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arXiv:1108.3803

Material Science for Quantum Computing with Atom Chips

R. Folman

Published Aug 18, 2011• 0 citations
arXivHTMLPDF

Abstract

In its most general form, the atom chip is a device in which neutral or charged particles are positioned in an isolating environment such as vacuum (or even a carbon solid state lattice) near the chip surface. The chip may then be used to interact in a highly controlled manner with the quantum state. I outline the importance of material science to quantum computing (QC) with atom chips, where the latter may be utilized for many, if not all, suggested implementations of QC. Material science is important both for enhancing the control coupling to the quantum system for preparation and manipulation as well as measurement, and for suppressing the uncontrolled coupling giving rise to low fidelity through static and dynamic effects such as potential corrugations and noise. As a case study, atom chips for neutral ground state atoms are analyzed and it is shown that nanofabricated wires will allow for more than $10^4$ gate operations when considering spin-flips and decoherence. The effects of fabrication imperfections and the Casimir-Polder force are also analyzed. In addition, alternative approaches to current-carrying wires are briefly described. Finally, an outlook of what materials and geometries may be required is presented, as well as an outline of directions for further study.

DOI
10.48550/arxiv.1108.3803

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In its most general form, the atom chip is a device in which neutral or charged particles are positioned in an isolating environment such as vacuum (or even a carbon solid state lattice) near the chip surface. The chip may then be used to interact in a highly controlled manner with the quantum state. I outline the importance of material science to quantum computing (QC) with atom chips, where the latter may be utilized for many, if not all, suggested implementations of QC. Material science is important both for enhancing the control coupling to the quantum system for preparation and manipulation as well as measurement, and for suppressing the uncontrolled coupling giving rise to low fidelity through static and dynamic effects such as potential corrugations and noise. As a case study, atom chips for neutral ground state atoms are analyzed and it is shown that nanofabricated wires will allow for more than 10410^4104 gate operations when considering spin-flips and decoherence. The effects of fabrication imperfections and the Casimir-Polder force are also analyzed. In addition, alternative approaches to current-carrying wires are briefly described. Finally, an outlook of what materials and geometries may be required is presented, as well as an outline of directions for further study.
The laser cooling, trapping and manipulating of neutral atoms has become a valuable tool for scientists, providing innovative ways to probe the nature of reality and giving rise to transformative devices in the fields of precise measurement and quantum information processing. Unlike traditional complex and bulky atomic experimental facilities, atom chips, through the design, fabrication of surface-patterned microstructures, and the integration of devices on the substrates, can precisely control the magnetic, electric or optical fields on a micro-nano scale with low power consumption. It can realize strong trapping as well as coherent atomic manipulation. Since atom chip was first proposed twenty years ago, it has built a robust quantum platform for miniaturizing and integrating quantum optics and atomic physics tools on a chip. In this paper, first, we briefly review the development history of atom chips, then introduce the basic knowledge of micro potential traps and micro guides based on on-chip current-carrying wires. Afterwards, the key technologies about the chip material, design, fabrication, characterization and integration of atom chips are discussed in detail. We not only focus on the currently most active and successful areas - current carrying wires, but also look at more visionary approaches such as to the manipulation of atoms with real nano structures, say, carbon nano tubes. The design and fabrication principles of ideal atom chips are discussed as well. In the forth part, the worldwide plans and research projects involving with atom chip technologies are summarized, showing that many countries see this as an important foundational technology. Following that, the major developments in the application fields including atom clocks, atom interferometer gyroscope, cold atom gravimeter, etc are described. Finally, the challenges faced by atom chips towards practical application are pointed out and the prospects for their subsequent development are depicted.
