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Science-2013-Carr-42-3.Pdf PERSPECTIVES PHYSICS A cloud of potassium atoms is tuned Negative Temperatures? to negative temperatures via a quantum phase transition. Lincoln D. Carr ltracold quantum gases present an A Positive temperature E Negative temperature exquisitely tunable quantum sys- ) Schematic experimental distribution ) tem. Applications include preci- E E ( ( U P P sion measurement ( 1), quantum simulations One-parameter thermal fit for advanced materials design ( 2), and new regimes of chemistry ( 3). Typically trapped k T k T B > 0 B < 0 in a combination of magnetic fi elds and laser Probability Probability beams, strongly isolated from the environ- E Low energy min E High energy max ment in an ultrahigh vacuum, and cooled to Energy E Energy E temperatures less than a microdegree above absolute zero, they are the coldest known B Repulsive superfluid C Mott insulator D Attractive superfluid material in the universe. The interactions Low energy, positive pressure Low energy, incompressible High energy, negative pressure between atoms in the gas can be tuned over Trap seven orders of magnitude and from repul- Low energy sive to attractive ( 4). The addition of stand- ing waves made from interfering lasers at optical wavelengths gives rise to an optical lattice, a crystal of light, periodic just like on February 10, 2013 the usual crystals made of matter. On page 52 of this issue, Braun et al. ( 5) use these special features of ultracold quantum gases to produce a thermodynamic oddity—nega- High energy tive temperature. Anti-trap Temperature is casually associated with hot and cold. How can something be “colder” Quantum phase transition Atoms Trap flipped to anti-trap, interactions Superfluid amplitude than absolute zero? The answer lies in a more Superfluid amplitude Optical lattice from repulsive to attractive envelope precise notion of temperature. Temperature is Less than zero. (A) Temperature is a one-parameter fi t: As the energy gets large, the probability that an atom www.sciencemag.org a single-parameter curve fi t to a probability will have that energy falls away exponentially. A quantum phase transition from a repulsive superfl uid (B) to distribution. Given a large number of parti- a Mott insulator (C) provides a bridge to an attractive superfl uid (D), resulting in negative pressure balanced cles, we can say each of them has a probabil- by negative temperature (E). ity to have some energy, P(E). Most will be in low-energy states and a few in higher-energy upper bound to kinetic energy via the forma- Braun et al. fi rst make their atoms repulsive states. This probability distribution can be fi t tion of a band gap, a sort of energetic barrier in a superfl uid phase. They tune them to a very well with an exponential falling away to to higher-energy states. The potential energy Mott insulating phase by simply turning up Downloaded from zero. Of course, the actual distribution may was made negative by the clever use of an the intensity of the optical lattice lasers, mak- be very noisy, but an exponential fi t is still anti-trap on top of the lattice, taking the shape ing the lattice deeper. Then they tune the inte- a good approximation (see the fi gure, panel of an upside-down parabola. Finally, the reactions to be attractive and at the same time A). Negative temperature means most parti- interactions were tuned to be attractive (neg- turn their trap upside down to be an anti-trap. cles are in a high-energy state, with a few in a ative). Thus, all three energies had an upper Finally, they melt the Mott insulator to obtain low-energy state, so that the exponential rises bound and, in principle, the atoms could pile an attractive superfl uid. These anti-traps have instead of falls (see the fi gure, panel E). up in high-energy states. been used before, to create a self-propagat- To create negative temperature, Braun et Braun et al. convinced their gas to undergo ing pulse of atoms that does not disperse (a al. had to produce an upper bound in energy, such a strange inversion using a quantum bright soliton) from attractive gases in one so particles could pile up in high-energy rather phase transition ( 6), an extension of the well- dimension ( 7, 8). However, attractive quan- than low-energy states. In their experiment, known thermodynamic concept of phase tran- tum gases in two and three dimensions can there are three important kinds of energy: sitions to a regime in which the temperature implode, rather spectacularly ( 9). This ten- kinetic energy, or the energy of motion in the is so low that it plays no role in the change dency to implode is called negative pressure. optical lattice; potential energy, due to mag- of phase. In this case, they worked with two The negative temperature is precisely what netic fi elds trapping the gas; and interaction phases, superfl uid and Mott