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arXiv:0708.3216 · Physical Review A

Robust creation of arbitrary-sized Dicke states of trapped ions by global addressing

I. E. Linington, Nikolay V. Vitanov

Published Jan 28, 2008• 41 citations
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Abstract

We propose a technique for the creation of maximally entangled symmetric Dicke states in an ion trap using adiabatic passage, which requires only a pair of chirped pulses from a single laser and is applicable to any number of ions and excitations. By utilizing a particular factorization of the Hilbert space for multilevel ladders we show that the problem can be reduced to ``bow-tie''-configuration energy-level crossings. This technique is naturally robust against fluctuations in the laser intensity and the chirp rate. Even when realistic heating rates are considered, we estimate that the overall fidelity should remain high (e.g., 98% for a ten-ion Dicke state), which represents a significant improvement over traditional approaches.

DOI
10.1103/physreva.77.010302

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We propose a technique for the creation of maximally entangled symmetric Dicke states in an ion trap using adiabatic passage, which requires only a pair of chirped pulses from a single laser and is applicable to any number of ions and excitations. By utilizing a particular factorization of the Hilbert space for multilevel ladders we show that the problem can be reduced to ``bow-tie''-configuration energy-level crossings. This technique is naturally robust against fluctuations in the laser intensity and the chirp rate. Even when realistic heating rates are considered, we estimate that the overall fidelity should remain high (e.g., 98% for a ten-ion Dicke state), which represents a significant improvement over traditional approaches.
We propose a simple technique for the generation of arbitrary-sized Dicke states in a chain of trapped ions. The method uses global addressing of the entire chain by two pairs of delayed but partially overlapping laser pulses to engineer a collective adiabatic passage along a multi-ion dark state. Our technique, which is a many-particle generalization of the stimulated Raman adiabatic passage technique, is decoherence free with respect to spontaneous emission and robust against moderate fluctuations in the experimental parameters. Furthermore, because the process is very rapid, the effects of heating are almost negligible under realistic experimental conditions. We predict that the overall fidelity of synthesis of a Dicke state involving ten ions sharing two excitations should approach 98% with currently achievable experimental parameters.
A simple technique for robust generation of vibrational Fock states in a chain of trapped ions is proposed. The method is fast and easy to implement, since only a single chirped laser pulse, simultaneously addressing all of the ions, is required. Furthermore, because the approach uses collective adiabatic passage, significant fluctuations in the intensity or frequency of the laser pulse can be tolerated, and the technique performs well even on the border of the Lamb-Dicke regime. We also demonstrate how this technique may be extended in order to create nonclassical superposition states of the ions' collective motion and Greenberger-Horne-Zeilinger states of their internal states. Because only a single laser pulse is required, heating effects arising under realistic experimental conditions are negligibly small.
We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique is fairly robust to parameter fluctuations and operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions; thus the implementation complexity grows only linearly with the size of the system. The approach does not require individual addressing of the ions in the trap and can be applied both inside and outside the Lamb–Dicke regime.
We propose a technique for robust and efficient navigation in the Hilbert space of entangled symmetric states of a multiparticle system with externally controllable linear and nonlinear collective interactions. A linearly changing external field applied along the quantization axis creates a network of well separated level crossings in the energy diagram of the collective states.One or more transverse pulsed fields applied at the times of specific level crossings induce adiabatic passage between these states. By choosing the timing of the pulsed field appropriately, one can transfer an initial product state of all N spins into (i) any symmetric state with n spin excitations and (ii) the N-particle analog of the Greenberger-Horne-Zeilinger state. This technique, unlike techniques using pulses of specific area, does not require precise knowledge of the number of particles and is robust against variations in the interaction parameters. We discuss potential applications in two-component Bose condensates and ion-trap systems.
Entangled states of two ions are realized by using an adiabatic process. Based on the proposal by Linington and Vitanov [Phys. Rev. A 77, 010302 (2008)], we have generated Dicke states in optical qubits of two 40Ca^{40}\mathrm{Ca}40Ca+{}^{+}+ ions by applying frequency-chirped optical pulses with time-dependent envelopes to perform rapid adiabatic passage on sideband transitions. One of the biggest advantages of adiabatic approaches is their robustness against variations in experimental parameters, which is verified by performing experiments for different pulse widths or peak Rabi frequencies. Fidelities exceeding 0.5, which is the threshold for inseparable states, are obtained over wide ranges of parameter values.
We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using adiabatic techniques. The inversion-about-average and oracle operators take the form of single off-resonant laser pulses. This is made possible by utilizing the physical symmetries of the trapped-ion linear crystal. The physical realization of the algorithm represents a dramatic simplification: each logical iteration (oracle and inversion about average) requires only two physical interaction steps, in contrast to the large number of concatenated gates required by previous approaches. This not only facilitates the implementation but also increases the overall fidelity of the algorithm.