as quantum memories for electron spin qubits.     

Long time evolution of a spin interacting with a spin bath in arbitrary magnetic field

We introduce a completely different method to calculate the evolution of a spin interacting with a sufficient large spin bath,especially suitable for treating the central spin model in a quantum dot(QD).With only an approximation on the envelope of central spin,the symmetry can be exploited to reduce a huge Hilbert space which cannot be calculated with computers to many small ones which can be solved exactly.This method can be used to calculate spin-bath evolution for a spin bath containing many(say,1000)spins,without a perturbative limit such as strong magnetic field condition,and works for long-time regime with sufficient accuracy.As the spin-bath evolution can be calculated for a wide range of time and magnetic field,an optimal dynamic of spin flip-flop can be found,and more sophisticated approaches to achieve extremely high polarization of nuclear spins in a QD could be developed.     

Quantum Speed Limit for Dynamics of Central Spin Model with Initial System-Bath Correlations

We investigate the quantum speed limit (QSL) time of an electronic spin coupled to a bath of nuclear spins. We consider three types of initial states with different correlations between the system and bath, i.e., quantum correlation, classical correlation, and no any correlation. Interestingly, we show that the QSL times of the central spin for these three types of initial correlations are identical when the couplings are homogeneous. However, it is remarkable different for inhomogenous couplings. The QSL time of the central spin is sensitive to the initial states, the average coupling strength, the distribution of the couplings between the system and bath and the number of the nuclear spins in the bath. Furthermore, we find that the coherence in the initial state has significant influences on the QSL time of the system, and can lead to the increase of QSL time for homogeneous couplings.     

Properties of specific electron helical states leads to spin filtering effect in dsDNA molecules

In a recent paper, Gohler et al. [1] report that a high efficiency electron spin filter can be constructed from an adsorbed monolayer of double-stranded DNA (dsDNA). Understanding the mechanisms responsible for spin filtering under these conditions has proven to be a challenge, as classical analysis fails to account for the high degree of polarization observed. In this paper we show that these observations can be understood since conduction electrons in the DNA molecule are characterized by specific helical states having a magnetic moment opposite to the direction of the electron wavevector. These helical states are fundamental to the quantum-mechanical properties of periodic structures with helical symmetry. Free electrons passing through the DNA monolayer interact with these helical states, but the strength of this interaction depends on the relative orientation of the electron spin and the magnetic moment associated with the possible helical states. One of these configurations leads to a negligible interaction resulting in high spin polarization in the transmitted electron beam. The overall effect is that the free electron flux component with a magnetic moment in an opposite direction to the magnetic moment of the helical states can pass through the dsDNA monolayer without absorption, while the other spin component is highly absorbed by dsDNA. This is consistent with the finding that a monolayer of single-stranded DNA does not exhibit similar spin filtering properties.     

Magnetic bloch electron states and spin polarization in 2D superlattices without an inversion center with Rashba spin-orbit interaction in an electron gas

The quantum states of carriers in 2D doubly periodic n-type semiconducting superlattices without spatial inversion symmetry in an external magnetic field are calculated in the one-electron approximation. It is shown that the spin-orbit interaction and spin splitting in the magnetic field may lead to the occurrence of the photovoltaic effect in a 2D electron gas without an inversion center and to a nonzero spin magnetization of the electron gas in the plane perpendicular to the magnetic field.     

Optical polarization of nuclei and ODNMR in GaAs/AlGaAs quantum wells

Optical orientation of electrons was used to polarize the crystal lattice nuclei in quantum-size heterostructures and to study the effect of the conduction band spin splitting on the spin states of quasi-two-dimensional (2D) electrons drifting in an external electric field. High (～1%) nuclear polarization was registered using polarized luminescence and ODNMR in single GaAs/AlGaAs quantum wells. Measurement was made of the hyperfine interaction fields created by polarized nuclei on electrons and by electrons on nuclei. The spin-lattice relaxation of nuclei on the non-degenerate 2D electron gas was calculated. A comparison of the theoretical and experimental longitudinal relaxation times permitted the conclusion that the localized charge carriers are responsible for nuclear polarization in quantum wells in the temperature range of 2–77 K. A new effect has been studied, i.e. induction of an effective magnetic field acting on 2D electron spins when electrons drift in an external electric field in the quantum well plane. This effective field B_eff is due to the spin splitting of the conduction band of 2D electrons. The paper discusses possible registration of an ODNMR signal when the field B_eff is modulated by an electric current during optical orientation.     

