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arXiv:1208.2287 · Physical Review Letters

Dynamical Suppression of Unwanted Transitions in Multistate Quantum Systems

Genko T. Genov, Nikolay V. Vitanov

Published Mar 26, 2013• 43 citations
arXivHTMLPDF

Abstract

We propose a method to suppress unwanted transition channels and achieve perfect population transfer in multistate quantum systems by using composite pulse sequences. Unwanted transition paths may be present due to imperfect light polarization, misalignment of the quantization axis, spatial inhomogeneity of the trapping fields, off-resonant couplings, etc., or they may be merely unavoidable, e.g., due to perturbing excitations in molecules and solids. Compensation of separate or simultaneous deviations in polarization, pulse area, and detuning is demonstrated, even when these deviations are unknown, in three-state V and Ξ (ladder) systems and in a four-state Y system.

DOI
10.1103/physrevlett.110.133002

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We propose a method to suppress unwanted transition channels and achieve perfect population transfer in multistate quantum systems by using composite pulse sequences. Unwanted transition paths may be present due to imperfect light polarization, misalignment of the quantization axis, spatial inhomogeneity of the trapping fields, off-resonant couplings, etc., or they may be merely unavoidable, e.g., due to perturbing excitations in molecules and solids. Compensation of separate or simultaneous deviations in polarization, pulse area, and detuning is demonstrated, even when these deviations are unknown, in three-state V and Ξ (ladder) systems and in a four-state Y system.
Summary form only given. Experiments in many fields of quantum physics require well-defined quantum states and well-defined interactions. For example, the basic ingredient of the quantum computer is a well-defined qubit - a two-state quantum system. Real quantum systems, however, possess many states and special care is needed to isolate just two of them. In real and artificial atoms this is usually done with polarized laser light, carefully aligned with the quantization axis. However, unwanted transition channels may still be present, which reduce the fidelity of the operations. For example, when an ultracold atomic ensemble held in an optical dipole trap is addressed by right circularly polarized light, many atoms often “see” an admixture of σ+ and σ- light (i.e., elliptical polarization [1]) since not all of them are exactly in the focus of the laser fields. Unwanted transitions may be present also due to imperfect polarization or alignment, off-resonant couplings, perturbing excitations in molecules and solids, etc.We propose a simple and efficient technique for automatic compensation of such errors, even without knowing their magnitudes, which uses composite pulse sequences [2-5] to dynamically suppress unwanted transitions, while simultaneously controlling the qubit in a robust way. We illustrate the technique in threeand four-state quantum systems forming linkages reminiscent of the letters V, Ξ and Y, but it can readily be adapted to more complex systems. By suitably choosing the phases of the constituent pulses, the unwanted transitions can be suppressed with very high fidelity, while compensation of deviations in laser polarizations, intensities and detunings can be done simultaneously. The accuracy, the flexibility and the simplicity of the proposed technique make it a potentially important tool in applications requiring high control fidelity, such as quantum information processing and quantum optics.transitions
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 a control method for off-resonant robust quantum information processing suited for quantum integrated photonics. We utilize detunings as control parameters to derive a family of composite pulses for high-fidelity complete population transfer. The presented detuning-modulated composite sequences can be implemented within the decay lifetime of the qubit and correct for control inaccuracies in various parameters including pulse strength, duration, detuning, phase jitter, Stark shift, and unwanted frequency chirps. We implement the proposed robust sequences in an integrated photonics platform to achieve complete light transfer insensitive to fabrication errors.
Abstract A scheme is proposed for achieving robust population inversion in five‐level systems by means of composite pulses. An example of such a system consists of the magnetic sublevels with angular momenta and . Through elaborately constructing the relative phases of pulse pairs, the composite sequences perform well in suppressing the uncorrelated pulse area errors. In particular, the five pulse‐pair sequence possesses good robustness and a short evolution time. The composite sequences are further designed to compensate for a single type of pulse area errors to any desired order. This work provides a high‐efficiency way for robust quantum state manipulation in five‐level systems.
Three-level systems appear in various quantum information processing platforms.In several control schemes, the excited level serves as an auxiliary state for implementing gate operations between the lower qubit states.However, extra excited levels give rise to unwanted transitions that cause leakage and other errors, degrading the gate fidelity.We focus on a coherent-population-trapping scheme for gates and design protocols that reduce the effects of the unwanted off-resonant couplings and improve the gate performance up to several orders of magnitude.For a particular setup of unwanted couplings, we find an exact solution, which leads to error-free gate operations via only a static detuning modification.In the general case, we improve gate operations by adding corrective modulations to the pulses, thereby generalizing the derivative removal by adiabatic gates protocol to systems.Our techniques enable fast and high-fidelity gates and apply to a wide range of optically driven platforms, such as quantum dots, color centers, and trapped ions.
We construct fast and stable control schemes for two- and three-level quantum systems. These schemes result in an almost perfect population transfer even in the presence of an additional, unwanted and uncontrollable transition. Such schemes are developed by first using the techniques of ‘shortcuts to adiabaticity' and then introducing and examining a measure of the scheme's sensitivity to an unwanted transition. We optimize the schemes to minimize this sensitivity and provide examples of shortcut schemes which lead to a nearly perfect population inversion even in the presence of unwanted transitions.