Synchronizing a single-electron shuttle to an external drive
Michael Möckel,
Darren R. Southworth,
Eva M. Weig,
Florian Marquardt
New Journal of Physics
16
043009
(2014)
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The nanomechanical single-electron shuttle is a resonant system in which a suspended metallic island oscillates between and impacts at two electrodes. This setup holds promise for one-by-one electron transport and the establishment of an absolute current standard. While the charge transported per oscillation by the nanoscale island will be quantized in the Coulomb blockade regime, the frequency of such a shuttle depends sensitively on many parameters, leading to <br>drift and noise. Instead of considering the nonlinearities introduced by the impact events as a nuisance, here we propose to exploit the resulting nonlinear dynamics to realize a highly precise oscillation frequency via synchronization of the shuttle self-oscillations to an external signal. We link the established phenomenological description of synchronization based on the ADLER equation to the microscopic nonlinear dynamics of the electron shuttle by calculating the effective ADLER constant analytically in terms of the microscopic parameters.
Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime (vol 4, 011015, 2014)
New Journal of Physics
16
085006
(2014)
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We provide a brief overview of the various topics addressed in this 'focus on' collection on optomechanics.
Cavity optomechanics
Markus Aspelmeyer,
Tobias J. Kippenberg,
Florian Marquardt
Reviews of Modern Physics
86
(4)
1391-1452
(2014)
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The field of cavity optomechanics is reviewed. This field explores the interaction between electromagnetic radiation and nanomechanical or micromechanical motion. This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation-pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity-quantum-optomechanics experiments. In addition, the perspectives for fundamental quantum physics and for possible applications of optomechanical devices are described.
Cavity Optomechanics Nano- and Micromechanical Resonators Interacting with Light Introduction
Markus Aspelmeyer,
Tobias J. Kippenberg,
Florian Marquardt
CAVITY OPTOMECHANICS: NANO- AND MICROMECHANICAL RESONATORS INTERACTING WITH LIGHT
1-4
(2014)
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We briefly guide the reader through the chapters of the book, highlighting the connections between the various approaches to cavity optomechanics.
Dissipative optomechanical squeezing of light
Andreas Kronwald,
Florian Marquardt,
Aashish A. Clerk
New Journal of Physics
16
063058
(2014)
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We discuss a simple yet surprisingly effective mechanism which allows the generation of squeezed output light from an optomechanical cavity. In contrast to the well known mechanism of 'ponderomotive squeezing', our scheme generates squeezed output light by explicitly using the dissipative nature of the mechanical resonator. We show that our scheme has many advantages over ponderomotive squeezing; in particular, it is far more effective in the good cavity limit commonly used in experiments. Furthermore, the squeezing generated in our approach can be directly used to enhance the intrinsic measurement sensitivity of the optomechanical cavity; one does not have to feed the squeezed light into a separate measurement device. As our scheme is very general, it could also e. g. be implemented using superconducting circuits.
Basic Theory of Cavity Optomechanics
Aashish A. Clerk,
Florian Marquardt
CAVITY OPTOMECHANICS: NANO- AND MICROMECHANICAL RESONATORS INTERACTING WITH LIGHT
5-23
(2014)
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This chapter provides a brief basic introduction to the theory used to describe cavity-optomechanical systems. This can serve as background information to understand the other chapters of the book. We first review the Hamiltonian and show how it can be approximately brought into quadratic form. Then we discuss the classical dynamics both in the linear regime (featuring optomechanical damping, optical spring, strong coupling, and optomechanically induced transparency) and in the nonlinear regime (optomechanical self-oscillations and attractor diagram). Finally, wediscuss the quantum theory of optomechanical cooling, using the powerful and versatile quantum noise approach.
Single-site-resolved measurement of the current statistics in optical
lattices
Stefan Kessler,
Florian Marquardt
Physical Review A
89
(6)
061601
(2014)
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At present, great effort is spent on the experimental realization of gauge fields for quantum many-body systems in optical lattices. At the same time, the single-site-resolved detection of individual atoms has become a new powerful experimental tool. We discuss a protocol for the single-site-resolved measurement of the current statistics of quantum many-body systems, which makes use of a bichromatic optical superlattice and single-site detection. We illustrate the protocol by a numerical study of the current statistics for interacting bosons in one and two dimensions and discuss the role of the on-site interactions for the current pattern and the ground-state symmetry for small two-dimensional lattices with artificial magnetic fields.
Decoherence in a double-dot Aharonov-Bohm interferometer: Numerical
renormalization group study
Bjoern Kubala,
David Roosen,
Michael Sindel,
Walter Hofstetter,
Florian Marquardt
Physical Review B
90
(3)
035417
(2014)
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Coherence in electronic interferometers is typically believed to be restored fully in the limit of small voltages, frequencies, and temperatures. However, it is crucial to check this essentially perturbative argument by nonperturbative methods. Here we use the numerical renormalization group to study ac transport and decoherence in an experimentally realizable model interferometer, a parallel double quantum dot coupled to a phonon mode. The model allows us to clearly distinguish renormalization effects from decoherence. We discuss finite-frequency transport and confirm the restoration of coherence in the dc limit.
Cavity Optomechanics Nano- and Micromechanical Resonators Interacting with Light Preface
Markus Aspelmeyer,
Tobias J. Kippenberg,
Florian Marquardt
CAVITY OPTOMECHANICS: NANO- AND MICROMECHANICAL RESONATORS INTERACTING WITH LIGHT
V-V
(2014)
Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime
Physical Review X
4
(1)
011015
(2014)
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Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Phys. Rev. Lett. 109, 253601 (2012)]. Here, we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime that correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation and is based on techniques borrowed from the laser theory due to Haake and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte Carlo simulations and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e., outside the single-photon strong-coupling regime, for strong cavity drive and rather large limit-cycle amplitudes. The approach taken here provides a natural starting point for further studies of quantum effects in optomechanics.
Contact
Theory Division Prof. Florian Marquardt
Max Planck Institute for the Science of Light Staudtstr. 2 91058 Erlangen, Germany