insulator. In a stabilizes the gas against negative pressure energy, due to interactions between the atoms superfl uid, the gas fl ows freely without vis- and implosion; the Mott insulator serves as in their gas. The lattice naturally gives an cosity and is coherent, like a laser, but made a bridge state between positive temperature of matter instead of light. In a Mott insula- and pressure, and negative temperature and Department of Physics, Colorado School of Mines, Boulder, tor, the atoms freeze into a regular pattern and pressure (see the fi gure, panels B to D). CO 80401, USA. E-mail: [email protected] become incompressible, similar to a solid. Braun et al.’s exploration of negative 42 4 JANUARY 2013 VOL 339 SCIENCE www.sciencemag.org Published by AAAS PERSPECTIVES temperature is part of a general theme of quantum mechanics. It is now believed that 3. L. D. Carr, D. Demille, R. Krems, J. Ye, New J. Phys. 11, pushing the limits of thermodynamics and a whole new concept is needed to deal with 055049 (2009). 4. S. E. Pollack et al., Phys. Rev. Lett. 102, 090402 (2009). quantum mechanics with ultracold quan- near-integrable quantum systems, casually 5. S. Braun et al., Science 339, 52 (2013). tum gases. Quantum phase transitions have called prethermalization, in which physical 6. L. D. Carr, Ed., Understanding Quantum Phase Transi- been explored intimately in these systems quantities after relaxation are described by tions (Taylor and Francis, New York, 2010). 7. L. D. Carr, Y. Castin, Phys. Rev. A 66, 063602 (2002). ( 2, 10). There is a special class of dynami- the fancy name “generalized Gibbs ensem- 8. L. Khaykovich et al., Science 296, 1290 (2002). cal systems, called integrable, that never ble” ( 12– 15). 9. E. A. Donley et al., Nature 412, 295 (2001). truly develop a temperature because their Thermodynamics is at the heart of chem- 10. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, I. Bloch, properties are different from those of a sys- istry, engineering, and many biological ques- Nature 415, 39 (2002). 11. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: tem in equilibrium with a thermal environ- tions. In ultracold quantum gases, the basic An Introduction (Wiley, New York, 1989). ment. Classically, integrability is opposed concepts of thermodynamics, positive or neg- 12. M. Rigol, V. Dunjko, V. Yurovsky, M. Olshanii, Phys. Rev. to chaos; chaotic dynamical systems ther- ative temperature, or whether a temperature Lett. 98, 050405 (2007). 13. A. C. Cassidy, C. W. Clark, M. Rigol, Phys. Rev. Lett. 106, malize and become thermodynamic. The concept is even relevant, are under intense 140405 (2011). borderline between integrability and chaos and profound exploration. 14. P. Calabrese, F. H. Essler, M. Fagotti, Phys. Rev. Lett. 106, is described by a famous and beautiful 227203 (2011). theory, called Kolmogorov-Arnold-Moser References 15. M. A. Cazalilla, A. Iucci, M. C. Chung, Phys. Rev. E. 85, 1. J. K. Stockton, K. Takase, M. A. Kasevich, Phys. Rev. Lett. 011133 (2012). (KAM) theory ( 11). To date, we do not 107, 133001 (2011). know whether there is a KAM theory for 2. M. Lewenstein et al., Adv. Phys. 56, 243 (2007). 10.1126/science.1232558 CHEMISTRY Metalloenzyme-like catalytic systems Bioinspired Oxidation Catalysts oxidize amines to imines under environmentally friendly conditions. on February 10, 2013 Martine Largeron and Maurice-Bernard Fleury mines are key intermediates in the synthe- that are rapidly dehydrogenated to nitriles simple copper/TEMPO (2,2,6,6-tetramethyl- sis of fi ne chemicals and numerous bio- (RC≡N) ( 5). Green processes have also been 1-piperidinyloxyl) system catalyzes the aer- Ilogically active compounds. They have developed that use biocompatible transition- obic oxidation of amines to imines at room traditionally been prepared through conden- metal catalysts, with dioxygen or air as the temperature, but is effi cient only for benzylic sation of amines with carbonyl compounds, sole oxidant. However, most of these methods amines ( 7). but the latter are extremely active and thus have limitations. For example, a solvent-free Naturally occurring metalloenzymes have difficult to handle. A powerful alternative copper-catalyzed synthesis of imines from long been recognized as attractive catalysts www.sciencemag.org strategy involves coupling primary alcohols primary amines uses air as a benign oxidant for aerobic oxidations because they can oper- and amines through catalytic alcohol activa- but requires high reaction temperatures ( 6). A ate under mild conditions with complete che- tion by temporary oxidation to an aldehyde ( 1). However, with few exceptions ( 2), these Copper amine oxidases Biomimetic catalytic systems aerobic oxidative reactions require high reac- H N R H N R tion temperatures and catalysts that contain 2 2 expensive and rare metals.
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