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

Abstract

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...

Highly coherent spin states in carbon nanotubes coupled to cavity photons

“…This measurement fitted by a Lorentzian has a full width at half maximum of γ FWHM = 2π × (498 ± 80) kHz which sets an upper bound of the decoherence rate γ S ≤ γ FWHM /2 = 2π × 249 kHz. Such a narrow line width is 2 orders of magnitude lower than that found in the valley-spin qubit in the previous work with carbon nanotubes 18,24 and compares favorably to the very recent figures of merit reported for Si-or GaAs-based platforms. [4][5][6] Specifically, our decoherence rate is about 2-4 times lower than the Si-based platforms and about 40 times lower than the GaAs platform.…”

“…Our measurements are therefore fully in agreement with the tabulated values for the hyperfine coupling expected in CNTs of A 0.1-0.5 μeV (see ref. 18 and reference therein). In addition to the decoherence rate, we also present the spin-photon coupling strength and the cooperativity of the spin-photon interface C ¼ ð2g 2 S Þ=ðκ γ S Þ À Á as a function of the detuning (Fig.…”

“…Whereas they are well documented in Si or GaAs, the coherence properties of single electronic spins in carbon nanotubes are still debated. 17,18 Here, we use a spin qubit scheme based on a carbon nanotube embedded in a microwave cavity. Our device is made using a stapling technique developed for cQED architectures, which produces ultraclean double quantum dot devices with near-ideal spectra.…”

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Gravity as a classical information channel: consequences and proposals towards detecting wave function collapse

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