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Kluwer Academic Publishers eBooks

Decoherence and Quantum Error Correction in Frequency Standards

Chiara Macchiavello, Susana F. Huelga, J. I. Cirac, ARTUR K. EKERT, Martin Bodo Plenio

Published Dec 19, 2005• 11 citations
Publisher

Abstract

The precision of frequency measurements performed on trapped ions in the presence of decoherence is analysed. In particular, standard Ramsey spectroscopy on uucorrelated ions and optimal measurements on maximally entangled states are proved to lead to the same resolution, while the best precision is achieved using partially entangled preparations. The use of symrnetrisation procedures is proposed and it is shown how this allows to overcome even the optimal precision achievable when both the initial preparation and the final measurement are optimized. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47097-7_45

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Kluwer Academic Publishers eBooks•Dec 19, 2005•1 citation
The precision of frequency measurements performed on trapped ions in the presence of decoherence is analysed. In particular, standard Ramsey spectroscopy on uucorrelated ions and optimal measurements on maximally entangled states are proved to lead to the same resolution, while the best precision is achieved using partially entangled preparations. The use of symrnetrisation procedures is proposed and it is shown how this allows to overcome even the optimal precision achievable when both the initial preparation and the final measurement are optimized. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of nnn two-level systems as well as different measurement procedures. We show that standard Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally entangled states provide the same resolution. The best resolution is achieved using partially entangled preparations with a high degree of symmetry.
Microwave spectroscopy using trapped and cooled ions can achieve precision and accuracy comparable to the best cesium frequency standards. We discuss standards based on 199Hg+ ions trapped in linear Paul traps: the Jet Propulsion Laboratory (JPL) standard, which uses up to 107 atoms confined near the trap axis, and the recently evaluated NIST standard, which uses approximately ten ions laser cooled and crystalized on the trap axis. We consider future directions in trapped ion frequency standard work, including the use of entangled states for achieving higher precision, and progress on trapped ion optical frequency standards. Finally, we discuss scientific and technical applications of extremely stable frequency standards.
Microwave spectroscopy using trapped and cooled ions can achieve precision and accuracy comparable to the best cesium frequency standards. We discuss standards based on 199Hg+ ions trapped in linear Paul traps: the Jet Propulsion Laboratory (JPL) standard, which uses up to 107 atoms confined near the trap axis, and the recently evaluated NIST standard, which uses approximately ten ions laser cooled and crystalized on the trap axis. We consider future directions in trapped ion frequency standard work, including the use of entangled states for achieving higher precision, and progress on trapped ion optical frequency standards. Finally, we discuss scientific and technical applications of extremely stable frequency standards.
We discuss strategies for quantum enhanced estimation of atomic transition frequencies with ions stored in Paul traps or neutral atoms trapped in optical lattices. We show that only marginal quantum improvements can be achieved using standard Ramsey interferometry in the presence of collective dephasing, which is the major source of noise in relevant experimental setups. We therefore analyze methods based on decoherence free subspaces and prove that quantum enhancement can readily be achieved even in the case of significantly imperfect state preparation and faulty detections.
This thesis describes new results on the entanglement of atomic spins in Ramsey interferometry, optical atomic clocks and trapped ions. It is divided into three parts: First, we investigate improvements to conventional Ramsey interferometry with entanglement and adding only rotations of the collective spin to adjust the signal and measurement directions. The geometric degrees of freedom, connected to the rotations, are analytically optimized for a large class of generalized Ramsey protocols to allow efficient optimization of all parameters. Besides a unification of existing approaches, the main result is that there is only one new protocol, where a previously unused double inversion is applied. Studies of the local sensitivity show that this protocol reaches the fundamental quantum Fisher information limit and is yet robust against errors during preparation and measurement. In the second section we investigate the conditions under which optical atomic clocks exhibit increased long-term stability when applying weakly entangled, spin squeezed states. We discuss the common case of an atomic clock with a single ensemble, typical Brownian frequency noise and finite dead time. Theoretical modelling of the servo loop allows quantitative predictions of the optimal stability for given values of dead time and laser noise, in very good agreement with numerical simulations of the closed feedback loop. The main result is that, even with the current most stable lasers, the clock stability can only be improved for ensembles below a critical atom number of about one thousand in optical Sr lattice clocks. Even with a future improvement of the laser performance by one order of magnitude, the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers. Thus the last section considers the robust generation of entanglement in ion traps. An error budget including relevant experimental error sources is calculated for state-of-the-art quantum gates, driven by oscillating microwave gradients in surface traps. Amplitude modulation of the driving fields is shown to efficiently counteract the current limitations from motional mode instability. The predicted increase of the gate quality was demonstrated by the group of C. Ospelkaus at PTB Braunschweig, who measured gates with errors as low as ~ 10^(-3). In a similar approach, interactions between spin and motion can also be generated by combining oscillating rf-fields with a static magnetic field gradient. Penning traps designed for precision spectroscopy already feature large magnetic field gradients at the edge of a magnetic bottle configuration. We present parameters and conditions under which laser-free coupling of spin and quantized motion for (anti-)protons is possible at these points, in a step towards quantum logic spectroscopy for (anti-)protons.
In this paper recent experiments with single trapped ions are reviewed. They deal with the spectrum of the resonance fluorescence of a single ion, the ion trap laser and with experiments towards a new frequency standard on the basis of a single In + ion. The experiments demonstrate essential ingredients necessary to realize quantum logic gates using trapped ions. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.