Adventures in attonewton force detection

Rugar, D.; Stipe, B. C.; Mamin, H. J.; Yannoni, C. S.; Stowe, T. D.; Yasumura, K.; Kenny, Thomas W.

doi:10.1007/s003390100729

Cited by 40 publications

(26 citation statements)

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“…Thin film interference has been employed as a simultaneous reflectance increasing and noise reducing strategy in ultrasensitive force detection 13,14 at millikelvin temperatures where thermal fluctuations dominate the noise floor. The advantage of a thin film interference scheme is twofold.…”

Section: ͑1͒mentioning

confidence: 99%

Thin film interference in the optomechanical response of micromechanical silicon cantilevers

Wilkinson

Gimzewski

2006

Applied Physics Letters

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The mechanical response of uncoated silicon microcantilevers is shown to modulate as a function of incident wavelength. Cantilever motion is measured interferometrically, using phase sensitive detection in response to a mechanically chopped excitation source. Thin film interference modeling shows that the fraction of absorbed light within the cantilever varies periodically over the range of 450–1000nm, in excellent agreement with the measurements. The results show that the optomechanical responsivity of these cantilevers can be tuned due to the effect via an appropriate selection of incident wavelength, incidence angle, lever thickness, and optical constants of the lever.

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Section: ͑1͒mentioning

confidence: 99%

Thin film interference in the optomechanical response of micromechanical silicon cantilevers

Wilkinson

Gimzewski

2006

Applied Physics Letters

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“…The characteristic adhesion force for a 1 um spherical particle is of the order of 0.1 dynes. It is a big force having in mind that modern techniques permit the measurement of a force a billion times smaller (Rugar, 2001). It is clear that this high loading leads to elastic or even plastic deformation of the material.…”

Section: Prefacementioning

confidence: 99%

Front Matter

'yanchuk

2002

Laser Cleaning

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“…Magnetic resonance force microscopy (MRFM) proposed a decade ago [1] is now approaching its ultimate goal: single spin detection [2]. The following question arises: To what extent can the MRFM be used for quantum measurement of spin states?…”

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confidence: 99%

“…The initial condition is assumed to be a product of the coherent quasiclassical wave function of the cantilever and the entangled state of the two spins, The chosen value of α corresponds to the quasiclassical state of the cantilever with the number of excitations n = |α| 2 = 200. The chosen value of η corresponds to the existing MRFM experiments with electron spins [2]. The time dependences (6) provide the conditions for the cyclic adiabatic inversion of the spin.…”

mentioning

confidence: 99%

“…One of the entangled spins drives the resonant cantilever vibrations, while the other remote spin does not interact directly with the quasiclassical cantilever. The Schrödinger cat state of the cantilever reveals two possible outcomes of the measurement for both entangled spins.Magnetic resonance force microscopy (MRFM) proposed a decade ago [1] is now approaching its ultimate goal: single spin detection [2]. The following question arises: To what extent can the MRFM be used for quantum measurement of spin states?…”

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confidence: 99%

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Magnetic-resonance force microscopy measurement of entangled spin states

et al. 2002

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We simulate magnetic resonance force microscopy measurements of an entangled spin state. One of the entangled spins drives the resonant cantilever vibrations, while the other remote spin does not interact directly with the quasiclassical cantilever. The Schrödinger cat state of the cantilever reveals two possible outcomes of the measurement for both entangled spins.Magnetic resonance force microscopy (MRFM) proposed a decade ago [1] is now approaching its ultimate goal: single spin detection [2]. The following question arises: To what extent can the MRFM be used for quantum measurement of spin states? The particular problem considered in this paper is the MRFM measurement of entangled spin states using a cyclic adiabatic inversion of the spin, which drives the resonant vibrations of the cantilever. We discuss the possibility of determining the state of a remote spin which is entangled with the spin interacting with the MRFM measurement apparatus.Diagram of an MRFM measurement of an entangled state of two spins in a chain of spins. S1 is a single measured spin which changes its direction under the action of the alternating magnetic field B1. S2 is the remote spin entangled with the spin S1. m is the magnetic moment of a ferromagnetic particle which is attached to the cantilever tip. The magnetic force on the cantilever tip (attractive or repulsive) depends on the direction of the spin S1. B0 is the permanent magnetic field which points in the positive z-direction.As an example, we consider a typical entangled state for two spatially separated spins,According to the conventional point of view, by measuring the left spin in the state | ↑ (or | ↓ ) we automatically collapse a remote right spin into the same state | ↑ (or | ↓ ). In the process of MRFM measurement (see Fig. 1) the direction of the measured spin, S 1 , changes periodically with the period of the cantilever vibrations. Thus, it is not clear what the direction of the entangled remote spin, S 2 , will be after the MRFM measurement.To study this problem, we simulated the quantum dynamics of this spin-cantilever system assuming that the measuring spin is initially entangled with the remote spin. The remote spin is not subjected to the action of the MRFM apparatus.The dimensionless quantum Hamiltonian of the spincantilever system in the rotating reference frame is [3],Here p z and z are the dimensionless momentum and coordinate of the cantilever tip; S 1 is the "first" measured spin; ǫ = ǫ(τ ) is the dimensionless amplitude of the radiofrequency (rf) field (where τ = ω c t is the dimensionless time and ω c is the cantilever frequency); η is the dimensionless constant of interaction between the cantilever and the spin, which is proportional to the magnetic field gradient produced by the ferromagnetic particle on the cantilever tip. The phase of the rf field is taken in the form (ωt + ϕ(t)), where ω is chosen equal to the Larmor frequency of the spin: ω = ω L . The time derivative,φ, changes periodically with the frequency of the cantilever vibrations, ω c . I...

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Adventures in attonewton force detection

Cited by 40 publications

References 0 publications

Thin film interference in the optomechanical response of micromechanical silicon cantilevers

Thin film interference in the optomechanical response of micromechanical silicon cantilevers

Front Matter

Magnetic-resonance force microscopy measurement of entangled spin states

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