The Formation of Two Supermassive Black Holes from A Single Collapsing Supermassive Star

From left to right: (top row) Christian Reisswig, Christian D. Ott, Ernazar Abdikamalov; (bottom row) Roland Haas, Philipp Mösta, Erik Schnetter

Authors: Christian Reisswig^1,*, Christian D. Ott^1,2,+, Ernazar Abdikamalov¹, Roland Haas¹, Philipp Moesta¹, Erik Schnetter^3,4,5

Affiliation:
¹TAPIR, California Institute of Technology, Pasadena, CA, USA
²Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo, Kashiwa, Japan
³Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
⁴Department of Physics, University of Guelph, Guelph, ON, Canada
⁵Center for Computation & Technology, Louisiana State University, Baton Rouge, LA, USA

^*NASA Einstein Fellow
⁺Alfred P. Sloan Research Fellow

The existence of supermassive black holes with masses a billion times the mass of our sun at high redshifts z>7 [1] is one of the mysteries in our understanding of the early history of the universe. At redshift z=7, the universe was less then one billion years old. This leads to a serious problem: how is it possible for black holes to acquire this tremendous amount of mass over a short timescale of just one billion years? A common theory of black hole growth assumes as a starting point the collapse of the very first stars, so called Population III stars. Population III stars may have had masses around 100 times the mass of our sun. The collapse of such a star can leave behind a black hole of similar mass that then grows via subsequent accretion of material from its surroundings. This process can yield quite massive black holes, but in order to reach supermassive scales within only one billion years, the accretion process must be rather extremely rapid to enable fast black hole growth. These high required accretion rates, however, seem to be difficult to be maintained due to, e.g. strong outgoing radiation that can blow away the surrounding gas that otherwise would be accreted onto the black hole [2]. The model, therefore, has difficulties of explaining the existence of very massive black holes in the early universe.

Another model which has recently regained attention is supermassive star collapse. Supermassive stars have originally been proposed by Hoyle & Fowler in the 1960s as a model for strong distant radio sources [3]. Such stars have masses up to a million times the mass of our sun and potentially formed in the monolithic collapse of primordial gas clouds that existed in the early universe [4, 5]. Unlike ordinary stars, which are mainly powered by nuclear burning, supermassive stars are mainly stabilized against gravity by their own photon radiation field that originates from the very high interior temperatures generated by gravitational contraction. During their short lives, they slowly cool due to the emitted photon radiation that keeps the stars in hydrostatic equilibrium. The colder stellar gas can be more easily compressed by the inward gravitational pull, and as a consequence, the stars slowly contract and become more compact. This process continues for a few million years until the stars reach sufficient compactness for gravitationally instability to set in. This general relativistic instability inevitably leads to gravitational collapse. One possible outcome of the collapse is a massive black hole containing most of the original mass of the star. Since the 'seed' mass of the nascent black hole is already pretty large, subsequent growth via accretion from the surroundings can easily push the black hole to supermassive scales within the available time without the need of extreme accretion rates and thus without any strong photon radiation that may blow away the surrounding accreting gas.

In our recent article published in Physical Review Letters [6], we study non-axisymmetric effects in the collapse of supermassive stars. The starting point of our models are supermassive stars which are at the onset of gravitational collapse. We use general relativistic hydrodynamic supercomputer simulations with fully dynamical non-linear space-time evolution to investigate the behavior and dynamics of collapsing supermassive stars. Such computer models have been considered in previous studies [7,8,9,10], however, mostly in axisymmetry.

 In an axisymmetric configuration, a supermassive star maintains a spherical shape during its collapse, which is possibly flattened due to rotation. In these previous studies, it has been shown that the possible outcome is either a single massive rotating black hole, or, alternatively, a powerful supernova explosion which completely disrupts the star. In our case, we select an initial stellar model which is rapidly rotating and leads to black hole formation. In fact, it is so rapidly rotating that the shape of our star is no longer spheroidal, but rather resembles the shape of a 'quasi'-torus where the maximum density is off-center and thus forming a central high-density ring (see upper left panel of Figure 1).

Figure 1: (To view higher resolution click on the image) The various stages encountered during the collapse of a supermassive star with an initial m=2 standing density wave perturbation. Each panel shows the density distribution in the equatorial plane.

