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      Quantum squeezing of motion in a mechanical resonator

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          Abstract

          As a result of the quantum, wave-like nature of the physical world, a harmonic oscillator can never be completely at rest. Even in the quantum ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. In this work, using microwave frequency radiation pressure, we both prepare a micron-scale mechanical system in a state near the quantum ground state and then manipulate its thermal fluctuations to produce a stationary, quadrature-squeezed state. We deduce that the variance of one motional quadrature is 0.80 times the zero-point level, or 1 dB of sub-zero-point squeezing. This work is relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultra-sensitive sensing of force and motion.

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          Sideband Cooling Micromechanical Motion to the Quantum Ground State

          The advent of laser cooling techniques revolutionized the study of many atomic-scale systems. This has fueled progress towards quantum computers by preparing trapped ions in their motional ground state, and generating new states of matter by achieving Bose-Einstein condensation of atomic vapors. Analogous cooling techniques provide a general and flexible method for preparing macroscopic objects in their motional ground state, bringing the powerful technology of micromechanics into the quantum regime. Cavity opto- or electro-mechanical systems achieve sideband cooling through the strong interaction between light and motion. However, entering the quantum regime, less than a single quantum of motion, has been elusive because sideband cooling has not sufficiently overwhelmed the coupling of mechanical systems to their hot environments. Here, we demonstrate sideband cooling of the motion of a micromechanical oscillator to the quantum ground state. Entering the quantum regime requires a large electromechanical interaction, which is achieved by embedding a micromechanical membrane into a superconducting microwave resonant circuit. In order to verify the cooling of the membrane motion into the quantum regime, we perform a near quantum-limited measurement of the microwave field, resolving this motion a factor of 5.1 from the Heisenberg limit. Furthermore, our device exhibits strong-coupling allowing coherent exchange of microwave photons and mechanical phonons. Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion, possibly even testing quantum theory itself in the unexplored region of larger size and mass.
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            emcee: The MCMC Hammer

            We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to \(\sim N^2\) for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.
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              Generation of Nonclassical Motional States of a Trapped Atom

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                Author and article information

                Journal
                10.1126/science.aac5138
                1507.01662

                Quantum physics & Field theory,Nanophysics
                Quantum physics & Field theory, Nanophysics

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