One Clock in Two Places Simultaneously

Ron Folman (photo credit: Naomi Weisman)

Author: Ron Folman

Affiliation: Ben-Gurion University of the Negev, Beer Sheva, Israel.

Link to atom chip group >>

Introduction:

This story is about Einstein’s theory of general relativity (GR) [1] and quantum mechanics (QM) [2]. These two theories constitute the physics revolutions of the 20th century, and there are numerous attempts to unify them or, at the very least, understand how they work together. This story is also about time. Some would claim that we are still far from really understanding time [3].

GR came to life in 1915, and was successful in explaining minute anomalies in the orbits of Mercury and other planets. In 1919, Sir Arthur Eddington was able, during a total solar eclipse, to verify a prediction of the theory when he headed an expedition which confirmed the deflection of light by the Sun. Some predictions, such as gravitational waves, remain unobserved. Another of the verified predictions of GR is that time is affected by gravity; it ticks at different rates depending on how close you are to a massive object. This has been confirmed for several decades now by sending rockets with clocks to large heights and recently, as atomic clocks became much more accurate, even by simply moving a clock a few centimeters higher in a lab. This effect was nicely displayed in the recent movie 'Interstellar'.

GR was always considered strange and hard to fathom. It is rumored that in one of his lectures on GR, Sir Eddington was asked by Ludwik Silberstain: "Professor Eddington, you must be one of three persons in the world who understands general relativity." Eddington paused, unable to answer. Silberstein continued "Don't be modest, Eddington!" Finally, Eddington replied "On the contrary, I'm trying to think who the third person is." It is quite amazing to see how less than a century later GR is an important part of our day-to-day life, as it is an essential part in the GPS navigation system.

QM is thought by many to be even weirder. It took away determinism, it allowed non-locality, and it even allowed objects to be in two places (or two states, e.g., of energy or of spin) at the same time. This seemed so ridiculous that one of the fathers of QM, Erwin Schrödinger came up with a thought experiment in which a cat is alive and dead at the same time, theoretically made possible due to QM. Other contributors to the birth of QM disliked it just as much. Einstein said that “God does not play with dice” and Louis de-Broglie believed determinism will come back in a more comprehensive theory. Niels Bohr said: “For those who are not shocked when they first come across quantum theory cannot possibly have understood it”. Yet, the theory is successfully withstanding endless testing for almost a century now.

It is quite strange that these two successful theories have not been put together into one simple description of the universe. It remains to be seen what exactly the interplay between the two is: for example, some claim that the crucial process of decoherence, which is responsible for defining the border between the quantum realm and the classical world (as our day-to-day world of large objects is known), is powered by GR [4]. Some even claim that the process of “wave-function collapse” is driven by GR [5]. This process is responsible for the fact that out of many possible outcomes which exist according to QM, we see only one when we make a measurement.

The experiment :

In the experiment we conducted, published recently in Science [6], we wanted to study the interplay between the two theories. Specifically we wanted to see what would happen if we take one clock and put it in two places in which time ticks at different rates, simultaneously. We then put the clock together again and observed it.

In order to do this we used a device called an atom chip (see our website for many relevant papers). It is a powerful tool in manipulating the internal and external degrees of freedom of ultra-cold atoms. Every atom in a cloud of ultra-cold atoms (a Bose-Einstein condensate at -273 deg. Celsius) was put in two places simultaneously (known in scientific language as a spatial quantum superposition [7]), by utilizing a device called an interferometer. In parallel, every atom was turned into an atomic clock by manipulating its internal (spin) degrees of freedom.

As we did not have sensitive enough clocks to observe the minute effect of GR, we induced an artificial time difference between the two locations occupied by the single clock (these two copies of the single clock are referred to in scientific language as wave-packets). Our proof-of-principle experiment indeed shows (as predicted by [8]) that time differences have a major effect on the quantum outcome expected from an interferometer (called an “interference pattern”). Specifically, we showed that time may act as a “which path” witness as if we measured in which of the two locations the clock is. Once such a measurement is made, QM tells us that the special state of quantum superposition is destroyed and the clock can no longer be in two places at the same time (this is called “complementarity”). However, we have also showed that if the hands of the clock in one wave-packet are rotated enough so that they again overlap the hands of the clock in the other wave-packet, we again cannot differentiate between the two locations and the superposition, and consequently the interference pattern is restored.

Technically, we used very strong magnetic gradients to construct a Stern-Gerlach type of interferometer, and also used similar gradients to induce the relative time lag (using the Zeeman effect). The atoms are laser-cooled and then additionally cooled by forced evaporation. The atoms are isolated from the environment by the fact that the whole experiment is conducted in a vacuum chamber. The final outcome of the experiment is registered with a CCD camera observing the atoms.

We now have a new tool at our disposal to investigate time and the interplay between GR and QM. What we will find is an open question. Usually, new tools bring new insight. The next step should be to use more accurate clocks and to separate the clock into positions farther apart so that we are able to see the effect of GR.

The Team :

The team included Ph.D. student Yair Margalit, post-doctoral fellows Dr. Zhifan Zhou and Dr. Shimon Machluf, and researchers Dr. Yonathan Japha and Dr. Daniel Rohrlich. In the picture are the first two authors of the paper: PhD student Yair Margalit (left) and post-doctoral fellow Zhifan Zhou (right).

Additional Thoughts :

It is perhaps appropriate to end a popular article with some broad thoughts and even speculations. It stands to reason that human kind knows much less than what it doesn’t know. Namely, we are just beginning to explore and understand the structure and dynamics of our world. History and Philosophy of science teach us that our understanding is constantly changing and no theory is the “end of the road”. Will we see extensions to GR or QM in our lifetime? Will they somehow be unified?

