Casimir effect:  60 years after......but still surprising

 

 
 
BRIEF INTRODUCTION: As device dimensions for Micro electro mechanical Systems (MEMS) decrease, forces such as the Casimir Effect  that are normally neglected in macrosystems have to be considered. Indeed, more than 50 years ago the eminent Dutch physicist H. Casimir discovered that two parallel conducting plates separated by a distance d attract each other with a force proportional to the surface area A. This is a prediction of quantum electrodynamics, which arise from the perturbation of zero point vacuum fluctuations of the electromagnetic field by the conducting plates. The fundamental nature of the Casimir effect and its implications, e.g. on surface forces, particle physics, cosmology as lead to wide theoretical work. The first experimental attempt to measure the Casimir force was inconclusive due to large error (~100 %). Recently, it became feasible high precision measurements of the Casimir force using a torsion pendulum,  an atomic force microscope, and a micromachined torsional device. The latter also revealed the possibility for novel actuators based on the Casimir force. The interpretation of the Casimir force in terms of changes in zero point vacuum electromagnetic energy suggests that it is a function of plate geometry that confines vacuum fluctuations.  Although we do not deal directly with such small distances in our everyday lives, they are important in nanoscale structures and microelectromechanical systems (MEMS). These are "intelligent" micron-sized devices in which mechanical elements and moving parts, such as tiny sensors and actuators, are carved into a silicon substrate. Electronic components are then wired on to the device to process information that it senses or to drive the movement of its mechanical parts. MEMS have many possible applications in science and engineering, and are already used as car air-bag pressure sensors.

Understanding the Casimir force: Although the Casimir force seems completely counterintuitive, it is actually well understood. In the old days of classical mechanics the idea of a vacuum was simple. The vacuum was what remained if you emptied a container of all its particles and lowered the temperature down to absolute zero. The arrival of quantum mechanics, however, completely changed our notion of a vacuum. All fields - in particular electromagnetic fields - have fluctuations. In other words at any given moment their actual value varies around a constant, mean value. Even a perfect vacuum at absolute zero has fluctuating fields known as "vacuum fluctuations", the mean energy of which corresponds to half the energy of a photon. However, vacuum fluctuations are not some abstraction of a physicist's mind. They have observable consequences that can be directly visualized in experiments on a microscopic scale. For example, an atom in an excited state will not remain there infinitely long, but will return to its ground state by spontaneously emitting a photon. This phenomenon is a consequence of vacuum fluctuations. Imagine trying to hold a pencil upright on the end of your finger. It will stay there if your hand is perfectly stable and nothing perturbs the equilibrium. But the slightest perturbation will make the pencil fall into a more stable equilibrium position. Similarly, vacuum fluctuations cause an excited atom to fall into its ground state.

The Casimir force is the most famous mechanical effect of zero-point-energy (ZPF) vacuum fluctuations. Consider the gap between two plane mirrors as a cavity. All electromagnetic fields have a characteristic "spectrum" containing many different frequencies. In a free vacuum all of the frequencies are of equal importance. But inside a cavity, where the field is reflected back and forth between the mirrors, the situation is different. The field is amplified if integer multiples of half a wavelength can fit exactly inside the cavity. This wavelength corresponds to a "cavity resonance". At other wavelengths, in contrast, the field is suppressed. Vacuum fluctuations are suppressed or enhanced depending on whether their frequency corresponds to a cavity resonance or not. The Casimir force is the most famous mechanical effect of vacuum fluctuations. Consider the gap between two plane mirrors as a cavity. All electromagnetic fields have a characteristic "spectrum" containing many different frequencies. In a free vacuum all of the frequencies are of equal importance. But inside a cavity, where the field is reflected back and forth between the mirrors, the situation is different. The field is amplified if integer multiples of half a wavelength can fit exactly inside the cavity. This wavelength corresponds to a "cavity resonance". At other wavelengths, in contrast, the field is suppressed. Vacuum fluctuations are suppressed or enhanced depending on whether their frequency corresponds to a cavity resonance or not. An important physical quantity when discussing the Casimir force is the "field radiation pressure". Every field - even the vacuum field - carries energy. As all electromagnetic fields can propagate in space they also exert pressure on surfaces, just as a flowing river pushes on a floodgate. This radiation pressure increases with the energy - and hence the frequency - of the electromagnetic field. At a cavity-resonance frequency the radiation pressure inside the cavity is stronger than outside and the mirrors are therefore pushed apart. Out of resonance, in contrast, the radiation pressure inside the cavity is smaller than outside and the mirrors are drawn towards each other. It turns out that, on balance, the attractive components have a slightly stronger impact than the repulsive ones. For two perfect, plane, parallel mirrors the Casimir force is therefore attractive and the mirrors are pulled together.  While the Casimir force is too small to be observed for mirrors that are several metres apart, it can be measured if the mirrors are within microns of each other. For example, two mirrors with an area of 1 cm2 separated by a distance of 1 µm have an attractive Casimir force of about 10-7 N - roughly the weight of a water droplet that is half a millimetre in diameter. Although this force might appear small, at distances below a micrometre the Casimir force becomes the strongest force between two neutral objects.

