Heavy-hole Spin Research Articles

Heavy-hole spin relaxation in quantum dots: Isotropic versus anisotropic effects

Heavy-hole spin relaxation in quantum dots: Isotropic versus anisotropic effects

Ballistic spin transport in DC-bias single top gate p-type narrow channel device with Zeeman–Rashba effects

The ballistic transport of holes in a p-type quasi-one-dimensional channel system is investigated without considering the coupling effect of the light and heavy holes. A top gate (TG) is used to form a potential barrier in the quantum channel with Zeeman–Rashba (ZR) effects. The Luttinger Hamiltonian and propagation matrix method are used to examine the relationship between the conductance and the incident hole energy. The results show that when the gate width L is large, an electron-like bound state (E-BS) structure is formed at the inflection point of the spin-down branch. When a positive gate potential energy is applied (U0>0), the light and heavy hole spins form an electron-like quasi-bound state (E-QBS) at the top of the branch under the hole spin. Conversely, when a negative gate potential energy (U0<0) is applied, the light and heavy hole spins form a hole-like quasi-bound state (H-QBS) structure at the bottom of the branch.

Coherence Characteristics of a GaAs Single Heavy-Hole Spin Qubit Using a Modified Single-Shot Latching Readout Technique.

We present an experimental study of the coherence properties of a single heavy-hole spin qubit formed in one quantum dot of a gated GaAs/AlGaAs double quantum dot device. We use a modified spin-readout latching technique in which the second quantum dot serves both as an auxiliary element for a fast spin-dependent readout within a 200 ns time window and as a register for storing the spin-state information. To manipulate the single-spin qubit, we apply sequences of microwave bursts of various amplitudes and durations to make Rabi, Ramsey, Hahn-echo, and CPMG measurements. As a result of the qubit manipulation protocols combined with the latching spin readout, we determine and discuss the achieved qubit coherence times: T1, TRabi, T2*, and T2CPMG vs. microwave excitation amplitude, detuning, and additional relevant parameters.

Quantum Control of Hole Spin Qubits in Double Quantum Dots

Hole spin qubits in semiconductor quantum dots (QDs) are promising candidates for quantum information processing due to their weak hyperfine coupling to nuclear spins, and to the strong spin-orbit coupling which allows for rapid operation time. We propose a coherent control on two heavy-hole spin qubits in a double QD by a fast adiabatic driving protocol, which helps to achieve higher fidelities than other experimentally commonly used protocols as linear ramping, $\pi$-pulses or Landau-Zener passages. Using fast quasiadiabatic driving via spin-orbit coupling, it is possible to reduce charge noise significantly for qubit manipulation and achieve high robustness for the qubit initialization. We also implement one and two-qubit gates, in particular, NOT, CNOT, and SWAP-like gates, of hole spins in a double QD achieving fidelities above $99\%$, exhibiting the capability of hole spins to implement universal gates for quantum computing.

Pressure effect on spin-resonant tunneling of holes in CdTe/Cd1-xMnxTe double-barrier heterostructure

Light Hole (LH) and Heavy Hole (HH) transmission, spin polarization and dwell time are theoretically studied in CdTe/CdMnTe heterostructures for different pressures. The transfer matrix method is used to find the transport properties taking Dresselhaus spin-orbit coupling into account. Sharp resonance peaks with high transmission probability are obtained for HH. A possibility to manipulate the spin-polarized dwell time of holes in this heterostructure using pressure is inferred from the results.

Pseudospin-electric coupling for holes beyond the envelope-function approximation

In the envelope-function approximation, interband transitions produced by electric fields are neglected. However, electric fields may lead to a spatially local $(k\text{\ensuremath{-}}\mathrm{independent})$ coupling of band (internal, pseudospin) degrees of freedom. Such a coupling exists between heavy-hole and light-hole (pseudo)spin states in III-V semiconductors, such as GaAs, or in group IV semiconductors (germanium, silicon,...) with broken inversion symmetry. Here, we calculate the electric-dipole (pseudospin-electric) coupling for holes in GaAs from first principles. We find a transition dipole of 0.5 debye, a significant fraction of that for the hydrogen-atom $1s\ensuremath{\rightarrow}2p$ transition. In addition, we derive the Dresselhaus spin-orbit coupling that is generated by this transition dipole for heavy holes in an asymmetric quantum well. A quantitative microscopic description of this pseudospin-electric coupling may be important for understanding the origin of spin splitting in quantum wells, spin coherence/relaxation $({T}_{2}^{*}/{T}_{1})$ times, spin-electric coupling for cavity-QED, electric-dipole spin resonance, and spin nonconserving tunneling in double quantum dot systems.

