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arXiv:2405.19536 · Physical Review Research

Generating Einstein-Podolsky-Rosen correlations for teleporting collective spin states in a two-dimensional trapped ion crystal

M. Miskeen Khan, Edwin Chaparro, Bhuvanesh Sundar, Allison L. Carter, J. J. Bollinger, Klaus Mølmer, Ana María Rey

Published Apr 17, 2025• 5 citations
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Abstract

We propose the use of phonon-mediated interactions as an entanglement resource to engineer Einstein-Podolsky-Rosen correlations and to perform teleportation of collective spin states in two-dimensional ion crystals. We emulate continuous variable quantum teleportation protocols between subsystems corresponding to different nuclear spin degrees of freedom. In each of them, a quantum state is encoded in an electronic spin degree of freedom that couples to the vibrational modes of the crystal. We show that high fidelity teleportation of spin-coherent states and their phase-displaced variant, entangled spin-squeezed states, and Dicke states, is possible for realistic experimental conditions in arrays from a few tens to a few hundred ions.

DOI
10.1103/physrevresearch.7.l022019

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We propose the use of phonon-mediated interactions as an entanglement resource to engineer Einstein-Podolsky-Rosen correlations and to perform teleportation of collective spin states in two-dimensional ion crystals. We emulate continuous variable quantum teleportation protocols between subsystems corresponding to different nuclear spin degrees of freedom. In each of them, a quantum state is encoded in an electronic spin degree of freedom that couples to the vibrational modes of the crystal. We show that high fidelity teleportation of spin-coherent states and their phase-displaced variant, entangled spin-squeezed states, and Dicke states, is possible for realistic experimental conditions in arrays from a few tens to a few hundred ions.
We report recent developments in our experiment to teleport light beams by utilizing Einstein-Podolsky-Rosen (EPR) entanglement for continuous quantum variables. We describe details of our experimental apparatus, including the generation of EPR entanglement from squeezed states of light. In addition, we have developed an explicit model for the teleportation of coherent states that includes the effect of diverse loss factors and limited degrees of entanglement, and that enables us to project the possibilities for achieving yet higher fidelities beyond the currently achieved value of 62% with our apparatus. Propects for other teleportation schemes will also be discussed.
Quantum many-body systems driven far from equilibrium can exhibit phase transitions, chaos and entanglement, but probing these phenomena in large, nearly closed systems remains challenging. The Dicke model, which couples an ensemble of two-level systems collectively to a single bosonic mode, provides a fundamental framework for exploring these phenomena in light-matter interactions. Here we show that a two-dimensional crystal of approximately 100 trapped ions realizes this model and accesses integrable dynamical phase transitions, signatures of chaotic dynamics and fluctuation-driven spin-phonon excitation growth. Adiabatic elimination of the vibrational mode reveals ferromagnetic and paramagnetic dynamical spin phases, whereas strong spin-phonon coupling produces irregular trajectories and local relaxation consistent with quantum thermalization. Following a quench from an unstable fixed point, correlated excitation growth precedes generalized vacuum Rabi collapses and revivals; calibrated calculations identify two-mode squeezing 2.6 dB below the standard quantum limit, supported by reconstruction from spin measurements. By connecting collective dynamical instabilities to experimentally accessible signatures of quantum correlations, these results establish large ion crystals as a scalable platform for investigating non-equilibrium light-matter dynamics and generating resources for quantum-enhanced sensing.
We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of subensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and demonstrate their viability even for small systems, while assessing limitations imposed by spin-motion entanglement and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.
We present a protocol for deterministically generating an optimal two-mode-squeezed state of distant free-space atomic ensembles. The protocol relies on two passes of a single coherent pulse through two separate atomic ensembles placed in homogeneous magnetic fields. In contrast to previous single-pass schemes, our approach significantly enhances the degree of entanglement due to the exponential behavior of the Einstein-Podolsky-Rosen variance. We also provide an efficient scheme to perform Bell measurement of atomic states, enabling the implementation of high-fidelity atomic quantum teleportation.
We demonstrate that collective continuous variables of two species of trapped ultracold bosonic gases can be Einstein-Podolsky-Rosen-correlated (entangled) via inherent interactions between the species. We propose two different schemes for creating these correlations--a dynamical scheme and a static scheme analogous to two-mode squeezing in quantum optics. We quantify the correlations by using known measures of entanglement and study the effect of finite temperature on these quantum correlations.
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter rrr and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter rrr.