Direct optimization of signal-to-noise ratio of CPMG-like sequences in inhomogeneous fields.

The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. In previous work we have developed short composite broadband refocusing pulses together with practical excitation pulses to realize such performance gains, and quantified them using the ratio of signal to noise power (SNR). In this work we systematically explore the performance of refocusing pulses as a function of the overall pulse length up to ten times the length of the regular 180° pulse. This is in the regime of non-adiabatic pulses. We introduce a new performance functional for numerical pulse optimization that directly maximizes SNR and study the effect of symmetry constraints on the pulses. We find that for the optimal pulses, the SNR per asymptotic echo increases with pulse length but, for typical echo spacings, the SNR per unit time is maximized for refocusing pulses that are between two and four times longer than the duration of the standard rectangular 180° pulse. The performance is limited by the control bandwidth and the inability of finding the global maximum. The best performance was obtained with symmetric phase-alternating (SPA) refocusing pulses optimized with our novel performance functional. To test them in the CPMG sequence, we also developed axis-matching excitation (AMEX) pulses for use with these SPA refocusing pulses and tested the new AMEX-SPA sequences experimentally in a grossly inhomogeneous field, observing excellent agreement with the theoretical expectations. One of these sequences produced over 4.5 times higher SNR per asymptotic echo and 3.9 times higher SNR per unit time than the standard CPMG sequence with the same instantaneous RF power level. We also found that the new sequences are at least as robust to changes in the RF field strength as the standard CPMG sequence.

Cavity cooling of an ensemble spin system.

We describe how sideband cooling techniques may be applied to large spin ensembles in magnetic resonance. Using the Tavis-Cummings model in the presence of a Rabi drive, we solve a Markovian master equation describing the joint spin-cavity dynamics to derive cooling rates as a function of ensemble size. Our calculations indicate that the coupled angular momentum subspaces of a spin ensemble containing roughly 10(11) electron spins may be polarized in a time many orders of magnitude shorter than the typical thermal relaxation time. The described techniques should permit efficient removal of entropy for spin-based quantum information processors and fast polarization of spin samples. The proposed application of a standard technique in quantum optics to magnetic resonance also serves to reinforce the connection between the two fields, which has recently begun to be explored in further detail due to the development of hybrid designs for manufacturing noise-resilient quantum devices.

Axis-matching excitation pulses for CPMG-like sequences in inhomogeneous fields.

The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. Here we introduce a new class of excitation pulses, so-called axis-matching excitation pulses, that optimize the response for a given refocusing pulse. These new excitation pulses are tailored to the refocusing pulses and take their imperfections into account. Rather than generating purely transverse magnetization, these pulses are designed to generate magnetization pointing along the axis of the effective rotation of the refocusing cycle. This approach maximizes the CPMG component and minimizes the CP component of the signal. Replacing a standard 90° pulse with a new excitation pulse matched to the 180° refocusing pulse increases the signal bandwidth and improves the echo amplitudes by 30% in inhomogeneous fields in comparison to the standard CPMG sequence. Larger gains are obtained with more advanced refocusing pulses. Recent work demonstrated that it is possible to increase the signal to noise ratio (SNR) of individual echoes by more than a factor of 1.5 (in power units) without increasing the duration or amplitude of the refocusing pulses. This was achieved by replacing the standard 180° refocusing pulse by a short phase alternating pulse and the standard 90° excitation pulse by a broadband excitation pulse. We show here that with suitable axis-matching excitation pulses, the SNR further increases by over a factor of 2. We discuss the underlying theory and present several practical implementations of purely phase modulated axis-matching excitation pulses for a number of different refocusing pulses that were derived using methods of optimal control. To gain the full benefit of these new excitation pulses, it is essential to replace the standard phase cycling scheme based on 180° phase shifts by a new scheme involving phase inversion. We tested the new pulses experimentally and observe excellent agreement with the theoretical expectations. We also demonstrate that an additional benefit of axis-matching excitation pulses is the decrease of the transient that appears in the amplitudes of the first few echoes, thus enabling better measurements of short relaxation times.

Bandwidth-limited control and ringdown suppression in high-Q resonators.

We describe how the transient behavior of a tuned and matched resonator circuit and a ringdown suppression pulse may be integrated into an optimal control theory (OCT) pulse-design algorithm to derive control sequences with limited ringdown that perform a desired quantum operation in the presence of resonator distortions of the ideal waveform. Inclusion of ringdown suppression in numerical pulse optimizations significantly reduces spectrometer deadtime when using high quality factor (high-Q) resonators, leading to increased signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To demonstrate the method, we experimentally measure the free-induction decay of an inhomogeneously broadened solid-state free radical spin system at high Q. The measurement is enabled by using a numerically optimized bandwidth-limited OCT pulse, including ringdown suppression, robust to variations in static and microwave field strengths. We also discuss the applications of pulse design in high-Q resonators to universal control of anisotropic-hyperfine coupled electron-nuclear spin systems via electron-only modulation even when the bandwidth of the resonator is significantly smaller than the hyperfine coupling strength. These results demonstrate how limitations imposed by linear response theory may be vastly exceeded when using a sufficiently accurate system model to optimize pulses of high complexity.

Application of optimal control to CPMG refocusing pulse design.

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B(0) and B(1) offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10t(180) that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of ±10% RF inhomogeneity.