The atoms in our lab are our teachers; they are teaching us new things every day. As we build a better dictionary from atom language to human language we will be able to understand more. They are teaching us about our physical universe and about how to understand the strange mysteries of QM. They are teaching us technology (clocks, magnetic sensors, gravitational sensors, navigation, quantum communications and quantum computing). Eventually they may even teach us things that have to do directly with who we are. For example, is there such a thing as free will? On this latter topic I invite the reader to see a very short and simplified film I made [9].

It makes me envious but also very happy to know that some of the young readers of this article will know much more than I ever will. I encourage the young reader to take up the adventure wholeheartedly.

References:
[1] “General relativity turns 100”, Special issue, Science, 347 (March 2015). Table of contents.
[2] “Foundations of quantum mechanics”, Insight issue, Nature Physics, 10 (April 2014).  Table of contents.
[3] Lee Smolin, "Time Reborn" (Mariner Books, 2014).
[4] Igor Pikovski, Magdalena Zych, Fabio Costa, Časlav Brukner, “Universal decoherence due to gravitational time dilation”, Nature Physics, 11, 668-672 (2015). Abstract.
[5] Roger Penrose, "The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics", Chapter 6 (New York: Oxford U. Press, 1989) ; Lajos Diósi, “Gravity-related wave function collapse: mass density resolution”, Journal of Physics: Conference Series, 442, 012001 (2013). Full Article ; Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P. Singh, Hendrik Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests”, Review of Modern Physics, 85, 471 (2013). Abstract.
[6] Yair Margalit, Zhifan Zhou, Shimon Machluf, Daniel Rohrlich, Yonathan Japha, Ron Folman, “A self-interfering clock as a 'which path' witness”, published online in 'Science Express' (August 6, 2015). Abstract.
[7] This new terminology is meaningful as all attempts to interpret the reality of this situation with day-to-day language have led to some sort of contradiction. The strange reality of the quantum world can perhaps only be accurately described by mathematics. Using words, which originate in our day-to-day (“classical”) experience, always fails those who attempt to harness them for the description of the quantum world. Perhaps one may alternatively state that the clock is in a state where it somehow “feels” how time “ticks” in several places at once.
[8] Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner, “Quantum interferometric visibility as a witness of general relativistic proper time”, Nature Communications, 2, 505 (2011). Abstract. 2Physics Article.
[9] “ ‘Are we alive?’ – a thought by Ron Folman”: YouTube Link.  

A Quantum Gas Microscope for Fermionic Atoms

The Fermi gas microscope group: (from left) graduate students Katherine Lawrence and Melih Okan, postdoc Thomas Lompe, graduate student Matt Nichols, Professor Martin Zwierlein, and graduate student Lawrence Cheuk. Photo credit: Jose-Luis Olivares/MIT.

Authors: Lawrence Cheuk and Martin Zwierlein

Affiliation: 
Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

Link to Ultracold Quantum Gases Group >>

What do electrons, protons, neutrons and even quarks have in common? They all are fermions, particles with half-integer spin. Unlike their bosonic counterparts, integer spin particles, fermions cannot occupy one and the same quantum state. This simple fact leads to the structure of our elements, where electrons have to avoid each other and occupy different orbits around the atomic nucleus, or at least differ in their spin orientation.

When many fermions interact strongly with each other, they can form complex matter with exotic properties, from atomic nuclei to solid state materials, to distant neutron stars. Their collective behavior leads to diverse phenomena such as the structure of the elements, high-temperature superconductivity and colossal magneto-resistance.

Yet our understanding of strongly-interacting Fermi systems is limited. In recent years, ultracold atomic Fermi gases have emerged as a pristine platform to study many-fermion systems. In particular, fermionic atoms trapped in an optical lattice formed by standing waves of light can simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations.

Yet our understanding of strongly-interacting Fermi systems is limited. In recent years, ultracold atomic Fermi gases have emerged as a pristine platform to study many-fermion systems. In particular, fermionic atoms trapped in an optical lattice formed by standing waves of light can simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations.

In the present work, recently published in Physical Review Letters [3], we have realized quantum gas microscope that images ultracold fermionic ⁴⁰K atoms with single-lattice-site resolution. Similar results have also been achieved at about the same time by researchers at University of Strathclyde and Harvard University [4,5].

Figure Caption: Fermionic ⁴⁰K atoms in a 2D optical lattice with 541nm spacing imaged using Raman sideband cooling. Image taken from [3].

In our experiment, we prepare a two-dimensional layer of ⁴⁰K atoms via laser cooling and forced evaporation. The atoms are then trapped in an optical lattice formed by retro-reflected laser beams, which form a standing wave with 541nm spacing. In order to resolve atoms with single-lattice-site resolution, we utilize a novel setup that incorporates a solid immersion lens into the vacuum window. This allows an enhancement in the numerical aperture, leading to higher resolution and enhanced light collection. In addition, optical aberrations that arise from a planar window are minimized in this setup.

In order to detect the atoms, we perform fluorescence imaging while simultaneously cooling the atoms. To make the atoms fluoresce, they are illuminated with near-resonant light. However, as the atoms emit photons, they experience heating from the recoil of photons. As the atoms are heated up, they hop between lattice sites and can even hop out of the lattice. In order to faithfully measure the occupation of the lattice sites, one must therefore eliminate the heating that arises when atoms fluoresce. We accomplish this via a technique known as Raman sideband cooling.

Raman sideband cooling, a technique first demonstrated in the 1990s, selectively transfers atoms from high-energy states to lower energy states via a two-photon Raman process. Atoms that are already in the lowest energy state, however, remain “dark” to the Raman light. By collecting photons that are scattered during this cooling process, we extract the position of the atoms while cooling the atoms. Hopping and atom loss are thus avoided. Furthermore, we have found that even after imaging the atoms with Raman sideband cooling, the atoms are predominantly in the lowest energy state. This invites the possibility of assembling low-entropy many-fermion states atom by atom.