Thermodynamics of a 4‐site Hubbard model by analytical diagonalization

By use of the conservation laws a four‐site Hubbard model coupled to a particle bath within an external magnetic field in z‐direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many‐particle states differing in electron number and spin if the electron density is away from half‐filling. The grand partition sum is calculated and the specific heat, the susceptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. For both the grand canonical and the canonical ensemble the high‐temperature crossing points of the specific heat are calculated. Whereas in the weak correlation regime the universal value calculated by second order perturbation theory for several Hubbard systems being in the thermodynamic limit is confirmed, these crossing points vanish for intermediate to strong correlation.     

Spin polarization of the neutral exciton in a single quantum dot

While efficient nuclear polarization has earlier been reported for the charged exciton in InAs/GaAs quantum dots at zero external magnetic field, we report here on a surprisingly high degree of circular polarization, up to ≈60%$\approx 60\%$, for the neutral exciton emission in individual InAs/GaAs dots. This high degree of polarization is explained in terms of the appearance of an effective nuclear magnetic field which stabilizes the electron spin. The nuclear polarization is manifested in experiments as a detectable Overhauser shift. In turn, the nuclei located inside the dot are exposed to an effective electron magnetic field, the Knight field. This nuclear polarization is understood as being due to the dynamical nuclear polarization by an electron localized in the QD. The high degree of polarization for the neutral exciton is also suggested to be due to separate in-time capture of electrons and holes into the QD.     

Spin-lattice relaxation in hyperfine-coupled systems: Applications to interstitial diffusion and molecular dynamics

The solid state diffusion of hydrogen, or of its pseudo-isotope muonium, provides an interesting example of spin-lattice relaxation in a 2-spin, 4-level system. The local field experienced by the interstitial atom fluctuates as it moves, inducing transitions between the coupled electron and nuclear spin states. Rate equations governing the populations of these states may be solved numerically to simulate the different relaxation functions which would be displayed by ESR, ENDOR and μSR spectroscopies and to assist in extracting motional correlation times from the experimental data. Spin relaxation in molecular radicals may be treated similarly, with different selection rules for different mechanisms: this paper treats the spin rotation mechanism and perturbation to anisotropic or isotropic components of the hyperfine interaction, caused by inter or intra-molecular motion. Conventional magnetic resonance monitors the population differences appropriate to particular transitions; only in sufficiently high fields do these distinguish the electronic and nuclear response. Muon spin relaxation is remarkable in separating out the nuclear spin projection whatever the degree of mixing of the spin states,via the asymmetry in the muon radioactive decay. Experimentally it has the advantage that measurements can be made over a wide range of field, from null external field up to thelevel crossing where the relaxation rate exhibits a striking peak.     

Modulated spin waves and robust quasi-solitons in classical Heisenberg rings

We investigate the dynamical behavior of finite rings of classical spin vectors interacting via nearest-neighbor isotropic exchange in an external magnetic field. Our approach is to utilize the solutions of a continuum version of the discrete spin equations of motion (EOM) which we derive by assuming continuous modulations of spin wave solutions of the EOM for discrete spins. This continuum EOM reduces to the Landau-Lifshitz equation in a particular limiting regime. The usefulness of the continuum EOM is demonstrated by the fact that the time-evolved numerical solutions of the discrete spin EOM closely track the corresponding time-evolved solutions of the continuum equation. It is of special interest that our continuum EOM possesses soliton solutions, and we find that these characteristics are also exhibited by the corresponding solutions of the discrete EOM. The robustness of solitons is demonstrated by considering cases where initial states are truncated versions of soliton states and by numerical simulations of the discrete EOM equations when the spins are coupled to a heat bath at finite temperatures.     

Electron–Nuclear Spin Dynamics in Semiconductor QDs

This work presents an overview of investigations of the nuclear spin dynamics in nanostructures with negatively charged InGaAs/GaAs quantum dots characterized by strong quadrupole splitting of nuclear spin sublevels. The main method of the investigations is the experimental measurements and the theoretical analysis of the photoluminescence polarization as a function of the transverse magnetic field (effect Hanle). The dependence of the Hanle curve profile on the temporal protocol of optical excitation is examined. Experimental data are analyzed using an original approach based on separate consideration of behavior of the longitudinal and transverse components of the nuclear polarization. The rise and decay times of each component of the nuclear polarization and their dependence on transverse magnetic field strength are determined. To study the role of the Knight field in the dynamic of nuclear polarization, a weak additional magnetic field parallel to the optical axis is used. We have found that, only taking into account the nuclear spin fluctuations, we can accurately describe the measured Hanle curves and evaluate the parameters of the electron–nuclear spin system in the studied quantum dots. A new effect of the resonant optical pumping of nuclear spin polarization in an ensemble of the singly charged (In,Ga)As/GaAs quantum dots subjected to a transverse magnetic field is discussed. Nuclear spin resonances for all isotopes in the quantum dots are detected in that way. In particular, transitions between the states split off from the ±1/2 doublets by the nuclear quadrupole interaction are identified.     

