Session V30: Focus Session: Semiconductor Qubits - Measurement

Single-donor spin qubits in silicon

The idea of using the spin of a single donor atom in silicon to encode quantum information goes back to the Kane proposal [1] in 1998. We have now resolved the technical challenges involved in the readout and control of the electron and nuclear spin of a single atom. The key breakthrough was the development of a device structure where the donor is tunnel-coupled to the island of an electrostatically-induced single-electron transistor [2]. This device allowed the single-shot readout of the electron spin with visibility $> 90\%$ and 3 $\mu$s readout time [3]. More recently we have integrated the single-shot readout device with a broadband microwave transmission line to coherently control the electron and nuclear spins. The resonance frequency of the electron is found by monitoring the excess spin-up counts while sweeping the microwave frequency. At any time, one of two possible frequencies is found to be in resonance with the electron spin, depending on the state of the nuclear spin. Alternately probing the two frequencies yields the (quantum nondemolition) single-shot readout of the nucleus, with fidelity $> 99.99\%$. Then we demonstrate the coherent control (Rabi oscillations) of both the electron and the nucleus, both detected in single-shot mode. The $\pi$-pulse fidelity is $\sim 70\%$ for the electron and $\sim 99\%$ for the nucleus. Hahn echo and multi-pulse dynamical decoupling sequences allow us to explore the true coherence of the qubits, yielding $T_{2e} \sim 200$ $\mu$s for the electron, and $T_{2n} \sim 60$ ms for the nucleus. These results are fully consistent with the bulk values for donors in a natural Si sample. Further improvements in qubit coherence can be expected by moving to isotopically pure $^{28}$Si substrates.\\[4pt] [1] B. E. Kane, Nature \textbf{393}, 133 (1998).\\[0pt] [2] A. Morello \textit{et al.}, Phys. Rev. B \textbf{80}, 081307(R) (2009).\\[0pt] [3] A. Morello \textit{et al.}, Nature \textbf{467}, 687 (2010).   

Quantum read-out and fast initialization of nuclear spin qubits with electric currents

Nuclear spin qubits have the longest coherence times in the solid state, but their quantum read-out and initialization is a great challenge. We present a theory for the interaction of an electric current with the nuclear spins of donor impurities in semiconductors [1]. The theory yields a sensitivity criterion for quantum detection of nuclear spin states using electrically detected magnetic resonance, as well as an all electrical method for fast nuclear spin qubit initialization.\\[4pt] [1] N. Stemeroff and R. de Sousa, Phys. Rev. Lett. {\bf 107}, 197602 (2011).   

Real-time readout and lifetime measurements of single-triplet states in a Si/SiGe double quantum dot

The singlet and triplet states of a two-electron double quantum dot can be used as the basis for a logical qubit that combines fast gating and robust readout via Pauli spin blockade. We present measurements of the lifetimes of these states in a Si/SiGe double dot at magnetic fields between 1T and 0T [1]. The lifetimes are found by analyzing the statistics of repeated single-shot measurements of the spin state of the system. This technique allows multiple relaxation processes to be observed simultaneously. At zero magnetic field we find that all four spin states have lifetimes of approximately 10ms. With increasing magnetic field the lifetimes of the S and T0 states show no noticeable change, while the lifetime of the T- state rises, reaching 3 seconds at 1T. [1] J. R. Prance, et al., e-print: arxiv.org/abs/1110.6431   

Calibrated State Tomography in Singlet-Triplet Qubits

Quantitative and accurate state tomography is becoming increasingly necessary in spin qubits to establish gate fidelities, entanglement measures, and optimize the increasingly complex gate sequences needed to perform experiments. In spin-qubits, to perform state tomography single-qubit rotations are used to map different axes of the Bloch sphere to the singlet-triplet axis, followed by projective measurement onto the singlet-triplet axis. Two orthogonal rotations are provided by two physically distinct mechanisms: magnetic field gradients and exchange rotations. The complex interplay between these mechanisms, noise sources, and pulse distortions make it difficult to accurately predict the angle and axis of rotations from first principles, leading to a circular problem: how can one calibrate tomographic rotations without any calibrated tomographic rotations? We describe and demonstrate a method which, using minimal assumptions, makes it possible to detect and correct for both axis errors in tomography and losses during the rotations associated with state tomography. This allows state tomography with unprecedented precision in these systems.   

Readout and Control Technology for Spin Qubits

Scale-up of spin qubits will require the development of new technological approaches that enable readout and control in multi-qubit device architectures. We report results demonstrating a fast readout method based on quantum capacitance that is well suited to detecting spin-states in qubit geometries beyond two quantum dots. Control protocols and device architectures for the selective rotation of single spins using on-chip transmission lines and ac-magnetic field gradients will be presented.   

Si/SiGe Quantum Dot Charge Sensing with Radio Frequency Single-Electron Transistor

We report the operation of a radio frequency superconducting single-electron transistor (rf-SSET) as a charge sensor for single and double Si/SiGe quantum dots (QDs). The charge sensitivity is on the order of $10^{-5}$ to $10^{-6}$ $e/\sqrt{Hz}$. In the reflectometry set-up, real-time electron tunneling events in a single QD are measured, which demonstrates a fast charge detection time of a few tens of microseconds. The stability diagram of a double QD is mapped out with the averaged reflected power of the rf-SSET. In addition, electron temperature is measured in a dilution refrigerator to be around 150 mK, allowing us to study spin blockade and Kondo effect.   

