Defying Gravity : Fascination of Levitation
Part 3 : Quantum levitation
The magnetic and acoustic levitation techniques that would defy gravity have been discussed in Parts 1 and 2 respectively in the current series on “Fascination of Levitation”. The present article, last in the series, discusses quantum levitation which involves small quantum force to make the technique useful for nano and micro electrochemical systems (NEMS and MEMS). The technology is in its infancy and still developing. In terms of familiarity spectrum, quantum levitation is diametrically at opposite end of the scale to the more established levitation techniques already discussed in the present series.
Quantum levitation involves quantum force which is expected to be small enough to levitate tiny components for easy processing to be used in NEMS and MEMS. However, the intricate part of quantum levitation is that the force involved displays attraction rather than levitation. A lack of levitation i.e. lifting capability would mean parts undergoing the treatment would attract each other and get stuck together called ” stiction” by a static friction. The adverse effect of quantum stiction in handling parts will restrict functionality and thereby limit further miniaturization of electrical and mechanical devices for NEMS and MEMS. This unfortunate situation to say the least is awkward in the present context, because it obviously denies the current interest on levitation.
Quantum levitation is thus an intriguing topic to write on, because, for a start, the subject matter cannot be directly dealt with due to attraction rather than levitation power of the quantum force. One has to look at the mechanism of quantum stiction first. Once understood, it is possible for the scientists to circumvent the problem by developing anti-stiction measures that would provide levitation for the nano world, and yet still applying the quantum force but in reversing i.e. repulsive mode. Both these aspects are discussed in the present article. This advancement of knowledge would facilitate friction-free handling of tiny parts via levitation.
Material scientists often experience friction from surface interactions during processing of closely spaced, tiny components mostly in nanotechnology. This would result in friction during movement of parts in the nano world which will ultimately lead to permanent adhesion hence stiction with loss of levitation. A theory known in science as Casimir force/effect is responsible for stiction. This attracting Casimir effect can be useful in some cases. But its serious adverse effect on levitation due to friction would cause parts in micromechanical and, even more severely, nanoscale devices to stick together. The use of correct, repulsive instead of direct quantum force should counteract quantum stiction and lead to frictionless levitation/lifting of tiny parts for their processing to be used in nano and micro machines of the future.
It is obvious that any discussion on quantum levitation would embrace an unorthodox approach of investigating the opposite effect first namely the quantum force responsible for stiction i.e. Casimir phenomenon. This should be followed by considering techniques to reverse the force for levitation. Based on basic physics, these aspects are discussed next in two separate sections.
2. Section 1 : Casimir phenomenon
Casimir phenomenon is a consequence of quantum physics at solid surfaces. It embodies quantum “attraction” which can be best described by considering what happens when two thin, uncharged parallel plates or mirrors (called Casimir plates) are placed very close to each other in vacuum with no external field. The initial consensus would be “nothing at all” since there is no force to play on them except gravity. However, quantum physics suggests otherwise with development of mutual attraction of the plates to each other in the presence of vacuum. This startling concept of attraction between the two plates although appears a bit odd, was first theoretically predicted in 1948 by the Dutch theoretical physicist Hendrick Casimir who considered the presence of a small but strong attractive effect dubbed the Casimir effect after his name, while the force between the two plates is known as the Casimir force. Based on quantum electrodynamics, this so-called Casimir phenomenon originates from alterations of tiny quantum oscillations/fluctuations of electromagnetic (EM) waves between and around the two uncharged Casimir plates in vacuum. This is explained later on (sec. 2E).
For a long time, Casimir effect was little more than a theoretical curiosity. This is because one does not deal directly with such small forces in everyday life. However, as the engineered devices continue to get smaller and smaller, the quantum forces are taken seriously. Experimental physicists in recent past realized the importance of Casimir force in nano and micro scale systems which have many possible applications in science and engineering (already used as air-bag pressure sensors). As a result, interest in the Casimir phenomenon had blossomed in recent years.
As mentioned earlier, development of an anti-stiction property is essential which would benefit frictionless handling of tiny parts via levitation. This feat of quantum levitation can only be achieved by reversing the attractive but unwanted Casimir force into a repulsive mode.
