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Quantum to Classical Crossover in Mechanical Systems
"Entanglement and intra-molecular cooling in biological systems"
"Mechanical resonators in the quantum regime"
I will describe recent experiments at UC Santa Barbara, representing about ten years' development of nanomechanical and quantum circuit technology, which culminated in our designing and then creating a mechanical resonator that could "easily" be operated in its quantum ground state, and further prepared in quantum (non-classical) states of mechanical vibration. Key requirements included a mechanical design that supported a microwave-frequency mechanical resonance; using a piezoelectric material in order to achieve very strong electromechanical coupling between the mechanical motion and the "electronic atom" we used to measure the resonator motion; and employing a Josephson junction, implemented as a phase quantum bit (aka an "electronic atom"), to measure and interact with the mechanical resonator. Operated at 25 mK on the mixing chamber of a dilution refrigerator, this integrated electromechanical system can be cooled to its quantum ground state without additional intervention. Then, employing the extraordinary nonlinearity provided by the Josephson qubit, and the coherent interactions of this qubit and the mechanical resonator, we were able to prepare and measure a single phonon (quantum of mechanical vibration) in the resonator.
Reference: "Quantum ground state and single-phonon control of a mechanical resonator", A.D. O'Connell et al., Nature 464, 697-703 (2010)
Andrew Cleland, Department of Physics, University of California, Santa Barbara CA 93106 USA
“Geometric phase kickback in a mesoscopic qubit-oscillator system”
I will discuss a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. I will show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. This study can be further extended to finite-temperature dissipative Markovian dynamics. I will finally discuss potential implementations in micro and nano-mechanical devices coupled to an effective two-level system. Rosario Fazio, Scuola Normale Superiore, Pisa. This work has been done in collaboration with M. S. Kim, G. M. Palma, M. Paternostro, G. Vacanti, and V. Vedral and supported by EU projects: GEOMDISS and QNEMS.
 G. Vacanti, R. Fazio, M. S. Kim, G. M. Palma, M. Paternostro, V. Vedral, arXiv:1108.0701
“Approaching the quantum regime with membrane-in-the-middle optomechanical devices”
“Cavity optomechanics with micromirrors”
The development of very high finesse optical cavities together with low-mass micro-mechanical resonators opens the way to the study of optomechanical systems in which the dynamical properties are governed by the radiation pressure exerted by light on mirrors. Different consequences of radiation pressure have already been observed and we present recent results concerning the optomechanical correlations between the radiation pressure and mirror motion, the laser cooling of micromirrors, and the development of very high-Q quartz micropillars and photonic crystal nanomembranes.
"Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode"
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is Œquantum coherent¹, i.e., if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate, quantum states are transferred from the optical field to the mechanical oscillator and vice versa, thus allowing control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at milli-Kelvin temperatures. Optical experiments have not attained this regime due to the large mechanical decoherence rates. Here we demonstrate for the first time quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of n=1.7 motional quanta, implying a ground state occupation of ca. 40%. Pulsed optical excitation reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibers. The results provide a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Jörg P. Kotthaus
“Improving Coherence of and Transduction to Nanomechanical Resonators”
Recent progress in the understanding of mechanisms that are responsible for the surprisingly highmechanical quality factors observed in prestressed string resonators will be discussed [1,2]. Thisopens a rational route towards improving the coherence of nanomechanical resonators and hints atthe dominating underlying microscopic mechanisms that limit coherence. Improving transduction tonanomechanical resonators is another essential prerequisite to achieve optimized coherent controlof resonators. Several recently developed schemes towards this goal, mainly employing local onchiptransduction, will be discussed [3-7]. These efforts aim at coherent control of NEMS both in theclassical [5-8] and quantum regime.
 S. S. Verbridge, H. G. Craighead, and J.M. Parpia, Appl. Phys. Lett. 92, 013112 (2008).
 Q. P. Unterreithmeier, T. Faust, and J. P. Kotthaus, Phys. Rev. Lett. 105, 027205 (2010).
 Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, Nature 458, 1001 (2009).
