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1. Coherently Coupled Mechanical Oscillators in the Quantum Regime

   https://doi.org/10.21203/rs.3.rs-1774123/v1  

   Hou, P-Y.; Wu, J.J.; Erickson, S.D.; Cole, D.C.; Zarantonello, G.; Brandt, A.D.; Wilson, A.C.; Slichter, D.H.; Leibfried, D. (July 2022, ArXivorg)

   Coupled harmonic oscillators are ubiquitous in physics and play a prominent role in quantum science. They are a cornerstone of quantum mechanics and quantum field theory, where second quantization relies on harmonic oscillator operators to create and annihilate particles. Descriptions of quantum tunneling, beamsplitters, coupled potential wells, "hopping terms", decoherence and many other phenomena rely on coupled harmonic oscillators. Despite their prominence, only a few experimental systems have demonstrated direct coupling between separate harmonic oscillators; these demonstrations lacked the capability for high-fidelity quantum control. Here, we realize coherent exchange of single motional quanta between harmonic oscillators -- in this case, spectrally separated harmonic modes of motion of a trapped ion crystal where the timing, strength, and phase of the coupling are controlled through the application of an oscillating electric field with suitable spatial variation. We demonstrate high-fidelity quantum state transfer, entanglement of motional modes, and Hong-Ou-Mandel-type interference. We also project a harmonic oscillator into its ground state by measurement and preserve that state during repetitions of the projective measurement, an important prerequisite for non-destructive syndrome measurement in continuous-variable quantum error correction. Controllable coupling between harmonic oscillators has potential applications in quantum information processing with continuous variables, quantum simulation, and precision measurements. It can also enable cooling and quantum logic spectroscopy involving motional modes of trapped ions that are not directly accessible. 

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2. Optimal encoding of oscillators into more oscillators

   https://doi.org/10.22331/q-2023-08-16-1082  

   Wu, Jing; Brady, Anthony J.; Zhuang, Quntao (August 2023, Quantum)

   Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also extend the applicability of error correction to continuous-variable states ubiquitous in quantum sensing and communication. In this work, we derive the optimal oscillator-to-oscillator codes among the general family of Gottesman-Kitaev-Preskill (GKP)-stablizer codes for homogeneous noise. We prove that an arbitrary GKP-stabilizer code can be reduced to a generalized GKP two-mode-squeezing (TMS) code. The optimal encoding to minimize the geometric mean error can be constructed from GKP-TMS codes with an optimized GKP lattice and TMS gains. For single-mode data and ancilla, this optimal code design problem can be efficiently solved, and we further provide numerical evidence that a hexagonal GKP lattice is optimal and strictly better than the previously adopted square lattice. For the multimode case, general GKP lattice optimization is challenging. In the two-mode data and ancilla case, we identify the D4 lattice—a 4-dimensional dense-packing lattice—to be superior to a product of lower dimensional lattices. As a by-product, the code reduction allows us to prove a universal no-threshold-theorem for arbitrary oscillators-to-oscillators codes based on Gaussian encoding, even when the ancilla are not GKP states. 

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3. Quantum enhanced metrology in the search for fundamental physical phenomena

   https://doi.org/10.21468/SciPostPhysLectNotes.40  

   Lehnert, Konrad (March 2022, SciPost Physics Lecture Notes)

   These notes summarize lectures given at the 2019 Les Houches summer school on Quantum Information Machines. They describe and review an application of quantum metrology concepts to searches for ultralight dark matter. In particular, for ultralight dark matter that couples as a weak classical force to a laboratory harmonic oscillator, quantum squeezing benefits experiments in which the mass of the dark matter particle is unknown. This benefit is present even if the oscillatory dark matter signal is much more coherent than the harmonic oscillator that it couples to, as is the case for microwave frequency searches for dark matter axion particles. 

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4. Inverse Elastic Scattering for a Random Source

   https://doi.org/10.1137/18M1235119  

   Li, J.; Li, P. (January 2020, SIAM journal on mathematical analysis)

   Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with a linear load. The source is modeled as a microlocally isotropic generalized Gaussian random function whose covariance operator is a classical pseudodifferential operator. The goal is to recover the principal symbol of the covariance operator from the displacement measured in a domain away from the source. For such a distributional source, we show that the direct problem has a unique solution by introducing an equivalent Lippmann--Schwinger integral equation. For the inverse problem, we demonstrate that, with probability one, the principal symbol of the covariance operator can be uniquely determined by the amplitude of the displacement averaged over the frequency band, generated by a single realization of the random source. The analysis employs the Born approximation, asymptotic expansions of the Green tensor, and microlocal analysis of the Fourier integral operators. 

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5. A driven Kerr oscillator with two-fold degeneracies for qubit protection

   https://doi.org/10.1073/pnas.2311241121  

   Venkatraman, Jayameenakshi; Cortiñas, Rodrigo G; Frattini, Nicholas E; Xiao, Xu; Devoret, Michel H (June 2024, Proceedings of the National Academy of Sciences)

   We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive. We find that when the detuning Δ between the frequency of the oscillator and the second subharmonic of the drive equals an even multiple of the Kerr coefficientK, $\mathrm{\Delta }/K=2m$, the oscillator displays $m+1$exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. These degeneracies can be explained by the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime, thus creating a protected cat qubit in the ground state manifold of our oscillator. Our results illustrate the relationship between degeneracies and noise protection in a driven quantum system. 

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