It is obvious that the term “quantum levitation” should be associated with quantum energy only. However, scientists from Tel Aviv University incorrectly popularise the same term while dealing with magnetic levitation using superconductor which involves local pinning/locking of magnetic field. Their argument is based on the link of superconductor to quantum physics. This is apparently a misnomer, because ideal quantum levitation should be linked directly to quantum energy such as repulsive Casimir force of the present text, rather than to an item in quantum physics.
B. Illustration of Casimir force in nature
Gecko’s ability to walk across ceilings in apparent defiance of gravity is a good example of Casimir force in real life. This unique feature illustrates how and why the movement of tiny nano-sized parts such as geckos’ toes enables individual gecko to achieve the extraordinary feat of sticking to a surface with just one toe. The picture above shows geckos’ feet and individual toes.
The sticking phenomenon is considered to be due to a simple electrostatic interactions (van der Waals or Casimir force in a more general sense) based upon a random location of electrons within their orbitals in the atoms on the surface of two compounds (geko’s feet and glass or ceiling material). The “dry glue” effect that enables gecko to walk across a ceiling or a smooth surface like glass is also sometimes believed to be due to tiny hairs on their toes that are so small that they are bonded on an atomic level to the atoms of the said surface.
C. Calculation of Casimir force
The small but strong attractive Casimir force F can be calculated between two parallel, plane plates of cross-sectional area A separated by a gap L, from the following relation :
F = (h*c*A*π^2)/ (2*π*240*L^4)
where apart from geometrical parameters A and L, the strength of the force F depends only on fundamental values namely Planck’s constant h (6.626 *10^-34 m^2*kg*sec^-1 or Joules.sec), and c the speed of electromagnetic waves i.e. light (3*10^8 m*sec^-1). It is obvious from the above relation that F will decrease rapidly with increasing gap L. For example, for two plates of 1 square centimetre area set at a micron apart i.e. A = 10^-4 m^2 and L = 10^-6 m, F will be 1.3*10^-7 N (N is Newton). This value for the same plates but separated by a larger gap of one centimetre i.e. L = 10^-2 m will be appreciably reduced down to 1.3*10^-23 N which is too weak to trace. In comparison, 1.3*10^-7 N at L = 10^-6 m although still small, is enough dominant force in the gap of the uncharged plates that is detectable by modern laboratory force measurements technique. (For the record, a force of 10^-7 N is roughly the weight of a water droplet that is half a millimetre in diameter.)
It is interesting to find out what happens when the calculation is taken further down the scale by considering a much closer gap in the nanometre range, say L =10nm or 10^-8m which is about a hundred times the typical size of an atom. The calculated Casimir force F reaches quite a high value at 1.3*10^5 N which per square metre is almost equivalent to 1 atmospheric pressure.
Measurement of F
Advances in instrumentation in recent times have now enabled the Casimir force F to be measured with greater accuracy than ever. In fact, despite the theoretical prediction some six decades ago in 1948, it was not until 1997 when the force was first measured in 0.6-6.0 μm range with an accuracy up to 5% of the predicted value. Advances in instrumentation such as atomic force microscopy which can sense forces as small as 10^-18 N, have now enabled scientists to measure F even with greater accuracy to within 1% of the expected theoretical value.
D. Basic parameters in physics and Casimir theory
An understanding of Casimir effect requires a basic knowledge of vacuum in space based on quantum field theory. The general perception of vacuum is that it is an empty space. But far from being empty, modern physics assumes that vacuum is full of fluctuating electromagnetic (EM) waves with wavelengths ranging from gamma rays (short wavelength, high frequency) to radio waves (long wavelength, low frequency) that can never be completely eliminated, like an ocean with unstoppable waves. As a result, instead of being empty, vacuum is more like a bubbling soup of various virtual particles like photons (quanta of light and other forms of EM radiations) popping into and out of existence. This dynamic phenomenon is termed as “vacuum fluctuation” or “quantum fluctuation” which refers to fluctuations of electromagnetic waves in vacuum. The mysterious Casimir force arises from the energy of virtual particles. At very short distances, vacuum fluctuations can lead to an attractive force (van der Waals forces) between atoms or molecules. It has been reported that Casimir’s original goal was to compute the van der Waals force between (polarisable) molecules of the metallic plates – author is not sure how.