Such a configuration is unstable to tiny density perturbations that may be present at the onset of collapse [10]. This instability is particularly strong for perturbations in the form of standing poloidal density waves with one (m=1) or two (m=2) maxima. Due to this instability, these perturbations grow exponentially during the collapse, and can lead to significant deformations away from axisymmetry. The nature of the instability typically leads to the formation of orbiting high-density clumps of matter inside the collapsing star (see upper right panel of Figure 1). Since the m=1 and m=2 perturbations grow fastest, either one or two high-density clumps will form, depending on the initial perturbation of the stellar density. These high density fragments continue to grow rapidly during the collapse, thus becoming denser and hotter. 

Once temperatures of more than one billion Kelvins are reached, a process sets, which is called electron-positron pair creation. The creation of particle pairs is possible because there is enough energy available in the surrounding gas to spontaneously create a particle and its anti-particle, in this case electrons and positrons. The pair creation process has the effect of taking out energy from the gas fragments, thus dramatically reducing their local pressure. The reduction in pressure support leads to a rapid increase in the central density within each fragment up to the point at which the fragments become so dense that event horizons appear around each of them (center left panel of Figure 1). In the case of an initial m=2 density perturbation, two black holes form that orbit each other. Since two black holes in close orbit emit very powerful gravitational radiation - ripples of space-time that travel at the speed of light - , the associated loss of energy causes the black hole orbits to shrink, leading to an inspiralling motion (red lines in the center left panel of Figure 1). The leading order mode of the corresponding emitted gravitational wave signal is shown in the lower panel Figure 2.

Figure 2: (To view higher resolution click on the image) The upper panel shows the time evolution of the density maximum until black hole formation. The center panel shows the mass and spin evolution of the black holes. The lower panel shows the emitted leading order gravitational wave signal.

It resembles the typical quasi-sinusoidal oscillatory signal expected from binary black hole mergers: as the orbit shrinks, the emitted radiation becomes higher in frequency. The inspiral continues until a common event horizon appears, marking the merger of the two black holes (lower left panel of Figure 1). The black hole merger remnant is initially deformed into a peanut shape, which quickly relaxes into a spherical shape by emitting exponentially decaying gravitational ring-down radiation. This is shown in the lower panel of Figure 2. The peak amplitude of the waveform corresponds to the black hole merger. From there, the signal quickly decays due to black hole ring-down. By the end of our simulation, the remnant black hole is rapidly rotating and is surrounded by a massive accretion disk (lower right panel of Figure 1).

The formation of two merging black holes requires a particular choice of initial stellar model parameters at the onset of collapse: (i) we require rapid rotation and (ii) a poloidal m=2 standing density wave perturbation must be present. This naturally leads to the question of the likelihood of our model. Recent cosmological simulations of collapsing primordial gas clouds - the potential birth sites for supermassive stars - indicate that rapid rotation is very likely [4]. Curiously, the same simulations also show that an m=2 deformation arises at the center of the clouds where the supermassive star will eventually form. Unfortunately, these simulations currently do not offer sufficient spatial resolution to investigate the formation of supermassive stars in the collapse of primordial gas clouds in detail. Further research will be necessary to self-consistently model the formation of supermassive stars that may inform us about the stellar conditions at the onset of collapse.


The new and exciting prediction that two black holes can form in the collapse of a single star gives rise to very efficient gravitational wave emission compared to models where only one black hole forms. The emitted gravitational radiation in our model configuration is so powerful that future space-borne gravitational wave observatories might see the signal from the edge of our universe. This has important implications for cosmology. If detected, the signal will inform us about the formation processes of supermassive stars and supermassive black holes in the early universe and will allow us to test the validity of the supermassive star collapse pathway to supermassive black hole formation.

Acknowledgements: This research is partially supported by NSF grant nos. PHY-1151197, AST-1212170, PHY-1212460, and OCI-0905046, by the Alfred P. Sloan Foundation, and by the Sherman Fairchild Foundation. CR acknowledges support by NASA through Einstein Postdoctoral Fellowship grant number PF2-130099 awarded by the Chandra X-ray center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. RH acknowledges support by the Natural Sciences and Engineering Council of Canada. The simulations were performed on the Caltech compute cluster Zwicky (NSF MRI award No. PHY-0960291), on supercomputers of the NSF XSEDE network under computer time allocation TG-PHY100033, on machines of the Louisiana Optical Network Initiative under grant loni_numrel08, and at the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy under contract DE-AC02-05CH11231.