 Q. P. Unterreithmeier, S. Manus, and J. P. Kotthaus, Appl. Phys. Lett. 94, 263104 (2009).
 Q. P. Unterreithmeier, T. Faust, S. Manus, and J. P. Kotthaus, Nano Letters 10, 887 (2010).
 G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus,and T. J. Kippenberg, Nature Physics 5, 909 (2009).
 T. Faust, P. Krenn, S. Manus, J. P. Kotthaus, and E. M. Weig, arxiv: 1109.1156v1
 Q. P. Unterreithmeier, T. Faust, and J. P. Kotthaus, Phys. Rev. B 81, 241405(R) (2010)
“MRI-AFM and a proposed experiment to measure gravity’s role in breaking the unitarity of quantum dynamics”
Authors: Andrea Vinante, Geert Wijts, Sasha Usenko, Jasper van Wezel and Tjerk H. Oosterkamp
We present the current state of the art in Magnetic Resonance Imaging by Atomic Force Microscopy (MRI-AFM), specifically the recent effort in Leiden to perform these experiments at lower temperatures. We have developed a method to detect the force sensor, a mechanical resonator with a resonant frequency of a few kHz and a spring constant k=10E-4 N/m, using a SQUID read-out . This method has been shown to be compatible with MRI-AFM experiments by applying it to the detection of electron spins at an oxidized silicon surface .
We then extrapolate to what might be achievable when applying these experiments on NV-centers. We propose an approach which may allow the creation of a superposition of states which will place a massive beam in a superposition of two states which is spatially separated by several nanometers.
With such an experiment one may begin to experimentally access the quantum to classical crossover, and thus force us to consider the possible ways in which the usual quantum dynamics may be affected.
The proposed experiment is aimed specifically at clarifying the role played by gravity, and may distinguish the resulting dynamics from that suggested by alternative scenarios for the quantum to classical crossover. We give an ad hoc theoretical description of the expected dynamics, and a discussion of the involved experimental parameter values and the proposed experimental protocol .
 O. Usenko, A. Vinante, G.H.J.C. Wijts, T.H. Oosterkamp: A superconducting quantum interference device based read-out of a subattonewton force sensor operating a millikelvin temperatures. Appl. Phys. Lett. 98 (2011) 133105
 A. Vinante, G. Wijts, O. Usenko, L. Schinkelshoek, and T.H. Oosterkamp, Magnetic Resonance Force Microscopy of paramagnetic electron spins at millikelvin temperatures, under review at Nature communications, arXiv:1105.3395
 J. van Wezel and T.H. Oosterkamp, Quantum Mechanics meets General Relativity in Nanoscale mechanical experiments. arXiv:0912.3675v2 [cond-mat.mes-hall], to be published in Proceedings of the Royal Society A
“Cavity optomechanics beyond the ground state – the potential of hybrid systems”
At least three groups have now achieved cooling of the center-of-mass motion of micromechanical oscillators close to their ground state, with mean phonon numbers substantially less than one. The coherent exchange of excitation between phonons and photons characteristic of the strong coupling regime has also been demonstrated. In a parallel development, Bose-Einstein condensates trapped inside high-Q optical resonators have been shown to behave under appropriate conditions much like optically driven mechanical oscillators, offering an alternative route to study the optomechanical properties of mesoscopic systems. And hybrid systems consisting of mechanical systems operating in the quantum regime coupled to atoms, molecules, or artificial atoms are likely to provide an additional testing ground to address questions ranging from fundamental physics to the development of novel field and force sensors. Advances past these trailblazing developments will involve a number of additional breakthroughs in what can loosely be called “beyond ground state’’ cavity optomechanics. These include the generation of nonclassical states of the phonon field (single and multimode squeezed states, number states, NOON states, entangled states, etc.) the development of schemes for the characterization of these states, protocols for state transfer between phonon and photon fields, including both optical and microwave fields. Hybrid systems, which can exploit the exquisite sensitivity of AMO measurements, promise to play an important role in these developments. The talk will review some recent advances in this direction, with particular emphasis on hybrid arrangements comprising coupled mechanical oscillators and quantum degenerate atomic systems.
