RESEARCH NEWS & VIEWS
1. Morton, D. C. et al. Nature 506, 221–224 (2014). 2. Huete, A. R. et al. Geophys. Res. Lett. 33, L06405 (2006). 3. Myneni, R. B. et al. Proc. Natl Acad. Sci. USA 104, 4820–4823 (2007). 4. Saleska, S. R., Didan, K., Huete, A. R. & da Rocha, H. R. Science 318, 612 (2007). 5. Samanta, A. et al. Geophys. Res. Lett. 37, L05401 (2010). 6. Samanta, A., Ganguly, S., Vermote, E., Nemani, R. R.
& Myneni, R. B. Environ. Res. Lett. 7, 024018 (2012). 7. Phillips, O. L. et al. Science 323, 1344–1347 (2009). 8. Koren, I., Kaufman, Y. J., Remer, L. & Martins, J. V. Science 303, 1342–1345 (2004). 9. Heiblum, R. H., Koren, I. & Feingold, G. Atmos. Chem. Phys. Disc. 13, 30013–30037 (2013). 10. Samanta, A., Ganguly, S., Vermote, E., Nemani, R. R. & Myneni, R. B. Earth Interact. 16, 1–14 (2012). 11. Huete, A. R. & Saleska, S. R. in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences Vol. XXXVIII, Part 8, 539–541 (Copernicus, 2010). This article was published online on 5 February 2014.
CONDENSED -MAT TER PHYSI C S
History matters for a stirred superfluid The observation of path dependence in the response of a superfluid to stirring promises potential applications in precision rotation sensing, and provides a test bed for microscopic theories of ultracold atomic gases. See Letter p.200 M AT T H E W J . D AV I S & K R I S T I A N H E L M E R S O N
H
ysteresis is the dependence of a system on not only its present surroundings, but also its history. It has been observed in many branches of science and engineering1, such as in the elasticity of materials, electronic circuits, biological processes, and even in macroeconomics. In many of these systems, hysteresis can be exploited for applications. On page 200 of this issue, Eckel et al.2 at the Joint Quantum Institute in Gaithersburg, Maryland, report the observation of hysteresis in the superfluid flow of an ultracold cloud of atoms known as a Bose–Einstein condensate. This result could prove an important step for developing atomtronic devices, in which atoms have an equivalent role to that of electrons in electronic devices. It could also provide a platform a
for investigating the microscopic origins of hysteresis and of the dissipative dynamics of Bose–Einstein condensates. Perhaps the best-known example of hysteresis is the response of the magnetization of a ferromagnetic material to an applied magnetic field. If the material is initially unmagnetized, slowly turning on a magnetic field will cause the material to become magnetized. However, subsequently reducing the magnetic field back to zero will leave the system with a net magnetization — the system is now in a different state from that in which it started, despite the environment being identical. More generally, systems that exhibit hysteresis consist of many interacting particles, allowing a complex myriad of states. Although the constituent particles and their interactions can be described by equations that are fully b
Stirrer
c
Phase 0
reversible in time, their collective behaviour is not. For example, for a single atom, the direction of its magnetic moment depends only on the applied magnetic field at that instant in time. However, in a ferromagnet, the collective behaviour of the atoms’ magnetic moments, which involves the formation of magnetic domains of uniform magnetization, does not. This hysteretic effect is the basis of modern magnetic-recording media such as hard disks. Superfluidity and superconductivity are macroscopic quantum phenomena that generally arise owing to the presence of a Bose– Einstein condensate (BEC), in which a huge number of identical interacting particles shares the same quantum-mechanical wavefunction. These quantum liquids are ‘super’ because, below a critical velocity, they can flow past obstacles without any friction or resistance3. When a BEC is confined to a toroidal (doughnut-shaped) container, the consequences are particularly interesting. One of the mathematical requirements of the wavefunction, which is characterized by an amplitude and a phase, is that it must be single-valued and continuous, and this means that the total change of a wavefunction’s phase about the doughnut must be an integer multiple of 2π. Quantum mechanics dictates that the speed of the particles in the ring is proportional to the rate of change of the phase about the container, which means that the circulation (the integral of the speed around the ring) of the superfluid is restricted to integer multiples of a constant — the circulation is quantized. Flows with speeds below the critical velocity last indefinitely, and are known as persistent currents3. For many researchers, this is the main feature of superfluidity and superconductivity. The team at the Joint Quantum Institute has been working with BECs in ring-shaped traps for the past few years, and has created and observed the persistence of flows4. The group has studied5 the decay of persistent flows following the introduction to the ring of an obstacle formed by a laser beam, creating a constriction (weak link) that the fluid