Classically, EM waves which originate from vibrations of electric and magnetic fields can never be completely exhausted. Unlike the mechanical waves of sound which need a (material) medium to transport their energy from one location to another, EM waves propagate through vacuum of the outer space at the speed of light without requiring any medium to help to travel. The concept of EM waves in vacuum is comparable with waves of various wavelengths in ocean which are always there in an ocean ranging from very big waves to small ripples that can never be stopped or exhausted.
Zero point energy (ZPE)
The Casimir attractive force cannot be explained by classical physics. Instead, it is purely a quantum effect involving zero-point oscillations of the EM field surrounding the surfaces. One would expect that if all the energy of light and heat are taken out from space, the energy in the vacuum should end up as zero i.e. ZPE. However, this is not necessarily the case. This is demonstrated by, for example, liquid helium which remains liquid rather than being frozen solid as the temperature is lowered down to absolute zero. This is because of irremovable ZPE of its atomic motions. (Helium will freeze if the pressure is increased to 25 atms.)
The EM waves come in all possible wavelengths, and their presence implies that empty space contains a certain amount of energy. The ever presence of EM waves (containing faster-than-light elementary sub-atomic energy particles referred to as tachyons)even in an apparently empty space in vacuum should provide certain amount of energy termed as vacuum energy which although in practice cannot be tapped, is always there. ZPE is thus the manifestation of vacuum energy which is small but positive. The vacuum state has ZPE which is the lowest quantized energy level of a quantum mechanical system that plainly shows itself as the static Casimir effect.
Interestingly, the ability of gecko to climb flat surfaces can in part be attributed to vacuum fluctuations and virtual particles. The attractive Casimir force between gecko’s toe and the surface has a quantum origin, as it arises from the quantum fluctuations of the zero energy states or vacuum states.
E. Casimir effect
The most straight-forward evidence of vacuum energy is the Casimir effect. As mentioned earlier, the theoretical prediction of attraction between the two parallel plates in vacuum was first proposed by Casimir. An extension of Casimir effect is the Casimir force F which is a consequence of quantum mechanics, theory of which describes the world of atoms and subatomic particles. According to the quantum theory, empty space is not empty, but filled with quantum vacuum that contains energetic particles like photons. The wavelengths of the photons that make up the electromagnetic field are affected by the gap between the Casimir plates, particularly when they are placed very close together within several nanometres in vacuum. This makes EM field between the plates different from that surrounding them. Some of the EM waves in terms of virtual photons would fill in the gap between the plates and will be bouncing back and forth, while others on the outside will not.
Casimir realised that vacuum energy in the gap between the plates can be calculated by counting only those photons whose wavelengths fit a whole number of times into the gap. Fluctuations of EM waves shown in blue colour in the artist’s sketch above become fewer by being squeezed within the gap as the two Casimir plates are brought closer to each other. The longer waves, shown in red on the outside of either plate are,
however, too big and will no longer fit into gap between the plates. The reflective surfaces of the plates block out entry into the gap of virtual photons of wavelengths longer than the separation distance. The total amount of ZPE or vacuum energy originating from EM waves between the plates become less than the amount elsewhere in the vacuum outside the plates.
The longer wavelengths thus remaining unconstrained would exert a stronger pressure on the outside of the surfaces. This will cause a pressure difference on either side of the plates. As the system tries to overcome this imbalance, the big waves will apply more pressure on the plates by squeezing and eventually sticking them together. This is manifested by a reduction of energy density in the gap between the plates compared with that on the outside, and like an external air pressure tending to collapse a slightly evacuated vessel, the Casimir force despite being a weak force, draws the plates towards each other introducing virtual attraction. Thus although F is smaller at larger gap (see calculation above), this attractive force would be significant at distances of micrometers or less causing parts to stick together.
The whole concept of Casimir effect arises from the sophisticated domain of quantum electrodynamics which stipulates, as explained above, an attractive Casimir force building up in the gap between the two uncharged plates. This is due to alteration of fluctuations of EM waves by the plates in the vacuum.
3. Section 2 : Reversing Casimir effect
Nanoengineered machines are progressively becoming popular with time, making it essential to sort out problems of stiction during handling of tiny components. In the nano-world, the major problem, as mentioned above, centres on the Casimir force which is responsible for ultimate cause of friction and hence stiction between parts. The only way to counteract this adverse stiction effect is to reverse the attractive Casimir force. The resulting repulsive force despite being still small would be strong enough to levitate tiny objects.
