Session E45: Hybrid Quantum Systems I

Charge dynamics and spin blockade in a hybrid double quantum dot in silicon

Hybrid architectures combining donor atoms and quantum dots in silicon can take advantage of fast gate voltage based spin manipulations to form a hybrid singlet-triplet qubit, with access to the quantum memory offered by the nuclear spin of the donor via the hyperfine interaction. Additionally, spin buses using quantum dot chains could mediate the transfer of quantum information between long-lived donor spins. We present an approach to a novel hybrid double quantum dot by coupling a donor to an artificial atom in a CMOS-compatible nanotransistor. Using gate-based RF-reflectometry, we probe the charge stability of the system and its quantum capacitance. Through microwave spectroscopy, we find a tunnel coupling of 2.7GHz and characterize the charge dynamics, revealing a charge $T_1$ of 100ns. We also show spin blockade at the inderdot transition and investigate the spin dynamics, opening up the possibility to operate this coupled system as a singlet-triplet qubit and to coherently transfer spin information between the quantum dot and the donor electron and nucleus.   

Controlling spin relaxation with a cavity

Spontaneous emission of radiation is one of the fundamental relaxation mechanisms for a quantum system. For spins, however, it is negligible compared to non-radiative relaxation~processes due to their weak coupling to the electromagnetic field. In 1946, Purcell~realized [1] that spontaneous emission is strongly enhanced when the quantum system is placed in a resonant cavity~- an effect now used to control the lifetime of systems with an electrical dipole [2]. Here, by coupling donor spins in silicon to a high quality factor superconducting microwave cavity of~small mode volume, we reach the regime where spontaneous emission constitutes the dominant spin~relaxation channel [3]. The relaxation rate is increased by three orders of magnitude when the spins are tuned to the cavity~resonance, showing it can be engineered and controlled on-demand. Our results provide a~novel way to initialize any spin into its ground state, with applications in magnetic resonance and quantum~information processing. They also show for the first time an alteration of spin dynamics by quantum fluctuations, a step towards the coherent magnetic coupling of a~spin to microwave photons. [1] E. M. Purcell, Phys.~Rev. 1946, 69, 681. \newline [2] P. Goy et al., PRL. 50, 1983. [3] A. Bienfait et al., arxiv~:1508.06148   

Coupling a Small Ensemble of Electrons on Helium to a Superconducting Circuit

Electrons on helium is a unique two-dimensional electron gas system formed at the interface of a quantum liquid (superfluid helium) and vacuum. If single electrons on helium can be isolated, the motional and spin states could form the building blocks for hybrid quantum computing [1,2]. Here we first review the strong coupling between a large electron ensemble and a microwave resonator [3]. Then we will describe methods to isolate small mesoscopic ensembles with less than 100 electrons in a micron-sized trap at the end of a quarter wavelength microwave cavity. Finally we will discuss the effect of helium fluctuations on the coherence of the hybrid circuit. [1] S. Lyon, Phys. Rev. A. 74, 5 (2006) [2] D.I. Schuster, et al. Phys. Rev. Lett. 105, 040503 (2010) [3] Ge Yang, et al., arXiv:1508.04847(2015)   

Magnetic resonance at the quantum limit

The detection and characterization of paramagnetic species by electron-spin resonance (ESR) spectroscopy has numerous applications in chemistry, biology, and materials science [1]. Most ESR spectrometers rely on the inductive detection of the small microwave signals emitted by the spins during their Larmor precession into a microwave resonator in which they are embedded. Using the tools offered by circuit Quantum Electrodynamics (QED), namely high quality factor superconducting micro-resonators and Josephson parametric amplifiers that operate at the quantum limit when cooled at 20mK [2], we report an increase of the sensitivity of inductively detected ESR by 4 orders of magnitude over the state-of-the-art, enabling the detection of 1700 Bismuth donor spins in silicon with a signal-to-noise ratio of 1 in a single echo [3]. We also demonstrate that the energy relaxation time of the spins is limited by spontaneous emission of microwave photons into the measurement line via the resonator [4], which opens the way to on-demand spin initialization via the Purcell effect. These results constitute a first step towards circuit QED experiments with magnetically coupled individual spins. [1] A. Schweiger and G. Jeschke, Principles of Pulse Electron Magnetic Resonance (Oxford University Press, 2001) [2] X. Zhou et al., Physical Review B 89, 214517 (2014). [3] A. Bienfait et al., arxiv~:1507.06831 [4] A. Bienfait et al., arxiv~:1508.06148   