The advent of fermion microscope will allow new studies of many-fermion systems in optical lattices, such as measurement of high order correlations and detection of magnetic ordering. Such studies could shed light on the behavior of other fermions, in particular, electrons. This may one day advance our understanding of the diverse phenomena that arise in complex solid-state systems.

References:
[1] Waseem S. Bakr, Jonathon I. Gillen, Amy Peng, Simon Fölling, Markus Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice", Nature, 462, 74 (2009). Abstract.
[2] Jacob F. Sherson, Christof Weitenberg, Manuel Endres, Marc Cheneau, Immanuel Bloch, Stefan Kuhr, "Single-atom-resolved fluorescence imaging of an atomic Mott insulator", Nature, 467, 68 (2010). Abstract.
[3] Lawrence W. Cheuk, Matthew A. Nichols, Melih Okan, Thomas Gersdorf, Vinay V. Ramasesh, Waseem S. Bakr, Thomas Lompe, Martin W. Zwierlein, "Quantum-Gas Microscope for Fermionic Atoms", Physical Review Letters, 114, 193001 (2015). Abstract.
[4] Maxwell F. Parsons, Florian Huber, Anton Mazurenko, Christie S. Chiu, Widagdo Setiawan, Katherine Wooley-Brown, Sebastian Blatt, Markus Greiner, "Site-Resolved Imaging of Fermionic ⁶Li in an Optical Lattice", Physical Review Letters, 114, 213002 (2015). Abstract.
[5] Elmar Haller, James Hudson, Andrew Kelly, Dylan A. Cotta, Bruno Peaudecerf, Graham D. Bruce, Stefan Kuhr, "Single-atom imaging of fermions in a quantum-gas microscope", arXiv:1503.02005v2 [cond-mat.quant-gas] (2015).

Site-Dependent Evolution of Electrical Conductance from Tunneling to Atomic Point Contact

Howon Kim (left) and Yukio Hasegawa

Authors: Howon Kim and Yukio Hasegawa

Affiliation: The Institute for Solid State Physics, University of Tokyo, Japan.

In our recent work [1], the evolution of electrical conductance was investigated from tunneling to atomic point contact whose atomic geometry was precisely defined using scanning tunneling microscopy (STM). We found that the conductance evolution depends on the contact site; for instance, on-top, bridge, or hollow ('hexagonal close packed, hcp' and 'face centered cubic, fcc') site in the close-packed lattice of the substrate, indicating the importance of the atomic configuration in the conductance of the atomic junctions.

Electronic conduction through atomic-sized metal contacts is of fundamental interest as a transport mechanism though the ultimately squeezed conductor [2]. Several seminal phenomena, such as quantization and step-wise variation [3, 4] in the conductance, have been reported using a method called break junction in which the conductance is measured just before the breaking moment of a nanometer-width thin wire. Since atomic geometry of the point contact cannot be controlled and the measured conductance fluctuates at every breaking, therefore, the obtained conductances are usually analyzed in a statistical manner. Scanning tunneling microscopy (STM) has also been utilized for the study of atomic point contacts, in which the contact is formed by pushing the probe tip toward the sample surface. Because of plastic deformation of the tip by the contact formation, however, quantitatively reliable and reproducible measurements have been difficult.

Figure 1. schematic showing the atomic geometry of the atomic point contacts formed at an on-top site (left) and a 3-fold hollow site (right) of a close-packed surface.

Here, in our study, making most of the capability of the atomically resolved imaging of STM, we measured the conductance of the atomic point contact in an atomically controlled manner. We first positioned the probe tip on a specific site, for instance, on-top, bridge, or hollow (fcc and hcp) site, in the crystallographic lattice of the substrate surface (Fig. 1), and then measured the conductance while moving the tip toward the substrate from tunneling to contact regimes. It is found that the conductance evolution depends significantly on the contact site. When the contact is formed, the hollow site has the largest conductance, and among the two hollow sites the hcp site is more conductive than fcc. When the tip is pulled from the contact by just 20-30 pm, a crossover occurs and the conductance at on-top site becomes the largest.

Figure 2: electrical conductance measured from tunneling (Δz = -20 pm) to contact (Δz = -60 pm) regimes. The measured conductance G is normalized by the quantum conductance G₀ given by 2e²/h (~77.5 μS). For each conductance trace, 10 traces taken at the corresponding sites marked in the atomically-resolved STM image (inset) are averaged.

The traces of the electrical conductance measured from tunneling to contact at on-top, bridge, fcc, and hcp sites of the Pb(111) surface are shown in Fig. 2. For each plot, 10 traces obtained from the corresponding marked sites in the inset STM image are averaged. At the tip displacement Δz of -50 ~ -60 pm from the tunneling (Δz = 0), the atomic contact is formed as the conductance shows saturation around the quantum conductance G₀ given by 2e²/h (~77.5 μS). The contact conductance shows strong site dependence; the conductance at the hcp site is largest and more than 50 % larger than the one measured at the on-top site. Around Δz = -30 ~ -40 pm, that is, when the tip is located above the substrate by 20 ~ 30 pm from the contact, the plot indicates the largest conductance at on-top site.

Figure 3. Spatial mappings of the conductance at various tip displacements (upper left) topographic STM image (3.0 X 3.0 nm²) taken simultaneously with 64 X 64 conductance traces. (lower left) conductance mapping at Δz = -32pm, where the largest conductance at on-top site is enhanced (Lower right) conductance mapping at Δz = -60 pm, that is, the contact regime, where hollow site, particularly hcp site, has large conductance. (upper right) schematics explaining the site dependence of the conductance. The atoms on which the chemical interaction is exerted are marked red.