References:
[1] Daniel J. Mortlock, Stephen J. Warren, Bram P. Venemans, Mitesh Patel, Paul C. Hewett, Richard G. McMahon, Chris Simpson, Tom Theuns, Eduardo A. Gonzáles-Solares, Andy Adamson, Simon Dye, Nigel C. Hambly, Paul Hirst, Mike J. Irwin, Ernst Kuiper, Andy Lawrence, Huub J. A. Röttgering, "A luminous quasar at a redshift of z = 7.085", Nature, 474, 616 (2011). Abstract.
[2] Marcelo A. Alavarez, John H. Wise, Tom Abel, "Accretion onto the first stellar-mass black holes", Astrophysical Journal Letters, 701:L133 (2009). Abstract.
[3] F. Hoyle, William A. Fowler, "Nature of strong radio sources", Nature, 197, 533 (1963). Abstract.
[4] Jun-Hwan Choi, Isaac Shlosman, Mitchell C. Begelman, "Supermassive black hole formation at high redshifts via direct collapse: physical processes in the early stage", Astrophysical Journal, 774:149, 18 (2013). Abstract.
[5] M. A. Latif, D. R. G. Schleicher, W. Schmidt, J. Niemeyer, "Black hole formation in the early Universe", Monthly Notices of the Royal Astronomical Society, 433, 1607-1618 (2013). Abstract.
[6] Christian Reisswig, Christian D. Ott, Ernazar Abdikamalov, Roland Haas, Philipp Moesta, "Formation and Coalescence of Cosmological Supermassive-Black-Hole Binaries in Supermassive-Star Collapse", Physical Review Letters, 111, 15, 151101 (2013). Abstract.
[7] Pedro J. Montero, Hans-Thomas Janka, Ewald Mueller, "Relativistic collapse and explosion of rotating supermassive stars with thermonuclear effects", Astrophysical Journal, 749:37, 14 (2012). Article.
[8] Motoyuki Sajio, Ian Hawke, "Collapse of differentially rotating supermassive stars: post black hole formation", Physical Review D, 80, 064001 (2009). Abstract.
[9] Masaru Sibata, Stuart L. Shapiro, "Collapse of a rotating supermassive star to a supermassive black hole: fully relativistic simulations", Astrophysical Journal, 572:L39 (2002). Article.
[10] Burkhard Zink, Nikolas Stergioulas, Ian Hawke, Christian D. Ott, Erik Schnetter, Ewald Mueller, "Nonaxisymmetric instability and fragmentation of general relativistic quasitoroidal stars", Physical Review D, 76, 024019 (2007). Abstract.

Combining Infrared Spectroscopy and Scanning Tunneling Microscopy

Graduate students working on the project (from left to right): Xiaoping Hong, Giang D. Nguyen, Ivan V. Pechenezhskiy

Authors:
Ivan V. Pechenezhskiy^1,2, Xiaoping Hong¹, Giang D. Nguyen¹, Jeremy E. P. Dahl³, Robert M. K. Carlson³, Feng Wang¹, and Michael F. Crommie^1,2

Affiliation:
¹Department of Physics, University of California at Berkeley, California, USA
²Materials Sciences Division, Lawrence Berkeley National Laboratory, California, USA
³Stanford Institute for Materials and Energy Science, Stanford University, California, USA

Scanning tunneling microscopy (STM) [1] is an outstanding tool for probing electronic structures and surface morphologies at the nanoscale. In a scanning tunneling microscope, a metallic tip moves above the surface in a raster-like manner and measures variations in the quantum mechanical tunneling current that exists in a nanometer-sized vacuum gap between the tip and the surface. These days STM is routinely used to explore metallic, semiconducting, and superconducting substrates, novel two-dimensional materials, as well as atomic and molecular adsorbates on these surfaces.

While STM allows us to image surfaces with unparalleled atomic resolution, one significant drawback of STM is the lack of chemical contrast. For the purpose of chemical recognition, however, vibrational spectroscopy (specifically infrared spectroscopy) can be used because precise knowledge of molecular vibrational modes often leads to identification of the corresponding molecular structures. A significant breakthrough in probing molecular vibrations with STM was made in 1998 with the invention of STM-based inelastic electron-tunneling spectroscopy (STM-IETS) [2]. However, STM-IETS has some disadvantages, such as its relatively poor spectral resolution which is dependent on temperature and bias modulation [3]. Therefore, combining STM with infrared spectroscopy to probe molecular vibrations is still an extremely appealing idea, and a successful combination has so far eluded scientists.