Hybrid Quantum Information Processing with Superconducting Circuits and Rydberg Atoms

Hybrid approaches to quantum information processing exploit the strengths of disparate quantum technologies to realize performance that exceeds what can be reached with any single technology on its own. Here we describe steps toward realization of a hybrid superconducting circuit – Rydberg atom quantum architecture that will marry a fast, high-fidelity superconducting quantum processor with a long-lived quantum memory based on trapped Rydberg atoms. The key challenge is development of a high-fidelity microwave photon – Rydberg atom interface. We have designed superconducting thin-film microwave resonators that allow trapping of single Rydberg atoms at a voltage antinode, where coupling to the zero-point fields of the resonator is strongest. We discuss the dependence of resonator quality factor and achievable coupling factor on device geometry. Finally, we present preliminary results of experiments to couple Rydberg atoms and superconducting linear resonators in a custom liquid helium cryostat.   

Photon-mediated interactions: a scalable tool to create and sustain entangled states of N atoms

We propose and study the use of photon-mediated interactions for the generation of steady-state entanglement between N atoms that are separated by arbitrary distances. Through the judicious use of coherent drives and the placement of the atoms in a network of Cavity QED systems, a balance between their unitary and dissipative dynamics can be precisely engineered to stabilize a long-range correlated state of qubits in the steady state. We discuss the general theory behind such a scheme, and present an example of how it can be used to drive a register of N atoms to a generalized W-state, and the entanglement sustained indefinitely. The achievable steady-state fidelities for entanglement and its scaling with the number of qubits are discussed for presently existing superconducting quantum circuits. While the protocol is primarily discussed for a superconducting circuit architecture, it is ideally realized in any Cavity QED platform that permits controllable delivery of coherent electromagnetic radiation to specified locations.   

Spin-cavity longitudinal coupling for two-qubit gates and measurement

We have studied the possibility of longitudinal coupling of various encoded quantum dot spin-qubits to a microwave resonator via modulation of voltage gates. A dynamical coupling of tens of MHz can be achieved. We investigate specific procedures for entangling gates using accumulated geometrics phases and calculate possible gate times and fidelities. Implications for qubit readout and continuous quantum monitoring are also considered.   

Magnetization detecting electron paramagnetic resonance spectroscopy using a dc-SQUID directly coupled to an electron spin ensemble

Electron parametric resonance (EPR) spectroscopy is one of the most widely-used tool to characterize materials containing unpaired electrons. In the case of conventional EPR spectrometers, the resonance is detected as a change of microwave transmittance of a cavity. In our method, on the other hand, magnetization of the sample induced by the resonance is detected by a direct current superconducting quantum interference device (dc-SQUID) magnetometer, which is bonded to the sample. Here, we report detection of electron spin polarization and EPR spectroscopy using a micrometer-sized dc-SQUID magnetometer. We measure temperature and in-plane magnetic field dependence of spin polarization ratio and it has good agreement to the hyperbolic tangent law. We also successfully demonstrate EPR spectroscopy by applying a continuous microwave signal to the sample with a on-chip microstrip. We estimate the sensing volume and the minimum distinguishable number of electron spins to be $\sim$ $10^{-10}$ cm$^{3}$ ($\sim$ 0.1 pl) and $\sim$ $10^6$, respectively. This result paves the way towards realizing highly sensitive EPR spectroscopy in nanometer-sized area.   

Coupling nanoscale spin ensembles to a SQUID embedded in superconducting circuits

Electron spin resonance is a ubiquitous phenomenon used for the characterization of paramagnetic materials and to coherently control electron spins as carriers of quantum information. The coupling strength between spins and RF magnetic fields can be increased by using microwave frequency resonators, realized either as 3D cavities or in planar geometries. Here, we study microwave resonators embedding a superconducting quantum interference device (SQUID), which couples to nearby electron spins of phosphorus donors in silicon. We compare different SQUID and resonator geometries aiming at enhanced spin sensitivity. We also study the coupled system in a sideband regime where the Zeeman energy is nonresonant with the cavity frequency, allowing for operation at lower DC magnetic fields.   

