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.

1 aMi, X.1 aBenito, M.1 aPutz, S.1 aZajac, D., M.1 aTaylor, J., M.1 aBurkard, Guido1 aPetta, J., R. uhttps://arxiv.org/abs/1710.0326501974nas a2200181 4500008004100000245005000041210004800091260001500139520145800154100001101612700001501623700001301638700001801651700001901669700001901688700001801707856006701725 2018 eng d00aA coherent spin–photon interface in silicon0 acoherent spin–photon interface in silicon c2018/02/143 aElectron 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.

1 aMi, X.1 aBenito, M.1 aPutz, S.1 aZajac, D., M.1 aTaylor, J., M.1 aBurkard, Guido1 aPetta, J., R. uhttps://www.nature.com/articles/nature25769#author-information02685nas a2200205 4500008004100000245006300041210006100104260001500165300001100180490000700191520207900198100002102277700001802298700002202316700001602338700001902354700001802373700001902391856006902410 2018 eng d00aHigh-fidelity quantum gates in Si/SiGe double quantum dots0 aHighfidelity quantum gates in SiSiGe double quantum dots c2018/02/15 a0854210 v973 aMotivated 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.

1 aGullans, M., J.1 aTaylor, J., M.1 aPetta, J., R. uhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.03530501439nas a2200205 4500008004100000245005100041210005100092260001500143300001200158490000800170520087500178100001801053700002201071700001301093700001601106700001901122700001901141700001801160856005501178 2018 eng d00aResonantly driven CNOT gate for electron spins0 aResonantly driven CNOT gate for electron spins c2018/01/26 a439-4420 v3593 aSingle-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.

1 aZajac, D., M.1 aSigillito, A., J.1 aRuss, M.1 aBorjans, F.1 aTaylor, J., M.1 aBurkard, Guido1 aPetta, J., R. uhttp://science.sciencemag.org/content/359/6374/43901662nas a2200217 4500008004100000245004300041210004300084260001500127300001100142490000600153520108300159100001601242700001501258700001601273700001901289700001101308700002101319700001901340700001801359856006701377 2016 eng d00aDouble Quantum Dot Floquet Gain Medium0 aDouble Quantum Dot Floquet Gain Medium c2016/11/07 a0410270 v63 aStrongly 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.

1 aStehlik, J.1 aLiu, Y.-Y.1 aEichler, C.1 aHartke, T., R.1 aMi, X.1 aGullans, Michael1 aTaylor, J., M.1 aPetta, J., R. uhttp://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.04102701372nas a2200181 4500008004100000245007800041210006900119260001500188300001100203490000800214520084100222100002101063700001601084700001701100700001801117700001901135856003601154 2016 eng d00aSisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot0 aSisyphus Thermalization of Photons in a CavityCoupled Double Qua c2016/07/25 a0568010 v1173 aA 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.

1 aGullans, Michael1 aStehlik, J.1 aLiu, Y., -Y.1 aPetta, J., R.1 aTaylor, J., M. uhttp://arxiv.org/abs/1512.0124801515nas a2200181 4500008004100000245007100041210006900112260001500181300001100196490000700207520099200214100001701206700001601223700002101239700001901260700001801279856003601297 2015 eng d00aInjection Locking of a Semiconductor Double Quantum Dot Micromaser0 aInjection Locking of a Semiconductor Double Quantum Dot Micromas c2015/11/02 a0538020 v923 a 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. 1 aLiu, Y., -Y.1 aStehlik, J.1 aGullans, Michael1 aTaylor, J., M.1 aPetta, J., R. uhttp://arxiv.org/abs/1508.0414701003nas a2200181 4500008004100000245006900041210006800110260001500178300001100193490000800204520048000212100002100692700001700713700001600730700001800746700001900764856003800783 2015 eng d00aPhonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser0 aPhononAssisted Gain in a Semiconductor Double Quantum Dot Maser c2015/05/13 a1968020 v1143 aWe 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. 1 aGullans, Michael1 aLiu, Y., -Y.1 aStehlik, J.1 aPetta, J., R.1 aTaylor, J., M. uhttp://arxiv.org/abs/1501.03499v301150nas a2200193 4500008004100000245004800041210004800089260001500137300001400152490000800166520063700174100001700811700001600828700001600844700002100860700001900881700001800900856003800918 2015 eng d00aSemiconductor double quantum dot micromaser0 aSemiconductor double quantum dot micromaser c2015/01/15 a285 - 2870 v3473 a 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. 1 aLiu, Y., -Y.1 aStehlik, J.1 aEichler, C.1 aGullans, Michael1 aTaylor, J., M.1 aPetta, J., R. uhttp://arxiv.org/abs/1507.06359v101375nas a2200181 4500008004100000245008800041210006900129260001400198490000700212520082100219100001901040700001801059700002001077700001501097700001901112700001801131856004401149 2007 eng d00aRelaxation, dephasing, and quantum control of electron spins in double quantum dots0 aRelaxation dephasing and quantum control of electron spins in do c2007/7/130 v763 aRecent 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. 1 aTaylor, J., M.1 aPetta, J., R.1 aJohnson, A., C.1 aYacoby, A.1 aMarcus, C., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0602470v2