High Magnetic Fields Coax New Discoveries from Topological Insulators

James Analytis [Photo courtesy: Stanford U.]

Using one of the most powerful magnets in the world, a small group of researchers has successfully isolated signs of electrical current flowing along the surface of a topological insulator, an exotic material with promising electrical properties. The research, led by James Analytis and Ian Fisher of the Stanford Institute of Materials and Energy Sciences, a joint SLAC-Stanford institute, was published last Sunday in Nature Physics [1]. The results provide a new window into how current flows in these exotic materials, which conduct along the exterior, while acting as insulators at the interior. At least in theory.

"This is a difficulty people in the field have been struggling with for two years," Fisher said. "The topological part is there but the insulator part isn't there yet." Chemical imperfections in the materials being tested have meant that the interior, or bulk, portions of topological insulators have been behaving more like metals than insulators.

Ian Fisher [Photo courtesy: Stanford U.]

In other words, while researchers have been trying to decipher the behavior of the electrons on the surface by observing the way they conduct current (called electronic transport), the electrons in the interior have also been conducting current. The difficulty arises in telling the two currents apart.

But, according to Fisher, the promise of useful applications for these exotic new materials—not to mention possible discoveries of fundamental new physics—rests on the ability to measure and control the electric current at the surface. In order to do so, Analytis, Fisher, and their group first had to reduce the amount of current running through the bulk of the material until the surface current could be detected, and then probe the physical properties of the electrons responsible for that surface current.

Analytis tackled the first problem by replacing some of the bismuth in bismuth selenide, a known topological insulator, with antimony, a lighter relative with the same number of electrons in its valence, or chemically reactive, shell. This provided a way to reduce the number of charge-carrying electrons in the interior of the sample.

But even after removing hundreds of billions of electrons, "we still didn't have an insulator," Analytis said. That's when he turned to Ross McDonald and the pulsed magnets at the Pulsed Field Facility, Los Alamos National Laboratory's branch of the National High Magnetic Field Laboratory.

Ross McDonald [Photo courtesy: National High Magnetic Field Laboratory, Tallahassee, FL]

Electrons in a uniform magnetic field follow circular orbits. As the electrons are subjected to higher and higher magnetic fields, they travel in tighter and tighter orbits, which are quantized, or separated into discrete energy levels, called Landau levels. Using a high-enough magnetic field to trap the bulk electrons in their lowest Landau level enabled Analytis to differentiate between the bulk electrons and the surface electrons, or, as Fisher put it, "get the bulk under control."

With McDonald's help, Analytis used one of Los Alamos' multi-shot pulsed magnets, so called because they deliver their full field strength in pulses lasting thousandths of a second. Analytis discovered that a moderate field of four Tesla (about twenty thousand times the strength of a refrigerator magnet) was sufficient to force the bulk conduction electrons into their lowest Landau level. Then he pushed the magnetic field to 65T to see what the surface electrons on the topological insulator would do.

The 100 Tesla multi-shot pulsed magnet at Los Alamos National Laboratory. James Analytis used a slightly less powerful magnet for the research covered in this article [Photo courtesy: National High Magnetic Field Laboratory, Tallahassee, FL].

He saw a clear signature from the Landau levels of the surface electrons. And, at the very highest magnetic fields, at which the surface electrons are pushed most closely together, Analytis detected signs that the electrons interacted with each other, instead of behaving like independent particles.

"It's beautiful," Fisher said. "It's unambiguous evidence that we can probe electronic transport in the surface of these materials." However, much of the difficulty in creating a truly insulating topological insulator remains.

"It feels like we've opened a door to the place [experimenters] want to be," he said, "but there's a lot more work to be done."

In the meantime, Analytis is moving ahead with his latest experiment—hitting the antimony-doped bismuth selenide with a staggering 85T—the highest magnetic field available in a multi-shot magnet anywhere in the world.

Reference
[1] James G. Analytis, Ross D. McDonald, Scott C. Riggs, Jiun-Haw Chu, G.S. Boebinger & Ian R. Fisher, "Two-dimensional surface state in the quantum limit of a topological insulator", Nature Physics, Published online November 21 (2010), doi:10.1038/nphys1861. Abstract.