Spin and reoccupation noise in a single quantum dot beyond the fluctuation-dissipation theorem

We report on the nonequilibrium spin noise of a single InGaAs quantum dot charged by a single hole under strong driving by a linearly polarized probe light field. The spectral dependency of the spin noise power evidences a homogeneous broadening and negligible charge fluctuations in the environment of the unbiased quantum dot. Full analysis of the spin noise spectra beyond the fluctuation-dissipation theorem yields the heavy-hole spin dynamics as well as the trion spin dynamics. Moreover, the experiment reveals an additional much weaker noise contribution in the Kerr rotation noise spectra. This additional noise contribution has a maximum at the quantum dot resonance and shows a significantly longer correlation time. Magnetic-field-dependent measurements in combination with theoretical modeling prove that this additional noise contribution unveils a charge reoccupation noise which is intrinsic in naturally charged quantum dots.

Hamiltonian term for a uniform dc electric field under the adiabatic approximation

In this work, we show that the disorder-free Kubo formula for the non-equilibrium value of an observable due to a DC electric field, represented by $E_x\hat{x}$ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-\textit{independent} perturbation $H_{MF}$. We derive the explicit expression for $H_{MF}$ and show that it originates from the adiabatic approximation to $\langle k|E_x\hat{x}$ in which transitions between the different eigenspinor states of a system are forbidden. The expression for $H_{MF}$ is generalized beyond the real spin degree of freedom to include other spin-like discrete degrees of freedom (e.g. valley and pseudospin). By direct comparison between Kubo formula and the time-independent perturbation theory, as well as the Sundaram-Niu wavepacket formalism, we show that $H_{MF}$ reproduces the effect of the E-field, i.e. $E_x\hat{x}$, up to the first order. This replacement suggests the emergence of a new spin current term that is not captured by the standard Kubo formula spin current calculation. We illustrate this via the exemplary spin current for the heavy hole spin 3/2 Luttinger system. Finally, we apply the formalism and derive an analogous $H_{MF}$ for the effects of a weakly position-dependent coupling to the spin-like internal degrees of freedom. This gives rise to an anomalous velocity as well as spin accumulation terms in spin$\otimes$pseudospin space in addition to those contained explicitly in the unperturbed Hamiltonian.

Decoupling a hole spin qubit from the nuclearspins.

A huge effort is underway to develop semiconductor nanostructures as low-noise hosts for qubits. The main source of dephasing of an electron spin qubit in a GaAs-based system is the nuclear spin bath. A hole spin may circumvent the nuclear spin noise. In principle, the nuclear spins can be switched off for a pure heavy-hole spin. In practice, it is unknown to what extent this ideal limit can be achieved. A major hindrance is that p-type devices are often far too noisy. We investigate here a single hole spin in an InGaAs quantum dot embedded in a new generation of low-noise p-type device. We measure the hole Zeeman energy in a transverse magnetic field with 10 neV resolution by dark-state spectroscopy as we create a large transverse nuclear spin polarization. The hole hyperfine interaction is highly anisotropic: the transverse coupling is <1% of the longitudinal coupling. For unpolarized, randomly fluctuating nuclei, the ideal heavy-hole limit is achieved down to nanoelectronvolt energies; equivalently dephasing times up to a microsecond. The combination of large and strong optical dipole makes the single hole spin in a GaAs-based device an attractive quantum platform.