2π
1
Superfluid circulation
91400 Orsay, France. e-mails: [email protected]; [email protected]
1→ 0
0→ 1
vc–
vc+
0 Stirrer speed →
Figure 1 | Hysteresis in a stirred superfluid2. a, A dilute-gas superfluid with a constant quantum-mechanical phase is initially held at rest in a ring-shaped trap. An obstacle rotating about the ring is then introduced, creating a constriction and stirring the superfluid. b, Above a critical stirrer speed (vc+), the stirring results in a transition from zero (0) to one (1) unit of circulation (the integral of the speed around the ring) in the superfluid, and the final phase of the system varies continuously from zero to 2π about the loop. Below vc+, the superfluid does not respond to the stirring. c, The transition from 0 to 1 occurs as the stirrer speed increases past vc+. However, on reversing the path, the transition from 1 to 0 takes place at the lower speed vc-. This cyclic path is an idealized example of hysteresis. 1 6 6 | N AT U R E | VO L 5 0 6 | 1 3 F E B R UA RY 2 0 1 4
© 2014 Macmillan Publishers Limited. All rights reserved
NEWS & VIEWS RESEARCH must pass through. More recently, the team has used6 the obstacle as a paddle-like stirrer to induce transitions from a state with no circulation to one with one or more quanta of circulation. In the current study, Eckel and colleagues begin with a superfluid at rest in the ring trap. The researchers turn on a stirrer rotating at constant speed, and leave it in the superfluid for two seconds (Fig. 1a). The stirrer is then withdrawn and the effect it has had on the superfluid is observed. For stirring speeds below a critical value, the authors find that the superfluid is oblivious to the stirring — it remains at rest in a state with no circulation. However, above this critical value, they find that the fluid transitions to a state in which it moves about the ring with one quantum of circulation (Fig. 1b). Next, Eckel et al. run their experiment in reverse: they begin with the superfluid rotating with one quantum of circulation. They stir it over the same range of speeds and directions as before, but because the stirrer is now moving more slowly than the superfluid, they look for transitions to the state in which the superfluid is at rest. Their key observation is that the stirring speed that returns the superfluid to rest can be smaller than the speed required to cause it to circulate in the first place — an example of hysteresis (Fig. 1c). Why is this result interesting? The researchers’ system is an atomtronic device analogous to a radio-frequency superconducting quantum interference device (SQUID) — a superconducting loop with one weak link. SQUIDs can exhibit hysteretic behaviour, and have applications in sensing vanishingly small magnetic fields. Owing to the mathematical analogy between magnetic fields for charged particles and rotation for neutral particles, atomtronic SQUIDs could prove to be exceptional rotation sensors. Although other researchers have demonstrated atomtronic SQUIDs7,8, Eckel et al. are the first to observe hysteresis in such a system. The authors suggest that this effect could play a crucial part in the design and application of atomtronic circuits, as it has in other electronic devices. Whether this is true remains to be seen. The level of control obtained during the experiment is impressive, and the data are remarkably clean. However, for atomtronic devices to prove genuinely useful and move out of the research lab, their reliability and robustness needs to continue to improve. Eckel and colleagues also simulate the stirring of the superfluid using the Gross– Pitaevskii model of BECs, which has proved remarkably adept at predicting the outcome of many experiments on dilute-gas superfluids3. And this is where the authors’ study gets particularly interesting. Although the simulations qualitatively reproduce the hysteretic behaviour, they predict critical stirring speeds that are too large by at least a factor of two.