Study of the QPC Back-action to Electron Spin Based Qubits

The electron spin states in quantum dots (QD) are potential for implementing qubits. Quantum point contacts (QPC) are widely used to read-out these spin states. However, any read-out procedure inevitably causes back-action to the measured qubits. In this work we studied the back-action of a QPC to the electron spin states in a single GaAs QD. We found that the non-equilibrium effect in the QPC real-time charge counting statistics is a benchmark of the QPC back-action strength. The back-action driven excitations to higher energy levels contribute extra features which enabled us to study the QD's internal structures. The excitations between the two Zeeman states for odd number of electrons and between the spin singlet-triplet states for even number of electrons are respectively studied. This provides a way to quantitatively evaluate the influence of back-action on Zeeman or singlet-triplet based spin qubits. The dependence of the relaxation time of various spin excited states on the back-action strength was also studied.   

Fast charge sensing in InAs nanowire double quantum dot devices

Fast and sensitive charge and spin state readout is one of the most important requirements for quantum computing. Radio frequency (rf) reflectometry [1] provides a simple and fast charge detection scheme for charge and spin state readout in double quantum dot (DQD) devices without a separate charge detector [2]. Here, we demonstrate charge sensing measurements in InAs nanowire DQD devices using rf-reflectometry. The source electrode of the nanowire DQD is directly coupled to the tank circuit. We correlate standard dc transport measurements with the tank circuit response. We drive the resonator at its resonant frequency and detect the reflected signal via a cryogenic and room temperature amplifier. Using rf-reflectometry, we can observe charging transitions even when the device tuned to a regime where current through the device is below the noise floor of the setup. The sensor enables the occupancy of the quantum dot to be probed down to a few electron regime. We present preliminary results of spin state readout using rf-reflectometry. \noindent \\ \noindent [1] R. J. Schoelkopf {\it et al.}, Science {\bf280}, 1238 (1998)\\ \noindent [2] K. D. Petersson {\it et al.}, Nano Lett. {\bf10}, 2789 (2010)\\   

Single charge sensing and transport in double quantum dots fabricated from commercially grown Si/SiGe heterostructures

We perform quantum Hall measurements on three types of commercially available modulation doped Si/SiGe heterostructures [1] to determine their suitability for depletion gate defined quantum dot devices. By adjusting the growth parameters, we are able to achieve two dimensional electron gases with low charge densities and high mobilities. We extract an electron temperature of 100 mK in the single quantum dot regime. Double quantum dots fabricated on these heterostructures show clear evidence of single charge transitions [2] as measured in dc transport and charge sensing. \\[4pt] [1] C. B. Simmons et al, Phys. Rev. Lett. 106, 156804 (2011).\\[0pt] [2] R. Hanson et al, Rev. Mod. Phys. 79, 1217 (2007).   

Charge sensing in a silicon MOS double quantum dot

We report charge sensing measurements on a double quantum dot fabricated in a silicon / silicon dioxide double top gated structure. Depletion gates are used to laterally define a double quantum dot, and each dot has an adjacent quantum point contact (QPC) electrometer for remote detection of the dot occupation. For charge sensing, two techniques have been employed. In one, the direct conductance of the QPC measured with a low frequency ac voltage bias, and in the other the differential change in QPC conductance is measured as an ac voltage is applied to a dot plunger gate. Simultaneous direct and differential charge sense measurements are performed using an amplitude modulation technique. We characterize the double dot using honeycomb stability diagrams and non-linear transport. Results are compared to detailed modeling of our device structure.   

Dispersive readout of spin blockade in a carbon nanotube double quantum dot

We probe the charge states of a carbon nanotube double quantum dot by coupling superconducting resonators to the leads and a gate of a device designed for operation as a spin-valley qubit. Multiplexed dispersive readout allows rapid reflectometry measurements of the device without the need for dedicated proximal charge sensors. In this way as-grown nanotubes may be used in a bottom-gated geometry to create low-disorder devices that are freely suspended and then insulated using atomic layer deposition. These techniques are demonstrated with measurements in the spin blockade regime. We acknowledge support from IBM, NSF-MWN, NSF-NRI through the INDEX Center, and Harvard University.   

Relaxation hotspots and fast reset of a single electron spin in a double quantum dot

We measure the relaxation time of a single electron spin in a double quantum dot as a function of the energy detuning between the two dots for Zeeman splitting larger than the tunnel coupling. Close to the charge degeneracy point at which the electron delocalizes over both dots we observe two ``hot spots'' at which relaxation times are enhanced by almost four orders of magnitude. We identify these hot spots to occur at degeneracies of orbital and spin excitations. The spin-orbit and hyperfine interaction in the GaAs host lattice efficiently mix degenerate spin states and in combination with fast orbital relaxation this can lead to a fast pumping of the electron spin to its ground state. The enhanced spin relaxation can be exploited to achieve a fast reset of the electron spin, which might prove useful in the context of spin based quantum information processing.