Hayashi<i>et al.</i>Reply:

Hayashi, Naoki; Kato, Tatsuhisa; Aoki, Takayuki; Ando, Tomohiro; Fukuda, Atsuo; Seomun, San‐Seong

doi:10.1103/physrevlett.91.239602

Cited by 77 publications

(164 citation statements)

References 15 publications

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“…1a for the case of the two lowest orbital states, n = 1, 2. Charge qubits based on double QDs [8] offer great tunability, but suffer from short coherence times (∼1 ns) [9]. Spin qubits on the contrary, enable long coherence times(∼1 µs) [10], but are much harder to control, as pointed out above.…”

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confidence: 99%

Coherent Single Electron Spin Control in a Slanting Zeeman Field

Tokura

Wiel

Obata³

et al. 2006

Phys. Rev. Lett.

270

306

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We consider a single electron in a 1D quantum dot with a static slanting Zeeman field. By combining the spin and orbital degrees of freedom of the electron, an effective quantum two-level (qubit) system is defined. This pseudo-spin can be coherently manipulated by the voltage applied to the gate electrodes, without the need for an external time-dependent magnetic field or spin-orbit coupling. Single qubit rotations and the C-NOT operation can be realized. We estimated relaxation (T1) and coherence (T2) times, and the (tunable) quality factor. This scheme implies important experimental advantages for single electron spin control.PACS numbers: 03.67. Lx, 85.30.Wx, Stimulated by electron-spin-based proposals for quantum computation [1], a growing interest has emerged in realizing the coherent manipulation of a single electron spin in a solid-state environment. The application of the electron's spin -rather than its charge -as a quantum bit (qubit) is motivated by its potentially long coherence time in solids and the fact that it comprises a natural two-level system. Single electron spin resonance (SESR) plays a key role in realizing electron-spin-qubit rotation. Importantly, SESR is also the prime tool for determining the single electron spin coherence time T 2 in confined solid-state systems such as quantum dots (QDs). The induced Rabi oscillations can be read out via electron transport [2] or optically [3], giving an estimate for T 2 . SESR was detected in paramagnetic defects in silicon [4] and for nitrogen vacancies in diamond [5], but not in semiconductor QDs so far. Realizing SESR in QDs is hard, not least because of the necessary high-frequency (∼10 GHz) magnetic field in a cryogenic (∼100 mK) setup. Waveguides and microwave cavities as used in conventional ESR [6], cause serious heating, limiting the operation temperature to ∼1 K. On-going work in our group focuses on generating ac magnetic fields by an on-chip microscopic coil [7].In this Letter, we propose a new SESR scheme that eliminates the need for an externally applied ac magnetic field, and with the potential of very high and tunable quality factors. An ac voltage is applied to let an electron in a QD oscillate under a static slanting Zeeman field. This effectively provides the electron spin with the necessary time-dependent magnetic field. Note the analogy with the Stern-Gerlach experiment, where the spin and orbital degrees of freedom are coupled by employing an inhomogenous magnetic field. The spatial oscillation of the electron within the QD involves the hybridization of orbital states, as schematically depicted in Fig. 1a for the case of the two lowest orbital states, n = 1, 2. Charge qubits based on double QDs [8] offer great tunability, but suffer from short coherence times (∼1 ns) [9]. Spin qubits on the contrary, enable long coherence times(∼1 µs) [10], but are much harder to control, as pointed out above. Here, we present a hybrid chargespin system that is promising both in terms of tunability and coherence. Analogously, the combination of...

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confidence: 99%

Coherent Single Electron Spin Control in a Slanting Zeeman Field

Tokura

Wiel

Obata³

et al. 2006

Phys. Rev. Lett.

270

306

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“…Such systems were amongst the first proposed for quantum computing [9] and numerous versions have evolved recently [6,[10][11][12]. We are attracted to charge-based systems for three reasons: (1) proven high-fidelity readout compatible with single-shot operations [13]; (2) potential for high-speed (∼ picosecond) operations [6]; and (3) the ability to define variable dimensionality Hilbert spaces by appropriate partitioning [14].…”

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confidence: 99%

Controlled phase gate for solid-state charge-qubit architectures

Schirmer

Greentree

2005

Phys. Rev. A

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We describe a mechanism for realizing a controlled phase gate for solid-state charge qubits. By augmenting the positionally defined qubit with an auxiliary state, and changing the charge distribution in the three-dot system, we are able to effectively switch the Coulombic interaction, effecting an entangling gate. We consider two architectures, and numerically investigate their robustness to gate noise.