This provides a real challenge for theorists — what is going wrong with the model? One issue is that the model does not allow for dissipation of energy, which is essential for hysteresis1. However, even adding dissipation to the model hardly changes the predictions. This result could perhaps have been anticipated from theoretical studies9 of an earlier experiment5 performed at the Joint Quantum Institute that found evidence of physics beyond the Gross–Pitaevskii model9 in the decay of persistent currents following the introduction of an obstacle. The team proposes a simple model of the energetics of vortex-pair creation in the presence of the stirrer that agrees rather well with their experimental results. It is up to theorists to try to work out whether this model is correct, and how it emerges from the full microscopic theory of BECs. Finally, hysteresis in real materials is often described by phenomenological models1. The complexity of these multi-particle systems generally precludes a description of hysteresis from first principles. In atomic BECs, in which the microscopic interactions between the atoms are well understood3 and the number of constituent particles is computationally tractable, it may
be possible to go beyond the Gross–Pitaevskii model and discern the ingredients needed to produce hysteresis and further exploit it for technological applications — the past can guide us towards a brighter future. ■ Matthew J. Davis is at the School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia. Kristian Helmerson is at the School of Physics, Monash University, Clayton, Victoria 3800, Australia. e-mail: [email protected] 1. Mayergoyz, I. D. Mathematical Models of Hysteresis and their Applications 2nd edn (Academic, 2003). 2. Eckel, S. et al. Nature 506, 200–203 (2014). 3. Leggett, A. J. Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Univ. Press, 2006). 4. Ryu, C. et al. Phys. Rev. Lett. 99, 260401 (2007). 5. Ramanathan, A. et al. Phys. Rev. Lett. 106, 130401 (2011). 6. Wright, K. C., Blakestad, R. B., Lobb, C. J., Phillips, W. D. & Campbell, G. K. Phys. Rev. Lett. 110, 025302 (2013). 7. Ryu, C., Blackburn, P. W., Blinova, A. A. & Boshier, M. G. Phys. Rev. Lett. 111, 205301 (2013). 8. Sackett, C. A. Nature 505, 166–167 (2014). 9. Mathey, A. C., Clark, C. W. & Mathey, L. Preprint at http://arxiv.org/abs/1207.0501 (2012).
C O N SER VAT I ON
Making marine protected areas work Globally consistent surveys of five factors influencing the success of marine protected areas — age, size, isolation, protection and enforcement — reveal that only when all five are present does nature thrive. See Letter p.216 BENJAMIN S. HALPERN
I
n the past few years, several huge marine protected areas (MPAs) have been created in the Pacific and Indian oceans, totalling more than 1.6 million square kilometres. That might sound like a large area, but even when combined with every other MPA on the planet, still less than around 2% of the world’s oceans are fully protected. In response to this conservation shortfall, coastal nations have committed to increasing the amount of protected area in their territorial waters to at least 10% by 2020. However, even if this target is met, the actual conservation value may be limited because MPAs often exist in name only — they do not truly provide protection. On page 216 of this issue, Edgar et al.1 provide key insights into why so many of the world’s MPAs are failing to meet their full potential and describe a clear path forward for achieving better conservation outcomes. The problems with existing protected areas are manifold. ‘Paper parks’, for which
protected-area boundaries exist in principle but are not enforced, have little conservation value. Unfortunately, there are a lot of paper parks2,3, and many other protected areas are only partially protected — activities such as recreational or hook-and-line fishing are allowed, leading to less conservation value than full protection4. Furthermore, nearly half of all MPAs are little bigger than a football field or have only recently been created5, limiting their ability to protect many species. It might seem as if we know a lot about what leads to MPA success or failure, but the simultaneous assessment of how various factors affect MPA success has been missing from previous studies. In other words, most studies tested one factor at a time, without controlling for the others. This is what makes Edgar and colleagues’ work particularly unusual. Using data from 87 MPAs around the world, all sampled with the same methods, the authors compared how the biomass, abundance and diversity of species in MPAs varied with all
1 3 F E B R UA RY 2 0 1 4 | VO L 5 0 6 | N AT U R E | 1 6 7
© 2014 Macmillan Publishers Limited. All rights reserved
1. Morton, D. C. et al. Nature 506, 221–224 (2014). 2. Huete, A. R. et al. Geophys. Res. Lett. 33, L06405 (2006). 3. Myneni, R. B. et al. Proc. Natl Acad. Sci. USA 104, 4820–4823 (2007). 4. Saleska, S. R., Didan, K., Huete, A. R. & da Rocha, H. R. Science 318, 612 (2007). 5. Samanta, A. et al. Geophys. Res. Lett. 37, L05401 (2010). 6. Samanta, A., Ganguly, S., Vermote, E., Nemani, R. R.
