Session L29: Focus Session: Semiconductor Qubits - Single and Multi-Qubit Demonstrations

Coherent control and detection of spin qubits in semiconductor with magnetic field engineering

Electrical control and detection of the spin qubits in semiconductor quantum dots (QDs) are among the major rapidly progressing fields for possible implementation of scalable quantum information processing. Coherent control of one-[1-3] and two-[4,5] spin qubits by electrical means had been demonstrated with various approaches. We have used an engineered magnetic field structure realized with proximal micro-magnets to transduce the spin and charge degrees of freedom and to selectively address one of the two spins [3]. We have demonstrated an all-electrical two-qubit gate consisting of single-spin rotations and interdot spin exchange in double QDs. A partially entangled output state is obtained by the application of the two-qubit gate to an initial, uncorrelated state. Our calculations taking into account of the nuclear spin fluctuation show the degree of entanglement. Non-uniform magnetic field also enables spin selective photon-assisted tunneling in double QDs, which then constitutes non-demolition spin read-out system in combination with a near-by charge detector [6]. \\[4pt] In collaboration with R. Brunner, Inst. of Phys., Montanuniversitaet Leoben, 8700, Austria, M. Pioro-Ladri\`{e}re, D\'{e}p. de Phys., Universit\'{e} de Sherbrooke, Sherbrooke, Qu\'{e}bec, J1K-2R1, Canada, T. Kubo, Y. -S. Shin, T. Obata, and S. Tarucha, ICORP-JST and Dep. of Appl. Phys., Univ. of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.\\[4pt] [1] F. H. Koppens, et al., Nature 442, 766 (2006).\\[0pt] [2] K. C. Nowack, et al., Science 318, 1430 (2007).\\[0pt] [3] M. Pioro-Ladri\`{e}re, et al., Nature Physics 4, 776 (2008).\\[0pt] [4] J. R. Petta, et al., Science 309, 2180 (2005).\\[0pt] [5] R. Brunner, et al., Phys. Rev. Lett. 107, 146801 (2011).\\[0pt] [6] Y. -S. Shin, et al., Phys. Rev. Lett. 104, 046802 (2010).   

Coherent Singlet-Triplet Oscillations in a Silicon-based Double Quantum Dot

We have performed coherent spin manipulation of a singlet-triplet qubit in a Si/SiGe double quantum-dot device fabricated in an undoped heterostructure. A charge stability diagram showed that the (0,0) charge state was reached and Pauli spin blockade was detected at the (1,1)-(0,2) anticrossing. A singlet-triplet splitting of $\sim $140 $\mu $eV in the (0,2) charge state provided a read-out window sufficiently wide for singlet-triplet discrimination. We used the S/T$_{-}$ spin funnel, Rabi oscillation, and $T_{2}$* pulsing experiments to measure (1,1) exchange energies spanning $\sim $0.6-700 neV over a large detuning range and measured a $T_{2}$* of 360 ns, consistent with theoretical expectations for our device. Sponsored by the United States Department of Defense. Approved for Public Release, Distribution Unlimited. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government.   

Tunable singlet-triplet splitting in a few-electron Si/SiGe quantum dot

The singlet-triplet energy splitting in a double quantum dot is an important parameter for singlet-triplet qubits, because it determines the energy gap for both initialization and readout. This splitting can also be used to perform gate operations in a newly proposed hybrid qubit [1]. We describe measurements in which we tune the singlet-triplet energy splitting by changing gate voltages on a Si/SiGe double quantum dot [2]. We argue that the energy is changed largely by lateral translation of the dot, which changes the local atomic structure that the electrons experience in the quantum dot, leading to variations in the valley-orbit coupling. We present calculations indicating the experimental results are consistent with the first excited state of the dot having non-zero valley-orbit coupling. [1] Z. Shi, et al., e-print: http://lanl.arxiv.org/abs/1110.6622. [2] Z. Shi, et al., e-print: http://lanl.arxiv.org/abs/1109.0511.   