The possibility of achieving levitation by reversing the Casimir effect has spurred lots of researches worldwide in recent times. A literature survey indicates following three basic approaches described below that could lead to develop repulsive quantum force. Although any success would help to minimize friction caused by the Casimir force during processing parts for NEMS and MEMS, the nanoworld still awaits for consistent experimental observation of the repulsive effect.
1. Use of perfect lens in metamaterial
Ulf Leonhardt and Thomas Philbin of the University of St.Andrews ( U.K) have worked out how to turn the normally “sticky” quauntam Casimir force from attraction to repulsion by using a specially developed “perfect”lens made from metamaterial with a negative index of refraction, sandwiched between the two Casimir plates in vacuum.
Definitions of “Perfect lens” and “metamaterial”
A perfect lens can focus an image with a resolution that is not restricted by the wavelength of light. It could be prepared from metamaterials which are artificially structured exotic photonic materials made from complex arrays of metal units and wires. Photonic crystals are periodic optical nanostructures that affect the propagation of EM waves such as photons in much the same way that ion lattices affect electrons in solids.
The metal units in metamaterials are smaller than the wavelength of light, so that they can be engineered to precisely how EM light waves travel around them. Metamaterials are thus designed to manipulate the EM spectrum in ways materials in nature cannot. They are characterised by negative index of refraction which can only be associated with negative values of electric permittivity Ɛ and magnetic permeability μ, preferably both equal to -1. With negative refractive index, such materials also known as left-handed metamaterials because they create left-handed electromagnetism, will bend the EM light waves in the opposite direction than expected. This will cause the Casimir force also to act in the opposite direction than normal, forcing the upper plate to levitate.
According to St Andrews scientists, inserting a “perfect lens” between the Casimir plates will disrupt the quantum fluctuations of the EM field. In particular, the negative index lens of metamaterials is able to modify ZPE of the EM field in the gap between surfaces, and thereby reversing the direction of the resulting mechanical force of the quantum vacuum, the Casimir force. The repulsive force thus created is strong enough to levitate an ultrathin aluminium mirror of 500 nm thick, causing it to hover above a perfect lens placed over a conducting plate. It is however, important to point out that although metamaterials are likely to reverse the Casimir effect, it is not easy to engineer such materials. It is thus unlikely that the above concept will come to fruition in the near future for levitation of small objects.
The above idea is extended by introducing the concept of strong chirality. A material is defined to be chiral if it lacks any plane of mirror symmetry, and also the structure of its mirror images cannot be superimposed atop each other. Human hands are examples of chiral objects because they lack of plane or centre of symmetry and are not superimposible. Chiral metamaterial is a new class of metamaterials which offers a simpler route to negative refractions via strong chirality and is thus believed to be the key material in reversing the attractive force. It has a complicated spiral structures and lacks mirror symmetry which is common among materials currently in use for making micromechanical devices. Strong chirality which does not exist in natural materials, can be obtained with metamaterials.
2. Interaction of materials immersed in a fluid
In a totally different approach to harness the repulsive Casimir force, Federico Capasso and his group at Harvard University consider plates being separated by a fluid, not vacuum. They found that repulsive quantum forces should result from materials with a certain relationship among their frequency-dependent dielectric functions ξ (which is a function of permittivity). They replaced the vacuum with a liquid of significantly different ξ from that of the plates themselves. When plates of high and low ξ values are separated by a fluid of intermediate ξ , the fluid will be drawn to the high ξ plate more strongly than the force with which the two plates are drawn to each other, so that there would be a net repulsion between the plates. This is believed to be due to a larger momentary polarization being induced in the fluid than in the low ξ plate. For example, bromobenzene was used as a fluid medium between gold-coated (100 nm thick) polystyrene sphere (39.8 μm diameter- attached to a cantilever to measure the repulsive force) and a silica plate. The dielectric functions are reported to be related as ξgold > ξ bromobenzene > ξsilica which makes the Casimir attraction between the liquid and the silica plate stronger than that between gold bead and silica.
As a result, fluid forces its way around the bead pushing it away from the silica plate. Artist’s impression of a repulsive quantum force is shown above. The next step will be to consider if future research can demonstrate repulsive forces with a liquid is more user friendly than bromobenzene in handling components in NEMS and MEMS.