Pierre Meystre, University of Arizona
“A single nitrogen-vacancy defect coupled to a nanomechanical oscillator"
We present a novel hybrid system consisting of a single Nitrogen Vacancy (NV) defect hosted in a diamond nanocrystal positioned at the extremity of a SiC nanowire. The nanowire acting as a nanoresonator is probed via time resolved nanocrystal fluorescence and photon correlation measurements. By immersing the system in a strong magnetic field gradient, we obtain a signature of a magnetic coupling between nanoresonator and the NV electronic spin. This is a first step towards entering two new fields of physics: single photon optomechanics and spin based nanomechanics.
“Decoherence in low-temperature solids’
Real progress in understanding decoherence in Nature has come with the confrontation between theory and experiments, on a variety of systems. This work has revealed that in condensed matter, most decoherence at low temperatures comes from localized environmental modes (spin impurities, nuclear spins, defects, disclocations, etc.), which can be modeled as a 'spin bath'. I will describe very recent examples from magnetic and electromechanical systems, and comment on the relationship to the 'quantum glass' problem. The spin bath is a new playground for theorists, but a headache for experimentalists. I discuss a number of theoretical approaches, and some strategies for suppressing environmental decoherence, along with recent experiments which show great promise in this direction. I conclude with a discussion of the rather subtle ‘crossover’ between the quantum and classical regimes.
“Carbon nanotube mechanical resonators coupled to charge and flux”
We study the motion of carbon nanotube resonators coupled to single electron charges, and to magnetic flux. Using a single electron transistor embedded in the nanotube to read out the motion of the high quality factor resonator (Q ~ 100000), we observe the static force exerted on the nanotube by a single electron, and frequency dips from a “single-electron spring”. Using a suspended carbon nanotube SQUID, we couple magnetic flux to the nanotube motion. We find a record-high critical current of 24 nA and supercurrents that persist to magnetic fields greater than 3T. The magnetic flux in the SQUID is tuned by a DC gate voltage, allowing us to directly observe static displacements of the nanotube with a responsivity of up to 0.4 mΦ/pm.
“Micromechanical motion in the quantum regime”
Accessing the full quantum nature of a macroscopic mechanical oscillator first requires elimination of its classical, thermal motion. The flourishing field of cavity optomechanics provides a nearly ideal architecture for both preparation and detection of mechanical motion at the quantum level. We realize a microwave cavity optomechanical system by coupling the motion of an aluminum membrane to the resonance frequency of a superconducting circuit . By exciting the microwave circuit below its resonance frequency, we damp and cool the membrane motion with radiation pressure forces, analogous to laser cooling of the motion of trapped ions. The microwave excitation serves not only to cool, but also to monitor the displacement of the membrane. A nearly shot-noise limited, Josephson parametric amplifier is used to detect the mechanical sidebands of this microwave excitation and quantify the thermal motion as it is cooled with radiation pressure forces to its quantum ground state . John Teufel, Affiliation: NIST Boulder.
 Teufel, J. D. et al. “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208 (2011).
 Teufel, J. D. et al. “Sideband cooling micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
Are put up in the corridor of the Lorentz Center for the duration of the workshop and can be discussed during the wine and cheese party on Tuesday and the breaks on all other days.
Darren Southworth, Ludwig-Maximilians-Universität
“Development of a Mechanical Single Electron Transistor”
We present progress in the development of a mechanical single electron shuttle. The shuttle is composed of a gold island on a silicon nitride beam situated in a gap between source and drain electrodes. Oscillation of the beam brings the island into contact with the electrodes, and in the presence of a DC bias charging of the island results in electron transport. The island is equipped with a gate electrode and the motion of the beam can be driven dielectrically.
The current design has potential to function as a mechanical single electron transistor at 4K.