Session M26: Semiconductor Qubits - RF Measurement and Hybridization

Circuit quantum electrodynamics with a spin qubit

Electron spins in quantum dots have been proposed as the building blocks of a quantum information processor. While both fast one and two qubit operations have been demonstrated, coupling distant spins remains a daunting challenge. In contrast, circuit quantum electrodynamics (cQED) has enabled superconducting qubits to be readily coupled over large distances via a superconducting microwave cavity. I will present our recent work aimed at integrating spin qubits with the cQED architecture.\footnote{K.D. Petersson et al., Nature 490, 380 (2012).} Our approach is to use spin qubits formed in strong spin-orbit materials such as InAs nanowires to enable a large effective coupling of the spin to the microwave cavity field. For an InAs nanowire double quantum dot coupled to the superconducting microwave cavity we achieve a charge-cavity coupling rate of $\sim 30$ MHz. Combining this large charge-cavity coupling rate with electrically driven spin qubit rotations we demonstrate that the cQED architecture can be used a sensitive probe of single spin dynamics. In another experiment, we can apply a source-drain bias to drive current through the double quantum dot and observe gain in the cavity transmission. We additionally measure photon emission from the cavity without any input field applied. Our results suggest that long-range spin coupling via superconducting microwave cavities is feasible and present new avenues for exploring quantum optics on a chip.   

Measuring the Charge Parity of an InAs Double Quantum Dot

We have fabricated tunable, few electron InAs nanowire double quantum dots (DQDs) which support rapid electrically driven single spin rotations.\footnote{M. D. Schroer, K. D. Petersson, M. Jung and J. R. Petta, Phys. Rev. Lett. \textbf{107}, 176811 (2011).} However, the measurement of nanowire DQDs presents an outstanding problem, typically relying on transport through the sample due to the lack of a local quantum point contact charge detector. We demonstrate a non-invasive charge sensing method based on a radio frequency measurement of the sample's complex admittance, which yields a fast and sensitive determination of the charge state.\footnote{M. Jung, M. D. Schroer, K. D. Petersson and J. R. Petta, Appl. Phys. Lett. \textbf{100}, 253508 (2012).} We show that this measurement is also sensitive to the spin state of the DQD, allowing a simple determination of the total charge parity in the sample.\footnote{M. D. Schroer, M. Jung, K. D. Petersson and J. R. Petta, Phys. Rev. Lett. \textbf{109}, 166804 (2012).} Radio frequency charge parity measurement may prove useful in high effective mass systems, such as Si/SiGe quantum dots, where the determination of the absolute charge number is not always feasible.   

Photon emission from a cavity-coupled double quantum dot

Circuit quantum electrodynamics (cQED) allows strong coupling between a microwave photon and a superconducting qubit. We recently demonstrated coupling of a double quantum dot (DQD) spin qubit to a high quality factor cavity in the cQED architecture, with a charge-cavity coupling rate of 30 MHz. Here we explore the same system, but with a finite source-drain bias applied across the DQD, which forces electrons to tunnel through the device. For specific experimental conditions, we observe gain in the cavity transmission. Moreover, in the absence of an input field, we directly measure photon emission from the cavity-coupled DQD. Our results are inconsistent with existing theoretical models, suggesting that contributions from phonons or cotunneling may be necessary to quantitatively describe the gain mechanism.   

Superconducting coplanar waveguide resonators for electron spin resonance applications

Superconducting coplanar waveguide (CPW) resonators are a promising alternative to conventional volume resonators for electron spin resonance (ESR) experiments where the sample volume and thus the number of spins is small. However, the magnetic fields required for ESR could present a problem for Nb superconducting resonators, which can be driven normal. Very thin Nb films (50 nm) and careful alignment of the resonators parallel to the magnetic field avoid driving the Nb normal, but flux trapping can still be an issue. Trapped flux reduces the resonator Q-factor, can lead to resonant frequency instability, and can lead to magnetic field inhomogeneities. At temperatures of 1.9 K and in a magnetic field 0.32 T, we have tested X-band resonators fabricated directly on the surface of a silicon sample. Q-factors in excess of 15,000 have been obtained. A thin layer of GE varnish applied directly to the resonator has been used to glue a sapphire wafer to its surface, and we still find Q-factors of 16,000 or more in the 0.32 T field. ESR applications of these resonators will be discussed.   

Microwave Measurements Electrons on Helium with Superconducting Coplanar Waveguide Resonators

Electrons on helium is a unique two-dimensional electron gas system formed at the interface of a quantum liquid (superfluid helium) and vacuum. The motional and spin states of single-electron quantum dots defined on such systems have been proposed for hybrid quantum computing [1,2]. Traditional AC transport experiments of electrons on helium are conducted at kilohertz frequencies. Here, we will present microwave measurements of electrons trapped in a 5GHz superconducting coplanar waveguide resonator with 1 MHz bandwidth. The effect of trapping parameters on the resonance, and experimental progress towards a single trapped electron regime will also be discussed.\\[4pt] [1] S. Lyon, Phys. Rev. A. 74, 5 (2006)\\[0pt] [2] D.I. Schuster, et al. Phys. Rev. Lett. 105, 040503 (2010)   

Photon mediated interaction between distant quantum dot circuits

Cavity QED allows one to study the interaction between light and matter at the most elementary level, by using for instance Rydberg atoms coupled to cavity photons. Recently, it has become possible to perform similar experiments on-chip, by using artificial two-level systems made from superconducting circuits instead of atoms. This circuit-QED offers unexplored potentialities, since other degrees of freedom than those of superconducting circuits could be used, and in particular, those of quantum dots. Such a hybrid circuit QED would allow one to study a large variety of situations not accessible with standard cavity QED, owing to the versatility of nanofabricated circuits. Here, we couple two quantum dot circuits to a single mode of the electromagnetic field in a microwave cavity. Our quantum dots are separated by 200 times their own size, with no direct tunnel and electrostatic couplings between them. We demonstrate their interaction mediated by the cavity photons. This could be used to scale up quantum bit architectures based on quantum dot circuits, and simulate on-chip phonon-mediated interactions between strongly correlated electrons.   

