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Quantum walks on a circle with optomechanical systems

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Abstract

We propose an implementation of a quantum walk on a circle in an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is obtained by applying Suzuki–Trotter decomposition. We numerically show that the system displays typical behaviors of quantum walks, namely the probability distribution evolves ballistically and the standard deviation of the phase distribution is linearly proportional to the number of steps. We also analyze the effects of decoherence by using the phase-damping channel on the coin space, showing the possibility to implement the quantum walk with present-day technology.

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Notes

  1. Usually in Hamiltonian (1) a linearization procedure is performed by assuming an undepleted cavity field, where the field operator is given by \(a\approx \alpha +\Delta a\), being \(\alpha \) a coherent amplitude and \(\Delta a\) a quantum fluctuation. Had we considered this linearization we would have ended up with the interaction term \(-\hbar g_0 (\alpha \Delta a^{\dagger }+\alpha ^* \Delta a) (b^{\dagger } + b)\), which turns out to lead to a quantum walk on a line given the displacement operator for the field \((\Delta a^{\dagger }+ \Delta a)\) for \(\alpha \) real. In this paper, we do not consider this procedure.

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Acknowledgments

JKM acknowledges financial supports from CNPq, Grants PCI-DB 302866/2014-0 and PDJ 165941/2014-6. RP acknowledges financial support from CNPq and FAPERJ. MCO acknowledges support by FAPESP and CNPq through the National Institute for Science and Technology of Quantum Information (INCT-IQ) and the Research Center in Optics and Photonics (CePOF).

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Author notes

  1. Jalil Khatibi Moqadam

    Present address: Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Campinas, SP, Brazil

Authors and Affiliations

  1. Laboratório Nacional de Computação Científica (LNCC), Petrópolis, RJ, Brazil

    Jalil Khatibi Moqadam & Renato Portugal

  2. Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Campinas, SP, Brazil

    Marcos Cesar de Oliveira

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  1. Jalil Khatibi Moqadam
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Correspondence to Renato Portugal.

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Moqadam, J.K., Portugal, R. & de Oliveira, M.C. Quantum walks on a circle with optomechanical systems. Quantum Inf Process 14, 3595–3611 (2015). https://doi.org/10.1007/s11128-015-1079-9

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