sign in sign up
<<
Home , Fermi gas

Optically Trapped Fermi

A few hundred thousand atoms, chilled to near , mimic the of other extreme systems, including and superconductors

John E. Thomas and Michael E. Gehm

he bowl is only a millimeter long trons inside an ordinary like cop- balloons by using a form of quantum Tand a tenth of a millimeter wide, no per. Even though the metal is , the trickery known as “strong interac- bigger than a piece of lint. Its walls are behave very much like a : tions” to expand the balloons greatly constructed of pure light, making this They are free to roam around (which in size. These interactions make the “optical bowl” an appropriately ethere- makes the metal conduct electricity), atoms affect one another at a much al container for the stuff sloshing but they have to fit into a strict energy greater distance than they ordinarily around inside: lithium atoms that have hierarchy—the same one found in the would. There are exciting indications, been chilled to less than a millionth of a degenerate Fermi gases we produced. not yet confirmed, that the strong in- degree above absolute zero. But you These gases are first cousins to an- teractions cause the atoms to form shouldn’t think of the sample trapped other strange quantum beast that ap- loose alliances called Cooper pairs. Su- in this vessel of light as just a cloud of pears at ultracold , called perconductivity and some forms of su- lithium (any more than you’d think of a a Bose-Einstein condensate. The re- perfluidity are the result of Cooper diamond as a mere lump of carbon). Its search group of Eric Cornell and Carl pairing. But before we describe some value lies not in the atoms that make it Wieman at the University of Colorado of the remarkable properties of the re- up but in the special way they are put at Boulder fashioned the first such con- sultant gas, let us take a moment to ex- together—in a remarkable configura- densate in 1995. (In 2001, Cornell and plain the significant technical hurdles tion known as a degenerate Fermi gas. Wieman shared a Nobel prize for their our group and others had to overcome. Such an assemblage constitutes a new work with Wolfgang Ketterle of the and is possibly the clos- Massachusetts Institute of Technology.) Chilling Out with Lasers est that scientists will ever come to hav- An atomic degenerate Fermi gas is The possibility of creating macroscopic ing on their desktops a neutron or a even trickier to create, because it pits quantum systems, such as degenerate piece of the quark matter that made up two precepts of quantum mechanics Fermi gases and Bose-Einstein conden- the early universe. against each other. On the one hand is sates, has come about largely because Although physicists had predicted Heisenberg’s famous uncertainty prin- of improvements in the technology of the existence of degenerate Fermi gases ciple, which says that the location of any optical cooling. In most experiments as long ago as the 1930s, nobody had particle becomes more ambiguous as its with ultracold gases, magnetic forces produced a fully independent one in speed becomes less uncertain. In an ul- ensnare the atoms. By contrast, optical the lab until five years ago. The closest tracold gas, the speed of the atoms is bowls use electric forces, which have model we had was the cloud of elec- known with unusual precision: It is the advantage that they can corral any close to zero. Therefore the atoms get kind of atom, whereas magnetic traps smeared out into blobs that are tens of work only for certain types. John E. Thomas was recently named Fritz London Distinguished Professor of Physics at Duke Uni- thousands of times larger than a normal In the simplest case, an optical bowl versity and is a Fellow of the American Physical room- atom. This blurring consists of an intense laser beam that is Society. He received his doctorate from the Massa- is no problem for a Bose-Einstein con- tightly focused into a high-vacuum re- chusetts Institute of Technology in 1979. His pri- densate, because it is made of “sociable” gion. The light draws cold atoms or mary area of research is quantum optics, and his atoms called , which like to over- molecules toward its focal point and research team was the first, in 2001, to achieve all- lap. But degenerate Fermi gases are confines them in a frictionless, heat- optical trapping of degenerate Fermi gases. made from solitary atoms called fermi- free environment, which is ideal for Michael E. Gehm received his Ph.D. in physics in ons (like the lithium in our trap), which studies of fundamental phenomena. 