In order to spatially demonstrate the site dependence, we performed real-space mappings of the conductance in the on-top enhancement region and in the contact regime. The upper-left panel of Fig. 3 is an STM image showing the atomic contrast taken simultaneously with the conductance traces. At a tip displacement Δz of -32pm, the conductance mapping (lower-left of Fig. 3) exhibits bright contrast at the on-top site, similarly to that in the topographic image. As the conductance mapping at Δz = 0 does not have any contrast, the bright contrast indicates the conductance enhancement at the on-top site. On the other hand, the conductance mapping in the contact regime (lower right of Fig. 3, Δz = -60pm) has its contrast reversed from that of the topographic one, indicating a larger conductance at the hollow site than at the on-top site. These results clearly demonstrate that the point contact conductance is quite sensitive to the atomic configuration.

When the distance between the tip and substrate is reduced, the attractive chemical interaction is exerted between the surface and tip apex atoms. This interaction presumably opens up the conduction channel and contributes to the development of the conductance. Schematics in the upper right panel of Fig. 3 show how the chemical interaction works in the case of contacts formed at on-top and hollow sites. When the tip approaches from the tunneling regime, the attractive interaction is exerted first at the on-top site (the force-exerted atoms are marked red in the schematics) because the substrate atoms are closer at on-top site than at hollow sites, thus making the on-top conductance enhanced. In the contact regime, however, the attractive force becomes stronger at hollow sites because of the greater number of involved atoms than the on-top site. This is probably the reason why conductance becomes larger there at the contact. Obviously, theoretical studies [5], simultaneous measurements of force and conductance by atomic force microscopy [6], and/or conduction channel analysis of the atomic point contact [7] are needed to elucidate the observed conductance behaviors.

References :
[1] Howon Kim and Yukio Hasegawa, "Site-dependent evolution of electrical conductance from tunneling to atomic point contact", Physical Review Letters, 114, 206801 (2015). Abstract.
[2] Nicolás Agraı̈t, Alfredo Levy Yeyati, Jan M. van Ruitenbeek, "Quantum properties of atomic-sized conductors", Physics Reports, 377, 81 (2003). Abstract.
[3] J. M. Krans, J. M. van Ruitenbeek, V. V. Fisun, I. K. Yanson, L. J. de Jongh; "The signature of conductance quantization in metallic point contacts", Nature, 375, 767 (1995). Abstract.
[4] L. Olesen, E. Lægsgaard, I. Stensgaard, F. Besenbacher, J. Schiøtz, P. Stoltze, K. W. Jacobsen, J. K. Nørskov; "Quantized conductance in an atom-sized point contact", Physical Review Letters, 72, 2251 (1994). Abstract.
[5] Jose Manuel Blanco, Cesar González, Pavel Jelínek, José Ortega, Fernando Flores, Rubén Pérez, "First-principles simulations of STM images: From tunneling to the contact regime", Physical Review B, 70, 085405 (2004). Abstract.
[6] Yoshiaki Sugimoto, Keiichi Ueda, Masayuki Abe, Seizo Morita "Three-dimensional scanning force/tunneling spectroscopy at room temperature", Journal of Physics : Condensed Matter, 24, 084008 (2012). Abstract.
[7] Howon Kim and Yukio Hasegawa, "Site-dependent conduction channel transmission in atomic-scale superconducting junctions", arXiv:1506.05528 [cond-mat.mes-hall].

Finding Optical Transitions for Testing a Fundamental Constant’s Constancy

From left to right: José, Alexander and Hendrik  discuss the spectral analysis -- standing next to the Heidelberg electron beam ion trap, where the results were obtained.

Authors: Alexander Windberger, Hendrik Bekker, José R. Crespo López-Urrutia

Affiliation: Max-Planck-Institut für Kernphysik, Heidelberg, Germany.

We studied the uncharted optical spectra of the highly charged ions W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺, and demonstrated generally applicable methods to identify the measured spectral lines. That allowed us to infer the transition energies for proposed ultra-stable frequency standards using Hf¹²⁺ and W¹⁴⁺ ions. In Ir¹⁷⁺, optical transitions with the highest sensitivity to a potential variation of the fine structure constant α ever predicted for a stable atomic system were determined. Highly advanced atomic structure calculations were benchmarked in the extreme regime of a triple level crossing.

Fundamental constants are taken as given by Nature. Our understanding of the origin of these constants is, however, rather poor: Their values are not set within the Standard Model but have to be determined empirically. Alternative theories, such as string or coupled dark energy theories, assume that fundamental constants emerge from dynamical fields and can vary at different times or places in the universe (see [1] for a review). Therefore, probing the stability of these constants allows us to search for physics beyond the Standard Model.

Our work focusses on testing a possible variation of the fine structure constant α, which characterizes the strength of interaction between charged particles and photons. Very small variations of α would lead to a detectable shift of wavelength, or color, of light which is emitted or absorbed by atoms. Following this approach the group of Webb et al. obtained the absorption spectra of interstellar clouds billions of light years away from us and in an extensive analysis found wavelength shifts for spectra observed at different angles [2]. This was interpreted as a spatial dipole-like variation of α.

We aim to test this extraordinary claim under well-defined laboratory conditions, preventing systematic uncertainties that the astrophysical observations might suffer from. Since the Earth, the Solar System, and our galaxy all move, a spatial variation translates into an effective temporal variation which was estimated at 10^-19/year [3]. Such a minuscule drift could be measured by monitoring the frequency ratio of two highly accurate optical atomic clocks. The clock transitions should be very sensitive to an α variation, but to nothing else. Highly charged ions fulfill these requirements. With an increasing ionic charge, the wavelengths of electronic transitions decrease and leave the range accessible to lasers. Systems with level crossings are an exception. When two or more configurations are almost equal in energy, optical transitions are possible. The level crossing of the 5s and 4f subshells predicted for Ir¹⁷⁺ should enable the highest sensitivity to the sought-after α variation in a stable atomic system [4].