There have been a number of attempts to combine light and STM for many different purposes [4]. However, in such studies, it is typically very difficult to separate useful information in measured signals from artifacts induced by the light heating up the tip. For example, one very common trick that is used to increase measurement sensitivity — light modulation in combination with phase-sensitive detection — does not work particularly well with STM since varying light intensity not only modulates the optical field at the junction but also modulates the tip-sample separation, and therefore the tunneling current. We realized that this problem can be bypassed if the laser light illumination is confined to a part of the surface away from the junction. The challenge, however, is to show that valuable information can still be obtained in this configuration. If so, all of the complex problems caused by the presence of light in the junction, such as tip thermal expansion, rectification and thermoelectric current generation [5], could be avoided.

How can one still do optical spectroscopy with an STM without direct illumination of the junction? The main idea behind our new spectroscopy technique is to use an STM tip as an extremely sensitive detector that measures surface expansion in the direction perpendicular to the surface. As the light frequency is tuned to a particular molecular vibrational resonance, the molecules absorb more light. The absorbed energy dissipates into the substrate and leads to substrate expansion. This expansion results in an increased tunneling current since the tip-sample separation decreases. In the actual setup, a feedback control system is used to keep the tunneling current constant by moving the tip away from the surface when the surface expands, and we measure the distance by which the tip retracts. Accordingly, when the substrate contracts, the tip moves closer to the surface to maintain the tunneling current. Recorded traces of the tip motion plotted versus laser light frequency immediately yield molecular absorption spectra. Attempts to make similar measurements have been made previously [6] but the recent progress, including demonstration of high spectral sensitivity in our measurements, only recently became possible thanks to our advances in designing and building a state-of-the-art tunable infrared laser with a stable power output (shown in Figure 1) [7].

Figure 1: IRSTM setup. An ultra-high vacuum chamber with a home-made STM is on the left and our home-made infrared laser based on an optic parametric oscillator is on the right.

In order to demonstrate the performance of the technique, referred to as infrared scanning tunneling microscopy (IRSTM) [8], we prepared samples of two different isomers of tetramantane by depositing these molecules on a Au(111) surface. These molecules, with chemical formula C₂₂H₂₈, belong to a class of molecules called diamondoids (as their structures closely-resemble that of diamond) [9]. When deposited on the gold surface, both isomers, [121]tetramantane and [123]tetramantane, form very similar single-layered close-packed assemblies as shown in Figure 2 (a, c). To obtain infrared spectra of these self-assembled structures, a beam of light from our tunable infrared laser was focused about 1 mm away from the tip-sample junction to a spot size of 1.2 mm in diameter. The spectra were recorded by tracing the motion of the tip while sweeping the laser frequency as described above. The measured IRSTM spectra for [121]tetramantane and [123]tetramantane are shown in Figure 2 (b, d). Several peaks corresponding to different modes of tetramantane CH-stretch vibrations are seen in the spectra and the spectra of the two isomers are clearly different. To compare with the STM-IETS technique, in Figure 2(b) the blue line shows an STM-IETS spectrum that has been previously obtained on a [121]tetramantane molecule [10]. In that work, STM-IETS resolution was not nearly enough to resolve any specific CH-stretch modes that exist in this frequency range. In contrast, Figure 2 demonstrates the remarkable chemical sensitivity of our new IRSTM technique.

Figure 2: (a) STM image of [121]tetramantane molecules on Au(111). (b) IRSTM spectrum (black line) of [121]tetramantane on Au(111). The blue line (with a single broad peak) shows an STM-IETS spectrum of [121]tetramantane on Au(111) from Ref. [10]. (c) STM image of [123]tetramantane molecules on Au(111). (d) IRSTM spectrum of [123]tetramantane on Au(111). Vibrational peaks for [123]tetramantane are seen to differ significantly from vibrational peaks for [121]tetramantane.

