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arXiv:0809.4287 · New Journal of Physics

Manipulating the quantum information of the radial modes of trapped ions: linear phononics, entanglement generation, quantum state transmission and non-locality tests

Alessio Serafini, Alex Retzker, Martin Bodo Plenio

Published Feb 4, 2009• 40 citations
arXivHTMLPDF

Abstract

We present a detailed study on the possibility of manipulating quantum information encoded in the 'radial' modes of arrays of trapped ions (i.e. in the ions' oscillations orthogonal to the trap's main axis). In such systems, because of the tightness of transverse confinement, the radial modes pertaining to different ions can be addressed individually. In the first part of the paper we show that, if local control of the radial trapping frequencies is available, any linear optical and squeezing operation on the locally defined modes—on single as well as on many modes—can be reproduced by manipulating the frequencies. Then, we proceed to describe schemes apt to generate unprecedented degrees of bipartite and multipartite continuous variable (CV) entanglement under realistic noisy working conditions and even restricting only to a global control of the trapping frequencies. Furthermore, we consider the transmission of the quantum information encoded in the radial modes along the array of ions, and show it to be possible to a remarkable degree of accuracy, for both finite-dimensional and CV quantum states. Finally, as an application, we show that the states which can be generated in this setting allow for the violation of multipartite non-locality tests, by feasible displaced parity measurements. Such a demonstration would be a first test of quantum non-locality for 'massive' degrees of freedom (i.e. for degrees of freedom describing the motion of massive particles).

DOI
10.1088/1367-2630/11/2/023007

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We present a detailed study on the possibility of manipulating quantum information encoded in the 'radial' modes of arrays of trapped ions (i.e. in the ions' oscillations orthogonal to the trap's main axis). In such systems, because of the tightness of transverse confinement, the radial modes pertaining to different ions can be addressed individually. In the first part of the paper we show that, if local control of the radial trapping frequencies is available, any linear optical and squeezing operation on the locally defined modes—on single as well as on many modes—can be reproduced by manipulating the frequencies. Then, we proceed to describe schemes apt to generate unprecedented degrees of bipartite and multipartite continuous variable (CV) entanglement under realistic noisy working conditions and even restricting only to a global control of the trapping frequencies. Furthermore, we consider the transmission of the quantum information encoded in the radial modes along the array of ions, and show it to be possible to a remarkable degree of accuracy, for both finite-dimensional and CV quantum states. Finally, as an application, we show that the states which can be generated in this setting allow for the violation of multipartite non-locality tests, by feasible displaced parity measurements. Such a demonstration would be a first test of quantum non-locality for 'massive' degrees of freedom (i.e. for degrees of freedom describing the motion of massive particles).
We propose an experimental architecture where an array of optical tweezers affords site-dependent control over the confining potential of a conventional radio-frequency ion trap. The site-dependent control enables programmable manipulation of phonon modes of ions, with many potential applications in quantum information processing (QIP) and thermodynamics. We describe protocols for programming the array of optical tweezers to attain a set of target phonon modes with high accuracy. We propose applications of such controls in simulating quantum thermodynamics of a particle of programmable effective mass via Jarzynski's equality and improving the efficiency of sympathetic cooling and quantum logic gates in a multispecies ion system of disparate masses. We discuss the required optical parameters in a realistic ion trap system and potential adverse effects of optical tweezers in QIP. Our scheme extends the utility of trapped ions as a platform for quantum computation and simulation.
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techniques, and quantum operations that allow various quantum simulations and quantum computation algorithms. We describe experiments using the vibrational modes, including the preparation of non-classical states, molecular vibronic sampling, and applications in quantum thermodynamics. We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.
Continuous-variable quantum computing utilizes continuous parameters of a quantum system to encode information, promising efficient solutions to complex problems. Trapped-ion systems provide a robust platform with long coherence times and precise qubit control, enabling the manipulation of quantum information through its motional and electronic degrees of freedom. In this work, quantum operations that can be generated in trapped-ion systems are employed to investigate applications aimed at state preparation in continuous-variable quantum systems.
The scaling of controlled quantum systems to large numbers of degrees of freedom is one of the long term goals of experimental quantum information science. Trapped-ion systems are one of the most promising platforms for building a quantum information processor with enough complexity to enable novel computational power, but face serious challenges in scaling up to the necessary numbers of qubits. In this thesis, I present both technical and operational advancements in the control of trapped-ion systems and their juxtaposition with photonic modes used for quantum networking. After reviewing the basic physics behind ion trapping, I then describe in detail a new method of implementing Raman transitions in atomic systems using optical frequency combs. Several dierent experimental setups along with simple theoretical models are reviewed and the system is shown to be capable of full control of the qubit-oscillator system. Two-ion entangling operations using optical frequency combs are demonstrated along with an extension of the operation designed to suppress certain experimental errors. I then give an overview of how spatially separated ions can be entangled using a photonic interconnect. Experimental results show that pulsed excitation of trapped ions provide an excellent single photon source that can be used as a heralded entangling gate between macroscopically separated systems. This heralded entangling gate is used to show a violation of a Bell inequality while keeping the detection loophole closed and can be used a source private random numbers. Finally, the coherent Coulomb force-based gates are combined with the probabilistic photon-based gates in a proof of concept experiment that shows the feasibility of a distributed ion-photon network.
We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximally Greenberger–Horne–Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglement of multiple coherent and squeezing states with desired amplitudes in a reasonable time.