No detailed knowledge of the electronic structure of these ion species existed. Most heavy highly charged ions, as Ir¹⁷⁺, are experimentally unexplored, and calculations are not sufficiently accurate for these complex systems. For our studies, we used the Heidelberg electron beam ion trap, which produces and traps the ions of interest. The continuously excited ions decay by emitting radiation, of which we analyzed the optical spectrum. An exemplary measurement can be seen in Fig. 1, showing the optical spectra of W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺ (atomic numbers Z=74-78). These ions encompass the whole predicted 5s-4f level crossing region.

Figure 1. (Click on the figure to view with higher resolution) Typical spectral map of Ir ions measured using the Heidelberg electron beam ion trap. For this measurement we acquired spectra at 10 V intervals of the electron beam acceleration potential. New groups of fluorescence lines start to appear when the electron beam energy reaches the ionization potential of an ionic charge state. The new charge state is produced more efficiently as the electron beam energy further increases, and the fluorescence lines become stronger until the ionization threshold of the next higher charge state is reached. At this point the ion population is transferred to the next charge state, which starts to fluoresce, while the former one disappears. This dependence of the fluorescence intensity on the acceleration potential is depicted in the right graph. It is notable that this section of the optical spectrum assigned to Ir¹⁷⁺ already shows a dense manifold of spectral lines. In order to derive the level structure from the spectrum, sophisticated identification schemes had to be applied.

Subsequently, we assigned the measured spectral lines to their corresponding electronic transitions to establish the level scheme [5]. Given the large theoretical uncertainties, a direct comparison of calculated and measured spectra is futile. Instead, we used three alternative methods to identify the spectral lines.

First, we exploited the fact that these ions are isoelectronic, since they have the same number of electrons, and thus similar atomic structures. Over a limited range of atomic numbers, the transition energies depend on the respective nuclear charge with a simple polynomial scaling. By comparison between the measured scaling functions and theoretical predictions we were able to reliably identify all underlying transitions as can be seen in Fig. 2.

Figure 2. (Click on the figure to view with higher resolution) Identification of isoelectronic transitions using their characteristic energy scaling. (a) Measured spectra of W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺ (black lines). An algorithm found nine isoelectronic transition energies that obey simple quadratic scaling laws (colored lines) as expected from theoretical considerations. (b) By comparing the experimentally determined constant offset A and the linear term B (full symbols) to the calculated ones (open symbols) an unambiguous identification of the underlying transitions could be achieved.

This method could be independently confirmed by measuring the identified transitions in Ir¹⁷⁺ with increased resolution and accuracy. The spectral lines revealed a characteristic line shape caused by the 8 T magnetic field present at the position of the trapped ions. The observed line shapes were individually modelled according to the Zeeman effect, leading to an independent verification in perfect agreement with the scaling method.

The identified transitions allowed us to test advanced atomic structure calculations for the first time in systems with such a complex level crossing of 4f ¹² 5s², 4f¹³ 5s, and 4f ¹⁴ configurations. We found that only relativistic multi-reference Fock-space coupled cluster calculations consistently showed a fair agreement with most of the observed lines.

A direct application is the determination of the transition energies of two proposed optical clock transitions with a potential relative frequency uncertainty of less than 10^-19 in W¹⁴⁺ and Hf¹²⁺ [6], another isoelectronic ion. Although we did not measure the spectrum of Hf¹²⁺, we were able to extrapolate the transition energy by applying the established energy scaling. Our experimental uncertainty is at least one order of magnitude smaller than that of predictions.

These clock transitions are exceptionally stable. However, they are not sensitive to a variation of the fine structure constant. For that, Ir¹⁷⁺ is ideal. By searching our data, we found closed transition cycles (Rydberg-Ritz principle) combining the identified with unidentified transitions. This enabled us to find two possible, but mutually excluding, candidates for the proposed α-sensitive transitions. We are currently performing more accurate measurements to remove this ambiguity.

Our method, line assignments by isoelectronic scaling of transitions (LINE ASSIST) is a straight-forward and general tool for exploring unknown spectra of highly charged ions. With the recent successful application of sympathetic cooling to highly charged ions [7], much higher accuracy can be achieved in future work: the ion temperature was reduced by nearly six orders of magnitude and the Doppler width accordingly. The experimental values for the transition energies obtained in the present work are needed for follow-up laser spectroscopy studies, applications as optical clock transitions, and testing the constancy of fundamental constants.

References:
[1] Jean-Philippe Uzan, "The fundamental constants and their variation: observational and theoretical status". Review of Modern Physics, 75, 403–455 (2003). Abstract.
[2] J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, M. B. Bainbridge, "Indications of a Spatial Variation of the Fine Structure Constant". Physical Review Letters, 107, 191101 (2011). Abstract.
[3] J.C. Berengut, V.V. Flambaum, "Manifestations of a spatial variation of fundamental constants in atomic and nuclear clocks, Oklo, meteorites, and cosmological phenomena". Europhysics Letters, 97, 20006 (2012). Abstract.
[4] J.C. Berengut, V.A. Dzuba, V.V. Flambaum, A. Ong, "Electron-Hole Transitions in Multiply Charged Ions for Precision Laser Spectroscopy and Searching for Variations in α". Physical Review Letters, 106, 210802 (2011). Abstract.
[5] A. Windberger, J.R. Crespo López-Urrutia, H. Bekker, N.S. Oreshkina, J.C. Berengut, V. Bock, A. Borschevsky, V.A. Dzuba, E. Eliav, Z. Harman, U. Kaldor, S. Kaul, U.I. Safronova, V.V. Flambaum, C.H. Keitel, P.O. Schmidt, J. Ullrich, O.O. Versolato, "Identification of the Predicted 5s−4f  Level Crossing Optical Lines with Applications to Metrology and Searches for the Variation of Fundamental Constants". Physical Review Letters, 114, 150801 (2015). Abstract.
[6] V. A. Dzuba, A. Derevianko, V.V. Flambaum, "High-precision atomic clocks with highly charged ions: Nuclear-spin-zero f ¹²-shell ions". Physical Review A, 86, 054501 (2012). Abstract.
[7] L. Schmöger, O.O. Versolato, M. Schwarz, M. Kohnen, A. Windberger, B. Piest, S. Feuchtenbeiner, J. Pedregosa-Gutierrez, T. Leopold, P. Micke, A.K. Hansen, T.M. Baumann, M. Drewsen, J. Ullrich, P.O. Schmidt, J.R. Crespo López-Urrutia, "Coulomb crystallization of highly charged ions". Science, 347, 1233 (2015). Abstract.

