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Vistas in Astronomy

Quantum measurements of trapped ions

Wayne M. Itano, James C Bergquist, J. J. Bollinger, Jonathan Magnolia Gilligan, Daniel J. Heinzen, F.L. Moore, Mark G. Raizen, David J. Wineland

Published Jan 1, 1993• 3 citations
Publisher
DOI
10.1016/0083-6656(93)90029-j

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Yb+ ion trapping and optimum planar trap geometries for scalable quantum technology

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Trapped ions in linear Paul traps are largely isolated from interaction with the environment. This property of trapped ions make them a primary choice for quantum technology. \nOver the last decade, trapped atomic ions in linear radio frequency Paul traps have shown to be an important tool to implement quantum algorithms. The scalability of linear ion \ntraps is required to handle large numbers of qubits, in order to implement useful quantum computation. Advance micro-fabrication technology allows the realisation of scalable ion traps. Further developments of micro-trap designs, for the purpose of scalable quantum technology, requires inter-disciplinary investigations of ion traps. Micro-scale ion trap designs typically require a versatile experimental setup. The first part of this thesis describes such an experimental setup including a chip bracket that can host macroscopic ion traps as well as advanced symmetric and asymmetric ion trap chips with up to 90 control electrodes. The system provides versatile optical access for both type of traps and the vacuum chamber is designed in a way so the ion traps can be replaced within a short amount of time. To test the working of the setup, a macroscopic ion trap with an ion-electrode distance of 310±10 μm is used to trap ytterbium ions (Yb+). The trap is characterised by measuring the heating rate, (n•), and spectral noise density SE(ω). A \nphotoionisation technique is used to ionise the different isotopes of Yb in our trap. Isotope selective photoionisation requires exact measurements of 1So↔1P1 transition for the different Yb isotopes. A technique to measure these resonant frequencies is described. \nThis technique works by observing and aligning fluorescence spots and by using this technique, the 1So↔1P1 transition frequencies for stable isotopes of Yb were measured with an accuracy of 60 MHz. These new measured transition frequencies for stable Yb isotopes differ from previously published work by 660 MHz. Furthermore, this technique can also be used to obtain the transition frequencies at different laser-atomic beam angles, typical for non-perpendicular laser-atomic beam angles. The second part of this thesis discusses the optimisation of surface trap geometries as they are being used to implement scalable ion trap designs which consist of a large number of trapping zones. The trap depth in surface traps is low compared to symmetric traps of similar dimensions. How to optimise the trap geometry to achieve maximum trap depth for a given ion height above the trap electrodes, is discussed. Fast and adiabatic ion shuttling operations in one dimension as well as ion separation and recombination processes are important for many quantum information implementations. The maximum speed of separation of trapped ions for adiabatic shuttling operations depends on the secular frequencies, the trapped ion experiences in the process. It will be shown how such ion trap structures have to be designed for fast ion separation process and linear shuttling. Numerical results of adiabatic shuttling operations for trapped ions in such trap structures are also presented.

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This thesis describes the development of two segmented ion trap systems for quantum information experiments and investigations of novel quantum measurements. We report successful loading of 40Ca+ ions in one of the trap systems and the successful demonstration of the partial collapse and revival of the wavefunction of an ion qubit using the system. We describe the operation of ion trap systems with segmented electrodes and develop a practical strategy for choosing the voltages to apply to the electrode segments to obtain desired trapping potentials and correct for stray fields. The linearity of the Laplace equation results in a linear map from the configuration space of electrode voltages to the function space of electric potentials in the trap. We decompose the electrode configuration space into basis vectors whose corresponding potentials have intuitive meaning. We describe attempts at loading Ca+ ions in a micro-scale segmented ion trap built at Lucent Technologies. The Lucent Trap is a planar ion trap fabricated using lithographic techniques on a silicon substrate. We experienced several problems with this trap and were unable to successfully load ions in it. A second ion trap, built at the University of Liverpool, is described. The Liverpool trap has miniature segmented electrodes constructed using conventional machining. We describe loading of Ca+ ions, and the demonstration of stable trapping with long ion lifetimes and stable electric and magnetic fields. The Liverpool trap is used to demonstrate non-projective “partial” measurements of a qubit wavefunction, which result in non-unitary, non-projective evolution of the wavefunction dubbed partial collapse. This effect can be reversed by performing another partial measurement, but only if the second measurement results in a particular outcome. When this outcome is observed, the qubit wavefunction is restored to the original state. An exact restoration occurs when both measurements are ideal, and we quantify the success of our demonstration by quantum process tomography. We obtain process fidelity >0.65 for a wide variation in strength of the partial collapse from 0−0.94 (where 0 leaves the system unaffected and 1 is the limit of a complete projective measurement).

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Unsharp positive operator-valued measurements allow a variety of measurement applications which minimally disrupt the state of the quantum system. Experimental schemes are proposed for implementing unsharp measurements on the qubit levels of a trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion and that of an auxiliary ion, using standard ion-trap quantum logic operations, and then realizing an unsharp measurement through projective measurement on the auxiliary atom. We analyze common sources of error and their effect on different applications of unsharp measurements.