2003, working in Thomas’s research group on Fer- according to Pauli’s exclusion principle Why would a focused beam of light mi gases. He is currently a postdoctoral fellow at cannot share space with their neighbors. attract atoms? The secret is that light is the Duke University Fitzpatrick Center for Pho- tonic and Communications Systems and at Duke’s As a result, making a degenerate Fermi an electromagnetic wave, consisting of Department of Electrical and Computer Engineer- gas is a lot like trying to pack balloons oscillating electric and magnetic fields. ing. Address for Thomas: Duke University De- into a closet. The electric field in a light beam exerts partment of Physics, Box 90305, Durham, NC Recently our group was able to a force on charged particles, such as the 27708-0305. Internet: [email protected] probe the quantum behavior of these electrons and inside an atom. © 2004 Sigma Xi, The Scientific Research Society. Reproduction 238 American Scientist, Volume 92 with permission only. Contact [email protected]. Figure 1. Experiments with ultracold Fermi gases help to illuminate the physics of various extreme systems, including the interior of neutron stars, such as the one left over from the supernova explosion that created the Crab Nebula (above). Neutron stars are prevented from collapsing into black holes by virtue of “Fermi ,” a consequence of the Pauli exclusion principle of quantum physics. (Image courtesy of the Eu- ropean Southern Observatory.)

An atom, however, has an equal num- the beam, a positively charged nucleus attraction that is slightly stronger than ber of electrons and protons, and thus in an atom below the beam will be the repulsion the cloud feels, is electrically neutral. A force nonethe- pulled upward, and the negatively and so there is a net upward force on less arises, for a somewhat subtle rea- charged electron cloud will be pushed the atom. If the situation were reversed, son: the field gradient. downward. The nucleus, being closer with the electric field pointing away If, for example, the electric field to the focus of the beam where the elec- from the beam, the nucleus would points upward and toward the focus of tric field is larger, then experiences an move farther away, and the electron © 2004 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2004 May–June 239 should be able to turn off the molasses after loading, and retain the atoms in the optical bowl for a very long time. Or so the theory goes. In practice, optical bowls did not work as expected until the late ‘90s, when our group fig- ured out what had been vexing them. The problem was that the atoms in an optical bowl slosh back and forth at a certain characteristic frequency: in our experiments, 6,600 times per second in the short direction and 230 times per second in the long direction. (The sec- ond frequency is lower because the at- traction to the center of the optical bowl is weaker in the axial direction.) The lasers then in use were not steady, and in particular they had an intensity Figure 2. Trapping neutral atoms in a cold, rarefied gas (orange cloud) can be accomplished using fluctuation at twice the frequency of an “optical bowl,” an intense laser (blue) that draws the atoms into the focus of the beam. The os- the atoms in the trap. cillating electric field of the laser causes the positively charged nucleus and the negatively To see the problem this causes, charged electrons of each atom to become slightly separated. Because the electric field (black ar- imagine an atom oscillating from side rows) is greatest near the focus, the force on the positive side of an atom is not completely bal- anced by the opposing force on the negative side. Below the beam, for example, the upward force to side, with the walls of the bowl vi- exerted on the top of an atom slightly exceeds the downward force on the bottom. Similarly, brating in and out. The atom gets a above the beam the downward force exerted on the bottom of an atom exceeds the upward push from the inward-moving side of force on the top. Thus in either case a net force arises (purple arrows), pulling the atoms inward. the bowl. By the time this atom reaches the other side (after one half of its peri- cloud would move closer. The net force is the second part of our three-step pro- od of oscillation), it