[The text is written by Lori Ann White of Stanford Linear Accelerator Laboratory (SLAC)]

Four-Fold Quantum Memory

Jeff Kimble (photo courtesy: Caltech Particle Theory Group)

Researchers at the California Institute of Technology (Caltech) have demonstrated quantum entanglement for a quantum state stored in four spatially distinct atomic memories.

Their work, described in the November 18 issue of the journal Nature [1], also demonstrated a quantum interface between the atomic memories—which represent something akin to a computer "hard drive" for entanglement—and four beams of light, thereby enabling the four-fold entanglement to be distributed by photons across quantum networks. The research represents an important achievement in quantum information science by extending the coherent control of entanglement from two to multiple (four) spatially separated physical systems of matter and light.

The proof-of-principle experiment, led by the William L. Valentine Professor and professor of physics H. Jeff Kimble, helps to pave the way toward quantum networks [2]. Similar to the Internet in our daily life, a quantum network is a quantum "web" composed of many interconnected quantum nodes, each of which is capable of rudimentary quantum logic operations (similar to the "AND" and "OR" gates in computers) utilizing "quantum transistors" and of storing the resulting quantum states in quantum memories. The quantum nodes are "wired" together by quantum channels that carry, for example, beams of photons to deliver quantum information from node to node. Such an interconnected quantum system could function as a quantum computer, or, as proposed by the late Caltech physicist Richard Feynman in the 1980s, as a "quantum simulator" for studying complex problems in physics.

Link to Professor Jeff Kimble's Quantum Optics group at Caltech >>

Quantum entanglement is a quintessential feature of the quantum realm and involves correlations among components of the overall physical system that cannot be described by classical physics. Strangely, for an entangled quantum system, there exists no objective physical reality for the system's properties. Instead, an entangled system contains simultaneously multiple possibilities for its properties. Such an entangled system has been created and stored by the Caltech researchers.

Previously, Kimble's group entangled a pair of atomic quantum memories and coherently transferred the entangled photons into and out of the quantum memories [3]. For such two-component—or bipartite—entanglement, the subsystems are either entangled or not. But for multi-component entanglement with more than two subsystems—or multipartite entanglement—there are many possible ways to entangle the subsystems. For example, with four subsystems, all of the possible pair combinations could be bipartite entangled but not be entangled over all four components; alternatively, they could share a "global" quadripartite (four-part) entanglement.

Hence, multipartite entanglement is accompanied by increased complexity in the system. While this makes the creation and characterization of these quantum states substantially more difficult, it also makes the entangled states more valuable for tasks in quantum information science.

[Image Credit: Nature/Caltech/Akihisa Goban] The fluorescence from the four atomic ensembles. These ensembles are the four quantum memories that store an entangled quantum state.

To achieve multipartite entanglement, the Caltech team used lasers to cool four collections (or ensembles) of about one million Cesium atoms, separated by 1 millimeter and trapped in a magnetic field, to within a few hundred millionths of a degree above absolute zero. Each ensemble can have atoms with internal spins that are "up" or "down" (analogous to spinning tops) and that are collectively described by a "spin wave" for the respective ensemble. It is these spin waves that the Caltech researchers succeeded in entangling among the four atomic ensembles.

The technique employed by the Caltech team for creating quadripartite entanglement is an extension of the theoretical work of Luming Duan, Mikhail Lukin, Ignacio Cirac, and Peter Zoller in 2001 for the generation of bipartite entanglement by the act of quantum measurement. This kind of "measurement-induced" entanglement for two atomic ensembles was first achieved by the Caltech group in 2005 [4].

In the current experiment, entanglement was "stored" in the four atomic ensembles for a variable time, and then "read out"—essentially, transferred—to four beams of light. To do this, the researchers shot four "read" lasers into the four, now-entangled, ensembles. The coherent arrangement of excitation amplitudes for the atoms in the ensembles, described by spin waves, enhances the matter–light interaction through a phenomenon known as superradiant emission.