Angular dependant micro-ESR characterization of a locally doped Gd$^{3+}$:Al$_{2}$O$_{3}$ hybrid system for quantum applications

Rare-earth doped crystals interfaced with superconducting quantum circuitry are an attractive platform for quantum memory and transducer applications. Here we present a detailed characterization of a locally implanted Gd$^{3+}$ in Al$_{2}$O$_{3}$ system coupled to a superconducting micro-resonator, by performing angular dependent micro-electron-spin-resonance (micro-ESR) measurements at mK temperatures. The device is fabricated using a hard Si$_{3}$N$_{4}$ mask to facilitate a local ion-implantation technique for precision control of the dopant location. The technique is found not to degrade the internal quality factor of the resonators which remains above $10^{5}$ (1). We find the measured angular dependence of the micro-ESR spectra to be in excellent agreement with the modelled Hamiltonian, supporting the conclusion that the dopant ions are successfully integrated into their relevant lattice sites whilst maintaining crystalline symmetries. Furthermore, we observe clear contributions from individual microwave field components of our micro-resonator, emphasising the need for controllable local implantation. $1)$ Wisby et al. Appl. Phys. Lett. \textbf{105}, 102601 (2014)   

Strong Coupling of a Donor Spin Ensemble to a Volume Microwave Resonator

We achieve the strong coupling regime between an ensemble of phosphorus donor spins (5e13 total donors) in highly enriched 28-Si (50 ppm 29-Si) and a standard dielectric resonator. Spins were polarized beyond Boltzmann equilibrium to a combined electron and nuclear polarization of 120 percent using spin selective optical excitation of the no-phonon bound exciton transition. We observed a spin ensemble-resonator splitting of $580\thinspace kHz$ (2g) in a cavity with a Q factor of 75,000 ($\kappa \ll \gamma \approx 120kHz$ where $\kappa $ and $\gamma $ are the external and internal resonator loss rates respectively). The spin ensemble has a long dephasing time ($9\thinspace \mu s)$ providing a wide window for viewing the time evolution of the coupled spin ensemble-cavity system described by the Tavis-Cummings model The free induction decay shows repeated collapses and revivals revealing a coherent and complete exchange of excitations between the superradiant state of the spin ensemble and the cavity (about 10 cycles are resolved). This exchange can be viewed as a swap of information between a long lived spin ensemble memory qubit ($T_{2}\approx 2\thinspace ms)$ and a cavity   

Suppressing gate errors through extra ions coupled to a cavity in frequency-domain quantum computation using rare-earth-ion-doped crystal

The rare-earth-ion-doped crystals, such as Pr$^{3+}$: Y$_2$SiO$_5$, are promising materials for scalable quantum computers, because the crystals contain a large number of ions which have long coherence time. The frequency-domain quantum computation (FDQC) enables us to employ individual ions coupled to a common cavity mode as qubits by identifying with their transition frequencies. In the FDQC, operation lights with detuning interact with transitions which are not intended to operate, because ions are irradiated regardless of their positions. This crosstalk causes serious errors of the quantum gates in the FDQC. When “resonance conditions” between eigenenergies of the whole system and transition-frequency differences among ions are satisfied, the gate errors increase. Ions for qubits must have transitions avoiding the conditions for high-fidelity gate. However, when a large number of ions are employed as qubits, it is difficult to avoid the conditions because of many combinations of eigenenergies and transitions. We propose new implementation using extra ions to control the resonance conditions, and show the effect of the extra ions by a numerical simulation. Our implementation is useful to realize a scalable quantum computer using rare-earth-ion-doped crystal based on the FDQC.   

Magneto-transport studies of a few hole GaAs double quantum dot in tilted magnetic fields.

Compared to equivalent electron devices, single-hole spins interact weakly with lattice nuclear spins leading to extended quantum coherence times. This makes p-type Quantum Dots (QD)~particularly attractive for practical quantum devices such as qubit circuits, quantum repeaters, quantum sensors etc. where long coherence time is required.~ Another property of holes is the possibility to tune their g-factor as a result of the strong anisotropy of the valance band.~ Hole g-factors can be conveniently tuned \textit{in situ} from a large value to almost zero by tilting the magnetic field relative to the 2D hole gas surface normal. [1] In this work we explore high-bias magneto-transport properties of a p-type double quantum dot (DQD) device fabricated from a GaAs/AlGaAs heterostructures using lateral split-gate technology.[2]~ A charge detection technique is used to monitor number of holes and tune the p-DQD in a single hole regime around (1,1) and (2,0) occupation states where Pauli spin-blockaded transport is expected. Four states are identified in quantizing magnetic fields within the high-bias current stripe -- three-fold triplet and a singlet which allows determining effective heavy hole g-factor as a function of the tilt angle from 90 to 0 degrees.~ ~[1]~ G. Ares et al., Phys.Rev. Lett. 110, .046602 (2013); [2] L. A. Tracy,et al., App. Phys. Lett. 104\textbf{, }123101 ~(2014).~