encounters the op- would once again be toward the focus. tocol. First, we cool several hundred posite wall of the bowl, which by this For reasons that are too complicated to million lithium atoms down to about time is again moving inward. So the explain here, the same phenomenon 150 millionths of a degree above ab- atom gets a push from that side. Over holds for atoms on the axis of the beam, solute zero, using a now-standard strat- and over the sides of the bowl keep but located in front of or behind the fo- egy called a magneto-optical trap. shoving the atom back and forth, cus. Thus, whichever direction the elec- This device uses six red laser beams, pumping it right out of the bowl in a tric field points, the atom always gets arranged in three orthogonal pairs. few seconds. pulled gently inward. Each of the pairs of beams slows the We overcame this problem in 1999 The key word here is “gently.” At lithium atoms in a single direction by using a custom-built laser designed to room temperature, or even well below, cleverly exploiting the Doppler effect. operate without jittering so much in in- the random thermal movements of an From the perspective of a moving tensity. With it, we succeeded in trap- atom will always overcome the feeble atom, the laser beam that propagates ping atoms for five minutes, hundreds tug of the laser. Therefore, to capture in the opposite direction seems to shift of times longer than with previous op- atoms in an optical bowl, one has to to a higher frequency, and the atom tical bowls. Since then, we have re- use a very intense laser and make the will see this as an increased “head- placed that laser with a more power- atoms very cold, so they do not move wind.” At the same time, the laser ful and extremely stable commercial too rapidly. The carbon dioxide laser in beam that travels in the same direction unit, and we can now keep the atoms our experiments has an intensity at its as the atom will shift to a lower fre- contained for almost seven minutes. focal point of 2 million watts per quency and create a reduced “tail- After we confine the atoms in the square centimeter, more than enough wind.” Because the effect increases bowl, they are still not cold enough for to cut through steel. Even at this inten- with the velocity of the atom, one can quantum effects to take over. For that, sity, the optical bowl is only deep think of the laser light as exerting a vis- they need to be chilled even more us- enough to confine an atom whose ini- cous force. This is why one of the in- ing the third and final step, called tial temperature is less than a thou- ventors of the magneto-optical trap, evaporative cooling. There is nothing sandth of a degree above absolute zero. the Nobel laureate Steven Chu of Stan- fancy about this stage; it is inspired by (Technically, individual atoms do not ford University, coined the very appro- the way a hot bowl of soup cools. have a temperature per se. However, priate nickname optical molasses. When two atoms collide, occasionally it’s easy enough to convert the kinetic Without the “molasses,” an atom they can pool their energy, and one of energy of an atom to a temperature passing into our optical bowl would them can gain enough oomph to es- equivalent, and this operation tells you shoot right out again, like a marble cape the trap or “evaporate.” The other how cold a gas must be to stay in the dropped into a teacup from a consider- one slows down. It then hits the other optical bowl.) able height. Having a magneto-optical atoms in the trap, cooling them, and Because the atoms have to be very trap is like filling the cup with honey the process continues. Eventually the cold already for us to capture them with first—the marble comes nearly to rest atoms get so cold that even two of a laser beam, setting up the optical bowl at the bottom of the bowl. Thus, we them together do not have enough en- © 2004 Sigma Xi, The Scientific Research Society. Reproduction 240 American Scientist, Volume 92 with permission only. Contact [email protected]. ergy for one of them to leave. At this point no more evaporation can take place, and the cooling stagnates. To overcome this problem, we slowly lower the intensity of the trapping laser beam—in effect, lowering the “lip” of the optical bowl—so that some of the warmer atoms can escape. We lose about two-thirds of the atoms in this way, but the remaining ones be- come cold enough to form a degener- ate Fermi gas.

