Electron spins in silicon quantum dots are attractive systems for quantum computing due to their long coherence times and the promise of rapid scaling using semiconductor fabrication techniques. While nearest neighbor exchange coupling of two spins has been demonstrated, the interaction of spins via microwave frequency photons could enable long distance spin-spin coupling and \"all-to-all\" qubit connectivity. Here we demonstrate strong-coupling between a single spin in silicon and a microwave frequency photon with spin-photon coupling rates g_s/(2π) \> 10 MHz. The mechanism enabling coherent spin-photon interactions is based on spin-charge hybridization in the presence of a magnetic field gradient. In addition to spin-photon coupling, we demonstrate coherent control of a single spin in the device and quantum non-demolition spin state readout using cavity photons. These results open a direct path toward entangling single spins using microwave frequency photons.

}, doi = {https://doi.org/10.1038/nature25769}, url = {https://arxiv.org/abs/1710.03265}, author = {X. Mi and M. Benito and S. Putz and D. M. Zajac and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {2148, title = {A coherent spin{\textendash}photon interface in silicon}, journal = {Nature}, year = {2018}, month = {2018/02/14}, abstract = {Electron spins in silicon quantum dots are attractive systems for quantum computing owing to their long coherence times and the promise of rapid scaling of the number of dots in a system using semiconductor fabrication techniques. Although nearest-neighbour exchange coupling of two spins has been demonstrated, the interaction of spins via microwave-frequency photons could enable long-distance spin\–spin coupling and connections between arbitrary pairs of qubits (\‘all-to-all\’ connectivity) in a spin-based quantum processor. Realizing coherent spin\–photon coupling is challenging because of the small magnetic-dipole moment of a single spin, which limits magnetic-dipole coupling rates to less than 1 kilohertz. Here we demonstrate strong coupling between a single spin in silicon and a single microwave-frequency photon, with spin\–photon coupling rates of more than 10 megahertz. The mechanism that enables the coherent spin\–photon interactions is based on spin\–charge hybridization in the presence of a magnetic-field gradient. In addition to spin\–photon coupling, we demonstrate coherent control and dispersive readout of a single spin. These results open up a direct path to entangling single spins using microwave-frequency photons.

}, doi = {10.1038/nature25769}, url = {https://www.nature.com/articles/nature25769$\#$author-information}, author = {X. Mi and M. Benito and S. Putz and D. M. Zajac and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {2147, title = {High-fidelity quantum gates in Si/SiGe double quantum dots}, journal = {Physical Review B}, volume = {97}, year = {2018}, month = {2018/02/15}, pages = {085421}, abstract = {Motivated by recent experiments of Zajac\ *et\ al.*\ [Science\ 359, 439 (2018)], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, nonadiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.

Electron-phonon coupling is known to play an important role in the charge dynamics of semiconductor quantum dots. Here we explore its role in the combined charge-photon dynamics of cavity-coupled double quantum dots. Previous work on these systems has shown that strong electron-phonon coupling leads to a large contribution to photoemission and gain from phonon-assisted emission and absorption processes. We compare the effects of this phonon sideband in three commonly investigated gate-defined quantum dot material systems: InAs nanowires and GaAs and Si two-dimensional electron gases (2DEGs). We compare our theory with existing experimental data from cavity-coupled InAs nanowire and GaAs 2DEG double quantum dots and find quantitative agreement only when the phonon sideband and photoemission processes during lead tunneling are taken into account. Finally, we show that the phonon sideband also leads to a sizable renormalization of the cavity frequency, which allows for direct spectroscopic probes of the electron-phonon coupling in these systems.

}, doi = {10.1103/PhysRevB.97.035305}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035305}, author = {M. J. Gullans and J. M. Taylor and J. R. Petta} } @article {2150, title = {Resonantly driven CNOT gate for electron spins}, journal = {Science}, volume = {359}, year = {2018}, month = {2018/01/26}, pages = {439-442}, abstract = {Single-qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. Although high-fidelity single-qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been challenging because of rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities greater than 99\%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 nanoseconds. We used the CNOT gate to generate a Bell state with 78\% fidelity (corrected for errors in state preparation and measurement). Our quantum dot device architecture enables multi-qubit algorithms in silicon.

