A semiconductor nanowire quantum dot with strong spin-orbit coupling (SOC) can be used to achieve a spin-orbit qubit. In contrast to a spin qubit, the spin-orbit qubit can respond to an external ac electric field, an effect called electric-dipole spin resonance. Here we develop a theory that can apply in the strong SOC regime. We find that there is an optimal SOC strength η(opt)=√2/2, where the Rabi frequency induced by the ac electric field becomes maximal. Also, we show that both the level spacing and the Rabi frequency of the spin-orbit qubit have periodic responses to the direction of the external static magnetic field. These responses can be used to determine the SOC in the nanowire.

One-dimensional (1D) hole gas confined in a cylindrical Ge nanowire has potential applications in quantum information technologies. Here, we analytically study the low-energy properties of this 1D hole gas. The subbands of the hole gas are two-fold degenerate. The low-energy subband wave-functions are obtained exactly, and the degenerate pairs are related to each other via a combination of the time-reversal and the spin-rotation transformations. In evaluating the effective g-factor of these low-energy subbands, the orbital effects of the magnetic field are shown to contribute as strongly as the Zeeman term. Also, near the center of the k z space, there is a sharp dip or a sharp peak in the effective g-factor. At the site k z = 0, the longitudinal g-factor g l is much less than the transverse g-factor g t for the lowest subband, while away from the site k z = 0, g l can be comparable to g t.

We study controllable exchange coupling between two singlet-triplet qubits. We start from the original second quantized Hamiltonian of a quadruple quantum dot system and obtain the effective spin-spin interaction between the two qubits using the projection operator method. Under a strong uniform external magnetic field and an inhomogeneous local micro-magnetic field, the effective interqubit coupling is of the Ising type, and the coupling strength can be expressed in terms of quantum dot parameters. Finally, we discuss how to generate various two-qubit operations using this controllable coupling, such as entanglement generation, and controlled-NOT gate.Comment: 9 pages, 3 figure

Understanding the spin dephasing mechanism is of fundamental importance in all potential applications of the spin qubit. Here we demonstrate a spin dephasing mechanism in a semiconductor quantum dot due to the 1/f charge noise. The spin-charge interaction is mediated by the interplay between the spin-orbit coupling and the asymmetrical quantum dot confining potential. The dephasing rate is proportional to both the strength of the spin-orbit coupling and the degree of the asymmetry of the confining potential. For parameters typical of the InSb, InAs, and GaAs quantum dots with a moderate well-height [Formula: see text] meV, we find the spin dephasing times are [Formula: see text] μs, 275 μs, and 55 ms, respectively. In particular, the spin dephasing can be enhanced by lowering the well-height. When the well-height is as small as [Formula: see text] meV, the spin depahsing times in the InSb, InAs, and GaAs quantum dots are decreased to [Formula: see text] μs, 18 μs, and 9 ms, respectively.

We show that a strong ‘spin’-orbit coupled one-dimensional hole gas is achievable via applying a strong magnetic field to the original two-fold degenerate (spin degeneracy) hole gas confined in a cylindrical Ge nanowire. Both strong longitudinal and strong transverse magnetic fields are feasible to achieve this goal. Based on quasi-degenerate perturbation calculations, we show the induced low-energy subband dispersion of the hole gas can be written as E = ℏ 2 k z 2 / ( 2 m h * ) + α σ z k z + g h * μ B B σ x / 2 , a form exactly the same as that of the electron gas in the conduction band. Here the Pauli matrices σ z,x represent a pseudo spin (or ‘spin’), because the real spin degree of freedom has been split off from the subband dispersions by the strong magnetic field. Also, for a moderate nanowire radius R = 10 nm, the induced effective hole mass m h * ( 0.065 ∼ 0.08 m e ) and the ‘spin’-orbit coupling α (0.35 ∼ 0.8 eV Å) have a small magnetic field dependence in the studied magnetic field interval 1 < B < 15 T, while the effective g-factor g h * of the hole ‘spin’ only has a small magnetic field dependence in the large field region.