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Physical Review A

Composite pulses for ultrabroad-band and ultranarrow-band excitation

Boyan T. Torosov, Elica S. Kyoseva, Nikolay V. Vitanov

Published Sep 8, 2015• 20 citations
Publisher

Abstract

We introduce ultrabroad-band composite pulses (CPs), which maximize (at the expense of a finite error tolerance $\ensuremath{\epsilon}$) the pulse area range wherein the population inversion remains above $1\ensuremath{-}\ensuremath{\epsilon}$. We present such CPs for error thresholds $\ensuremath{\epsilon}=0.01$, 0.001, and 0.0001 in two versions: CPs with different pulse areas of the constituent pulses, used as control parameters, and with equal pulse areas. The former CPs naturally outperform the CPs of identical pulses, which in turn outperform conventional broad-band CPs obtained by annulling the population inversion derivatives at a single point. Moreover, we derive double-compensation CPs, which correct errors in both the pulse area and the detuning. They outperform the corresponding conventional CPs as well. By using the same error-tolerance approach, we construct ultranarrow-band CPs, which squeeze the population inversion in as narrow a range as possible while keeping the excitation outside this range below the error threshold $\ensuremath{\epsilon}$.

DOI
10.1103/physreva.92.033406

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We introduce ultrabroad-band composite pulses (CPs), which maximize (at the expense of a finite error tolerance \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ) the pulse area range wherein the population inversion remains above 1\ensuremath−\ensuremathϵ1\ensuremath{-}\ensuremath{\epsilon}1\ensuremath−\ensuremathϵ. We present such CPs for error thresholds \ensuremathϵ=0.01\ensuremath{\epsilon}=0.01\ensuremathϵ=0.01, 0.001, and 0.0001 in two versions: CPs with different pulse areas of the constituent pulses, used as control parameters, and with equal pulse areas. The former CPs naturally outperform the CPs of identical pulses, which in turn outperform conventional broad-band CPs obtained by annulling the population inversion derivatives at a single point. Moreover, we derive double-compensation CPs, which correct errors in both the pulse area and the detuning. They outperform the corresponding conventional CPs as well. By using the same error-tolerance approach, we construct ultranarrow-band CPs, which squeeze the population inversion in as narrow a range as possible while keeping the excitation outside this range below the error threshold \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ.
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 one 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 Pr3+:Y2SiO5{\text{Pr}}^{3+}\text{:}{\text{Y}}_{2}{\text{SiO}}_{5}Pr3+:Y2​SiO5​ crystal.
We derive composite pulse sequences that achieve high-fidelity excitation of two-state systems in an optically dense, inhomogeneously broadened ensemble. The composite pulses are resistant to distortions due to the backaction of the medium they propagate in and are able to create high-fidelity inversion to optical depths $\ensuremath{\alpha}z>10$. They function well with smooth pulse shapes used for coherent control of optical atomic transitions in quantum computation and communication. They are an intermediary solution between single $\ensuremath{\pi}$-pulse excitation schemes and adiabatic passage schemes, being far more error tolerant than the former but still considerably faster than the latter.
Abstract We construct composite half- π pulses that are simultaneously robust to systematic mistracking of the control phases and to small pulse-area deviations. We extend the errant-phase composite-pulse approach from population-inversion ( π ) gates to π / 2 rotations, which are intrinsically more sensitive to phase miscalibration because they rely on controlled interference to create a specific superposition. The phases of the constituent pulses are chosen to cancel, order by order, the leading error terms associated with a correlated phase-scaling parameter while preserving broadband tolerance to pulse-area errors. We provide explicit non-anagram phase solutions for odd-length sequences and verify their performance by numerical simulations of the full composite propagator.
We propose a protocol for robust quantum state engineering using composite pulses (CPs) in four-level systems. The analytical expression of the propagator is derived for the implementation of universal single-qubit gates and the maximum superposition state. By carefully designing the relative phases between pulses, the CP sequences can compensate for the pulse area error to any desired order. We present two classes of CP sequences, one generating robust population inversion and the other generating robust superposition states. As applications, we employ the well-designed CP sequences to achieve the conversion of the W and Greenberger-Horne-Zeilinger states with high fidelity in a Rydberg atomic system. It is shown that the CP sequences yield excellent robustness with respect to the pulse area errors, and they possess a short evolution time.
Composite pulses---sequences of pulses with well-defined relative phases---are an efficient, robust, and flexible technique for coherent control of quantum systems. Composite sequences can compensate for a variety of experimental errors in the driving field (e.g., in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g., inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate for systematic errors in the composite phases. In the first type of such composite sequences, which compensate for pulse area errors, relative phase errors of over 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate for simultaneous pulse area and detuning errors, relative phase errors of over 5% can be compensated.
We introduce high-fidelity passband (PB) composite pulse sequences constructed by concatenation of recently derived arbitrarily large and arbitrarily accurate broadband B\mathcal{B}B and narrowband N\mathcal{N}N composite sequences. Our PB sequences allow us to produce flexible and tunable nearly rectangular two-state inversion profiles as a function of the individual pulse area because the width and the rectangularity of these profiles can be adjusted at will. Moreover, these PB sequences suppress excitation around pulse area 0 and $2\ensuremath{\pi}$, and suppress deviations from complete population inversion around pulse area $\ensuremath{\pi}$ to arbitrarily high orders. These features make them a valuable tool for high-fidelity qubit operations in the presence of relatively strong amplitude noise. We construct two types of PB pulses: N(B)\mathcal{N}(\mathcal{B})N(B), in which a broadband pulse is nested into a narrowband pulse, and B(N)\mathcal{B}(\mathcal{N})B(N), in which a narrowband pulse is nested into a broadband pulse; the latter sequences deliver narrower profiles. We derive exact analytic formulas for the composite phases of the PB pulses and exact analytic formulas for the inversion profiles. These formulas allow an easy estimation of the experimental resources needed for any desired qubit inversion profile.