Electric dipole spin resonance measurement of spin-orbit anisotropy in InSb nanowire quantum dots

Indium antimonide nanowires are considered a leading platform for the generation of Majorana fermion bound states, and as hosts of spin-orbit quantum bits based on single electrons. Both efforts are motivated by the strong spin-orbit interaction in the bulk InSb. Here we present measurements of the strength and orientation of the effective spin-orbit magnetic field in InSb nanowire double quantum dots. Spin-orbit interaction induces avoided level crossings between triplet (1,1) and singlet (0,2) double dot states. These avoided crossings are observed in the spectrum of the electric dipole spin resonance performed on strongly-coupled double dots. We find that the spin-orbit field is oriented perpendicular to the nanowire axis, and parallel to the substrate plane. This orientation is consistent with Rashba spin-orbit interaction and is favorable for Majorana experiments. The strength of spin-orbit interaction is characterized by the spin-orbit length which we estimate to be 200 nm. This translates into a temperature scale of 3K for the observation of Majorana states.   

Coherent manipulation of spin-orbit quantum bits in InSb nanowires

Semiconductor nanowires with strong spin-orbit coupling are becoming an attractive platform for spin-based quantum computation. Here we demonstrate coherent transitions between spin-orbit doublet states of individual electrons in indium antimonide (InSb) nanowire quantum dots induced by gigahertz-frequency electric fields. The spin-orbit doublet states form a qubit which initialization and detection relies on Pauli blockade in the double quantum dot (1,1) configuration. The maximum Rabi frequency exceeds 100 MHz and more than 10 periods of coherent oscillations are observed. We estimate fidelities of single qubit rotations and analyze qubit decoherence times by performing spin echo sequence. The two qubits in a double quantum dot are individually addressable due to different g-factors. The coupling between the qubits can be mediated by exchange interaction. The fidelities of single qubit rotations are sufficiently high to permit the implementation of two-qubit quantum gates such as controlled-not (C-NOT) or controlled-phase (C-Phase).   

Spin Relaxation and Manipulation in Spin-orbit Qubits

We derive a generalized form of the Electric Dipole Spin Resonance (EDSR) Hamiltonian in the presence of the spin-orbit interaction for single spins in an elliptic quantum dot (QD) subject to an arbitrary (in both direction and magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi frequency as a function of the magnetic field for sufficiently large Zeeman energies, and present a microscopic expression for the anisotropic electron g-tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a double quantum dot (DQD). Finally, we calculate two-electron-spin relaxation rates due to phonon emission, for both in-plane and perpendicular magnetic fields. Our results have immediate applications to current EDSR experiments on nanowire QDs, g-factor optimization of confined carriers, and spin decay measurements in DQD spin-orbit qubits.   

Spin coherence in Multi-electron GaAs double dots

Experimental investigation of spin manipulation and readout in multi-electron double quantum dots is reported. For occupations of order 10 electrons, spin blockade in both transport and pulsed-gate measurements is identified. Exchange rotations, dynamical decoupling, S/T+ beamsplitter experiments, and single-shot readout can all be implemented similar to the single-electron case. These demonstrations are relevant for the practical operation and scaling of GaAs spin qubits.   

Fast Exchange Oscillations in Quantum Dot Spin Qubits

The exchange splitting, J, is an important tool in semiconductor spin qubits, as it can drive both single qubit rotations and two qubit entangling operations. However, qubits operating under exchange can be dephased by electrical noise, as J is a function of the local electrostatic environment. We investigate the exchange interaction in a singlet-triplet qubit created in double quantum dot by measuring exchange oscillations ranging in frequency over three orders of magnitude. In particular, we resolve exchange oscillations at frequencies up to 30GHz, where both electrons occupy the same quantum dot. Here, J saturates to approximately the singlet-triplet splitting, and no longer depends on the electrostatic environment. In this regime exchange oscillations are insensitive to electrical noise. Since semiconductor spin qubits are usually limited by dephasing, these potentially dephasing-free exchange oscillations offer a new regime for studying quantum control in spin qubits.   