Measurement of spin coherence using Raman scattering

Ramsey interferometry provides a natural way to determine the coherence time of most qubit systems. Recent experiments on quantum dots however, demonstrated that dynamical nuclear spin polarization can strongly influence the measurement process, making it difficult to extract the $T_2^*$ coherence time using optical Ramsey pulses. Here, we demonstrate an alternative method for spin coherence measurement that is based on first-order coherence of photons generated in spin-flip Raman scattering. We show that if a quantum emitter is driven by a weak monochromatic laser, Raman coherence is determined exclusively by spin coherence, allowing for a direct determination of spin $T_2^*$ time. When combined with coherence measurements on Rayleigh scattered photons, our technique enables us to identify coherent and incoherent contributions to resonance fluorescence, and to minimize the latter. We verify the validity of our technique by comparing our results to those determined from Ramsey interferometry for electron and heavy-hole spins.

Quantum computing with acceptor spins in silicon

The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin–orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin–orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin–orbit induced dipole–dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin–orbit terms are responsible for sweet spots in the dephasing time as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin–orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.

Controlled tunneling-induced dephasing of Rabi rotations for high-fidelity hole spin initialization

We report the sub-picosecond initialization of a single heavy hole spin in a self-assembled quantum dot with >98.5 % fidelity and without external magnetic field. Using an optically adressable charge and spin storage device we tailor the relative electron and hole tunneling escape timescales from the dot and simultaneously achieve high-fidelity initialization, long hole storage times and high efficiency readout via a photocurrent signal. We measure electric field-dependent Rabi oscillations of the neutral and charged exciton transitions in the ultrafast tunneling regime and demonstrate that tunneling induced dephasing (TID) of excitonic Rabi rotations is the major source for the intensity damping of Rabi oscillations in the low Rabi frequency, low temperature regime. Our results are in very good quantitative agreement with quantum-optical simulations revealing that TID can be used to precisely measure tunneling escape times and extract changes in the Coulomb binding energies for different charge configurations of the quantum dot. Finally, we demonstrate that for sub-picosecond electron tunneling escape TID of a coherently driven exciton transition facilitates ultrafast hole spin initialization with near-unity fidelity.

Maximizing the purity of a qubit evolving in an anisotropic environment

We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlet-triplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical results for spin-echo envelope modulations of arbitrary spin components of a hole spin in a quantum dot, going beyond a standard secular approximation. We account for general dynamics in the presence of a pure-dephasing process and identify a crossover timescale at which it is again advantageous to initialize the qubit in the non-interacting ground state. Finally, we consider a general two-axis dynamical decoupling sequence and determine initial conditions that maximize purity, minimizing leakage to the environment.

Optical spin noise of a single hole spin localized in an (InGa)As quantum dot.

We advance spin noise spectroscopy to the ultimate limit of single spin detection. This technique enables the measurement of the spin dynamic of a single heavy hole localized in a flat (InGa)As quantum dot. Magnetic field and light intensity dependent studies reveal even at low magnetic fields a strong magnetic field dependence of the longitudinal heavy hole spin relaxation time with an extremely long T1 of ≥180 μs at 31mT and 5K. The wavelength dependence of the spin noise power discloses for finite light intensities an inhomogeneous single quantum dot spin noise spectrum which is explained by charge fluctuations in the direct neighborhood of the quantum dot. The charge fluctuations are corroborated by the distinct intensity dependence of the effective spin relaxation rate.

Spin-orbit splitting of valence subbands in semiconductor nanostructures

We propose the 14-band $\mathbf k \cdot \mathbf p$ model to calculate spin-orbit splittings of the valence subbands in semiconductor quantum wells. The reduced symmetry of quantum well interfaces is incorporated by means of additional terms in the boundary conditions which mix the $\Gamma_{15}$ conduction and valence Bloch functions at the interfaces. It is demonstrated that the interface-induced effect makes the dominating contribution to the heavy-hole spin splitting. A simple analytical expression for the interface contribution is derived. In contrast to the 4$\times$4 effective Hamiltonian model, where the problem of treating the $V_z k_z^3$ term seems to be unsolvable, the 14-band model naturally avoids and overcomes this problem. Our results are in agreement with the recent atomistic calculations [J.-W. Luo et al., Phys. Rev. Lett. {\bf 104}, 066405 (2010)].