& Myneni, R. B. Environ. Res. Lett. 7, 024018 (2012). 7. Phillips, O. L. et al. Science 323, 1344–1347 (2009). 8. Koren, I., Kaufman, Y. J., Remer, L. & Martins, J. V. Science 303, 1342–1345 (2004). 9. Heiblum, R. H., Koren, I. & Feingold, G. Atmos. Chem. Phys. Disc. 13, 30013–30037 (2013). 10. Samanta, A., Ganguly, S., Vermote, E., Nemani, R. R. & Myneni, R. B. Earth Interact. 16, 1–14 (2012). 11. Huete, A. R. & Saleska, S. R. in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences Vol. XXXVIII, Part 8, 539–541 (Copernicus, 2010). This article was published online on 5 February 2014.
CONDENSED -MAT TER PHYSI C S
History matters for a stirred superfluid The observation of path dependence in the response of a superfluid to stirring promises potential applications in precision rotation sensing, and provides a test bed for microscopic theories of ultracold atomic gases. See Letter p.200 M AT T H E W J . D AV I S & K R I S T I A N H E L M E R S O N
H
ysteresis is the dependence of a system on not only its present surroundings, but also its history. It has been observed in many branches of science and engineering1, such as in the elasticity of materials, electronic circuits, biological processes, and even in macroeconomics. In many of these systems, hysteresis can be exploited for applications. On page 200 of this issue, Eckel et al.2 at the Joint Quantum Institute in Gaithersburg, Maryland, report the observation of hysteresis in the superfluid flow of an ultracold cloud of atoms known as a Bose–Einstein condensate. This result could prove an important step for developing atomtronic devices, in which atoms have an equivalent role to that of electrons in electronic devices. It could also provide a platform a
for investigating the microscopic origins of hysteresis and of the dissipative dynamics of Bose–Einstein condensates. Perhaps the best-known example of hysteresis is the response of the magnetization of a ferromagnetic material to an applied magnetic field. If the material is initially unmagnetized, slowly turning on a magnetic field will cause the material to become magnetized. However, subsequently reducing the magnetic field back to zero will leave the system with a net magnetization — the system is now in a different state from that in which it started, despite the environment being identical. More generally, systems that exhibit hysteresis consist of many interacting particles, allowing a complex myriad of states. Although the constituent particles and their interactions can be described by equations that are fully b
Stirrer
c
Phase 0
reversible in time, their collective behaviour is not. For example, for a single atom, the direction of its magnetic moment depends only on the applied magnetic field at that instant in time. However, in a ferromagnet, the collective behaviour of the atoms’ magnetic moments, which involves the formation of magnetic domains of uniform magnetization, does not. This hysteretic effect is the basis of modern magnetic-recording media such as hard disks. Superfluidity and superconductivity are macroscopic quantum phenomena that generally arise owing to the presence of a Bose– Einstein condensate (BEC), in which a huge number of identical interacting particles shares the same quantum-mechanical wavefunction. These quantum liquids are ‘super’ because, below a critical velocity, they can flow past obstacles without any friction or resistance3. When a BEC is confined to a toroidal (doughnut-shaped) container, the consequences are particularly interesting. One of the mathematical requirements of the wavefunction, which is characterized by an amplitude and a phase, is that it must be single-valued and continuous, and this means that the total change of a wavefunction’s phase about the doughnut must be an integer multiple of 2π. Quantum mechanics dictates that the speed of the particles in the ring is proportional to the rate of change of the phase about the container, which means that the circulation (the integral of the speed around the ring) of the superfluid is restricted to integer multiples of a constant — the circulation is quantized. Flows with speeds below the critical velocity last indefinitely, and are known as persistent currents3. For many researchers, this is the main feature of superfluidity and superconductivity. The team at the Joint Quantum Institute has been working with BECs in ring-shaped traps for the past few years, and has created and observed the persistence of flows4. The group has studied5 the decay of persistent flows following the introduction to the ring of an obstacle formed by a laser beam, creating a constriction (weak link) that the fluid