"The emitted light from each atom in an ensemble constructively interferes with the light from other atoms in the forward direction, allowing us to transfer the spin wave excitations of the ensembles to single photons," says Akihisa Goban, a Caltech graduate student and coauthor of the paper. The researchers were therefore able to coherently move the quantum information from the individual sets of multipartite entangled atoms to four entangled beams of light, forming the bridge between matter and light that is necessary for quantum networks.

The Caltech team investigated the dynamics by which the multipartite entanglement decayed while stored in the atomic memories. "In the zoology of entangled states, our experiment illustrates how multipartite entangled spin waves can evolve into various subsets of the entangled systems over time, and sheds light on the intricacy and fragility of quantum entanglement in open quantum systems," says Caltech graduate student Kyung Soo Choi, the lead author of the Nature paper. The researchers suggest that the theoretical tools developed for their studies of the dynamics of entanglement decay could be applied for studying the entangled spin waves in quantum magnets.

Further possibilities of their experiment include the expansion of multipartite entanglement across quantum networks and quantum metrology. "Our work introduces new sets of experimental capabilities to generate, store, and transfer multipartite entanglement from matter to light in quantum networks," Choi explains. "It signifies the ever-increasing degree of exquisite quantum control to study and manipulate entangled states of matter and light."

In addition to Kimble, Choi, and Goban, the other authors of the paper, "Entanglement of spin waves among four quantum memories," are Scott Papp, a former postdoctoral scholar in the Caltech Center for the Physics of Information now at the National Institute of Standards and Technology in Boulder, Colorado, and Steven van Enk, a theoretical collaborator and professor of physics at the University of Oregon, and an associate of the Institute for Quantum Information at Caltech.

References
[1] K.S. Choi, A. Goban, S.B. Papp, S.J. van Enk, H. J. Kimble, "Entanglement of spin waves among four quantum memories", Nature 468, 412-416 (18 November 2010). Abstract.
[2] H.J. Kimble, "The quantum internet", Nature 453, 1023-1030 (19 June 2008). Abstract.
[3] K. S. Choi, H. Deng, J. Laurat, H. J. Kimble, "Mapping photonic entanglement into and out of a quantum memory", Nature 452, 67-71 (6 March 2008). Abstract.
[4] C.W. Chou, H. de Riedmatten, D. Felinto, S.V. Polyakov, S.J. van Enk, H.J. Kimble, "Measurement-induced entanglement for excitation stored in remote atomic ensembles", Nature 438, 828-832 (8 December, 2005). Abstract.

Hanbury Brown and Twiss Interferometry with Interacting Photons

Left to right: Eran Small, Yoav Lahini, Yaron Bromberg and Yaron Silberberg

[This is an invited article based on a recently published work by the authors
-- 2Physics.com]

Authors: Yoav Lahini, Yaron Bromberg, Eran Small and Yaron Silberberg
Affiliation: Department of Physics of Complex Systems, the Weizmann Institute of Science, Rehovot, Israel.

The next time you go out on a sunny day, take a minute to consider the sunlight you see reflected from the ground near you. If you could have frozen time, you would see that actually, the light pattern on the ground is not homogenous, but rather it is speckled – it is made out of patches of light and darkness, similar to the speckle pattern you see when a laser light hits a rough surface like a wall. For sunlight, the typical speckle size is around 100 microns, but that is not the reason why the sunlight speckles are not observed in everyday life. The real reason is that this speckle pattern changes much faster than the human eye – and in fact, faster than any man made detector – can follow. As a result we see an averaged, smeared homogenous light reflected around us.

To understand this phenomenon, and its relation to the Hanbury-Brown and Twiss effect and the birth of quantum optics, let’s first consider the sun as observed by a spectator on earth. The sun is an incoherent light source – that is, there is no fixed phase relation between the rays of light coming from different parts of the sun’s surface. In fact, it is more accurate to say that there is a phase relation between the rays only that this phase difference continuously fluctuates. The rate of the phase fluctuations is very fast, typically on the scale of femtoseconds. Nevertheless, let’s assume for a moment that we could freeze time while looking at the sunlight on Earth. What would we see? Since everything is “frozen”, the phase between all the rays coming from the sun is fixed, and the rays will interfere. The result of such interference of many rays with a random phase leads to the speckle pattern – patches of light and darkness. Bright regions are formed where the rays interfere constructively, and dark regions where the rays interfere destructively. The typical size of the patches is determined by the distance over which constructive interference changes to destructive. This happens when the path lengths from the emitters on the sun (or any incoherent source) to the Earth change by about half a wavelength. In fact it can be shown that the typical size of such speckle, if one could ever be photographed, goes like the wavelength over the angular size of the source, as seen from the earth [1]. This means that the size of a typical speckle is larger the further the distance between the source and the observer - the speckles diffract, their size increases as they propagate.