Vibrational spectra of molecules on surfaces can be used to study molecule-molecule and molecule-substrate interactions. Using IRSTM we have been able to observe the notable influence of molecule-molecule interactions between tetramantane molecules on their vibrational spectra. To investigate molecule-molecule and molecule-substrate interactions in detail, IRSTM measurements were also performed on monolayers formed by the simplest diamondoid molecule, which is called adamantane. These measurements were supported by first-principle calculations and new interesting insights have been reported in another recent study [11].

While IRSTM allows atomic-scale imaging and the probing of vibrational modes of molecules in the same setup, the phenomenal spatial resolution inherent to conventional STM measurements cannot (yet) be attributed to the IRSTM vibrational spectra. The measured signal in IRSTM comes from excitations of all molecules that are illuminated by the laser beam, i.e. from roughly a trillion molecules in our measurements. Though extension of IRSTM to the single-molecule limit will not be trivial, and will require some bright ideas, there is a lot of room for improvement in the current technique. In addition, the indirect measurement of absorbed heat in a scanning probe microscopy setup could be applied to a number of other important technological applications.

References:
[1] Gerd Binnig and Heinrich Rohrer, “Scanning tunneling microscopy — from birth to adolescence”, Reviews of Modern Physics, 59, 615 (1987). Abstract.
[2] B. C. Stipe, M. A. Rezaei, W. Ho, “Single-Molecule Vibrational Spectroscopy and Microscopy”, Science, 280, 1732 (1998). Abstract.
[3] L. J. Lauhon and W. Ho, “Effects of temperature and other experimental variables on single molecule vibrational spectroscopy with the scanning tunneling microscope”, Review of Scientific Instruments, 72, 216 (2001). Abstract.
[4] Stefan Grafström, “Photoassisted scanning tunneling microscopy”, Journal of Applied Physics, 91, 1717 (2002). Abstract.
[5] M. Völcker, W. Krieger, T. Suzuki, and H. Walther, “Laser‐assisted scanning tunneling microscopy”, Journal of Vacuum Science & Technology, B 9, 541 (1991). Abstract.
[6] D. A. Smith and R. W. Owens, “Laser-assisted scanning tunnelling microscope detection of a molecular adsorbate”, Applied Physics Letters, 76, 3825 (2000). Abstract.
[7] Xiaoping Hong, Xinglai Shen, Mali Gong, Feng Wang, “Broadly tunable mode-hop-free mid-infrared light source with MgO:PPLN continuous-wave optical parametric oscillator”, Optics Letters, 37, 4982 (2012). Abstract.
[8] Ivan V. Pechenezhskiy, Xiaoping Hong, Giang D. Nguyen, Jeremy E. P. Dahl, Robert M. K. Carlson, Feng Wang, Michael F. Crommie, “Infrared Spectroscopy of Molecular Submonolayers on Surfaces by Infrared Scanning Tunneling Microscopy: Tetramantane on Au(111)”, Physical Review Letters, 111, 126101 (2013). Abstract.
[9] J. E. Dahl, S. G. Liu, and R. M. K. Carlson, “Isolation and Structure of Higher Diamondoids, Nanometer-Sized Diamond Molecules”, Science, 299, 96 (2003). Abstract.
[10] Yayu Wang, Emmanouil Kioupakis, Xinghua Lu, Daniel Wegner, Ryan Yamachika, Jeremy E. Dahl, Robert M. K. Carlson, Steven G. Louie, Michael F. Crommie, “Spatially resolved electronic and vibronic properties of single diamondoid molecules”, Nature Materials, 7, 38 (2008). Abstract.
[11] Yuki Sakai, Giang D. Nguyen, Rodrigo B. Capaz, Sinisa Coh, Ivan V. Pechenezhskiy, Xiaoping Hong, Feng Wang, Michael F. Crommie, Susumu Saito, Steven G. Louie, Marvin L. Cohen, “Intermolecular interactions and substrate effects for an adamantane monolayer on the Au(111) surface”, arXiv:1309.5090. 

A New Nuclear ‘Magic’ Number in Exotic Calcium Isotopes

David Steppenbeck

Author: David Steppenbeck

Affiliation: Center for Nuclear Study, University of Tokyo, Japan

Physicists have come one step closer to understanding unstable atomic nuclei. A team of researchers from the University of Tokyo and RIKEN, among other institutions in Japan and Italy, has provided direct evidence for a new nuclear ‘magic’ number in the radioactive calcium isotope ⁵⁴Ca (a bound system of 20 protons and 34 neutrons). In an article published in the journal 'Nature' [1], they show that ⁵⁴Ca is the first known nucleus where N = 34 is a magic number.

