Maximal Rabi frequency of an electrically driven spin in a disordered magnetic field

Széchenyi, Gábor; Pályi, András

doi:10.1103/physrevb.89.115409

Cited by 24 publications

(41 citation statements)

References 29 publications

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“…The transition rate depends on ϕ and ϕ only through S (lin) c,K +κ,c,K +κ (K + G), which is invariant under the exchange of ϕ and ϕ polar angle of κ and κ as seen from Eq. (23). This proves the first equality in Eq.…”

Section: Appendix B: Proof Of Eqs (8a) and (8b)supporting

confidence: 54%

“…Recently, ways to control and measure the valley degree of freedom (or valley index, for short) in these materials have been proposed [1][2][3][4][5][6][7][8] and tested experimentally [9][10][11][12][13][14][15][16]. The valley index is also being actively considered as a carrier of quantum information [14,[17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Valley relaxation in graphene due to charged impurities

Boross

Pályi

2015

Phys. Rev. B

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Monolayer graphene is an example of materials with multivalley electronic structure. In such materials, the valley index is being considered as an information carrier. Consequently, relaxation mechanisms leading to loss of valley information are of interest. Here, we calculate the rate of valley relaxation induced by charged impurities in graphene. A special model of graphene is applied, where the p z orbitals are two-dimensional Gaussian functions, with a spatial extension characterized by an effective Bohr radius a eB . We obtain the valley relaxation rate by solving the Boltzmann equation, for the case of noninteracting electrons, as well as for the case when the impurity potential is screened due to electron-electron interaction. For the latter case, we take into account local-field effects and evaluate the dielectric matrix in the random phase approximation. Our main findings are as follows: (i) The valley relaxation rate is proportional to the electronic density of states at the Fermi energy. (ii) Charged impurities located in the close vicinity of the graphene plane, at distance d 0.3Å, are much more efficient in inducing valley relaxation than those farther away, the effect of the latter being suppressed exponentially with increasing graphene-impurity distance d. (iii) Both in the absence and in the presence of electron-electron interaction, the valley relaxation rate shows pronounced dependence on the effective Bohr radius a eB . The trends are different in the two cases: In the absence (presence) of screening, the valley relaxation rate decreases (increases) for increasing effective Bohr radius. This last result highlights that a quantitative calculation of the valley relaxation rate should incorporate electron-electron interactions as well as an accurate knowledge of the electronic wave functions on the atomic length scale.

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Section: Appendix B: Proof Of Eqs (8a) and (8b)supporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Valley relaxation in graphene due to charged impurities

Boross

Pályi

2015

Phys. Rev. B

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“…As expected, Rabi frequency increases with microwave power, but saturates at the highest power suggesting a contribution of short-range disorder to the EDSR mechanism [39]. With coherent manipulation established, we measure dephasing using a Ramsey sequence of two bursts per pulse cycle separated by time τ S [ Fig.…”

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confidence: 99%

Hyperfine and Spin-Orbit Coupling Effects on Decay of Spin-Valley States in a Carbon Nanotube

et al. 2017

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The decay of spin-valley states is studied in a suspended carbon nanotube double quantum dot via leakage current in Pauli blockade and via dephasing and decoherence of a qubit. From the magnetic field dependence of the leakage current, hyperfine and spin-orbit contributions to relaxation from blocked to unblocked states are identified and explained quantitatively by means of a simple model. The observed qubit dephasing rate is consistent with the hyperfine coupling strength extracted from this model and inconsistent with dephasing from charge noise. However, the qubit coherence time, although longer than previously achieved, is probably still limited by charge noise in the device.The co-existence in carbon nanotubes of spin and valley angular momenta opens a host of possibilities for quantum information [1][2][3][4], coherent coupling to mechanics [5,6], and on-chip entanglement [7,8]. Spin-orbit coupling [9] provides electrical control, but introduces a relaxation channel. However, measurements of dephasing and decoherence [10][11][12] show that spin and valley qubit states couple surprisingly strongly to lattice nuclear spins and to uncontrolled electric fields, e.g. from thermal switchers. Realising these possibilities requires such effects to be mitigated. Here we study leakage current in a Pauli blockaded double quantum dot to identify spin-orbit and hyperfine contributions to spin-valley relaxation [3,13,14]. By suspending the nanotube, we decouple it from the substrate [11]. Measuring a spinvalley qubit defined in the double dot, we find dephasing and decoherence rates nearly independent of temperature, and show that charge noise cannot explain the observed dephasing, supporting the conclusion that despite the low density of 13 C spins, hyperfine interaction causes rapid dephasing in nanotubes [10,11].The measured device [ Fig. 1(a-b)] is a carbon nanotube suspended by stamping between two contacts and over five gate electrodes G1-G5 [3,[15][16][17]. Gate voltages V G1 − V G5 , together with Schottky barriers at the contacts, define a double quantum dot potential. The dot potentials are predominantly controlled by gates G1 (for the left dot) and G4-5 (for the right dot), while the interdot tunnel barrier is controlled by gates G2-3. For fast manipulation, gates G1 and G5 are connected via tees to waveform generator outputs and a vector microwave source. The device is measured in a magnetic field B = (B X , B Y , B Z ), with Z chosen along the nanotube and X normal to the substrate. Experiments were in a dilution refrigerator at 15 mK unless stated.To map charge configurations of the double quantum dot, we measure the current I through the nanotube with source-drain bias V SD = 8 mV applied between the contacts [ Fig. 1(c)]. As a function of V G1 and V G4 , the honeycomb Coulomb peak pattern is characteristic of a double quantum dot, with honeycomb vertices marking transitions between particular electron or hole occupations [18]. A horizontal stripe of suppressed current around V G4 = 200 mV indicates depl...

