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Register a new userZero-Temperature Casimir Fluctuations and the Limits of Force Microscope Sensitivity
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Authors
John A. Sidles
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It is predicted that in force microscopy the quantum fluctuations responsible for the Casimir force can be directly observed as temperature-independent force fluctuations having spectral density $9pi/(40ln(4/e)) hbar delta k$, where $hbar$ is Plancks constant and $delta k$ is the observed change in spring constant as the microscope tip approaches a sample. For typical operating parameters the predicted force noise is of order $10^{-18}$ Newton in one Hertz of bandwidth. The Second Law is respected via the fluctuation-dissipation theorem. For small tip-sample separations the cantilever damping is predicted to increase as temperature is reduced, a behavior that is reminiscent of the Kondo effect.
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We study the zero and finite temperature Casimir force acting on a perfectly conducting piston with arbitrary cross section moving inside a closed cylinder with infinitely permeable walls. We show that at any temperature, the Casimir force always tends to move the piston away from the walls and towards its equilibrium position. In the case of rectangular piston, exact expressions for the Casimir force are derived. In the high temperature regime, we show that the leading term of the Casimir force is linear in temperature and therefore the Casimir force has a classical limit. Due to duality, all these result also hold for an infinitely permeable piston moving inside a closed cylinder with perfectly conducting walls.
The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic details of the system which effectively set a large-momentum cutoff in the underlying field theory, rendering it potentially large. This raises the question how the properties of the force variance are reflected in experimentally observable quantities, such as the thickness of a wetting film or the position of a suspended colloidal particle. Here, based on a rigorous definition of the instantaneous force, we analyze static and dynamic correlations of the CCF for a conserved fluid in film geometry for various boundary conditions within the Gaussian approximation. We find that the dynamic correlation function of the CCF is independent of the momentum cutoff and decays algebraically in time. Within the Gaussian approximation, the associated exponent depends only on the dynamic universality class but not on the boundary conditions. We furthermore consider a fluid film, the thickness of which can fluctuate under the influence of the time-dependent CCF. The latter gives rise to an effective non-Markovian noise in the equation of motion of the film boundary and induces a distinct contribution to the position variance. Within the approximations used here, at short times, this contribution grows algebraically in time whereas, at long times, it saturates and contributes to the steady-state variance of the film thickness.
Several experimental demonstrations of the Casimir force between two closely spaced bodies have been realized over the past two decades. Extending the theory to incorporate the behavior of the force between two superconducting films close to their transition temperature has resulted in competing predictions. To date, no experiment exists that can test these theories, partly due to the difficulty in aligning two superconductors in close proximity, while still allowing for a temperature-independent readout of the arising force between them. Here we present an on-chip platform based on an optomechanical cavity in combination with a grounded superconducting capacitor, which overcomes these challenges and opens up the possibility to probe modifications to the Casimir effect between two closely spaced, freestanding superconductors as they transition into a superconducting state. We also perform preliminary force measurements that demonstrate the capability of these devices to probe the interplay between two widely measured quantum effects: Casimir forces and superconductivity.
We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwells equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the lower bound, implying that nanostructuring is of limited use for increasing attraction. In contrast, the possibility of repulsion is observed even for isotropic dipoles, and is routinely found to be several orders of magnitude larger than any known design, including recently predicted geometries involving conductors with sharp edges. Our results have ramifications for the design of surfaces to trap, suspend, or adsorb ultracold gases.
Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular gratings in regimes not accessible before. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.
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