The atomic nucleus, a quantum system composed of protons and neutrons, exhibits shell structures analogous to that of electrons orbiting in an atom. In stable, naturally occurring nuclei, large energy gaps exist between ‘shells’ that fill completely when the number of protons or neutrons is equal to 2, 8, 20, 50, 82 or 126 [2]. These are commonly referred to as the nuclear ‘magic’ numbers. Nuclei that contain magic numbers of both protons and neutrons are dubbed ‘doubly magic’ and these systems are more inert than others since their first excited states lie at relatively high energies.

However, recent studies have indicated that the traditional magic numbers (listed above) are not as robust as was once thought and may even change in nuclei that lie far from the stable isotopes on the Segrè chart. It is now known that while some magic numbers can disappear, other new ones can present themselves [3]. A few noteworthy examples of such phenomena are the vanishing of the N = 28 (neutron number 28) traditional magic number in ⁴²Si and the appearance of a new magic number at N = 16 in very exotic oxygen isotopes, one that is not observed in stable isotopes.

The explanation for such behaviour lies in the interplay between nucleons (protons and neutrons) in the nucleus and the ‘shuffling’ of nucleonic orbitals relative to one another, which is often referred to as ‘shell evolution’. In radioactive isotopes with extreme proton-to-neutron ratios, these orbitals may shuffle around so much to the extent that previously large energy gaps between orbitals can become rather small (causing the traditional magic numbers to disappear) while new enlarged energy gaps can sometimes appear (the onset of new magic numbers).

Nuclei around exotic calcium isotopes on the Segrè chart have also received much recent attention and experiments on ⁵²Ca, ⁵⁴Ti and ⁵⁶Cr have provided substantial evidence for a new magic number at N = 32. Another new magic number has been predicted to occur at N = 34 in the very exotic calcium isotope ⁵⁴Ca, but difficulties in producing this isotope in the laboratory have hindered experimental input—that is, until now. Owing to the world’s highest intensity radioactive beams being produced at the Radioactive Isotope Beam Factory [4] in Japan, the team of researchers was able to study the structure of the ⁵⁴Ca nucleus for the first time.

Figure 1: Detectors in the DALI2 γ-ray detector array used in the experimental study of ⁵⁴Ca. [Photo credit: Satoshi Takeuchi]

A primary beam of ⁷⁰Zn³⁰⁺ ions at an energy of 345 MeV/nucleon and an intensity of 6 X 10¹¹ ions per second was fragmented to produce a fast radioactive beam that contained ⁵⁵Sc and ⁵⁶Ti. These radioactive nuclei were directed onto a 1-cm-thick Be target to produce ⁵⁴Ca by removing one proton from ⁵⁵Sc or two protons from ⁵⁶Ti. The ⁵⁴Ca nuclei were produced either in their ground states or in excited states. In the case of the latter, the excited states decayed rapidly by emitting γ-ray photons to shed their excess energy. The energies of the γ rays were measured using an array of 186 sodium iodide detectors (Fig. 1) that surrounded the Be target. In turn, the Doppler-corrected γ-ray energies were used to deduce the energies of the nuclear excited states, which provide information on the nuclear structure.

The results of the study [1] indicate that the first excited state in ⁵⁴Ca lies at a relatively high energy, which not only highlights the doubly magic nature of this nucleus but confirms the presence of a new magic number at N = 34 in very exotic systems for the first time, ending over a decade of debate on the matter since its first prediction [5]. From a more general standpoint, understanding the nucleon-nucleon forces and evolution of nuclear shells in unstable nuclei plays a key role in the understanding of astrophysical processes such as nucleosynthesis in stars.