2π
1
Superfluid circulation
91400 Orsay, France. e-mails: [email protected]; [email protected]
1→ 0
0→ 1
vc–
vc+
0 Stirrer speed →
Figure 1 | Hysteresis in a stirred superfluid2. a, A dilute-gas superfluid with a constant quantum-mechanical phase is initially held at rest in a ring-shaped trap. An obstacle rotating about the ring is then introduced, creating a constriction and stirring the superfluid. b, Above a critical stirrer speed (vc+), the stirring results in a transition from zero (0) to one (1) unit of circulation (the integral of the speed around the ring) in the superfluid, and the final phase of the system varies continuously from zero to 2π about the loop. Below vc+, the superfluid does not respond to the stirring. c, The transition from 0 to 1 occurs as the stirrer speed increases past vc+. However, on reversing the path, the transition from 1 to 0 takes place at the lower speed vc-. This cyclic path is an idealized example of hysteresis. 1 6 6 | N AT U R E | VO L 5 0 6 | 1 3 F E B R UA RY 2 0 1 4
© 2014 Macmillan Publishers Limited. All rights reserved
NEWS & VIEWS RESEARCH must pass through. More recently, the team has used6 the obstacle as a paddle-like stirrer to induce transitions from a state with no circulation to one with one or more quanta of circulation. In the current study, Eckel and colleagues begin with a superfluid at rest in the ring trap. The researchers turn on a stirrer rotating at constant speed, and leave it in the superfluid for two seconds (Fig. 1a). The stirrer is then withdrawn and the effect it has had on the superfluid is observed. For stirring speeds below a critical value, the authors find that the superfluid is oblivious to the stirring — it remains at rest in a state with no circulation. However, above this critical value, they find that the fluid transitions to a state in which it moves about the ring with one quantum of circulation (Fig. 1b). Next, Eckel et al. run their experiment in reverse: they begin with the superfluid rotating with one quantum of circulation. They stir it over the same range of speeds and directions as before, but because the stirrer is now moving more slowly than the superfluid, they look for transitions to the state in which the superfluid is at rest. Their key observation is that the stirring speed that returns the superfluid to rest can be smaller than the speed required to cause it to circulate in the first place — an example of hysteresis (Fig. 1c). Why is this result interesting? The researchers’ system is an atomtronic device analogous to a radio-frequency superconducting quantum interference device (SQUID) — a superconducting loop with one weak link. SQUIDs can exhibit hysteretic behaviour, and have applications in sensing vanishingly small magnetic fields. Owing to the mathematical analogy between magnetic fields for charged particles and rotation for neutral particles, atomtronic SQUIDs could prove to be exceptional rotation sensors. Although other researchers have demonstrated atomtronic SQUIDs7,8, Eckel et al. are the first to observe hysteresis in such a system. The authors suggest that this effect could play a crucial part in the design and application of atomtronic circuits, as it has in other electronic devices. Whether this is true remains to be seen. The level of control obtained during the experiment is impressive, and the data are remarkably clean. However, for atomtronic devices to prove genuinely useful and move out of the research lab, their reliability and robustness needs to continue to improve. Eckel and colleagues also simulate the stirring of the superfluid using the Gross– Pitaevskii model of BECs, which has proved remarkably adept at predicting the outcome of many experiments on dilute-gas superfluids3. And this is where the authors’ study gets particularly interesting. Although the simulations qualitatively reproduce the hysteretic behaviour, they predict critical stirring speeds that are too large by at least a factor of two.