Spin noise in the anisotropic central spin model

Spin-noise measurements can serve as direct probe for the microscopic decoherence mechanism of an electronic spin in semiconductor quantum dots (QD).We have calculated the spin-noise spectrum in the anisotropic central spin model using a Chebyshev expansion technique which exactly accounts for the dynamics up to an arbitrary long but fixed time in a finite size system. In the isotropic case, describing QD charged with a single electron, the short-time dynamics is in good agreement with a quasi-static approximation for the thermodynamic limit. The spin-noise spectrum, however, shows strong deviations at low frequencies with a power-law behavior. In the Ising limit, applicable to QDs with heavy-hole spins, the spin-noise spectrum exhibits a threshold behavior above the Larmor frequency. In the generic anisotropic central spin model we have found a crossover from a Gaussian type of spin-noise spectrum to a more Ising-type spectrum with increasing anisotropy in a finite magnetic field. In order to make contact with experiments, we present ensemble averaged spin-noise spectra for QD ensembles charged with single electrons or holes. The Gaussian-type noise spectrum evolves to a more Lorentzian shape spectrum with increasing spread of characteristic time-scales and g-factors of the individual QDs.

Creation of entangled spin qubits between distant quantum dots

We theoretically show that an entangled state can be prepared between distant heavy-hole spin qubits by using III\char21{}V semiconductor quantum dots (QDs) in cascaded cavities. In this scheme, using quantum state transfer between photons and carrier spins, the local spin-singlet state in a virtually excited trion is stretched into the two separated QDs via a single-photon transmission. We calculate the effective Liouville equation and determine the optimal conditions for entanglement creation. We also discuss the possibility of distributing entangled electron spins in the same manner.

Holes in germanium quantum wells: spin relaxation and temperature dynamics

AbstractWe use fs‐pump white‐light‐supercontinuum probe spectroscopy with appropriate polarization configurations to investigate the hole spin and hole cooling dynamics in Germanium quantum wells in the vicinity of the Γ valley. We observe heavy hole spin flip times of up to 1.7 ps at 10, 300 fs after the excitation. Additionally, a strong, late bleaching (Δ ∼10 ps) at the lower‐lying energies indicates post‐injection heating of the hole system. This effect is virtually independent of the surplus energies of electrons and carrier density as long as no higher bands are involved by direct or two‐photon absorption. It is a direct manifestation of energy transfer from thermalizing electrons in the L valleys to the hole system. This mechanism is supported by microscopic simulations based on the semiconductor Bloch equations, clearly identifying the cooling of the hole system. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Dynamical magnetic and nuclear polarization in complex spin systems: semi-magnetic II–VI quantum dots

Dynamical magnetic and nuclear polarization in complex spin systems is discussed on the example of transfer of spin from exciton to the central spin of magnetic impurity in a quantum dot in the presence of a finite number of nuclear spins. The exciton is described in terms of electron and heavy-hole spins interacting via exchange interaction with magnetic impurity, via hyperfine interaction with a finite number of nuclear spins and via dipole interaction with photons. The time evolution of the exciton, magnetic impurity and nuclear spins is calculated exactly between quantum jumps corresponding to exciton radiative recombination. The collapse of the wavefunction and the refilling of the quantum dot with a new spin-polarized exciton is shown to lead to the build up of magnetization of the magnetic impurity as well as nuclear spin polarization. The competition between electron spin transfer to magnetic impurity and to nuclear spins simultaneous with the creation of dark excitons is elucidated. The technique presented here opens up the possibility of studying optically induced dynamical magnetic and nuclear polarization in complex spin systems.

Effects of valence band mixing on hole spin coherence via hole-nuclei hyperfine interaction in InAlAs quantum dots

The effects of valence band mixing on the hole spin coherence in self-assembled InAlAs quantum dots are investigated. The valence band mixing induces not only optical anisotropy in the quantum dot emissions but also heavy hole spin dephasing via the hyperfine interaction with the lattice nuclei. We evaluated the degree of valence band mixing for a number of In0.75Al0.25As/Al0.3Ga0.7As quantum dots from experiments. The magnitude of valence band mixing does not show a clear dependence on the photoluminescence energy, and it is less than 0.25 in our sample. Although the direct measurement with experimental methods has not been carried out at this stage, the effect of valence band mixing on the hole spin coherence is discussed in detail by the calculations.