Frequency (field) dependent NMR relaxation rate in the interrupted metallic strand model

We calculate the nuclear magnetic resonance rate T^?1₁ arising from the electron-nuclear hyperfine contact interaction, within the interrupted metallic strand model. The electron levels are assumed to have an energy half width Γ and a mean spacing Δ₀ and it is assumed that all segments have the same nuclear spin temperature. In the limit Γ ? Δ₀, T^?1₁ has nearly the same behaviour for kT ? Δ₀ and kT?Δ₀. It is proportional to temperature but has a Lorentzian magnetic field dependence with halfwidth H= Γ/μ_B. At low fields it is enhanced over the value for a normal metal by the factor Δ₀/Γ.This anomalous behaviour arises from the suppression of electron spin flip processes by a magnetic field and should always occur when electronic states are localised, that is when there is a locally discrete electron energy spectrum. Therefore it may be relevant not only to certain linear chain conductors but to other cases of electron localisation.The present model provides an additional possible source of frequency dependence of T₁ in linear chain materials. In certain materials especially those containing defects, it may be more appropriate than the currently accepted mechanism which involves electron spin diffusion in one dimension.     

Quantum anomalous hall effect in Hg1-yMnyTe quantum wells

The quantum Hall effect is usually observed when a two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum anomalous Hall effect, can be realized in Hg{1-y}Mn{y}Te quantum wells, without an external magnetic field and the associated Landau levels. This effect arises purely from the spin polarization of the Mn atoms, and the quantized Hall conductance is predicted for a range of quantum well thickness and the concentration of the Mn atoms. This effect enables dissipationless charge current in spintronics devices.     

Coherent state transfer between an electron and nuclear spin in (15)N@C(60)

Electron spin qubits in molecular systems offer high reproducibility and the ability to self-assemble into larger architectures. However, interactions between neighboring qubits are "always on," and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both effectively turn on or off interqubit coupling mediated by dipolar interactions and benefit from the long nuclear spin decoherence times (T(2n)). We transfer qubit states between the electron and (15)N nuclear spin in (15)N@C(60) with a two-way process fidelity of 88%, using a series of tuned microwave and radio frequency pulses and measure a nuclear spin coherence lifetime of over 100 ms.     

Experimental signature of phonon-mediated spin relaxation in a two-electron quantum dot

We observe an experimental signature of the role of phonons in spin relaxation between triplet and singlet states in a two-electron quantum dot. Using both the external magnetic field and the electrostatic confinement potential, we change the singlet-triplet energy splitting from 1.3 meV to zero and observe that the spin relaxation time depends nonmonotonously on the energy splitting. A simple theoretical model is derived to capture the underlying physical mechanism. The present experiment confirms that spin-flip energy is dissipated in the phonon bath.     

The family of topological Hall effects for electrons in skyrmion crystals

Hall effects of electrons can be produced by an external magnetic field, spin–orbit coupling or a topologically non-trivial spin texture. The topological Hall effect (THE) – caused by the latter – is commonly observed in magnetic skyrmion crystals. Here, we show analogies of the THE to the conventional Hall effect (HE), the anomalous Hall effect (AHE), and the spin Hall effect (SHE). In the limit of strong coupling between conduction electron spins and the local magnetic texture the THE can be described by means of a fictitious, “emergent” magnetic field. In this sense the THE can be mapped onto the HE caused by an external magnetic field. Due to complete alignment of electron spin and magnetic texture, the transverse charge conductivity is linked to a transverse spin conductivity. They are disconnected for weak coupling of electron spin and magnetic texture; the THE is then related to the AHE. The topological equivalent to the SHE can be found in antiferromagnetic skyrmion crystals. We substantiate our claims by calculations of the edge states for a finite sample. These states reveal in which situation the topological analogue to a quantized HE, quantized AHE, and quantized SHE can be found.     

Cyclotron dynamics of electron wave packets in topological insulators in an external magnetic field

The evolution of electron wave packets formed from surface states in topological insulators located in an external magnetic field is studied. The electron and spin densities of the wave packets under consideration are calculated analytically and are visualized. The influence of the main characteristics of the wave packets (the spin polarization) on the splitting and the change in their forms with time is considered.