Quantum Effects According to quantum mechanics, all matter exhibits both particle-like and wavelike properties. When a particle, such as an electron or even a whole atom, is considered as a wave, it is said to have a “de Broglie wavelength,” which determines the effective “size” of the particle. The de Broglie wave- length varies inversely with momen- tum. Increasing the , as in a particle accelerator, makes the wave- length of the particle very small. (This is why physicists use accelerators to probe very tiny features within an atom—such as its electrons, protons and .) When the momentum is very small, as in our optical trap, the atom spreads out like a balloon. At these extremely low temperatures, the balloon is about a micrometer in diam-

Figure 3. Formation and study of a degenerate Fermi gas begins with a cloud of lithium atoms, which are slowed by the six inward- directed laser beams of a magneto-optical trap (red at top), a device that is said to create an “optical molasses.” (The ringlike arrows indi- cate the flow of current in an adjacent pair of coils, which generates a magnetic field.) Once these atoms are cooled to 150 millionths of a degree above absolute zero, they can be con- fined in the “optical bowl” created by a single focused laser beam (blue). Because the restor- ing force perpendicular to the beam is greater than along the beam, the bowl produces a cig- ar-shaped cloud of atoms (center). Gradually decreasing the intensity of this beam allows some of the atoms to escape, cooling those that remain, which eventually reach 50 bil- lionths of a degree above zero. At this tem- perature the gas becomes degenerate, a highly organized state that acts somewhat like a sin- gle “mega-atom.” The authors study this phe- nomenon by turning off the laser that forms the optical bowl, allowing the cloud to ex- pand. They obtain a sequence of pictures of the evolving cloud using short pulses of laser light (yellow at bottom), which pass through the gas before being projected onto an imag- ing device (green). The behavior of the cloud as it expands preserves a “memory” of its time as a degenerate Fermi gas. © 2004 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2004 May–June 241 eter—a length that is large enough to bosons resolve with a good microscope. When the de Broglie wavelength gets large enough, the balloons start to touch one another and then try to over- lap. At that point, the gas is called “de- generate,” and its behavior starts to be energy energy governed by quantum rules rather Fermi than the rules of classical physics. energy Yin and Yang Since the 1930s, physicists have real- ized that quantum particles fall into tk tk tk extent oftk motion extent of motion two categories: bosons and fermions. Identical bosons are gregarious parti- Figure 4. All atoms in a Bose-Einstein condensate attain the same energy level, the lowest one cles, preferring to occupy the same en- available (left), whereas only two atoms (with opposite nuclear ) can share one energy lev- ergy states as their neighbors. Photons el in a degenerate Fermi gas (right). As a result, the atoms in such a gas occupy a series of in- (particles of light) behave this way, for creasing energy levels, up to a level that corresponds to the Fermi temperature of the gas. The example in lasers, where photons of a higher the energy level of an atom, the broader its oscillatory motion within the trap. certain energy stimulate atoms to re- lease more photons of the same energy. The particles that make up ordinary 4,000 — matter—protons, neutrons and elec- trons—are fermions, and they behave quite differently. As the physicists En- 2,000 — rico Fermi and P. A. M. Dirac discov- ered, these particles are introverts. Two fermions with the same “spin” cannot be at the same energy level and occupy 0 — the same region of space. (The spin of a particle has to do with the way it lines up in a magnetic field. It comes in two –2,000 — varieties: spin up and spin down.) This behavior, too, has major consequences

scattering length (units of Bohr radii) in everyday life. It explains the period- –4,000 — ic table. The second row of the periodic table, for instance, has eight elements — — — — — — — — — because the second electron shell has 0 20 40 60 80 100 120 140 slots for eight electrons. Two electrons can never share the same slot, because they are fermions. molecules strong free atoms Larger composite particles, such as stable interactions stable atoms or molecules, act like fermions if they are made of an odd number of fermions, and like bosons if they are made up of an even number. Thus lithium-6, with 3 protons, 3 neutrons molecule and 3 electrons, is a composite ,