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“…However, both scenarios of EDSR (i.e., based on a micromagnet or spin-orbit coupling) are in a physical regime distinct from Refs. [13][14][15], because δh xy is typically much smaller than the drive b. To see this, we notice that Eq.…”

mentioning

confidence: 99%

“…[10] has demonstrated striking deviations from the ESR behavior, including a crossover from power-law to gaussian decay. It is also known that the electron motion, as well as the presence of the drive, can have substantial effects on spin dynamics and decoherence [13][14][15][16][17]. These considerations motivate us to provide here a detailed characterization of EDSR dephasing induced by the hyperfine interaction, paying special attention to the large-amplitude regime.…”

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confidence: 99%

Dephasing due to Nuclear Spins in Large-Amplitude Electric Dipole Spin Resonance

2016

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We have analyzed effects of the hyperfine interaction on electric dipole spin resonance when the amplitude of the quantum-dot motion becomes comparable or larger than the quantum dot's size. Away from the well known small-drive regime, the important role played by transverse nuclear fluctuations leads to a gaussian decay with characteristic dependence on drive strength and detuning. A characterization of spin-flip gate fidelity, in the presence of such additional drive-dependent dephasing, shows that vanishingly small errors can still be achieved at sufficiently large amplitudes. Based on our theory, we analyze recent electric-dipole spin resonance experiments relying on spin-orbit interactions or the slanting field of a micromagnet. We find that such experiments are already in a regime with significant effects of transverse nuclear fluctuations and the form of decay of the Rabi oscillations can be reproduced well by our theory.PACS numbers: 85.35. Be,03.65.Yz Introduction. The interest in coherent manipulation of single electron spins has stimulated intense research efforts, leading to a great degree of control in a variety of nanostructures [1, 2]. For electrons in quantum dots, electron spin resonance (ESR) was first demonstrated in Ref. [3]. However, full electric control of local spins might be a better strategy for complex architectures of many quantum dots, envisioned to realize quantum information processing [4]. Thus, electric dipole spin resonance (EDSR) was developed relying on either spin-orbit couplings [5,6] or the inhomogeneous magnetic field induced by a micromagnet [7,8]. The effectiveness of EDSR is highlighted by recent experiments, which could demonstrate Rabi oscillations with frequencies larger than 100 MHz for both approaches [9,10]. To further improve the performance of such spin manipulation schemes, it is important to characterize relevant dephasing mechanisms, and especially those which might become dominant at strong electric drive. In fact, as it will become clear in the following, a sufficiently strong drive is able to induce significant and yet unexplored modifications on how typical dephasing sources affect EDSR. For this reason, while representing the main limitation for accurate spin manipulation, dephasing is still poorly understood in large-amplitude regime of EDSR (i.e., when the amplitude of motion becomes comparable to the quantum dot's size).

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Maximal Rabi frequency of an electrically driven spin in a disordered magnetic field

Cited by 24 publications

References 29 publications

Valley relaxation in graphene due to charged impurities

Valley relaxation in graphene due to charged impurities

Hyperfine and Spin-Orbit Coupling Effects on Decay of Spin-Valley States in a Carbon Nanotube

Dephasing due to Nuclear Spins in Large-Amplitude Electric Dipole Spin Resonance

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