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**1 - 7**of**7**### Dynamical decoupling sequence construction as a filterdesign problem

- Journal of Physics B: Atomic, Molecular and Optical Physics
, 2011

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### c ○ Rinton Press HIGH-FIDELITY QUANTUM CONTROL USING ION CRYSTALS IN A PENNING TRAP

, 2009

"... We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser ..."

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We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled [1], and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays [5, 6, 7, 8]. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials [9, 10]. We discuss the use of two-dimensional 9Be + ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz ground-state electron spin flip transition, which we drive using microwaves [11, 12]. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement [1] on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary highfidelity rotations (τπ ∼200 µs). Randomized Benchmarking [13] demonstrates an error per gate (a Pauli-randomized π/2 and π pulse pair) of 8±1×10−4. Ramsey interferometry and spin-locking [14] measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical free-induction decay coherence time of T2 ∼2 ms, and a limiting T1ρ ∼688 ms. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the error-suppressing capabilities of dynamical

### Non-Ergodic Nuclear Depolarization in Nano-Cavities.

, 2003

"... Recently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of a gas in a closed nano-cavities are independent of the spacing between all spins. We derive exact time-dependent polarization for all spins in spin- 1 2 ensemble with spatially ..."

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Recently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of a gas in a closed nano-cavities are independent of the spacing between all spins. We derive exact time-dependent polarization for all spins in spin- 1 2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin, P1(0) = 1 then the exact spin dynamics of the model is shown to exhibit a periodical short pulses of the polarization of the first spin, the effect being typical of the systems having a large number, N, of spins. If N ≫ 1, then within the period 4π/g ( 2π/g) for odd (even) N-spin clusters, with g standing for spin coupling, the polarization of spin 1 switches quickly from unity to the time independent value, 1/3, over the time interval about (g √ N) −1, thus, almost all the time, the spin 1 spends in the time independent condition P1(t) = 1/3. The period and the width of the pulses determine the volume and the form-factor of the ellipsoidal cavity. The formalism is adopted to the case of time varying nano-fluctuations of the volume of the cavitation nano-bubbles. If the volume V (t) is varied by the Gaussian-in-time random noise then the envelope of the polarization peaks goes irreversibly to 1/3. The polarization dynamics of the single spin exhibits the Gaussian ( or exponential) time dependence when the correlation time of the fluctuations of the nano-volume is larger ( or smaller) than the 〈(δg) 2 〉 −1/2, where the 〈(δg) 2 〉 is the variance of the g(V (t)) coupling. Finally, we report the exact calculations of the NMR line shape for the N-spin gaseous aggregate. PACS numbers: 05.30.-d, 76.20.+q 1 1

### JOURNAL OF MAGNETIC RESONANCE 75, 1 lo- 124 ( 1987) Theory of Multiple-Pulse NMR at Low and Zero Fields

, 1987

"... Coherent averaging with time-dependent magnetic fields at low and zero static magnetic fields encounters several features which are unfamiliar in high-field magnetic resonance. The principal differences are that magnetic field pulses act generally on all spin species in the sample and that the Hamil ..."

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Coherent averaging with time-dependent magnetic fields at low and zero static magnetic fields encounters several features which are unfamiliar in high-field magnetic resonance. The principal differences are that magnetic field pulses act generally on all spin species in the sample and that the Hamiltonian contains additional terms that are normally discatded in a high static magnetic field. We illustrate how the full Hamiltonian or different terms of the Hamiltonian may be averaged to zero by sequences of 90 ” rotations around the x, y, and z axes. The two limiting cases of ideal delta-function pulses and windowless sequences are treated. We also show that the duality between rotations of space coordinates and spin coordinates allows one to replace spatial reorientations of the sample, such as magic-angle spinning, by time-dependent magnetic fields. Sequences of delta-function pubes at zero field are analogous to recursive expansion schemes of multiple-pulse sequences at high field. The terms of the full Hamiltonian appear also in the average Hamiltonian of high-field pulse sequences and can be manipulated by the same sequence of configurations as

### JOURNAL OF MAGNETIC RESONANCE 80,96- 111 (1988) Multiple-Pulse Sequences for Precise Transmitter Phase Alignment

, 1987

"... We show that arbitrary RF phase shifts can be measured precisely using the nuclear spins to monitor the phase of the RF field. Other imperfections like resonance offset, RF inhomogeneity, or symmetric phase transients are removed by the action of the multiple-puise sequence and have little influence ..."

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We show that arbitrary RF phase shifts can be measured precisely using the nuclear spins to monitor the phase of the RF field. Other imperfections like resonance offset, RF inhomogeneity, or symmetric phase transients are removed by the action of the multiple-puise sequence and have little influence on the measurements. Phase shifts can be trimmed to the desired value with an uncertainty of less than 10 millidegrees in favorable CaSeS. 0 1988 Academic Press, Inc.

### SOLID STATE NMR CHEMICAL SHIFfS AS AN ALTERNATIVE TO DIFFRACTION DATA IN TIlE DETERMINATION OF

, 1988

"... I would like to express my heartfelt thanks to Professor Mary Frances Richardson for her supervision, teaching, and assistance. In addition, I would like to thank DrJ. S. Hartman for his valuable discussion on the subject of nmr, and Dr. S. M. Rothstein for his help and encouragement. Thanks are als ..."

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I would like to express my heartfelt thanks to Professor Mary Frances Richardson for her supervision, teaching, and assistance. In addition, I would like to thank DrJ. S. Hartman for his valuable discussion on the subject of nmr, and Dr. S. M. Rothstein for his help and encouragement. Thanks are also offered to Tim, Donna, and Beatrice for their friendly help with acquisition of nmr spectra, and to the departmental faculties and graduate students for their valuable advice. Finally, I am grateful to NSERC for the financial support to this program. ii ABSTRACf Silicon carbide, which has many polytypic modifications of a very simple and very symmetric structure, is an excellent model system for exploring, the relationship between chemical shift, long-range dipolar shielding, and crystal structure in network solids. A simple McConnell equation treatment of bond anisotropy effects in a poly type predicts chemical shifts for silicon and carbon sites