skip to main content


Title: Coherently Coupled Mechanical Oscillators in the Quantum Regime
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.  more » « less
Award ID(s):
2016244
NSF-PAR ID:
10340299
Author(s) / Creator(s):
; ; ; ; ; ; ; ;
Date Published:
Journal Name:
ArXivorg
ISSN:
2331-8422
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Ultracold molecules have been proposed as a candidate platform for quantum science and precision measurement because of their rich internal structures and interactions. Direct laser-cooling promises to be a rapid and efficient way to bring molecules to ultracold temperatures. However, for trapped molecules, laser-cooling to the quantum motional ground state remains an outstanding challenge. A technique capable of reaching the motional ground state is Raman sideband cooling, first demonstrated in trapped ions and atoms. Here we demonstrate Raman sideband cooling of CaF molecules trapped in an optical tweezer array. Our protocol does not rely on high magnetic fields and preserves the purity of molecular internal states. We measure a high ground-state fraction and achieve low motional entropy per particle. The low temperatures we obtain could enable longer coherence times and higher-fidelity molecular qubit gates, desirable for quantum information processing and quantum simulation. With further improvements, Raman sideband cooling will also provide a route to quantum degeneracy of large molecular samples, which could be extendable to polyatomic molecular species. 
    more » « less
  2. The chief objective of this paper is to explore energy transfer mechanism between the sub-systems that are coupled by a nonlinear elastic path. In the proposed model (via a minimal order, two degree of freedom system), both sub-systems are defined as damped harmonic oscillators with linear springs and dampers. The first sub-system is attached to the ground on one side but connected to the second sub-system on the other side. In addition, linear elastic and dissipative characteristics of both oscillators are assumed to be identical, and a harmonic force excitation is applied only on the mass element of second oscillator. The nonlinear spring (placed in between the two sub-systems) is assumed to exhibit cubic, hardening type nonlinearity. First, the governing equations of the two degree of freedom system with a nonlinear elastic path are obtained. Second, the nonlinear differential equations are solved with a semi-analytical (multi-term harmonic balance) method, and nonlinear frequency responses of the system are calculated for different path coupling cases. As such, the nonlinear path stiffness is gradually increased so that the stiffness ratio of nonlinear element to the linear element is 0.01, 0.05, 0.1, 0.5 and 1.0 while the absolute value of linear spring stiffness is kept intact. In all solutions, it is observed that the frequency response curves at the vicinity of resonant frequencies bend towards higher frequencies as expected due to the hardening effect. However, at moderate or higher levels of path coupling (say 0.1, 0.5 and 1.0), additional branches emerge in the frequency response curves but only at the first resonant frequency. This is due to higher displacement amplitudes at the first resonant frequency as compared to the second one. Even though the oscillators move in-phase around the first natural frequency, high amplitudes increase the contribution of the stored potential energy in the nonlinear spring to the total mechanical energy. The out-of-phase motion around the second natural frequency cannot significantly contribute due to very low motion amplitudes. Finally, the governing equations are numerically solved for the same levels of nonlinearity, and the motion responses of both sub-systems are calculated. Both in-phase and out-of-phase motion responses are successfully shown in numerical solutions, and phase portraits of the system are generated in order to illustrate its nonlinear dynamics. In conclusion, a better understanding of the effect of nonlinear elastic path on two damped harmonic oscillators is gained. 
    more » « less
  3. null (Ed.)
    Dipole–phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO + , and discuss progress towards experimental realization. We also further develop the theory of DPQL to include state preparation and measurement and entanglement of multiple molecular ions. 
    more » « less
  4. BACKGROUND Electromagnetic (EM) waves underpin modern society in profound ways. They are used to carry information, enabling broadcast radio and television, mobile telecommunications, and ubiquitous access to data networks through Wi-Fi and form the backbone of our modern broadband internet through optical fibers. In fundamental physics, EM waves serve as an invaluable tool to probe objects from cosmic to atomic scales. For example, the Laser Interferometer Gravitational-Wave Observatory and atomic clocks, which are some of the most precise human-made instruments in the world, rely on EM waves to reach unprecedented accuracies. This has motivated decades of research to develop coherent EM sources over broad spectral ranges with impressive results: Frequencies in the range of tens of gigahertz (radio and microwave regimes) can readily be generated by electronic oscillators. Resonant tunneling diodes enable the generation of millimeter (mm) and terahertz (THz) waves, which span from tens of gigahertz to a few terahertz. At even higher frequencies, up to the petahertz level, which are usually defined as optical frequencies, coherent waves can be generated by solid-state and gas lasers. However, these approaches often suffer from narrow spectral bandwidths, because they usually rely on well-defined energy states of specific materials, which results in a rather limited spectral coverage. To overcome this limitation, nonlinear frequency-mixing strategies have been developed. These approaches shift the complexity from the EM source to nonresonant-based material effects. Particularly in the optical regime, a wealth of materials exist that support effects that are suitable for frequency mixing. Over the past two decades, the idea of manipulating these materials to form guiding structures (waveguides) has provided improvements in efficiency, miniaturization, and production scale and cost and has been widely implemented for diverse applications. ADVANCES Lithium niobate, a crystal that was first grown in 1949, is a particularly attractive photonic material for frequency mixing because of its favorable material properties. Bulk lithium niobate crystals and weakly confining waveguides have been used for decades for accessing different parts of the EM spectrum, from gigahertz to petahertz frequencies. Now, this material is experiencing renewed interest owing to the commercial availability of thin-film lithium niobate (TFLN). This integrated photonic material platform enables tight mode confinement, which results in frequency-mixing efficiency improvements by orders of magnitude while at the same time offering additional degrees of freedom for engineering the optical properties by using approaches such as dispersion engineering. Importantly, the large refractive index contrast of TFLN enables, for the first time, the realization of lithium niobate–based photonic integrated circuits on a wafer scale. OUTLOOK The broad spectral coverage, ultralow power requirements, and flexibilities of lithium niobate photonics in EM wave generation provides a large toolset to explore new device functionalities. Furthermore, the adoption of lithium niobate–integrated photonics in foundries is a promising approach to miniaturize essential bench-top optical systems using wafer scale production. Heterogeneous integration of active materials with lithium niobate has the potential to create integrated photonic circuits with rich functionalities. Applications such as high-speed communications, scalable quantum computing, artificial intelligence and neuromorphic computing, and compact optical clocks for satellites and precision sensing are expected to particularly benefit from these advances and provide a wealth of opportunities for commercial exploration. Also, bulk crystals and weakly confining waveguides in lithium niobate are expected to keep playing a crucial role in the near future because of their advantages in high-power and loss-sensitive quantum optics applications. As such, lithium niobate photonics holds great promise for unlocking the EM spectrum and reshaping information technologies for our society in the future. Lithium niobate spectral coverage. The EM spectral range and processes for generating EM frequencies when using lithium niobate (LN) for frequency mixing. AO, acousto-optic; AOM, acousto-optic modulation; χ (2) , second-order nonlinearity; χ (3) , third-order nonlinearity; EO, electro-optic; EOM, electro-optic modulation; HHG, high-harmonic generation; IR, infrared; OFC, optical frequency comb; OPO, optical paramedic oscillator; OR, optical rectification; SCG, supercontinuum generation; SHG, second-harmonic generation; UV, ultraviolet. 
    more » « less
  5. 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.

     
    more » « less