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Experimental quantum error correction with trapped ions

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Bulletin of the American Physical Society•Mar 21, 2013•0 citations
Trapped ions in linear Paul traps are largely isolated from interaction with the environment. This property of trapped ions make them a primary choice for quantum technology. \nOver the last decade, trapped atomic ions in linear radio frequency Paul traps have shown to be an important tool to implement quantum algorithms. The scalability of linear ion \ntraps is required to handle large numbers of qubits, in order to implement useful quantum computation. Advance micro-fabrication technology allows the realisation of scalable ion traps. Further developments of micro-trap designs, for the purpose of scalable quantum technology, requires inter-disciplinary investigations of ion traps. Micro-scale ion trap designs typically require a versatile experimental setup. The first part of this thesis describes such an experimental setup including a chip bracket that can host macroscopic ion traps as well as advanced symmetric and asymmetric ion trap chips with up to 90 control electrodes. The system provides versatile optical access for both type of traps and the vacuum chamber is designed in a way so the ion traps can be replaced within a short amount of time. To test the working of the setup, a macroscopic ion trap with an ion-electrode distance of 310±10 μm is used to trap ytterbium ions (Yb+). The trap is characterised by measuring the heating rate, (n•), and spectral noise density SE(ω). A \nphotoionisation technique is used to ionise the different isotopes of Yb in our trap. Isotope selective photoionisation requires exact measurements of 1So↔1P1 transition for the different Yb isotopes. A technique to measure these resonant frequencies is described. \nThis technique works by observing and aligning fluorescence spots and by using this technique, the 1So↔1P1 transition frequencies for stable isotopes of Yb were measured with an accuracy of 60 MHz. These new measured transition frequencies for stable Yb isotopes differ from previously published work by 660 MHz. Furthermore, this technique can also be used to obtain the transition frequencies at different laser-atomic beam angles, typical for non-perpendicular laser-atomic beam angles. The second part of this thesis discusses the optimisation of surface trap geometries as they are being used to implement scalable ion trap designs which consist of a large number of trapping zones. The trap depth in surface traps is low compared to symmetric traps of similar dimensions. How to optimise the trap geometry to achieve maximum trap depth for a given ion height above the trap electrodes, is discussed. Fast and adiabatic ion shuttling operations in one dimension as well as ion separation and recombination processes are important for many quantum information implementations. The maximum speed of separation of trapped ions for adiabatic shuttling operations depends on the secular frequencies, the trapped ion experiences in the process. It will be shown how such ion trap structures have to be designed for fast ion separation process and linear shuttling. Numerical results of adiabatic shuttling operations for trapped ions in such trap structures are also presented.
This thesis describes the development of two segmented ion trap systems for quantum information experiments and investigations of novel quantum measurements. We report successful loading of 40Ca+ ions in one of the trap systems and the successful demonstration of the partial collapse and revival of the wavefunction of an ion qubit using the system. We describe the operation of ion trap systems with segmented electrodes and develop a practical strategy for choosing the voltages to apply to the electrode segments to obtain desired trapping potentials and correct for stray fields. The linearity of the Laplace equation results in a linear map from the configuration space of electrode voltages to the function space of electric potentials in the trap. We decompose the electrode configuration space into basis vectors whose corresponding potentials have intuitive meaning. We describe attempts at loading Ca+ ions in a micro-scale segmented ion trap built at Lucent Technologies. The Lucent Trap is a planar ion trap fabricated using lithographic techniques on a silicon substrate. We experienced several problems with this trap and were unable to successfully load ions in it. A second ion trap, built at the University of Liverpool, is described. The Liverpool trap has miniature segmented electrodes constructed using conventional machining. We describe loading of Ca+ ions, and the demonstration of stable trapping with long ion lifetimes and stable electric and magnetic fields. The Liverpool trap is used to demonstrate non-projective “partial” measurements of a qubit wavefunction, which result in non-unitary, non-projective evolution of the wavefunction dubbed partial collapse. This effect can be reversed by performing another partial measurement, but only if the second measurement results in a particular outcome. When this outcome is observed, the qubit wavefunction is restored to the original state. An exact restoration occurs when both measurements are ideal, and we quantify the success of our demonstration by quantum process tomography. We obtain process fidelity >0.65 for a wide variation in strength of the partial collapse from 0−0.94 (where 0 leaves the system unaffected and 1 is the limit of a complete projective measurement).
Unsharp positive operator-valued measurements allow a variety of measurement applications which minimally disrupt the state of the quantum system. Experimental schemes are proposed for implementing unsharp measurements on the qubit levels of a trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion and that of an auxiliary ion, using standard ion-trap quantum logic operations, and then realizing an unsharp measurement through projective measurement on the auxiliary atom. We analyze common sources of error and their effect on different applications of unsharp measurements.