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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Quantum non-Gaussianity of multi-phonon states of a single atom

Lukáš Podhora, Lukáš Lachman, Tuan Pham Minh, Adam Lešundák, Ondřej Čı́p, L. Slodička, Radim Filip

Published Jun 21, 2021• 0 citations
Publisher

Abstract

Quantum non-Gaussian (QNG) mechanical states from inherently nonlinear quantum processes are already required in quantum sensing, become essential in quantum thermodynamics, and also open directions in quantum computing with continuous variables. The discrete building blocks of such states are the energy eigenstates - Fock states. Despite the progress in their experimental preparation, the remaining energy uncertainty can still invisibly cause loss of the critical quantum non-Gaussian aspects of the phonon distribution relevant for the applications.

DOI
10.1109/cleo/europe-eqec52157.2021.9542529

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Quantum non-Gaussian (QNG) mechanical states from inherently nonlinear quantum processes are already required in quantum sensing, become essential in quantum thermodynamics, and also open directions in quantum computing with continuous variables. The discrete building blocks of such states are the energy eigenstates - Fock states. Despite the progress in their experimental preparation, the remaining energy uncertainty can still invisibly cause loss of the critical quantum non-Gaussian aspects of the phonon distribution relevant for the applications.
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Quantum non-Gaussian mechanical states are already required in a range of applications. The discrete building blocks of such states are the energy eigenstates-Fock states. Despite progress in their preparation, the remaining imperfections can still invisibly cause loss of the aspects critical for their applications. We derive and apply the most challenging hierarchy of quantum non-Gaussian criteria on the characterization of single trapped-ion oscillator mechanical Fock states with up to 10 phonons. We analyze the depth of these quantum non-Gaussian features under intrinsic mechanical heating and predict their requirement for reaching quantum advantage in the sensing of a mechanical force.
Quantum coherence between energy eigenstates of harmonic oscillators is essential for quantum physics. Even the most elementary binary superpositions of the ground and the higher eigenstate are highly required for quantum sensing, thermodynamics, and computing. We derive upper bounds for quantum coherences achieved by classical and Gaussian states and operations and, subsequently, obtain a hierarchy of the thresholds for the off-diagonal elements necessary to reach genuine quantum non-Gaussian coherences. The presented analysis demonstrates that certification based solely on estimation of coherences can cover the quantum non-Gaussian states, which are undetectable by the criteria based solely on the estimation of the corresponding state populations. We experimentally demonstrate the unambiguous observation of quantum non-Gaussian coherences in mechanical vibrations of a single calcium ion up to the superposition of zero and six phonons. The analysis of the robustness with respect to pure dephasing in a motional Ramsey experiment demonstrates the feasibility of their storage for up to more than 20 ms for superpositions with a large energy difference of participating number states. The presented observations prove that atomic oscillations go deeply into a diverse area of discrete quantum non-Gaussian coherent phenomena critical for their applications.
Quantum non-Gaussianity (QNG) corresponds to an essential resource in many prospective applications of quantum technologies. QNG states of light have been demonstrated in a broad range of experimental platforms with various complementary advantages [1]. However, in order to allow for their direct and efficient utilization for interaction with the target quantum system, their degrees of freedom have to be well-defined and controllable. This imposes a requirement on the generation of QNG light in a single optical mode. While the intrinsic single-photon sources including trapped ions, atoms, or molecules, naturally offer a close-to a single mode emission, their technologically more accessible counterparts including majority of the solid-state emitters and sources based on heralded generation of nonclassical states in various parametric nonlinear processes typically provide a multi-mode output. Although several demonstrations of a single-mode operation of nonclassical light sources based on these platforms have been recently demonstrated, an unambiguous observation of a single-mode QNG light has never been presented.
Optomechanics with levitated nanoparticles is a promising way to combine very different types of quantum non-Gaussian aspects induced by continuous dynamics in a nonlinear or time-varying potential with the ones coming from discrete quantum elements in dynamics or measurement. First, it is necessary to prepare quantum non-Gaussian states using both methods. The nonlinear and time-varying potentials have been widely analyzed for this purpose. However, feasible preparation of provably quantum non-Gaussian states in a single mechanical mode using discrete photon detection has not been proposed yet for optical levitation. We explore pulsed optomechanical interactions combined with non-linear photon detection techniques to approach mechanical Fock states and confirm their quantum non-Gaussianity. We also predict the conditions under which the optomechanical interaction can induce multiple-phonon addition processes, which are relevant for nnn-phonon quantum non-Gaussianity. The practical applicability of quantum non-Gaussian states for sensing phase-randomized displacements is shown. Besides such applications, generating quantum non-Gaussian states of levitated nanoparticles can help to study fundamental questions of quantum thermodynamics, and macroscopic quantum effects.
Abstract Quantum non-Gaussian states of phononic systems coupled to light are essential for fundamental studies of single-phonon mechanics and direct applications in quantum technology. Although nonclassical mechanical states have already been demonstrated, the more challenging quantum non-Gaussianity of such states remains limited. Using photon counting detection, we propose the quantum non-Gaussian generation of few-phonon states of low-temperature vibrating superfluid Helium. We predict the quantum non-Gaussian depth of such phononic states and investigate their robustness under relevant mechanical heating. As the quality of such phononic states is very high, we confirm a single-phonon bunching capability to further classify such states for future mechanical experiments. Moreover, we predict increasing capability for force sensing and thermometry for increasing heralded phonon numbers.