References:
[1] D. Steppenbeck, S. Takeuchi, N. Aoi, P. Doornenbal, M. Matsushita, H. Wang, H. Baba, N. Fukuda, S. Go, M. Honma, J. Lee, K. Matsui, S. Michimasa, T. Motobayashi, D. Nishimura, T. Otsuka, H. Sakurai, Y. Shiga, P.-A. Söderström, T. Sumikama, H. Suzuki, R. Taniuchi, Y. Utsuno, J. J. Valiente-Dobón, K. Yoneda. "Evidence for a new nuclear ‘magic number’ from the level structure of ⁵⁴Ca". Nature 502, 207–210 (2013). Abstract.
[2] Maria Goeppert Mayer. "On closed shells in nuclei. II". Physical Review, 75, 1969–1970 (1949). Abstract.
[3] David Warner. "Nuclear Physics: Not-so-magic numbers". Nature, 430, 517–519 (2004). Abstract.
[4] http://www.nishina.riken.jp/RIBF/
[5] Takaharu Otsuka, Rintaro Fujimoto, Yutaka Utsuno, B. Alex Brown, Michio Honma, Takahiro Mizusaki. "Magic numbers in exotic nuclei and spin-isospin properties of the NN interaction". Physical Review Letters, 87, 082502 (2001). Abstract.

Nanoscale Fourier-Transform Magnetic Resonance Imaging

(Clockwise from Top Left) John M. Nichol, Tyler R. Naibert, Raffi Budakian, Lincoln J. Lauhon

Authors:
John M. Nichol¹, Tyler R. Naibert¹, Eric R. Hemesath², Lincoln J. Lauhon², Raffi Budakian¹

Affiliation:
¹Dept of Physics, University of Illinois at Urbana-Champaign, USA
²Dept of Materials Science and Engineering, Northwestern University, USA

Magnetic resonance imaging (MRI) has had a profound impact on biology and medicine [1]. Key to its success has been the unique ability to combine imaging with nuclear magnetic resonance spectroscopy—a capability that has led to a host of powerful modalities for imaging. Common examples include spin-relaxation weighted imaging [2], chemical shift imaging [2], and functional MRI [3]. These and most other modern MRI techniques involve applying a combination of sophisticated radiofrequency and static magnetic field pluses to image the sample. These “pulsed” magnetic resonance methods [4] enable highly-efficient imaging by acquiring data from the entire sample at all times.

The spatial resolution of inductive MRI remains limited to millimeter lengths scales in common practice and to a few micrometers in the highest-resolution experimental instruments [5]. Although it remains a significant challenge, there is considerable interest to extend these powerful spectroscopic and imaging capabilities to the nanometer scale as the capability to perform nanoscale MRI would revolutionize biology and medicine. Promising work towards this goal includes force-detected magnetic resonance [6], which has been used to perform three-dimensional imaging of single tobacco mosaic virus particles with 5 nm resolution [7], and nitrogen-vacancy-based magnetic resonance [8, 9], which has been used to detect proton resonance in volumes as small as (5 nm)³ [10, 11]. The difficulties associated with the detection of nanometer-size volumes of nuclear spins, however, have required techniques such as these -- that are strikingly different from conventional inductive MRI. Moreover, it remains difficult to apply classic pulsed magnetic resonance techniques to nanometer-size samples.

In a recent proof-of-concept experimental work [12], we demonstrate a new technique, which allows us to perform pulsed nuclear magnetic resonance imaging and spectroscopy with nanometer-scale spatial resolution. Two unique components central to this work are (1) the ability to generate intense time-dependent magnetic fields on the nanometer scale, and (2) the development of a novel spin manipulation protocol, which allows us to encode the quantum spin noise in nanometer-scale ensembles of nuclear spins.

In particular, we perform nanometer-scale solid-state Fourier-transform MRI with roughly 10-nm spatial resolution. Fourier-transform imaging [13, 14], a pulsed magnetic resonance technique that relies on coherent manipulation of spins in the sample, is the most common method of MRI because it is highly efficient [15]. We use a nanometer-scale metal wire, or constriction, to generate intense static and radiofrequency magnetic field gradient pulses, which create temporal correlations in the statistical spin fluctuations in the sample. The correlations are recorded for a set of pulse configurations and Fourier-transformed to give the spin density. The sample used in this study is a nanometer-sized volume of polystyrene, a solid organic material containing a high proton density (Fig. 1).

Figure 1. Schematic of the experimental apparatus. A silicon nanowire coated with polystyrene is positioned near a constriction in a lithographically fabricated Ag wire. Electric current through the constriction generates static and radiofrequency magnetic field pulses, which are used to image protons in the polystyrene coating.