Radioactive Iron - An Astrophysical Clock for Nucleosynthesis

Anton Wallner (photo credit: Stuart Hay, ANU)

Author: Anton Wallner^1,2

Affiliation:
¹Dept of Nuclear Physics, Australian National University, Canberra, Australia,
²VERA Laboratory, Faculty of Physics, University of Vienna, Austria.

Massive stars may end their life in a supernova explosion - one of the most violent events in our galaxy. Supernovae are thus massive exploding stars that return a large fraction of the star’s material back to the interstellar medium. Nucleosynthesis in massive stars shapes therefore the elemental abundance pattern and the galactic chemical evolution, e.g. our solar system is the product of many preceding star generations [1].

Extraterrestrial material in the form of interstellar dust can also enter the solar system and may be deposited on Earth [2]. Their nucleosynthetic history is locked in its isotopic signatures. Interstellar matter will contain stable isotopes but also freshly produced radionuclides. Thus, the existence of fresh radionuclides in the interstellar medium serves as radioactive clocks for their recent production.

Radioactive iron-60 (Fe-60) is a radionuclide with a half-life of about 2 million years. It is predominantly formed in massive stars at the end of their lives just before and during a supernova and then distributed by the explosion into the interstellar space. Fe-60 is thus an ideal candidate to monitor supernova explosions and recent element synthesis.

Since this radioactive iron is not naturally present on Earth, trace amounts of this isotope are a particularly sensitive astrophysical marker. Supernova-produced iron from the interstellar medium can be captured by the Earth on its way through the Milky Way. If one finds this radioactive iron-60 in the terrestrial environment (apart from artificial production), it must come from cosmic explosions; more precisely from the last few million years, otherwise it would have long since decayed.

With its half-life in the million year range, Fe-60 is suitable for dating astrophysical events, such as supernova explosions. The usability of this isotope, in particular as an astrophysical clock, was however limited, because the lifetime of this nuclide was not exactly known - an important prerequisite to serve as a chronometer. There were two measurements so far, one from 1984 [3] and another very precise one from 2009 [4], but both were almost a factor of 2 different.

Iron-60 – a monitor for element synthesis and nearby supernova explosions

This isotope has a variety of applications in astrophysics. The main reason is, it is observed in space through its radioactive decay and it is not naturally present on Earth.

Researchers can virtually monitor live nucleosynthesis in massive stars, e.g. active regions of element formation and also the distribution of ejected stellar material in the Milky Way. Iron-60 can be observed directly in our Milky Way via space-born satellites through its decay and the characteristic radiation emitted (similar to another radioactive isotope, Al-26) [5,6]. These observations clearly demonstrate its presence in the interstellar medium. Such radionuclides were produced 'recently", i.e. within a few half-lives. As their decay is observed, one needs the half-life to calculate the number of atoms present in the interstellar medium.

Knie et al., in a pioneering work at the Technical University of Munich, Germany, found Fe-60 at the ocean floor in a manganese crust indicating a possible near-Earth supernova activity about 2 to 3 million years ago [7,8]. Iron-60 was present at the birth of our solar system, more than four billion years ago. This is evidenced today in pre-solar material by overabundances of Fe-60’s decay products [9].

Establishing a connection between these observations of the radioactive decay of Fe-60 and the number of iron-60 atoms, however, requires a precise knowledge of its life-time, that is, its half-life.

How to measure a half-life of millions of years?

Firstly, one needs a sufficient number of atoms. We, a team of scientists from Australia, Switzerland and Austria [10] used artificially produced iron-60 extracted from nuclear waste of an accelerator facility in Switzerland. This iron fraction was separated by specialists in Switzerland and then analyzed for its Fe-60 content. The number of radioactive atoms must be measured in absolute terms, and this is a difficult task and was probably the reason for the discrepancy in earlier measurements.

Figure caption: Identification spectra with a clear separation of the main background Ni-60 from Fe-60: single atom counting of Fe-60 at the ANU - each point represents a single atom. Combining up to 5 different detector signals results in an unsurpassed sensitivity of Fe-60/Fe = 4 X 10^-17 (A. Wallner et al., [10]).

We used a very sensitive method to accurately determine the low number of Fe-60 atoms in their sample: accelerator mass spectrometry (AMS) [11,12], a technique that counts atoms directly and that is used for example, also for radiocarbon dating. The Fe-60 measurements were carried out at the Heavy Ion Accelerator Facility at the Australian National University in Canberra, one of the world's most sensitive facilities to detect tiny traces of rare elements in our environment. With this extremely sensitive facility no background could influence our results. Further, we counted Fe-60 relative to another radioactive iron isotope, namely Fe-55. Fe-55 is well known and easier to measure. By using the same measurement setup for Fe-60 and Fe-55, we are confident that potential unknown errors were minimized in our work.

The new value for the half-life of Fe-60 [10] shows a good agreement with the precise measurement by Rugel et al. from the year 2009 [4]. According to our result, they had done a very good job! Combining both measurements, this allows now the use of Fe-60 as a precise cosmic clock. It eliminates a long-standing discrepancy and thus establishes this radionuclide as a precise astrophysical chronometer.