As noted earlier, the sun will create a speckle pattern on Earth with a typical speckle size of 100 microns, while a distant star (with a much smaller angular size) will create a speckle size of a few meters and even kilometers. So in theory, if the speckle size can be somehow measured, it will allow to determine the angular size of stars, or any other incoherent light source.

In 1956, two astronomers, Hanbury Brown and Twiss, did just that [2]. They found a way to determine the typical speckle size in starlight with just two detectors instead of a camera. The trick was to use two fast detectors, and look into the noise measured by the two detectors, instead of the averaged signal as we usually do in the lab. So how does it work? The intensities measured by the two detectors are noisy, since the speckle pattern that impinges on the detectors continuously varies. But, as long as the two detectors are separated by a distance smaller than the typical speckle size, they will be illuminated most of the time by the same speckle. The signals measured by the two detectors will therefore be noisy but correlated, i.e. the two signals will fluctuate together. However, if the two detectors are separated by a distance larger than the typical speckle size, the signals' fluctuations will be totally uncorrelated, since each detector sees different speckles. Therefore the distance in which noise in the two detectors becomes uncorrelated is a measure of the typical speckle size, and therefore a measure of the angular size of the observed star.

Hanbury Brown and Twiss (HBT) proved their theory several times [3,4], by giving accurate measures of the angular size of several stars using radio and optical interferometry. These experiments gave rise to a vigorous debate about the nature of light: it is easy to prove the HBT effect if you think of light as classical waves, but what happens if you try to take the particle view of light? How can two photons, coming from two distant atoms on the surface of a star and measures by two distant detectors on the surface of the earth, be correlated? The answer to this question was given only after a few years by the Nobel Prize laureate Roy Glauber [5], an answer that marked the birth of the field of Quantum Optics.

Since those days, the HBT technique was adopted and used in many different fields in physics as a tool to remotely measure properties of different sources. For example, the HBT method was used to measure the properties subatomic particles created in nuclear collisions [6], of Bose-Einstein Condensates (BEC) in lattice potentials [7,8] and other systems [9-13]. In a work recently published in Nature Photonics [14], we note that these modern uses of HBT interferometry rely on an assumption that there are no interactions between the particles on their way from the source to the detectors. Such interactions (or nonlinear effects in the case of classical waves) would affect the correlations while the particles (or waves) propagate from the source to the detectors. The assumption of no interactions is probably valid in the astronomical case (although due to the very long distances involved that might also be questioned), but is not necessarily true for atom-matter waves released from their confining potential, or for charged sub-atomic particles propagating from the point of interest to the detection.

To see how one can cope with such complications we analyzed the effect of interactions on the resulting HBT correlation by considering light propagation in a nonlinear medium – a scenario physically similar to matter waves released from a confining potential (the equations describing the dynamics of matter waves are identical, in certain limits, to the equations used in our paper). Using a spatial light modulator and diffusers we mimicked a spatially incoherent light source in a controlled manner, and measured the HBT correlations after propagation of the speckle field in a nonlinear medium. We investigated both repulsive and attractive interactions, in two and three dimensional space. Using these measurements, we have shown how the interactions modify the measured HBT correlations. While the fact the interactions modify correlations is expected, our work provides an intuitive picture for the source of this modification. The key idea is to follow the propagation of the speckle patterns in the nonlinear medium. As discussed above, when there are no interactions the speckles diffract along the propagation. But in the presence of interactions, or nonlinearity, each speckle can turn into what is known as a soliton – a self trapped entity, with a size that does not change along the propagation. This means that the size of the speckles is no longer a measure for the angular size of the source. It is in fact a measure for the strength of the interactions.