}, doi = {10.1126/science.aao5965}, url = {http://science.sciencemag.org/content/359/6374/439}, author = {D. M. Zajac and A. J. Sigillito and M. Russ and F. Borjans and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {1815, title = {Double Quantum Dot Floquet Gain Medium}, journal = {Physical Review X}, volume = {6}, year = {2016}, month = {2016/11/07}, pages = {041027}, abstract = {Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here we show that a single electron in a periodically driven DQD functions as a \"Floquet gain medium,\" where population imbalances in the DQD Floquet quasi-energy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intra-cavity photon number n_c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current -- one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of non-classical light and thermalization of driven quantum systems.

}, doi = {10.1103/PhysRevX.6.041027}, url = {http://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041027}, author = {J. Stehlik and Y.-Y. Liu and C. Eichler and T. R. Hartke and X. Mi and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1692, title = {Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/07/25}, pages = {056801}, abstract = {A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.056801}, url = {http://arxiv.org/abs/1512.01248}, author = {Michael Gullans and J. Stehlik and Y. -Y. Liu and J. R. Petta and J. M. Taylor} } @article {1500, title = {Injection Locking of a Semiconductor Double Quantum Dot Micromaser}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/11/02}, pages = {053802}, abstract = { Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models. }, doi = {10.1103/PhysRevA.92.053802}, url = {http://arxiv.org/abs/1508.04147}, author = {Y. -Y. Liu and J. Stehlik and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1332, title = {Phonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/05/13}, pages = {196802}, abstract = {We develop a microscopic model for the recently demonstrated double quantum dot (DQD) maser. In characterizing the gain of this device we find that, in addition to the direct stimulated emission of photons, there is a large contribution from the simultaneous emission of a photon and a phonon, i.e., the phonon sideband. We show that this phonon-assisted gain typically dominates the overall gain which leads to masing. Recent experimental data are well fit with our model. }, doi = {10.1103/PhysRevLett.114.196802}, url = {http://arxiv.org/abs/1501.03499v3}, author = {Michael Gullans and Y. -Y. Liu and J. Stehlik and J. R. Petta and J. M. Taylor} } @article {1499, title = {Semiconductor double quantum dot micromaser}, journal = {Science}, volume = {347}, year = {2015}, month = {2015/01/15}, pages = {285 - 287}, abstract = { The coherent generation of light, from masers to lasers, relies upon the specific structure of the individual emitters that lead to gain. Devices operating as lasers in the few-emitter limit provide opportunities for understanding quantum coherent phenomena, from THz sources to quantum communication. Here we demonstrate a maser that is driven by single electron tunneling events. Semiconductor double quantum dots (DQDs) serve as a gain medium and are placed inside of a high quality factor microwave cavity. We verify maser action by comparing the statistics of the emitted microwave field above and below the maser threshold. }, doi = {10.1126/science.aaa2501}, url = {http://arxiv.org/abs/1507.06359v1}, author = {Y. -Y. Liu and J. Stehlik and C. Eichler and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1359, title = {Relaxation, dephasing, and quantum control of electron spins in double quantum dots}, journal = {Physical Review B}, volume = {76}, year = {2007}, month = {2007/7/13}, abstract = {Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here, we present a detailed theory for electron spin dynamics in two-electron double dot systems that was used to guide these experiments and analyze experimental results. The theory treats both charge and spin degrees of freedom on an equal basis. Specifically, we analyze the relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron system. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits. }, doi = {10.1103/PhysRevB.76.035315}, url = {http://arxiv.org/abs/cond-mat/0602470v2}, author = {J. M. Taylor and J. R. Petta and A. C. Johnson and A. Yacoby and C. M. Marcus and M. D. Lukin} }