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arXiv:1511.06155 · Physical Review A

Composite pulses for high-fidelity population inversion in optically dense, inhomogeneously broadened atomic ensembles

G. Demeter

Published Feb 22, 2016• 22 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.93.023830

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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 \ensuremathαz>10\ensuremath{\alpha}z>10\ensuremathαz>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 \ensuremathπ\ensuremath{\pi}\ensuremathπ-pulse excitation schemes and adiabatic passage schemes, being far more error tolerant than the former but still considerably faster than the latter.
Population inversion from an initial quantum state to a desired quantum state represents an exciting new frontier for quantum manipulation; that frontier is endowed with a strong interdisciplinary character and connections to other scientific fields, including atomic, molecular, and optical physics, as well as in solid-state devices, for fundamental studies, nuclear magnetic resonance and other spectroscopic techniques, metrology, interferometry, optical control of chemical reactions or quantum-information applications. Two-level systems are ubiquitous in these areas, and the driving of a population inversion is an important operation. So far various schemes for population transfer to a target state from an initial state have been proposed in theory and implemented in experiment. To be useful, such methods must, of course, be reliable, fast, and robust. Most literatures on two-level models investigated population inversion, which could be modelled by infinite-time processes. In this paper, by using a composite adiabatic passage (CAP) technique—in which the single pulse driving the quantum transition is replaced by a sequence of pulses with well-defined control phases, we investigate the population inversion problem of two-level quantum system with a finite duration. We take a sinusoidally varying pulse model that continuously vanishes at the beginning and the end of the finite duration as an example. The high-fidelity population inversion of the two-level system with finite duration is achieved. We discuss the effects of both coupling strength and detuning strength on the transition probability. It is found that this protocol could suppress the oscillations in the transition probability and reduce the admissible error bellow the 10 -4 quantum computation benchmark. The fidelity can arrive at 1, even with simple three- and five-composite pulse sequences. The protocol combines the advantages of adiabatic passage and composite pulses techniques. By choosing the composite phases appropriately, a high-fidelity, fast, stable and extremely robust complete population inversion is achieved for the finite-time two-level model. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp as long as the latter satisfy the symmetry property. Furthermore, the classical Hamiltonian is applied to describe the dynamic properties of the quantum system and further verify the effectiveness and feasibility of the proposed CAP technique. The results we present here are general and in principle apply to any two- and multi-level quantum systems. The accuracy of the CAP technique and its robustness against parameter variations make the protocol suitable for ultrahigh-fidelity quantum manipulation. We believe that the protocol can be widely used in many different areas of science, ranging from the quantum information, the quantum chemical, and the quantum optics to the ultracold atomic and molecular physics.
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.
In this work, we exploit the idea of composite pulses to achieve robust population inversion in a three-level quantum system. The scheme is based on the modulation of the coupling strength, while the other physical parameters remain unchanged. The composite pulses sequence is designed by vanishing high-order error terms, and can compensate the systematic errors to any desired order. In particular, this scheme keeps a good performance under the disturbance of waveform deformations. This trait ensures that population inversion can be nearly obtained even when the pulse sequence has a short jump delay. As an example, we employ the designed composite pulse sequence to prepare the WWW state in a robust manner in the superconducting circuits. The numerical results show that the fidelity can still maintain a high level in a decoherence environment.
We evaluate various sources of errors that occur when attempting to produce a specified coherent change of a two-state quantum system using six popular coherent control techniques: resonant excitation, adiabatic following, composite adiabatic passage, universal composite pulses, shortcut to adiabaticity, and single-shot shaped pulses. As error sources, we consider spatial intensity distribution, transit time variation, inhomogeneous broadening, Doppler broadening, unwanted chirp, and shape errors, as well as errors generated by counter-rotating terms. For the various error types, different techniques emerge as the best performers, but overall we find that universal composite pulses perform most consistently and are most resilient to errors compared to all other procedures.
Abstract In this work, we propose a composite pulses (CPs) scheme by modulating phases to achieve high fidelity population transfer in three-level systems. To circumvent the obstacle that not enough variables are exploited to eliminate the systematic errors in the transition probability, we put forward a cost function to find the optimal value. The cost function is independently constructed either in ensuring an accurate population of the target state, or in suppressing the population of the leakage state, or both of them. The results demonstrate that population transfer is implemented with high fidelity even when existing the deviations in the coupling coefficients. Furthermore, our CPs scheme can be extensible to arbitrarily long pulse sequences. As an example, we employ the CPs sequence for achieving the three-atom singlet state in an atom-cavity system with ultrahigh fidelity. The final singlet state shows robustness against deviations and is not seriously affected by waveform distortions. Also, the singlet state maintains a high fidelity under the decoherence environment.
The proposal for quantum computing with rare-earth-metal-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected frequency channels. We show that a class of Gaussian composite pulses and complex sech pulses provide accurate qubit $\ensuremath{\pi}$ rotations, which are at the same time channel selective on a 5 MHz frequency scale and tolerant to $\ifmmode\pm\else\textpm\fi{}0.5\mathrm{MHz}$ deviations of the transition frequency of ions within a single channel. Rotations in qubit space of arbitrary angles and phases are produced by sequences of $\ensuremath{\pi}$ pulses between the excited state of the ions and coherent superpositions of the qubit states.