Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes

Genes, Claudiu; Vitali, David; Tombesi, Paolo; Gigan, Sylvain; Aspelmeyer, Markus

doi:10.1103/physreva.77.033804

Cited by 565 publications

(456 citation statements)

References 40 publications

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“…(20,21). In these quadratures, the amplifier equations can be written as (dropping here the added-noise terms)…”

Section: Amplificationmentioning

confidence: 99%

“…[9]). Considering a thermally populated bath, the noise spectrum assumes the form [8] S ξ (ω) = γ m ω ω m coth ω kT + 1…”

Section: Noise: Input Field Correlators and The Quantum Limitmentioning

confidence: 99%

“…The theoretical framework suitable for description of the amplification is closely related to the methodology used to describe the sideband cooling in optomechanical systems [17,18,[20][21][22][23]. We describe the system in terms of quantum Langevin equations with the aim of analyzing the effect of the pumping on the signal, and especially to detail the effects of different types of fluctuations coupling to the system.…”

mentioning

confidence: 99%

“…On the other hand, if only one observable is measured, for example position, or a single quadrature such as either amplitude or phase of oscillations, noise in this measurement can be squeezed below the quantum limit at the expense of increased noise in the other quadrature. In this case, the amplifier is said to be phase-sensitive.While most modern transistors operate several orders of magnitude above the fundamental noise limit, superconducting Josephson junction parametric amplifiers [3, 4,8,9], working near the absolute zero of temperature, have found uses at the level of only a few added quanta at microwave frequencies.Approaching the quantum limit with a mechanical amplifier has remained fully elusive, moreover, there is little work whatsoever on amplifying electrical signals by mechanical means [10], foremost due to the typically small electromechanical interaction. In this work, we describe a way to approach quantum-limited microwave amplification, now with a mechanical device.…”

mentioning

confidence: 99%

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Microwave amplification with nanomechanical resonators

Massel

Heikkilä

Pirkkalainen

et al. 2011

Nature

286

216

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Sensitive measurement of electrical signals is at the heart of modern science and technology. According to quantum mechanics, any detector or amplifier is required to add a certain amount of noise to the signal, equaling at best the energy of quantum fluctuations [1, 2]. The quantum limit of added noise has nearly been reached with superconducting devices which take advantage of nonlinearities in Josephson junctions [3, 4]. Here, we introduce a new paradigm of amplification of microwave signals with the help of a mechanical oscillator. By relying on the radiation pressure force on a nanomechanical resonator [5][6][7], we provide an experimental demonstration and an analytical description of how the injection of microwaves induces coherent stimulated emission and signal amplification. This scheme, based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices, and, at the same time, has a high potential to reach quantum limited operation. With a measured signal amplification of 25 decibels and the addition of 20 quanta of noise, we anticipate near Since the early days of quantum mechanics, the effect of quantum zero point fluctuations on measurement accuracy has been actively investigated. When measuring a position x of an object, one necessarily disturbs its subsequent motion by introducing a disturbance to the momentum p. The imprecision and disturbance are related by the fundamental limit ∆x∆p ≥ /2 owing to the Heisenberg uncertainty principle. A proper compromise between the two leads to the lowest added noise power per unit bandwidth ω/2 which equals the quantum fluctuations of the system itself at the signal frequency ω. On the other hand, if only one observable is measured, for example position, or a single quadrature such as either amplitude or phase of oscillations, noise in this measurement can be squeezed below the quantum limit at the expense of increased noise in the other quadrature. In this case, the amplifier is said to be phase-sensitive.While most modern transistors operate several orders of magnitude above the fundamental noise limit, superconducting Josephson junction parametric amplifiers [3, 4,8,9], working near the absolute zero of temperature, have found uses at the level of only a few added quanta at microwave frequencies.Approaching the quantum limit with a mechanical amplifier has remained fully elusive, moreover, there is little work whatsoever on amplifying electrical signals by mechanical means [10], foremost due to the typically small electromechanical interaction. In this work, we describe a way to approach quantum-limited microwave amplification, now with a mechanical device. Our system consists of a mechanical resonator affected by radiation pressure forces due to an electromagnetic field confined in a lithographically patterned thin-film microwave cavity. Depending on the configuration, it is capable of either phase-sensitive, or phase-insensitive amplification.Our system of two coupled linear oscillators form...

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“…(20,21). In these quadratures, the amplifier equations can be written as (dropping here the added-noise terms)…”

Section: Amplificationmentioning

confidence: 99%

“…[9]). Considering a thermally populated bath, the noise spectrum assumes the form [8] S ξ (ω) = γ m ω ω m coth ω kT + 1…”

Section: Noise: Input Field Correlators and The Quantum Limitmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Microwave amplification with nanomechanical resonators

Massel

Heikkilä

Pirkkalainen

et al. 2011

Nature

286

216

View full text Add to dashboard Cite

show abstract

“…This class of models with photon number -mirror displacement (Nx) type of coupling used for mirror-photon entanglement [52], entanglement cooling of a mirror [53] and entanglement of test masses and standard quantum limit [54] is very different from the class with bilinear coupling in QBM studies (Beware of inconsistencies in the usual master equations for this problem, see [55]). …”

Section: B Decoherence and Disentanglementmentioning

confidence: 99%

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

2008

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In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two-harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [Hu, Paz and Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N , harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations and dissipation of mesoscopic objects towards the construction of a theoretical framework for macroscopic quantum phenomena.

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Ultrahigh‐Resolution Optical Fiber Thermometer Based on Microcavity Opto‐Mechanical Oscillation

Liu

Jiang

Liu

et al. 2022

Advanced Photonics Research

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High‐resolution temperature measurement is nerve‐wracking obstruction for precise characterization of many physical, chemical, and biological processes. To solve this problem, a novel microcavity–optomechanical–oscillation‐based thermometer is proposed. The microcavity serving as a link parametrically couples the mechanical resonator and optical resonator in the same structure and provides a natural and highly sensitive temperature transduction mechanism and ultrahigh‐resolution optical demodulation. The mathematical model of geometrical parameters, mechanics, and material properties for temperature response mechanism is established and verified experimentally. The proposed thermometer has a thermal sensitivity of 11 300 Hz °C−1 and an ultrahigh‐temperature resolution of 1 × 10−4 °C, to the best of one's knowledge, which is the highest temperature resolution with a silica cavity.

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Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes

Cited by 565 publications

References 40 publications

Microwave amplification with nanomechanical resonators

Microwave amplification with nanomechanical resonators

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

Ultrahigh‐Resolution Optical Fiber Thermometer Based on Microcavity Opto‐Mechanical Oscillation

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