A single-electron transistor incorporated as part of a nanomechanical resonator represents an extreme limit of electron-phonon coupling. While it allows for fast and sensitive electromechanical measurements, it also introduces backaction forces from electron tunnelling which randomly perturb the mechanical state. Despite the stochastic nature of this backaction, under conditions of strong coupling it is predicted to create self-sustaining coherent mechanical oscillations. Here, we verify this prediction using time-resolved measurements of a vibrating carbon nanotube transistor. This electromechanical oscillator has intriguing similarities with a laser. The single-electron transistor, pumped by an electrical bias, acts as a gain medium while the resonator acts as a phonon cavity. Despite the unconventional operating principle, which does not involve stimulated emission, we confirm that the output is coherent, and demonstrate other laser behaviour including injection locking and frequency narrowing through feedback. arXiv:1903.04474v1 [cond-mat.mes-hall]

In an optomechanical setup, the coupling between cavity and resonator can be increased by tuning them to the same frequency. We study this interaction between a carbon nanotube resonator and a radio-frequency tank circuit acting as a cavity. In this resonant regime, the vacuum optomechanical coupling is enhanced by the dc voltage coupling the cavity and the mechanical resonator. Using the cavity to detect the nanotube's motion, we observe and simulate interference between mechanical and electrical oscillations. We measure the mechanical ring down and show that further improvements to the system could enable the measurement of mechanical motion at the quantum limit.

Only single-electron transistors with a certain level of cleanliness, where all states can be properly accessed, can be used for quantum experiments. To reveal their exceptional properties, carbon nanomaterials need to be stripped down to a single element: graphene has been exfoliated into a single sheet, and carbon nanotubes can reveal their vibrational, spin and quantum coherence properties only after being suspended across trenches1–3. Molecular graphene nanoribbons4–6 now provide carbon nanostructures with single-atom precision but suffer from poor solubility, similar to carbon nanotubes. Here we demonstrate the massive enhancement of the solubility of graphene nanoribbons by edge functionalization, to yield ultra-clean transport devices with sharp single-electron features. Strong electron–vibron coupling leads to a prominent Franck–Condon blockade, and the atomic definition of the edges allows identifying the associated transverse bending mode. These results demonstrate how molecular graphene can yield exceptionally clean electronic devices directly from solution. The sharpness of the electronic features opens a path to the exploitation of spin and vibrational properties in atomically precise graphene nanostructures.

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...

We report microwave-driven photon-assisted tunneling in a suspended carbon nanotube double quantum dot. From the resonant linewidth at a temperature of 13 mK, the charge dephasing time is determined to be 280 ± 30 ps. The linewidth is independent of driving frequency, but increases with increasing temperature. The moderate temperature dependence is inconsistent with expectations from electron-phonon coupling alone, but consistent with charge noise arising in the device. The extracted level of charge noise is comparable with that expected from previous measurements of a valley-spin qubit, where it was hypothesized to be the main cause of qubit decoherence. Our results suggest a possible route towards improved valley-spin qubits.