Summary form only given. We report on the experimental realisation of traps and guides for neutral atoms on a nanofabricated chip. Our main results are: (a) Trap parameters with a transverse ground state size below 100 nm and frequencies of above 100 kHz (as required by QIP proposals) have been achieved. (b) We could trap and guide atoms exclusively with the fields created on the chip. (c) We have shown that a wide variety of magnetic potentials may be realised, such as quadrupole fields for a MOT, 3D minima for trapping, 2D minima for guiding, and beam splitters. (d) It has been shown that standard nanofabrication techniques and materials may he utilised to build these atom chips. The wires on the surface can stand sufficiently high current densities in vacuum and at room temperature.
We report on the experimental realisation of traps and guides for neutral atoms on a nanofabricated chip. Our main results are: (a) Trap parameters with a transverse ground state size below 100 nm and frequencies of above 100 kHz (as required by QIP proposals) have been achieved. (b) We could trap and guide atoms exclusively with the fields created on the chip. (c) We have shown that a wide variety of magnetic potentials may be realised, such as quadrupole fields for a MOT, 3D minima for trapping, 2D minima for guiding, and beam splitters. (d) It has been shown that standard nanofabrication techniques and materials may he utilised to build these atom chips. The wires on the surface can stand sufficiently high current densities in vacuum and at room temperature.
Abstract The limitations for the coherent manipulation of neutral atoms with fabricated solid state devices, so-called ‘atom chips’, are addressed. Specifically, we examine the dominant decoherence mechanism, which is due to the magnetic noise originating from the surface of the atom chip. It is shown that the contribution of fluctuations in the chip wires at the shot noise level is not negligible. We estimate the coherence times and discuss ways to increase them. Our main conclusion is that future advances should allow for coherence times as long as 1 second, a few µm away from the surface. PACS: 03.75.-b Matter waves – 32.80.Lg Mechanical effects of light on atoms and ions – 03.67.Lx Quantum computation – 05.40.-a Fluctuation phenomena and noise In the quest for physical implementations of quantum information processing, “atom chips ” are currently of great interest.
The power of quantum computation derives from algorithmic methods that exploit the availability of quantum superposition and entanglement to perform computations that are intractable with classical devices. The race is on to develop hardware that will unleash the promise of quantum algorithms. A handful of different types of hardware are currently being developed with the greatest efforts directed at superconducting, quantum-dot, trapped-ion, photonic, and neutral-atom approaches [1]. While all approaches have strengths and weaknesses, and are at different stages of development, the challenge of creating a practical design that can be scaled to a million or more qubits has not yet been met with any of the existing platforms. One may wonder if we really need a million qubits for a useful quantum computer. The answer depends on our ambition level. On the one hand it is widely believed that a quantum computer with less than 100 reliable qubits will be able to demonstrate a quantum advantage for a well defined computational problem [2]. Demonstration of a quantum computational advantage will generate great excitement in the halls of academia, but will have little broader import. A problem of great practical interest such as ab initio design of chemicals for increasing the yield of fertilizers for crop production, to name but one example, may also require just a few hundred qubits, provided computational sequences with circuit depth of 1010 or more operations can be reliably performed [3]. However, given the current performance of qubit hardware, which has demonstrated error rates not less than ∼10−3, computations with depth 1010 will only produce random outcomes of negligible value. The solution lies in the construction of error-correction circuitry operating on logical qubits, each composed of many physical qubits, which will enable logical error rates many orders of magnitude smaller than physical error rates. Although error correction is remarkably efficient for classical computing devices—Hamming codes detect and correct errors while only requiring roughly 10% overhead in the number of physical bits—quantum error correction is notoriously expensive. New approaches to error correction are the subject of intensive research with one promising direction being the development of codes that are optimized to suppress the dominant error mechanism in a particular physical platform [4,5]. Nevertheless, with physical error rates of 10−4, a plausible target for current qubit systems, the overhead required to reach logical error rates of 10−10 may be measured in thousands of physical qubits for each logical qubit. Thus