As another additional outcome we encourage other groups to repeat such kind of measurements. With respect to the difficulty of performing measurements of long half-lives, independent and complementary techniques are essential for settling open and difficult-to-solve questions.

References:
[1] R. Diehl, D.H. Hartmann and N. Prantzos (eds.), "Astronomy with Radioactivities", Lecture Notes in Physics, vol. 812, Springer, Berlin (2011). Google Books Preview.
[2] A. Wallner, T. Faestermann, C. Feldstein, K. Knie, G. Korschinek, W. Kutschera, A. Ofan, M. Paul, F. Quinto, G. Rugel, P. Steier, "Abundance of live ²⁴⁴Pu in deep-sea reservoirs on Earth points to rarity of actinide nucleosynthesis", Nature Communications, 6:5956; DOI: 10.1038/ncomms6956 (2015). Full Article.
[3] Walter Kutschera, Peter J. Billquist, Dieter Frekers, Walter Henning, Kenneth J. Jensen, Ma Xiuzeng, Richard Pardo, Michael Paul, Karl E. Rehm, Robert K. Smither, Jan L. Yntema, Leonard F. Mausner, "Half-life of 60Fe", Nuclear Instruments and Methods in Physics Research, Section B, 5, 430 (1984). Abstract.
[4] G. Rugel, T. Faestermann, K. Knie, G. Korschinek, M. Poutivsev, D. Schumann, N. Kivel, I. Günther-Leopold, R. Weinreich, and M. Wohlmuther, "New Measurement of the ⁶⁰Fe Half-Life", Physical Review Letters, 103, 072502 (2009). Abstract.
[5] W. Wang, M. J. Harris, R. Diehl, H. Halloin, B. Cordier, A.W. Strong, K. Kretschmer, J. Knödlseder, P. Jean, G. G. Lichti, J. P. Roques, S. Schanne, A. von Kienlin, G. Weidenspointner, and C. Wunderer, "SPI observations of the diffuse ⁶⁰Fe emission in the galaxy", Astronomy & Astrophysics, 469, 1005 (2007). Abstract.
[6] Roland Diehl, "Nuclear astrophysics lessons from INTEGRAL", Reports on Progress in Physics. 76, 026301 (2013). Abstract.
[7] K. Knie, G. Korschinek, T. Faestermann, E. A. Dorfi, G. Rugel, A. Wallner, "⁶⁰Fe Anomaly in a Deep-Sea Manganese Crust and Implications for a Nearby Supernova Source", Physical Review Letters, 93, 171103 (2004). Abstract.
[8] C. Fitoussi, G. M. Raisbeck, K. Knie, G. Korschinek, T. Faestermann, S. Goriely, D. Lunney, M. Poutivtsev, G. Rugel, C. Waelbroeck, A. Wallner, "Search for Supernova-Produced ⁶⁰Fe in a Marine Sediment", Physical Review Letters, 101, 121101 (2008). Abstract.
[9] A. Shukolyukov, G.W. Lugmair, "⁶⁰Fe in eucrites", Earth and Planetary Science Letters, 119, 159 (1993). Abstract ; A. Shukolyukov, G.W. Lugmair, "Live iron-60 in the early solar system", Science, 259, 1138 (1993). Abstract.
[10] A. Wallner, M. Bichler, K. Buczak, R. Dressler, L. K. Fifield, D. Schumann, J. H. Sterba, S. G. Tims, G. Wallner, W. Kutschera, “Settling the half-life of ⁶⁰Fe – fundamental for a versatile astrophysical chronometer”, Physical Review Letters, 114, 041101 (2015). Abstract.
[11] Hans-Arno Synal, "Developments in accelerator mass spectrometry", International Journal of Mass Spectrometry, 349–350, 192 (2013). Abstract.
[12] Walter Kutschera, "Applications of accelerator mass spectrometry", International Journal of Mass Spectrometry, 349–350, 203 (2013). Abstract.

Collisions of Matter-Wave Solitons

[Left to right] De Luo, Jason Nguyen, and Randy Hulet

Authors: 
Jason H.V. Nguyen¹, Paul Dyke², De Luo¹, Boris A. Malomed³, Randall G. Hulet¹

Affiliations:
¹Department of Physics and Astronomy, Rice University, Houston, Texas, USA
²Centre of Quantum and Optical Science, Swinburne University of Technology, Melbourne, Australia
³Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Israel

Link to Hulet Atom Cooling Group >>

Solitons are localized wave disturbances that propagate without changing shape or spreading out. This remarkable effect depends on a self-attraction created by the medium the solitons propagate in. If the self-attraction increases with the size of the wave amplitude, solitons with larger amplitude are “squeezed” harder to keep them from spreading out, while smaller amplitude, broader solitons require a gentler squeeze. Solitons have been observed in a variety of wave phenomena, including pulses of light traveling in optical fibers, ocean waves, and in many other diverse phenomena, perhaps even in the collective oscillations of protein and DNA molecules. The largest known soliton-like object is the Great Red Spot on Jupiter.

We study matter-wave solitons, which are much rarer. Quantum mechanics tells us that matter can exhibit wave-like or particle-like behavior, depending on the circumstances. Perhaps the most exotic are collective matter waves known as Bose-Einstein condensates consisting of millions of atoms cooled to near absolute zero temperature, where the atoms act in unison and behave as if they had a common purpose. These Bose-Einstein condensates are matter-wave solitons when the interactions between atoms in the condensate are attractive, and when they are confined in a one-dimensional guide.

Early experiments studying matter-wave solitons examined properties of single solitons [1] and soliton trains [2]. In our experiment, originally published in Nature Physics [3], we create two nearly identical matter-wave solitons consisting of approximately 28000 lithium atoms per soliton. They are separated by 26 micrometers using a cylindrically focused laser beam, which acts as a barrier, and are held at opposite sides of a one-dimensional guide formed by an infrared laser beam. The guide is curved along its axis, forming a bowl-shaped potential, so that when we turn the barrier off, the solitons fall inward and collide multiple times as they oscillate back and forth.