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“…In a gatedefined quantum dot the number of electrons can be reduced down to one [3,4]; such single-electron QDs may form the basis of qubits in quantum computation schemes [5,6]. High frequency operations on QD systems have been used to observe fundamental electronic phenomena such as coherent charge oscillations [7], single-and multiple-spin dynamics [8][9][10], excited-state spectra [11], and elastic tunneling behavior [12], and will be necessary for quantum computation applications in semiconductor systems.In typical QD experiments, the QDs were defined by static surface gates, and high frequency operations were achieved by applying voltage pulses to the gates. However, an alternative method has received recent attention: to use a dynamic QD defined by a surface acoustic wave (SAW) where high frequency operations are performed by moving the QD past static surface gates at a high velocity [13,14].…”

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confidence: 99%

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Energy-Dependent Tunneling from Few-Electron Dynamic Quantum Dots

et al. 2007

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We measure the electron escape rate from surface-acoustic-wave dynamic quantum dots (QDs) through a tunnel barrier. Rate equations are used to extract the tunneling rates, which change by an order of magnitude with tunnel-barrier-gate voltage. We find that the tunneling rates depend on the number of electrons in each dynamic QD because of Coulomb energy. By comparing this dependence to a saddlepoint-potential model, the addition energies of the second and third electron in each dynamic QD are estimated. The scale ( a few meV) is comparable to those in static QDs as expected. DOI: 10.1103/PhysRevLett.99.156802 PACS numbers: 73.23.Hk, 73.50.Rb, 73.63.Kv Quantum dots (QDs) in semiconductor systems, where electrons are confined in zero-dimensional states, have been the object of much recent attention [1,2]. In a gatedefined quantum dot the number of electrons can be reduced down to one [3,4]; such single-electron QDs may form the basis of qubits in quantum computation schemes [5,6]. High frequency operations on QD systems have been used to observe fundamental electronic phenomena such as coherent charge oscillations [7], single-and multiple-spin dynamics [8][9][10], excited-state spectra [11], and elastic tunneling behavior [12], and will be necessary for quantum computation applications in semiconductor systems.In typical QD experiments, the QDs were defined by static surface gates, and high frequency operations were achieved by applying voltage pulses to the gates. However, an alternative method has received recent attention: to use a dynamic QD defined by a surface acoustic wave (SAW) where high frequency operations are performed by moving the QD past static surface gates at a high velocity [13,14]. Because GaAs is piezoelectric, the strain wave of a SAW on a GaAs=AlGaAs heterostructure is accompanied by an electric potential modulation, which forms a series of oneor few-electron dynamic QDs in an empty quasi-onedimensional channel [15,16]. Previous experiments have attempted to observe interactions in dynamic QDs defined by SAWs [17], but to our knowledge the tunneling behavior necessary to observe complex quantum phenomena has not been seen.In this Letter we report measurements of the nonequilibrium escape rate from one-and few-electron dynamic QDs defined by a SAW. This measurement has been carried out in static quantum dots over second [18] and millisecond [12] time scales, but the dynamic QD arrangement allows us to directly observe electron tunneling on subnanosecond time scales. The SAW-defined dynamic QDs carry electrons along the channel to a tunnel barrier, where the electrons can escape from the QD into a neighboring two-dimensional electron gas (2DEG). Observation of the tunneling current allows us to determine the tunnel rate of electrons leaving the dynamic QD, which is found to depend on the number of electrons in the dot. By fitting these rates to a simple model, we determine the addition energy of the dynamic QD. This is, to our knowledge, the first direct measurement of dynamic QD energies.T...

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Hayashiet al.Reply:

Cited by 77 publications

References 15 publications

Coherent Single Electron Spin Control in a Slanting Zeeman Field

Coherent Single Electron Spin Control in a Slanting Zeeman Field

Controlled phase gate for solid-state charge-qubit architectures

Energy-Dependent Tunneling from Few-Electron Dynamic Quantum Dots

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