 

New physics on the horizon? The Casimir effect could also play a role in accurate force measurements between the nanometre and micrometre scales. Newton's inverse-square law of gravitation has been tested many times at macroscopic distances by observing the motion of planets. But no-one has so far managed to verify the law at micron length scales with any great precision. Jens Gundlach and colleagues at Washington, for example, have used a torsion pendulum to determine the gravitational force between two test masses separated by distances from 10 mm down to 220 µm. Their measurements confirmed that Newtonian gravitation operates in this regime but that the Casimir force dominates at shorter distances. At any rate such tests are important because many theoretical models that attempt to unify the four fundamental forces of nature predict the existence of previously undiscovered forces that would act at such scales. Any deviation between experiment and theory could hint at the existence of new forces. But all is not lost even if both values agree: the measurements would then put new limits on existing theories.

Real materials: The problem with studying the Casimir effect is that real mirrors are not like the perfectly smooth plane mirrors. In particular, real mirrors do not reflect all frequencies perfectly. They reflect some frequencies well - or even nearly perfectly - while others are reflected badly. In addition, all mirrors become transparent at very high frequencies. When calculating the Casimir force the frequency-dependent reflection coefficients of the mirrors have to be taken into account - a problem first tackled by Evgeny Lifshitz in the mid-1950s, and then by Julian Schwinger and many others. It turns out that the measured Casimir force between real metallic mirrors that are 0.1 µm apart is only half the theoretical value predicted for perfect mirrors. If this discrepancy is not taken into account when comparing experimental data with theory, then an experimental measurement could erroneously be interpreted as a new force.

Finite conductivity: The problem with studying the Casimir effect is that real mirrors are not like the perfectly smooth plane mirrors. In particular, real mirrors do not reflect all frequencies perfectly. They reflect some frequencies well - or even nearly perfectly - while others are reflected badly. In addition, all mirrors become transparent at very high frequencies. When calculating the Casimir force the frequency-dependent reflection coefficients of the mirrors have to be taken into account (first tackled by Evgeny Lifshitz in the mid-1950s, and then by Julian Schwinger and others). It turns out that the measured Casimir force between real metallic mirrors that are 0.1 µm apart is only half the theoretical value predicted for perfect mirrors. If this discrepancy is not taken into account when comparing experimental data with theory, then an experimental measurement could erroneously be interpreted as a new force . 
Finite temperature: Another problem with calculating the expected Casimir force for a real system is the fact that experiments are never carried out at absolute zero - as originally envisaged in Casimir's calculations - but at room temperature. This causes thermal - as well as vacuum - fluctuations to come into play. These thermal fluctuations can produce their own radiation pressure and create a bigger Casimir force than expected. For example, the Casimir force between two plane mirrors 7 µm apart is twice as large at room temperature than at absolute zero. Fortunately, thermal fluctuations at room temperature are only important at distances above 1 µm, below which the wavelength of the fluctuations is too big to fit inside the cavity. Although the temperature dependence of the Casimir force has not yet been studied in detail experimentally, it must be included in calculations of the force at separations above 1 µm. 

Surface roughness: A third and final problem in calculating the Casimir force is that real mirrors are not perfectly smooth. Most mirrors are made by coating a substrate with a thin metal film using the technique of sputtering, e-beam, thermal deposition etc.  The deposition process produces films with a roughness of 1-20 nm (or even more depending also on the deposited film thickness etc.). While such roughness is invisible to the naked eye, it does affect measurements of the Casimir force, which is very sensitive to small changes in distance. In our work we investigate the influence of self-affine roughness on the Casimir energy for plate-plate/sphere geometry. The plate roughness is characterized by the rms roughness amplitude w, the lateral correlation length x, and the roughness exponent H. Application on the pull-in voltages  to MEMS/NEMS switches are currently  in progress taking into account the effect of electrostatic forces.

Measurements of the Casimir & Capillary forces  are in progress by the use of the Pico-Force AFM: The MultiMode PicoForce scanning probe microscope system brings unprecedented accuracy and flexibility to molecular biology and nanoscale materials research. With its innovative force-measurement features, proven SPM technology, and high-speed fifth-generation NanoScope V controller, the MultiMode PicoForce is ideally suited for a broad variety of studies, from protein unfolding and antigen-antibody binding to membrane elasticity. The system's handheld PicoAngler tool allows users to manually explore tip-sample interactions with incredible ease. This innovative tool is particularly useful for single-molecule force spectroscopy, providing highly sensitive approach and retraction of the cantilever tip. PicoForce AFM Datasheet

 

 

Our recent papers on Casimir/Surface  forces

 

Ph.D Thesis : Peter van Zwol (Dynamic surface roughening and the Casimir force in MEMS/NEMS, Cluster 3 M2I, in progress)
Collaboration: Dr. V. B. Svetovoy (MESA+, Tweente University, NL)
Participation in the ESF Network  CASMIR
 
Theory papers on surface forces - MEMS / NEMS

Pull-in characteristics of electromechanical switches in the presence of Casimir forces: Influence of self-affine surface roughness

Phase maps of microelectromechanical switches in the presence of electrostatic and Casimir forces

Surface roughness influence on the pull-in voltage of microswitches in presence of thermal and quantum vacuum fluctuations

Adhesion stability of rough elastic films in presence of quantum vacuum fluctuations

Capillary condensation and quantum vacuum effects on the pull-in voltage of electrostatic switches with self-affine rough plates

Contact angle influence on the pull-in voltage of electrostatic switches in presence of capillary condensation and quantum vacuum effects

 
Interesting references for general audience
Feel the Force
Casimir Forces: Still surprising after 60 years