This provides a real challenge for theorists — what is going wrong with the model? One issue is that the model does not allow for dissipation of energy, which is essential for hysteresis1. However, even adding dissipation to the model hardly changes the predictions. This result could perhaps have been anticipated from theoretical studies9 of an earlier experiment5 performed at the Joint Quantum Institute that found evidence of physics beyond the Gross–Pitaevskii model9 in the decay of persistent currents following the introduction of an obstacle. The team proposes a simple model of the energetics of vortex-pair creation in the presence of the stirrer that agrees rather well with their experimental results. It is up to theorists to try to work out whether this model is correct, and how it emerges from the full microscopic theory of BECs. Finally, hysteresis in real materials is often described by phenomenological models1. The complexity of these multi-particle systems generally precludes a description of hysteresis from first principles. In atomic BECs, in which the microscopic interactions between the atoms are well understood3 and the number of constituent particles is computationally tractable, it may
be possible to go beyond the Gross–Pitaevskii model and discern the ingredients needed to produce hysteresis and further exploit it for technological applications — the past can guide us towards a brighter future. ■ Matthew J. Davis is at the School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia. Kristian Helmerson is at the School of Physics, Monash University, Clayton, Victoria 3800, Australia. e-mail: [email protected] 1. Mayergoyz, I. D. Mathematical Models of Hysteresis and their Applications 2nd edn (Academic, 2003). 2. Eckel, S. et al. Nature 506, 200–203 (2014). 3. Leggett, A. J. Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Univ. Press, 2006). 4. Ryu, C. et al. Phys. Rev. Lett. 99, 260401 (2007). 5. Ramanathan, A. et al. Phys. Rev. Lett. 106, 130401 (2011). 6. Wright, K. C., Blakestad, R. B., Lobb, C. J., Phillips, W. D. & Campbell, G. K. Phys. Rev. Lett. 110, 025302 (2013). 7. Ryu, C., Blackburn, P. W., Blinova, A. A. & Boshier, M. G. Phys. Rev. Lett. 111, 205301 (2013). 8. Sackett, C. A. Nature 505, 166–167 (2014). 9. Mathey, A. C., Clark, C. W. & Mathey, L. Preprint at http://arxiv.org/abs/1207.0501 (2012).
C O N SER VAT I ON
Making marine protected areas work Globally consistent surveys of five factors influencing the success of marine protected areas — age, size, isolation, protection and enforcement — reveal that only when all five are present does nature thrive. See Letter p.216 BENJAMIN S. HALPERN
I
n the past few years, several huge marine protected areas (MPAs) have been created in the Pacific and Indian oceans, totalling more than 1.6 million square kilometres. That might sound like a large area, but even when combined with every other MPA on the planet, still less than around 2% of the world’s oceans are fully protected. In response to this conservation shortfall, coastal nations have committed to increasing the amount of protected area in their territorial waters to at least 10% by 2020. However, even if this target is met, the actual conservation value may be limited because MPAs often exist in name only — they do not truly provide protection. On page 216 of this issue, Edgar et al.1 provide key insights into why so many of the world’s MPAs are failing to meet their full potential and describe a clear path forward for achieving better conservation outcomes. The problems with existing protected areas are manifold. ‘Paper parks’, for which
protected-area boundaries exist in principle but are not enforced, have little conservation value. Unfortunately, there are a lot of paper parks2,3, and many other protected areas are only partially protected — activities such as recreational or hook-and-line fishing are allowed, leading to less conservation value than full protection4. Furthermore, nearly half of all MPAs are little bigger than a football field or have only recently been created5, limiting their ability to protect many species. It might seem as if we know a lot about what leads to MPA success or failure, but the simultaneous assessment of how various factors affect MPA success has been missing from previous studies. In other words, most studies tested one factor at a time, without controlling for the others. This is what makes Edgar and colleagues’ work particularly unusual. Using data from 87 MPAs around the world, all sampled with the same methods, the authors compared how the biomass, abundance and diversity of species in MPAs varied with all
1 3 F E B R UA RY 2 0 1 4 | VO L 5 0 6 | N AT U R E | 1 6 7
© 2014 Macmillan Publishers Limited. All rights reserved