The magnetic resonance sensor we use is an ultra-sensitive silicon-nanowire mechanical oscillator [16], and the sample is mounted on the tip of the nanowire (Fig. 1). In addition to providing pulses for magnetic resonance, the metal constriction also produces a magnetic field gradient that oscillates at the silicon nanowire mechanical resonance frequency. The force of interaction between the protons in the sample and the magnetic field gradient from the constriction induces an angstrom-scale vibration of the nanowire, which we measure using a fiber-optic interferometer [17]. The silicon nanowire is an exceptionally sensitive mechanical oscillator and is well-suited to detecting the minute forces originating from small ensembles of nuclear spins [16].

Looking forward, our technique establishes a paradigm by which all other pulsed magnetic resonance techniques can be implemented for nanoscale imaging and spectroscopy. Constrictions capable of producing two orthogonal static gradients could be fabricated, and such devices would enable full three-dimensional imaging. A small coil near the sample could also provide a uniform radiofrequency field throughout the sample, which would enable the use of solid-state nuclear magnetic resonance spectroscopy techniques. More generally, our approach serves as a model for leveraging these and other sophisticated pulsed magnetic resonance tools to aid nanoscale MRI in its progress toward atomic-scale imaging.

References:
[1] R. R. Ernst, G. Bodenhausen, and A. Wokaun, "Principles of Nuclear Magnetic Resonance in One and Two Dimensions" (Oxford University Press, New York, 1997).
[2] D. D. Stark and W. G. Bradley, Magnetic Resonance Imaging (C.V. Mosby Co., St. Louis, 1988).
[3] Seiji Ogawa, Tso-Ming Lee, Asha S. Nayak, Paul Glynn, "Oxygenation-sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields", Magnetic Resonance in Medicine, 14, 68 (1990). Abstract.
[4] R. R. Ernst and W. A. Anderson, "Application of Fourier Transform Spectroscopy to Magnetic Resonance", Review of Scientific Instruments, 37, 93 (1966). Abstract.
[5] L. Ciobanu, D. A. Seeber, and C. H. Pennington, "3D MR microscopy with resolution 3.7μm by 3.7μm by 3.7μm", Journal of Magnetic Resonance, 158, 178 (2002). Abstract.
[6] J. A. Sidles, J. L. Garbini, K. J. Bruland, D. Rugar, O. Zuger, S. Hoen, C. S. Yannoni, "Magnetic resonance force microscopy", Review of Modern Physics, 67, 249 (1995). Abstract.
[7] C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, "Nanoscale magnetic resonance imaging", Proceedings of the National Academy of Sciences of USA, 106, 1313 (2009). Article.
[8] C. L. Degen, "Scanning magnetic field microscope with a diamond single-spin sensor", Applied Physics Letters, 92, 243111 (2008). Abstract.
[9] J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, M. D. Lukin, "High-sensitivity diamond magnetometer with nanoscale resolution", Nature Physics, 4, 810 (2008). Abstract.
[10] H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, D. Rugar, "Nanoscale Nuclear Magnetic Resonance with a Nitrogen-Vacancy Spin Sensor", Science 339, 557 (2013). Abstract.
[11] T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, "Nuclear Magnetic Resonance Spectroscopy on a (5-Nanometer)³ Sample Volume", Science 339, 561 (2013). Abstract.
[12] John M. Nichol, Tyler R. Naibert, Eric R. Hemesath, Lincoln J. Lauhon, Raffi Budakian, "Nanoscale Fourier-Transform Magnetic Resonance Imaging", Physical Review X, 3, 031016 (2013). Abstract.
[13] Anil Kumar, Dieter Welti, Richard R Ernst, "NMR Fourier zeugmatography", Journal of Magnetic Resonance, 18, 69 (1975). Abstract.
[14] D. I. Hoult, "Rotating frame zeugmatography", Journal of Magnetic Resonance, 33, 183 (1979). Abstract.
[15] P. Brunner and R. R. Ernst, "Sensitivity and performance time in NMR imaging", Journal of Magnetic Resonance, 33, 83 (1979). Abstract.
[16] John M. Nichol, Eric R. Hemesath, Lincoln J. Lauhon, Raffi Budakian, "Nanomechanical detection of nuclear magnetic resonance using a silicon nanowire oscillator", Physical Review B, 85, 054414 (2012). Abstract.
[17] John M. Nichol, Eric R. Hemesath, Lincoln J. Lauhon, Raffi Budakian, "Displacement detection of silicon nanowires by polarization-enhanced fiber-optic interferometry", Applied Physics Letters, 93, 193110 (2008). Abstract.