Experimental observation of a speckle pattern propagating in a nonlinear medium. In the interaction free case, the width of a typical speckle is inversely proportional to the width of the source, W. In the presence of interactions, one needs to take into account the strength of the intensity fluctuations as well. Image credit: Adi Natan
But perhaps more importantly, we provide a new framework that can include interactions in HBT interferometry. We found that the information on the source can still be retrieved if the interactions are taken into account correctly. We show that in the presence of interactions the angular size of the source can be recovered, but one needs in addition to the spatial correlation also to measure the strength of the signals' fluctuations. Intuitively, this stems from the fact that speckles which have became “solitons” still propagate at different angles. Since these “speckolitons” keep their size along the propagation, the chance that a speckoliton will hit the detectors goes down as the distance from the source to the detector increases. But the intensity the speckolitons carries is much higher than the intensity of a linear speckle which diffracts along the propagation. Careful analysis of this phenomena leads to the conclusion that in the presence of interactions the intensity fluctuations carry the missing information on the angular size of the source.

One can measure the strength of the fluctuations by simply looking at the variance of the detectors' readouts, which is closely related to the contrast of the bright to dark patches in the speckle pattern. As a possible application, consider HBT interferometry with trapped BEC. A recent paper [7] identified the complication of using HBT interferometry arising due to interactions during the time-of-flight, after the condensate is released from the trap. That paper suggests an intricate manipulation of the condensate during the time-of-flight, to scale out the effects of interactions. Our paper provides a framework to include the interactions in the analysis, without the need for such complicated experiments.

References:
[1] Goodman, J. W. , "Speckle Phenomena in Optics" (Roberts & Co., 2007)
[2] Hanbury Brown, R. &. Twiss, R. Q. "A test of a new type of stellar interferometer on Sirius", Nature 178, 1046–1048 (1956). Abstract.
[3] Hanbury Brown, R. &. Twiss, R. Q. Correlations between photons in two coherent beams of light. Nature 177, 27–29 (1956). Abstract.
[4] Hanbury Brown, R. "The Intensity Interferometer: Its Application to Astronomy" (Taylor & Francis, 1974).
[5] Glauber, R. G. "Photon correlations", Phys. Rev. Lett. 10, 84–86 (1963). Abstract.
[6] Baym, G. "The physics of Hanbury Brown–Twiss intensity interferometry: from stars to nuclear collisions", Acta. Phys. Pol. B 29, 1839–1884 (1998). Article.
[7] Simon Fölling, Fabrice Gerbier, Artur Widera, Olaf Mandel, Tatjana Gericke & Immanuel Bloch, "Spatial quantum noise interferometry in expanding ultracold atom clouds", Nature 434, 481–484 (2005). Abstract.
[8] Altman, E., Demler, E. & Lukin, M. D. "Probing many body correlations of ultra-cold atoms via noise correlations", Phys. Rev. A 70, 013603 (2004). Abstract.
[9] M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, C. I. Westbrook, "Hanbury Brown Twiss effect for ultracold quantum gases", Science 310, 648–651 (2005). Abstract.
[10] Oliver, W. D., Kim, J., Liu J. & Yamamoto, Y. "Hanbury Brown and Twiss-type experiment with electrons", Science 284, 299–301 (1999). Abstract.
[11] Kiesel, H., Renz, A. & Hasselbach, F. "Observation of Hanbury Brown–Twiss anticorrelations for free electrons", Nature 418, 392–394 (2002). Abstract.
[12] T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect & C. I. Westbrook, "Comparison of the Hanbury Brown–Twiss effect for bosons and fermions", Nature 445, 402–405 (2007). Abstract.
[13] I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu & V. Umansky, "Interference between two indistinguishable electrons from independent sources", Nature 448, 333–337 (2007). Abstract.
[14] Bromberg, Y., Lahini, Y., Small, E. & Silberberg, Y. Hanbury Brown and Twiss interferometry with interacting photons. Nature Photonics 4, 721-726 (2010). Abstract.