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arXiv:0807.3500

Spatial correlation functions for the collective degrees of freedom of many trapped ions

Nicolas C. Menicucci, Gerard J Milburn

Published Jul 22, 2008• 0 citations
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Abstract

Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions have the experimental advantage of each having their own "built-in" motional detector: electronic states that can be coupled, via an external laser, to the ion's vibrational motion. The post-interaction electronic state can be read out with high efficiency, giving a stochastic measurement record whose classical correlations reflect the quantum correlations of the ions' collective vibrational state. Here we calculate this general result, then we discuss the long detection-time limit and specialize to Gaussian states, and finally we compare the results for thermal versus squeezed states.

DOI
10.48550/arxiv.0807.3500

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Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions have the experimental advantage of each having their own "built-in" motional detector: electronic states that can be coupled, via an external laser, to the ion's vibrational motion. The post-interaction electronic state can be read out with high efficiency, giving a stochastic measurement record whose classical correlations reflect the quantum correlations of the ions' collective vibrational state. Here we calculate this general result, then we discuss the long detection-time limit and specialize to Gaussian states, and finally we compare the results for thermal versus squeezed states.
We present a simple method that can be used to directly measure the squeezing of the quantum motional states of a trapped ion. Through the use of the interaction between the trapped ion and classical lasers, one can design a required coupling between the internal electronic and external vibrational degrees of freedom of the ion and can transfer information of the expectation value of a vibrational operator to the atomic internal populations. Thus measurement of squeezing on the quantum motional state can directly be realized. By adjusting the phases of the interacting lasers, one can measure the squeezing of both position and momentum quadratures.
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta.Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task.For many applications, linear chains of ions in conventional traps are ideally suited to address this problem.However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems.Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields.We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal.As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap.Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion.Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.
We present experimental results of using trapped ions for the study of energy transport and quantum correlations in many-body systems. We investigate energy propagation by locally exciting one end of an ion chain and then observing the subsequent dynamics. The experimental results agree with the presented normal mode model of ion motion, and signify the first steps towards realizing theoretical proposals of studying many-body physics with the motional degree of freedom of trapped ions. Additionally, we present a method for detecting correlations between an open quantum system and its environment by acting only locally on the open system. We implement this method using a single trapped ion and discuss our current work towards extending the results to larger systems. Lastly, we demonstrate how the presented method for local detection of quantum correlations can be used for detection of quantum phase transitions.
Quantum technology with atomic, molecular and optical systems has advanced to a stage that single particles can be manipulated precisely so that quantum information processing is no longer elusive. In fact, a great number of quantum information protocols have been demonstrated with small scaled systems. The remaining task is to build large scale practical devices. However it turns out that scaling up is highly nontrivial in the quantum world. A protocol valid in principle could face enormous technical challenges when the system size is increased. Therefore new ideas and smart designs that bypass the technical obstacles are extremely useful in this field. In this dissertation we tackle several specific problems in quantum information processing with trapped ions and cold atomics gases. For ions, we first present a scalable implementation scheme for the recently proposed concept of Boson sampling, which holds the promise of outperforming classical computers in the near future. The scheme is based on the technically mature linear Paul trap and the transverse motional phonons of the ions are manipulated with laser to perform sampling. A complete recipe is provided and the technical requirements are discussed. Then we go back to the conventional circuit model for computation and discuss a method to perform individual ion addressing quantum gates with Gaussian beams. We describe the so-called spatial refocusing technique to significantly narrow down the beams with coherent interference. We also extend the original quantum gate formalism to include the effect of micromotion. We demonstrate high fidelity gates in the presence of significant micromotion. This paves the way to the development of a two dimensional ion crystal quantum processor with hundreds of ions inside a single trap. On the other hand, we explore precision measurement with a cold atom interferometer. Combining a spin-spin interaction Hamiltonian and coherent spin rotation pulses, we construct optimized pulse sequences for spin squeezing to approach the Heisenberg limit of noise. Finally we investigate the general problem of state detection with faulty detectors. We develop a statistical procedure to recover the true correlation from noisy data.
Laser-ion interactions that collectively couple the pseudo-spins of a string of trapped ions to one of the string's vibrational modes [1] have been used by us to entangle a pair of40Ca+ions with very high fidelity [2–4]. In addition, we experimentally confirmed that this gate mechanism allows for entangling ions without having recourse to ground state cooling [3]. This opens the way to performing an entangling gate after having applied an operation which does not preserve the ions' motional state like for example state detection.
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