a quantum computer able to perform deep calculations on a few hundred logical qubits could require a million physical qubits. A consequence of the cost of quantum error correction is that any viable approach to large-scale quantum computing needs to combine high-fidelity quantum logic operations with a capability for integrating large numbers of physical qubits. From this perspective neutral-atom qubits appear particularly promising [6] as they have already demonstrated control of more qubits than any other platform with recent experiments in 1D [7], 2D [8,9], and 3D [10] geometries showing control of up to 50 atomic qubits. Large qubit arrays can potentially be prepared in 1D, 2D, or 3D geometries. The number of proximal qubits increases with the dimensionality, which is advantageous for implementation of error correction code words, and points towards a preference for 2D or 3D arrays. On the other hand, the added overhead of compensating crosstalk incurred when targeting atoms inside a 3D volume makes parallel operations on multiple qubits challenging. A 2D geometry, as shown schematically in Fig. 1, may be an optimal choice since qubit control and measurement can be performed with lasers propagating normal to the plane of the array so that individual qubit sites can be addressed independently. With demonstrated array periods of a few micrometers we require a footprint of less than 1 mm2 for 104 qubits. Conceptual picture of a 2D neutral-atom qubit array. a) High-numerical-aperture lenses project several different wavelengths of light for control and measurement of the qubits. Specific choices of optical wavelengths depend on the atomic species. Not shown are optics for initial laser cooling, transport to the array, beam scanning, and imaging for qubit measurement. b) Averaged fluorescence image of 49 atomic qubits on a 2D grid with |3.8 μm3.8 \, {\mu} \rm {m}3.8μm| spacing [8]. From a fundamental perspective the prospects for scaling neutral-atom systems are particularly promising due to the exceptionally large ratio between coherent and incoherent coupling rates. Neutral-atom qubits are encoded in hyperfine ground states for which coherence times of the order of 10 s have been demonstrated [10]. This implies a dephasing rate |γ∼0.1 s−1\gamma \sim 0.1 \, \rm s^{-1}γ∼0.1s−1|⁠. The coherent coupling that enables quantum logic operations is switched on by exciting atoms to high-lying Rydberg states with principal quantum number close to 100 [11,12]. Rydberg excited atoms at spacings of a few micrometers in an optical lattice interact coherently with rates |g>109 s−1g > 10^9\, \rm s^{-1}g>109s−1|⁠. The ratio between desired coherent coupling and residual incoherent dephasing of g/γ ∼ 1010 establishes a figure of merit that is enabling for scalability. To our knowledge only trapped ions can claim a similar g/γ ratio [13], but without a correspondingly direct path towards controlling thousands of qubits in a single processing unit. Although the g/γ ratio is exceptionally favorable for neutral-atom qubits a complete set of universal gate operations has not yet been demonstrated with high fidelity. Single-qubit gates in large 2D and 3D arrays have reached fidelity |F∼0.999{\mathcal {F}}\sim 0.999F∼0.999| [8,10]. However, the highest demonstrated fidelity for two-qubit entanglement mediated by Rydberg-state interactions is |F<0.8{\mathcal {F}}< 0.8F<0.8| [6,14,15], a value that is well short of the theoretical limit of |F>0.9999{\mathcal {F}}> 0.9999F>0.9999| [16,17]. There is healthy optimism within the research community working with neutral-atom qubits that combining improved laser sources with reduced noise, better cooling to reduce motional dephasing, and control of stray electric fields that perturb Rydberg atoms will lead to substantially improved gate fidelity in the near future. Recent results with better filtering of laser phase noise have already demonstrated remarkable improvement in ground–Rydberg entanglement [18]. The outlook for the next few years appears very promising. We anticipate that with advances in lasers, optical lattices for atom trapping, deterministic rearrangement and loading of atoms in multi-dimensional arrays [19,20], and optics for fast beam scanning it will be possible to increase the number of physical qubits in a single neutral-atom module to at least 104. A challenging yet plausible path to a million-qubit processor can then be contemplated by connecting 100 such modules with atom–photon entanglement channels [21]. Beyond the potential for advancing the state of the art in computation, development of techniques for single-atom control inside large multi-atom arrays will enable other applications of quantum science including metrology and time-keeping. Rydberg interactions that are at the heart of a neutral-atom quantum computer may lead to multi-atom entanglement and Heisenberg scaling of atomic-clock precision [22]. This work was supported by the NSF and ARL CDQI.