Experimental realization of an order-finding algorithm with an NMR quantum computer

We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.     

Simultaneous soft pulses applied at nearby frequencies

The rotation of a spin subject to an on-resonance soft pulse and simultaneously to a soft pulse at a nearby frequency may strongly deviate from the desired rotation expected for a single on-resonance pulse. The deviation is the result of transient frequency shifts of the spin caused by the off-resonance irradiation. We show that the resulting error can be corrected by shifting the frequency of the on-resonance pulse in such a way that it tracks the shift of the spin frequency. Experimentally, the effectiveness of this simple and intuitive method is demonstrated for simultaneous inversions at nearby frequencies in the case of both coupled and uncoupled spins. Simulations predict that the correction technique is effective for arbitrary pulse shapes and tip angles and is particularly useful when the frequency window of the shaped pulse is two to eight times the frequency separation between the chemical shifts of the two spins.     

Manifestations of phase-coherent transport in graphene

The electronic transport properties of graphene exhibit pronounced differences from those of conventional two dimensional electron systems investigated in the past. As a consequence, well established phenomena such as the integer quantum Hall effect and weak localization manifest themselves differently in graphene. Here we present an overview of recent experiments that we have performed to probe phase coherent transport. In particular, we have investigated in great detail Josephson supercurrent and superconducting proximity effect in junctions consisting of a graphene layer in between superconducting electrodes. We have also used the same devices to measure aperiodic conductance fluctuations and weak localization. The experimental results clearly indicate that low-temperature transport in graphene is phase coherent on a ∼ 1μm length scale, irrespective of the position of the Fermi level. We discuss the different behavior of Josephson supercurrent and weak localization in terms of the unusual properties of the electronic states in graphene upon time reversal symmetry.     

Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

A two-dimensional steady-sate analysis of semi-infinite brittlecrack growth at a constant subcritical rate in an unboundedfully-coupled thermoelastic solid under mixed-mode thermomechanicalloading is made. The loading consists of normal and shear tractionsand heat fluxes applied as point sources (line loads in theout-of-plane direction). A related problem is solved exactly in an integral transformspace, and robust asymptotic forms used to reduce the originalproblem to a set of integral equations. The equations are partiallycoupled and exhibit operators of both Cauchy and Abel types,yet can be solved analytically. The temperature change field at a distance from the moving crackedge is then constructed, and its dominant term is found tobe controlled by the imposed heat fluxes. The role of this termis, indeed, enhanced if the heat fluxes serve to render thecrack as a net heat source/sink for the solid, as opposed tobeing a transmitter of heat across its plane. More generally,the influence of the thermoelastic coupling on this field, aswell as other functions, is found to increase with crack speed.     

Spin echo of a single electron spin in a quantum dot

We report a measurement of the spin-echo decay of a single electron spin confined in a semiconductor quantum dot. When we tip the spin in the transverse plane via a magnetic field burst, it dephases in 37 ns due to the Larmor precession around a random effective field from the nuclear spins in the host material. We reverse this dephasing to a large extent via a spin-echo pulse, and find a spin-echo decay time of about 0.5 micros at 70 mT. These results are in the range of theoretical predictions of the electron spin coherence time governed by the electron-nuclear dynamics.     

Synthetic magnetic opals

We present studies of novel nanocomposites of BiNi impregnated into the structure of opals as well as inverse opals. Atomic force microscopy and high resolution elemental analyses show a highly ordered structure and uniform distribution of the BiNi filler in the matrix. These BiNi-based nanocomposites are found to exhibit distinct ferromagnetic-like ordering with transition temperature of about 675 K. As far as we know there exists no report in literature on any BiNi compound which is magnetic.     

Generating entanglement and squeezed states of nuclear spins in quantum dots

We present a scheme for achieving coherent spin squeezing of nuclear spin states in semiconductor quantum dots. The nuclear polarization dependence of the electron spin resonance generates a unitary evolution that drives nuclear spins into a collective entangled state. The polarization dependence of the resonance generates an area-preserving, twisting dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips. Our estimates of squeezing times indicate that the entanglement threshold can be reached in current experiments.     

Universal phase shift and nonexponential decay of driven single-spin oscillations

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear-spin bath. Because of the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of approximately pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit.     

Single-shot readout of electron spin states in a quantum dot using spin-dependent tunnel rates

We present a method for reading out the spin state of electrons in a quantum dot that is robust against charge noise and can be used even when the electron temperature exceeds the energy splitting between the states. The spin states are first correlated to different charge states using a spin dependence of the tunnel rates. A subsequent fast measurement of the charge on the dot then reveals the original spin state. We experimentally demonstrate the method by performing readout of the two-electron spin states, achieving a single-shot visibility of more than 80%. We find very long triplet-to-singlet relaxation times (up to several milliseconds), with a strong dependence on the in-plane magnetic field.     

Zeeman energy and spin relaxation in a one-electron quantum dot

We have measured the relaxation time, T1, of the spin of a single electron confined in a semiconductor quantum dot (a proposed quantum bit). In a magnetic field, applied parallel to the two-dimensional electron gas in which the quantum dot is defined, Zeeman splitting of the orbital states is directly observed by measurements of electron transport through the dot. By applying short voltage pulses, we can populate the excited spin state with one electron and monitor relaxation of the spin. We find a lower bound on T1 of 50 micros at 7.5 T, only limited by our signal-to-noise ratio. A continuous measurement of the charge on the dot has no observable effect on the spin relaxation.