energy whereas lithium-7, with one more neu- tron, is a composite . At ordinary free atoms temperatures the two isotopes have identical chemical properties, but at su- percold temperatures, their different 85 quantum personalities emerge. magnetic field (millitesla) When a gas of composite bosons, say one made up of lithium-7, is chilled in Figure 5. Feshbach resonance changes the behavior of a degenerate Fermi gas. This phenomenon an optical bowl, a sudden transition oc- causes the distance at which the atoms influence one another—their “scattering length”—to in- curs at the onset of degeneracy (the crease dramatically when a magnetic field of a particular strength is applied (top). (A positive scattering length corresponds to repulsion; negative to attraction.) In the case of 6Li atoms, Fesh- “transition temperature”). Suddenly bach resonance takes place at 85 millitesla. In a weaker magnetic field, a molecule has a lower en- the gas changes from a classical one, ergy than a pair of free atoms. In a stronger field, free atoms are energetically favored (bottom). with the atoms in various energy states, Near resonance, free atoms and those bound in a molecule act similarly, which accounts for the to one in which they all have the same substantially increased scattering length, or what physicists call “strong interactions.” energy—the least that the container al- © 2004 Sigma Xi, The Scientific Research Society. Reproduction 242 American Scientist, Volume 92 with permission only. Contact [email protected]. lows. That is, all of the atoms oscillate expansion of an ordinary gas expansion of a strongly interacting gas with the lowest energy and the longest wavelength possible. They vibrate in unison, like a single mega-atom. This is a Bose-Einstein condensate. When a gas of composite fermions, say one made up of lithium-6, is cooled to the transition temperature (called the “Fermi temperature” for compressed expanded compressed expanded fermions), a different transition takes place: The atoms begin to arrange Figure 6. Strongly interacting Fermi gases behave very differently from normal gases when themselves in an orderly fashion, two they expand. In an ordinary gas, the atoms interact very rarely after they are released from a compressed state. In the Fermi gas, the atoms oscillate inside “quantum balloons,” which ex- in the lowest energy state allowed, two pand along with the atomic spacing. Therefore the atoms continue to exert Fermi pressure on in the next lowest, and so on—just as one another, an interaction that operates over comparatively large distances. the electrons in a regular atom do. The result is a degenerate Fermi gas, which fected very much by its neighbors. This Fermi gas really contains two popula- might be thought of as a different kind is not the case in a strongly interacting tions of fermions, some with spin up of mega-atom. degenerate Fermi gas, where the atoms and others with spin down. The prohi- Soon after Cornell and Wieman cre- jostle against one another and exist in a bition on sharing the same space does ated the first Bose-Einstein condensate, more or less constant state of collision. not apply to two fermions with oppo- investigators began trying to produce “Collision” is perhaps too violent a site spin. Normally lithium-6 atoms the first degenerate Fermi gas of atoms. word for this kind of behavior, so with opposite spin barely notice each (Recall that degenerate Fermi gases quantum physicists usually employ other, and so their scattering length is made of electrons already existed, in the more neutral term “interaction.” near zero. any metallic conductor.) In 1999, Debo- But one should not confuse these very When we turn on a magnetic field, it rah Jin of the University of Colorado long-distance interactions with classi- changes the internal magnetic energy succeeded with potassium-40, using a cal forces. An interaction arises when of an atom, which behaves like a bar modified version of Cornell and Wie- two particles literally try to share the magnet. When the total energy of an man’s magnetic trapping techniques. same real estate and either do it ami- opposite-spin pair of atoms matches Unfortunately, Jin’s method does not cably (as in the case of bosons) or that of a two-atom molecule, they can apply to all atoms, and it took other fight over it (as in the case of fermi- interact very strongly. In a sense, the groups a longer time to develop more ons). The distance at which the parti- magnetic field fools the atoms into general techniques. In 2001 Randy cles first start to “notice” one another thinking they are in a molecule. The Hulet’s group at Rice University, is called the scattering length, and an phenomenon is called a “Feshbach res- Christophe Salomon’s at École normale interaction is said to be strong if it has onance,” after the late MIT physicist supérieure, and Ketterle’s at