Phonon-Mediated Population Inversion in a Driven Double Quantum Dot

We examine phonon emission processes in a double quantum dot, configured as either a single or two-electron charge qubit and driven with resonant microwave excitation. Fast readout using a proximal rf quantum point contact (rf-QPC) enables charge sensing with high resolution and allows fine phonon-related features to be observed in microwave spectroscopy data. Spontaneous phonon emission is observed to produce level broadening and population inversion of a two-level system, a phenomena predicted theoretically but previously unreported. For the two-electron configuration, microwave transitions are shown to be spin-dependent, consistent with the well-understood mechanism of Pauli-blockade in double quantum dots.   

Dispersive Readout of a Few-Electron Double Quantum Dot with Fast rf Gate-Sensors

We report the dispersive charge-state readout of a double quantum dot in the few-electron regime using the $in$ $situ$ gate electrodes as sensitive detectors. We benchmark this gate-sensing technique against the well established quantum point contact (QPC) charge detector and find comparable performance with a bandwidth of $\sim$ 10 MHz and an equivalent charge sensitivity of $\sim$ 6.3 $\times$ $10^{-3}$ e/$\sqrt{\mathrm{Hz}}$. Dispersive gate-sensing alleviates the burden of separate charge detectors for quantum dot systems and promises to enable readout of qubits in scaled-up arrays.   

Spectroscopy of a GaAs Double Dot Qubit with Dispersive Readout

We report microwave spectroscopy of a GaAs double dot qubit device using the dispersive gate sensor (DGS) readout technique. In contrast to charge sensing methods based on quantum point contacts (QPCs) or single electron transistors (SETs), the DGS detection method senses the tunneling of charge between states that are near degenerate in energy. Microwave excitation applied to the surface gates enables this readout approach to resolve low energy spectroscopic features not apparent in transport or standard charge sensing measurements. We discuss the origin of these features and the use of this technique for characterizing semiconductor qubit systems.   

Radio frequency charge sensing in a Si double quantum dot device

Coherent spin manipulation has recently been demonstrated in a variety of silicon based devices.\footnote{B. M. Maune \emph{et al.}, Nature \textbf{481}, 344 (2012).}$^,$\footnote{J. J. Pla \emph{et al.}, Nature \textbf{489}, 541 (2012).} We fabricate accumulation mode double quantum dot devices and use radio frequency reflectometry to perform fast charge sensing in the few-electron regime. Our devices employ a nearby single quantum dot as a charge sensor. Charge transitions in the double dot result in a $\sim$60\% relative change in the charge sensor conductance when the sensor is operated in the Coulomb blockade regime, compared to a $\sim$1\% conductance change when the sensor is operated as a traditional quantum point contact. Further development of these techniques may enable us to perform single shot spin readout in a silicon quantum dot.   

Transport and Charge Manipulation in a Single Electron Silicon Double Quantum Dot

Silicon is one of the most promising candidates for ultra-coherent qubits due to its relatively early position in periodical table and the absence of nuclear spin in its naturally abundant isotope. Here we demonstrate a reliable recipe that enables us to reproducibly fabricate an accumulation mode few electron double quantum dot (DQD). We demonstrate tunable interdot tunnel coupling at single electron occupancy in the device. The charge state of the qubit is monitored by measuring the amplitude of the radio frequency signal that is reflected from a resonant circuit coupled to a charge sensor. By applying microwave radiation to the depletion gates, we probe the energy level structure of the DQD using photon assisted tunneling (PAT). We apply bursts of microwave radiation and monitor the dependence of the PAT peak height on the burst period to extract the charge relaxation time, T$_{1}$. By experimentally tuning the charge qubit Hamiltonian, we measure the tunnel coupling and detuning dependence of T$_{1}$.   

Progress towards microwave readout of a silicon double quantum dot

Microwave resonators coupled to quantum systems have been used for fast dispersive measurement in several different architectures in solid state and atomic physics. The electronic states of a semiconductor quantum dot represent a promising candidate for quantum information processing. Our work is geared toward developing a fast, non-demolition readout of a semiconductor qubit in silicon through coupling to a superconducting microwave resonator. We report progress on a novel design of a lateral   

Fabrication and measurement of an RF-QPC in an undoped Si/SiGe heterostructure

We perform radio-frequency reflectometry measurements on a quantum point contact fabricated in an undoped accumulation-mode Si/SiGe heterostructure. This device is a promising candidate for high-bandwidth charge sensing in Si/SiGe, and it provides the capability for fast qubit readout in this material. We show operation of the device with a well-defined resonance that can be modulated by a nearby gate. We will discuss design challenges that are particular to accumulation-mode structures and how they can be resolved.