Coherent electrical manipulation of a quantum dot qubit

We demonstrate the initialization and coherent manipulation of a spin-based qubit in a InAs quantum dot (QD), implementing a spin-flip gate with a fidelity of 97\%. We will discuss new measurements on the effect of fluctuating nuclear magnetic field which have implications on state initialisation, operation fidelity, and qubit storage time. An exciton spin-state is initialised by absorption of an incident polarised photon. The exciton state of QDs has two spin-eigenstates separated by fine-structure splitting ($s$), which can be manipulated using applied electric field. Superposition spin-states precess around the Bloch-sphere with an angular frequency $|s|/\hbar$. An electric field is used to vary the rate and axis of the spin-state precession, and thus control the time-evolution of the stored qubit. Nuclear magnetic field fluctuations induce additional random variations in $s$, the effects of which we investigate to understand the ideal initialisation and storage regime. Subsequent radiative decay maps the spin of the exciton onto the polarisation of the emitted photon. These results demonstrate a photon-spin interface, which has potential applications in scalable optical quantum computing schemes.   

Fabrication and Characterization of Si MOS-Based Triple Quantum Dot Devices

We have fabricated electrostatically defined, few electron triple quantum dot (TQD) devices in a silicon metal-oxide-semiconductor structure. The devices show good electrical stability and gate controllability. We have obtained charge stability diagrams for identifying the charging states of the TQD. In this talk, we will describe the technical challenges in the TQD fabrication and present the experimental results of tuning three dots into a resonance. We will also discuss the prospect of these devices to encode a spin qubit that uses exchange interaction alon and possible ways to perform coherent manipulations within the tunable range of inter-dot tunneling of these devices. The work is supported by ARO.   

Pairwise control of exchange interaction between individual spins in a triple quantum dot

The original spin qubit proposal [1] suggested a linear array of spins for quantum computations and the exchange interaction for 2 qubit operations. An essential component of the proposal was the ability to control pairwise the exchange interaction between neighbouring pairs of spins. In this work we experimentally demonstrate such a pairwise control of the exchange interaction between three spins localized in a triple quantum dot (TQD) device. The TQD potential was formed using electrostatic lateral split-gate technology on a GaAs/GaAlAs heterostructure with a high-mobility two-dimensional electron gas [2]. We employ fast pulsing technique based on the Landau-Zener-Stuckelberg (LZS) approach for creating and manipulating coherent superpositions of three spin quantum states [3]. We show that we are able to maintain coherence when increasing the exchange coupling of one spin with another while simultaneously decreasing its coupling with the third.\\[4pt] [1] D. Loss, and D.P. DiVincenzo, Phys. Rev. A57, 120-126 (1998).\\[0pt] [2] L. Gaudreau , et al., Appl. Phys. Lett. v.95, 193101 (2009). \\[0pt] [3] J.R. Petta, H. Lu, and A.C. Gossard, Science v.327, 669-672 (2010).   

Entanglement of Two Singlet-Triplet Qubits

Semiconductor spin qubits are promising candidates for quantum computation because of their potential for scalability. However, their weak interaction with the environment, which leads to long coherence times, makes two-qubit operations challenging. We perform the first two-qubit operation between singlet-triplet qubits. The two qubit operation relies on the capacitive coupling between two adjacent qubits to generate a CPHASE gate. In order to combat low frequency noise we use a dynamically decoupled gate that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography we measure the two-qubit density matrix and show that the operation produces the expected state. We extract a concurrence of 0.44 and a Bell state fidelity of 0.72, each providing definitive proof of entanglement.   

Two-axis Control and Readout of an Exchange-Only Spin Qubit in a GaAs Triple Quantum Dot

The initialization, full control, and readout of a GaAs triple quantum dot exchange qubit is demonstrated. Appropriate depletion gate design has enabled control and single-shot readout along multiple Bloch sphere axes in a three electron device. Rotations around both non-orthogonal control axes are projected along three separate Bloch sphere axes, and quality factors $(Q \equiv \omega / T_2^*)$ of 500 are observed. Finally, we analyze decoherence and dynamical decoupling schemes unique to this system.