Universal composite pulses for efficient population inversion with an arbitrary excitation profile

Abstract

We introduce a method to rotate arbitrarily the excitation profile of universal broadband composite pulse sequences for robust high-fidelity population inversion. These pulses compensate deviations in any experimental parameter (e.g. pulse amplitude, pulse duration, detuning from resonance, Stark shifts, unwanted frequency chirp, etc.) and are applicable with any pulse shape. The rotation allows to achieve higher order robustness to any combination of pulse area and detuning errors at no additional cost. The latter can be particularly useful, e.g., when detuning errors are due to Stark shifts that are correlated with the power of the applied field. We demonstrate the efficiency and universality of these composite pulses by experimental implementation for rephasing of atomic coherences in a Pr 3+ :Y2SiO5 crystal.

Composite pulses for high fidelity population transfer in three-level systems

“…Unlike the case of two-level systems [30][31][32][33][34][35][36][37][38], there exists a population leakage from the ground states to the excited state in the three-level system. Thus, we need to suppress population leakage (i.e., the population of the excited state |e ) as well.…”

“…Note that the design procedure of the phases is more complicated in three-level systems than that in two-level systems [30][31][32][33][34][35][36][37][38], since there are two coefficients [C (1) N,1 and C (1) N,2 ] in the first-order term while there are six coefficients [C (2) N,k and D (2) N,k , k = 1, 2, 3] in the second-order term, and so forth. Particularly, when considering the small number of pulses, which is often the practical case, it does not have sufficient phases to eliminate the systematic errors up to the desired order.…”

“…The CPs technique, comprised of a well-organized train of constant pulses with determined pulse areas and relative phases, was conceived in early nuclear magnetic resonance (NMR) [18][19][20][21]. To date, this technique has been used extensively in QIP [22][23][24][25][26][27][28][29][30][31]. One unique feature of CPs is that the pulse sequence is available to compensate for the systematic error in any physical parameters (e.g., pulse duration, pulse amplitude, detuning, Stark shift, etc.)…”

Composite pulses for high fidelity population transfer in three-level systems

“…= 0. Note that the design procedure of the phases is more complicated in three-level systems than that in two-level systems [30][31][32][33][34][35][36][37][38], since there are two coefficients [C (1) N,1 and C (1) N,2 ] in the first-order term while there are six coefficients [C (2) N,k and D (2) N,k , k = 1, 2, 3] in the second-order term, and so forth. Particularly, when considering the small number of pulses, which is often the practical case, it does not have sufficient phases to eliminate the systematic errors up to the desired order.…”

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

“…A large amount of solutions have been proposed in the literature to date, with their own advantages and limitations [25] in terms of pulse duration and energy or efficiency of the control protocol. Among recent propositions for two-level quantum systems, we mention composite pulses [26,27,28,29,30], procedures based on shortcut controls [31,32,33], learning control [34,35] and optimal control methods [36,37,38,39,40,4,41,42,43]. As an illustrative example of this control issue, we consider in this study the control of two-level quantum systems with different resonance offsets, which can be viewed as a reference problem for robust protocols in quantum control.…”