MIT a large scattering length. In recent Herman Feshbach, who first predicted achieved success using magnetically years, several groups have demon- it. When the magnetic field is tuned trapped bosons to cool fermions con- strated the possibility of changing the correctly, the atoms can notice each tained in the same trap. Hulet and Sa- scattering length—making it as large other at what is, in atomic terms, an in- lomon showed that fermionic lithium-6 as desired, and even changing it from credibly long distance. gas occupies a much larger volume attractive to repulsive—by applying How long, exactly? One limitation is than bosonic lithium-7. This difference a magnetic field. the de Broglie wavelength; if two makes sense, because the fermions are Why does this work? To begin with, atoms are farther apart than the de forced to adopt many different energy we should explain that our degenerate Broglie wavelength, they will be obliv- levels—and some thus must move in orbits of large radius, whereas the bosons all crowd into the lowest energy state and have a small radius of motion. At the same time, our group at Duke also managed to produce degen- erate Fermi gases colder than one- tenth of the Fermi temperature, using all-optical cooling methods. These highly degenerate Fermi gases are quite stable, and they exhibit spectacu- lar properties when we introduce the trapped cloud release anisotropic expansion “strong interactions” that we men- tioned in the introduction. Figure 7. Theory predicts that strongly interacting Fermi gases should expand anisotropically after release from an optical trap. Because pressure falls off most abruptly radially outward The Magic of Strong Interactions from the axis of the elongate cloud, the gas expands more rapidly in this direction than along In an ordinary gas, collisions between the axis (black arrows). The gas thus changes shape over time, shifting from cigar (left) to atoms are quite rare and short-lived, bulging pumpkin (right). The presence or absence of such shape-changing expansion can and hence any particular atom is not af- serve as a litmus test for strong interactions—and perhaps for . © 2004 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2004 May–June 243 100 200 400 600 800 1,000 1,500 2,000 microseconds microseconds microseconds microseconds microseconds microseconds microseconds microseconds

400 microseconds

400 microseconds 1,000

1,000 2,000 atom density atom density 2,000

–200 –100 0 100 200 300 –200 –100 0 100 200 transverse coordinate (micrometers) axial coordinate (micrometers)

Figure 8. Experimental data confirm the anisotropic expansion of a cloud of 6Li atoms. Sequential images capture the change in shape and den- sity of the gas cloud as it warms. The gas remains degenerate, and strongly interacting, for about 400 microseconds after release (shown in the first three frames). After 400 microseconds, the high initial velocity of the atoms causes the cloud to continue changing shape in the same man- ner, although the atoms are no longer strongly interacting. Quantitative measurements derived from these images show that the atoms spread out much more rapidly transverse to the axis of the cloud (left graph) than along it (right graph). ious of each other for sure, like two bal- it. That is, the pressure gradient deter- theories of quark matter or neutron loons that pass by each other. So in any mines the outward force, which is stars. Indeed, the remarkable shape- Fermi gas, the scattering length can be largest in the narrow directions of the shifting behavior we observe is similar no larger than the de Broglie wave- cigar. In an ordinary gas, the atoms to the dynamical behavior predicted re- length, which in turn can be no bigger would soon stop pressing against one cently for a quark-gluon . than the spacing between particles (be- another as they escaped. But in our As another example, we have done cause otherwise some of the same-spin strongly interacting Fermi gas, the experiments to determine the “net in- fermions would overlap). atoms themselves (really their quantum teraction energy” in a strongly interact- But at supercold temperatures, the de “balloons”) keep expanding to match ing Fermi gas, which is simply the total Broglie wavelength grows until it the spacing between them, and the energy of attraction or repulsion of a matches the spacing between atoms. pressure gradient does not go away for given particle to all other particles near Also, when the magnetic field is suitably a long time. The metamorphosis contin- enough to interact with it. In a universal arranged, the Feshbach resonance ues even after the gas stops interacting, system, one can show that this quantity makes the scattering length increase to because the radial velocity of the atoms is