3. Changes in geometry and material properties
A most puzzling aspect of the Casimir theory is that the force is a function of geometry. If the plates are replaced by hemispherical shells, the force becomes repulsive. Spherical surfaces somehow “enhance” the number of virtual photons. There is no simple or intuitive way to tell which way the force will go before carrying out complicated calculations.
It is considered that although the Casimir force pushes identical plates together, changes in the geometry and material properties of one of the plates can reverse the direction of the force. Based on theoretical calculation, a nanometre-thick plate made from a material called yttrium iron garnet (YIG) could levitate half a micrometer above a gold plate. Levitation apparently improves, at least theoretically, with increasing repulsive force as the YIG plate gets thinner. This is convenient because with thinner plate, the weight is reduced which would result in the force getting strong enough to levitate it. There is yet to have consistent practical demonstration of such effect
4. Final remarks
The natural quantum force namely the Casimir force is undesirable in the miniature world of NEMS and MEMS. This is because such force is unfortunately responsible for the ultimate cause of friction, hence stiction which would not yield to quantum levitation of parts in making tiny devices. The problem has to be tackled in a roundabout way by first investigating the mechanism of the quantum stiction of the Casimir force. This is to be followed by developing levitation via introducing anti-stiction measures. Thus the present topic on quantum levitation is addressed with an unorthodox approach due to lack of, unlike other established levitation methods, any direct guideline.
Casimir phenomenon is the result of one of the most interesting macroscopic effects of vacuum fluctuations/oscillations in a quantum electromagnetic field. The effect has extended the microscopic gecko’s criterion of interatomic van der Waals force to the attraction between macroscopic structures in a vacuum. The force is powerful and attractive when the gap between the objects is very small i.e. in the nanometre range. This is because the very close objects alter the quantum fluctuations in the vacuum.
With engineered devices getting smaller and smaller, development of reversal of this uncannily eerie quantum Casimir force can be used one day to hold molecules aloft i.e. levitate them, creating virtually friction-free parts for processing nano or micro devices. The repulsive effect which has yet to be consistently confirmed experimentally could help minimize the friction in micro or nano sized machines caused by the Casimir force. The MEMS combine mechanical structures with electronics on a single chip such as the one that triggers the airbag in a car, contains both mechanical elements for measuring violent de-acceleration and the electronics needed for deciding when to explode the airbag.
Though it is possible in principle to quantum levitate humans, scientists are a long way off attaining such feats. Current technology is only applicable to miniature objects since the quantum force is small and act only over short ranges.
Some useful sources
1. Proc.Royal Netherlands Academy of Arts & Sci., B51,793, 1948 2. http://physics.about.com/od/quantumphysics/f/QuantumLevitation.htm 3. U.Leonhardt and T.Philbin, New J.Phys.Vol.9,August, 254,2007 4. S.K.Lamoreaux, Physics Today, February, pp.40-45, 2007
5.http://www.scholarpedia.org/article/Casimir_Force 6. S.K.Lamoreaux, Scholapedia, 6(10),9746, 2011 7.http://www.hep.caltech.edu/~phys199/lectures/lect5_6_cas.pdf , 8.http://math.ucr.edu/home/baez/physics/Quantum/casimir.html 9. S.K.Lamoreaux, Phys.Rev.Letters, Vol.78, p.5, 1997 10. J.Miller, Physics Today, February, pp 19 - 22, 2009 11. U.Mohideen and A.Roy, Phys.Rev.Lett., Vol.81, 4549, 1998 12. A.Lambrecht, Physics World, September, p. 29, 2002 13. R.Zhao et.al. Phy.Rev.Lett., Vol.103 (10), 103602, 2009 14.http://dx.doi.org/10.1103/PhysRevLett.102.023901 15. J.N.Mundy et.al Nature, Jan.8, 457(7226): 170, 2009 16.http://physics.aps.org/story/v2/st28 17. N.Inui, J.Appl.Phys. Vol.111, (7) 074304, 2012 : DOI : 10.1063/1.3698619 18.http://www.nature.com/news/2009/090107/full/news.2009.4.html 19.http://math.ucr.edu/home/baez/physics/Quantum/casimir.html 20.http://www.freegrab.net/zpeintro.htm