Laser-free method for creation of two-mode squeezed state and beam-splitter transformation with trapped ions

• URL: http://arxiv.org/abs/2303.05831v1
• Date: Fri, 10 Mar 2023 10:11:35 GMT
• Title: Laser-free method for creation of two-mode squeezed state and beam-splitter transformation with trapped ions
• Authors: Bogomila S. Nikolova and Peter A. Ivanov
• Abstract summary: We propose a laser-free method for creation of a phonon two-mode squeezed state and a beam-splitter transformation. We show that a Heisenberg limit of precision can be achieved when the initial state with $n$ phonons evolves under the action of the beam-splitter transformation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a laser-free method for creation of a phonon two-mode squeezed state and a beam-splitter transformation, using time-varying electric fields and non-linear couplings between the normal modes in a linear ion crystal. Such non-linear Coulomb-mediated interactions between the collective vibrational modes arise under specific trap-frequency conditions in an ion trap. We study the quantum metrological capability for parameter estimation of the two quantum states and show that a Heisenberg limit of precision can be achieved when the initial state with $n$ phonons evolves under the action of the beam-splitter transformation. Furthermore, we show that the phonon non-linearity and the spin-dependent force can be used for creation of a three-qubit Fredkin gate.

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