proportional to the average kinetic en- its maximum possible value: the de- continues to be greater than the axial ve- ergy of the constituent particles. Broglie wavelength. So when we com- locity as the atoms coast freely. Then, The constant of proportionality, de- bine cold temperature with a precisely the cloud continues to expand much noted beta, has important conse- tuned magnetic field, the scattering more rapidly in the radial direction than quences for the mechanical stability of length, the de Broglie wavelength and it does lengthwise, so it visibly changes such a system. The kinetic energy gives the interparticle spacing are all the same. shape, from a “cigar” to a “pancake.” rise to an effective repulsion between Our group was the first to observe a With the strong interactions, degen- the interacting fermions, which is remarkable thing that happens when erate Fermi gases also exhibit what known as the Fermi pressure. This you prepare such a gas and then re- physicists call universal behavior, becom- pressure tends to keep fermions apart move the container by turning off the ing a model for many other natural and is responsible for the stability of optical bowl. Initially, the trapped atom- physical systems. In other words, any neutron stars against gravitational col- ic gas has the shape of the optical strongly interacting Fermi system (any lapse and for the mechanical stability bowl—a long, narrow cigar. When the system in which scattering length of our trapped gas. However, the net atoms are released, the atomic gas ex- equals interparticle spacing) should act interaction energy also provides a pres- pands rapidly in the narrow (radial) di- in like ways. It does not matter whether sure, which can be inward or outward, rection of the cigar, while standing near- the fermions are atoms, electrons, depending on the sign of the propor- ly still in the long (axial) direction! This quarks or something else. The way tionality constant. If beta were less than is a consequence of the pressure forces these systems interact in bulk will al- –1, the inward pressure due to the in- on the gas: Each small part of the gas is ways be similar. That is why the degen- teraction energy would exceed the out- pushed out by the pressure behind it erate Fermi gas in our laboratory can ward Fermi pressure, and the system and inward by the pressure in front of become a table-top tool to test the latest would collapse. © 2004 Sigma Xi, The Scientific Research Society. Reproduction 244 American Scientist, Volume 92 with permission only. Contact [email protected]. Nuclear physicists have struggled for may help in that quest. Physicists have tures comparable to the Fermi tem- thirty years to compute beta. That task known since the 1950s that conductors perature. But if the scale model does is extremely difficult because the re- become superconducting when oppo- work—if Cooper pairs can exist at a quired calculations involve the interac- site-spin electrons pair up and start large fraction of the Fermi tempera- tion of many particles. The best estimate flowing together through the atomic ture—then the same thing might be obtained from theory is about –0.5. That lattice. Similarly, a fermionic , possible in a conductor: It is conceiv- is, the net interaction energy should ex- such as helium-3, becomes a superfluid able that scientists might one day ert an inward force that is only half the when its atoms pair up in the same fashion materials that superconduct strength of the outward Fermi pressure, way. These loose associations, which all the way up to 2,000 degrees or which is consistent with the obvious are not as permanent as molecular more—not just room temperature but fact that neutron stars are stable. Need- bonds, are known as Cooper pairs. a good deal warmer. less to say, one can’t just grab of piece of For all known superconductors, It may be too much to dream of such a and check out whether Cooper pairs become stable only at a an ultrahigh-temperature supercon- this value is exactly –0.5. But now we temperature vastly below the Fermi ductor happening anytime soon. But have measured beta in our laboratory, temperature—roughly 10 to 100 de- we can hope at least that the insights and Salomon and Rudolf Grimm of the grees above absolute zero, or one- gleaned from recent work on degener- University of Innsbruck have since hundredth to one-thousandth of the ate Fermi gases will lead to an era of made similar measurements. Fermi temperature. (The Fermi tem- new super-high-temperature super- From our first experiments, we have perature of a metal—construed as a de- conducting materials. estimated that beta is about –0.26. Re- generate Fermi gas—is extremely high cently, Salomon obtained –0.3 at a because it contains so many electrons, Bibliography somewhat higher temperature, and or fermions. Thus every energy level is Andrews, M. R., C. G. Townsend, H.-J. Mies- Grimm obtained values closer to –0.5. It occupied up to a very high energy. The ner, D. S. Durfee, D. M. Kurn and W. Ketter- is too early to pronounce a definite ver- most energetic electrons, the ones in le. 1997. Observation of interference be- tween two Bose condensates. Science dict, as both the experimental and theo- the conduction band, have an equiva- 275:637–641. retical estimates may still have system- lent temperature of 10,000 degrees.) Collins, G. P. 2003. The next big chill. Scientific atic errors. What is encouraging is that Recently, three theoretical groups American (October) 289(4):26–28. the values are reasonably close—close have predicted that strongly interact- DeMarco, B., and D. S. Jin. 1999. Onset of Fermi enough anyway that experimentalists ing Fermi gases can become superflu- degeneracy in a trapped atomic gas. Science and theorists will have something to ids at temperatures up to half of the 285:1703–1706. talk about over the next few years. Fermi temperature. If the theory is cor- Granade, S. R., M. E. Gehm, K. M. O’Hara and J. E. Thomas. 2002. All-optical production rect, such systems will produce the of a degenerate Fermi gas. Physical Review The Quest for Superfluidity highest-temperature Cooper pairs Letters 88:120405. Sandro Stringari, a theorist at the Uni- known to physics (highest tempera- Grimm, R., M. Weidemüller and Y. B. Ovchin- versity of Trento in Italy, first predicted ture as a fraction of the Fermi temper- nikov. 2000. Optical dipole traps for neutral the “shape-changing” behavior in ature, that is). Several groups, includ- atoms. Advances in Atomic, Molecular & Op- 2002, before anyone had managed to ing ours, have now produced such tical Physics 42:95–165. produce a strongly interacting degen- gases at temperatures well below one- Ketterle, W., D. S. Durfee and D. M. Stamper- Kurn. 1999. Making, probing and under- erate Fermi gas. He argued, further, tenth of the Fermi temperature, so a standing Bose-Einstein condensates. In Bose- that the shape-changing was a possi- high-temperature superfluid may al- Einstein Condensation in Atomic Gases, ed. M. ble signature of superfluidity. ready have been created. However, Inguscio, S. Stringari and C. E. Wieman. Superfluids, which were first discov- unambiguous proof of its existence Amsterdam: IOP Press, pp. 67–176. ered in the 1930s, are substances that flow has so far eluded all experiments. O’Hara, K. M., S. R. Granade, M. E. Gehm, T. without friction. The atoms in superfluids Perhaps it seems like cheating to A. Savard, S. Bali, C. Freed and J. E. Thomas. 1999. Ultrastable CO2 laser trap- act like the electrons in superconductive call a gas a “high-temperature” super- ping of lithium fermions. Physical Review materials, which flow with zero resis- fluid when its actual temperature is Letters 82:4204–4207. tance. In principle, superconducting less than a millionth of a degree above O’Hara, K. M., S. L. Hemmer, M. E. Gehm, S. wires can be harnessed for all sorts of absolute zero. To understand why not, R. Granade and J. E. Thomas. 2002. Obser- useful purposes, for example, to transmit consider this analogy. The develop- vation of a strongly interacting degenerate Fermi gas of atoms. Science 298:2179–2182. electricity long distances without any en- ment of a new airplane proceeds from Truscott, A. G., K. E. Strecker, W. I. McAlexan- ergy loss. In practice, though, ordinary sketches on paper to scale models to a der, G. B. Partridge and R. G. Hulet. 2001. superconductors only operate at temper- working prototype. In our case, the Observation of Fermi pressure in a gas of atures a few degrees above absolute zero. “paper sketch” is the concept of a uni- trapped atoms. Science 291:2570–2572. Even the so-called “high-temperature” versal Fermi system. The “scale mod- superconductors, discovered since the el” is a strongly interacting degenerate 1980s, have to be chilled to liquid- Fermi gas. It is scaled down both in nitrogen temperatures. It is no exaggera- physical size and in temperature. The For relevant Web links, consult this tion to say that the search for a room-tem- universality principle means that this issue of American Scientist Online: perature superconductor is a holy grail of scaling should not fundamentally http://www.americanscientist.org/ condensed-matter physics. change the properties of the system. If IssueTOC/issue/601 To the extent that the atoms in a su- the scale model did not work, we perfluid imitate the electrons in a su- would have reason to suspect that perconductor, degenerate Fermi gases Cooper pairs cannot form at tempera- © 2004 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2004 May–June 245