A defining property of ideal solitons is that they pass through one another without changing their shape, amplitude, or velocity [4,5,6]. Yet, when we did the experiment, we observed violent collisions that produced interference minima and maxima in the collision region. We found the character of the collision and the interference depended on a property of a wave known as its “phase”, in agreement with the general theory of solitons. In the case that the solitons were nearly in-phase, they appear to merge during the collision and then pass through one another. When solitons were nearly out-of-phase, however, we were faced with the contradiction that solitons appeared to closely approach each other, but then to bounce off each other.

Figure 1: (a) Time evolution showing a full period of oscillation (τ=32 ms) for the case when the solitons are nearly in-phase. At the 1/4 and 3/4 points the solitons appear to merge and afterwards pass through one another. (b) Similar to (a) except for the case when the solitons are nearly out-of-phase. At the 1/4 and 3/4 points the solitons appear to be separated by a small gap, after which they appear to bounce off each other.

Since all solitons are expected to pass through one another, not just the ones with the “correct” phase, we did an experiment with “tagged” solitons: one soliton was made smaller to distinguish it from the other. Upon repeating the experiment, we discovered that even the out-of-phase solitons passed through one another. The interference at the point of collision had created a node, or empty space between solitons that only created the appearance of reflection.

Figure 2: Time evolution showing a full period of oscillation (τ=32 ms) with tagged solitons that are nearly out of phase. At the 1/4 and 3/4 points the solitons maintain a minimum gap between them during the collision, however afterwards we observe that the solitons pass through one another as they did in the nearly in-phase case.

Since solitons depend on self-attraction, they can collapse into high density compact objects when their density becomes too large. By controlling the strength of the interaction, we observed that in-phase soliton collisions can result in collapse, as the increasing density during collision causes their self-attraction to be overwhelming. In addition to the two solitons annihilating each other in this way, we also observed that a pair of solitons may merge into a single, smaller soliton.

Although independent solitons have been well-understood for some time, their interaction has brought new insights. In the future, we will explore how solitons can be made into an interferometer, much like a matter-wave version of a laser gyro. To do this, we will use a sheet of light as a beam-splitter for solitons, where solitons have a quantum mechanical probability to be reflected or transmitted, each taking separate paths around a closed loop.

References:
[1] L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, “Formation of a matter-wave bright soliton”, Science, 296, 1290-1293 (2002). Abstract.
[2] Kevin E. Strecker, Guthrie B. Partridge, Andrew G. Truscott, Randall G. Hulet, “Formation and propagation of matter-wave soliton trains”, Nature, 417, 150-153 (2002). Abstract.
[3] Jason H. V. Nguyen, Paul Dyke, De Luo, Boris A. Malomed, Randall G. Hulet, “Collisions of matter-wave solitons”, Nature Physics, 10, 918-922 (2014). Abstract.
[4] N.J. Zabusky & M.D. Kruskal. “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states”, Physical Review Letters, 15, 240 (1965). Abstract.
[5] V.E. Zakharov, A.B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media”, Soviet Physics JETP, 34, 62 (1972). Full Article.
[6] G.L. Lamb, “Elements of soliton theory”, New York, Wiley (1980).

Antineutrino Monitoring for the Iranian Heavy Water Reactor

[From Left to Right] Eric Christensen, Patrick Huber, Patrick Jaffke, Thomas E. Shea

Authors: Eric Christensen¹, Patrick Huber¹, Patrick Jaffke¹, Thomas E. Shea²

Affiliation:
¹Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia, USA
²TomSheaNuclear Consulting Services, Gorgengasse 10/25, 1190 Vienna, Austria

Antineutrino reactor monitoring has been proposed in the 1970s; steady progress in detector technology will make this technology practically feasible within 1-2 years. In this contribution we investigate how this decades-old idea can be applied to the recent situation in Iran, more specifically we discuss the benefits of using antineutrinos to monitor the heavy water reactor at Arak, the IR-40. One of the key findings is that a detector situated outside the reactor building would meet the verification goals identified by the International Atomic Energy Agency for plutonium production or diversion from declared inventories.

All nuclear reactors produce plutonium during operation, however only very specific types of reactors are suitable for the production of weapons-grade plutonium. Historically, all plutonium used in nuclear weapons has been obtained from either heavy water or graphite moderated reactors fueled with natural uranium. At the beginning of their respective weapons programs these reactors typically had a thermal power output in the 20-250 MW_th range, which is considerably less than typical commercial power reactors. As shown in previous work [1,2] reactors with a power output in this range represent a particularly suitable target for antineutrino reactor monitoring.

Iran is constructing a 40 MW_th heavy water moderated, natural uranium fueled reactor at Arak, the so-called IR-40. Given its design characteristics, this reactor is ideally suited to make weapons-usable plutonium with an annual output of about 10 kg. It is estimated that about 4 kg of plutonium are sufficient to make a simple explosive device with a yield upwards of several kilotons of TNT equivalent [3]. Iran states that the IR-40 will be used exclusively for peaceful purposes, in particular isotope production for medical applications. Nonetheless, the IR-40 is, after the uranium enrichment program, one of the key issues in the ongoing negotiations between Iran and the P5+1 countries (i.e., these are the five permanent members of the UN Security Council: United States, Russia, China, United Kingdom, France plus Germany). A possible solution could be the conversion of the reactor to operate with enriched uranium reducing its plutonium output significantly without limiting its ability to provide isotopes for civilian applications [4].

Any agreement reached about the the future of the IR-40 will present a challenge for effectively monitoring its implementation. The historic example of the first nuclear crisis in the Democratic People's Republic of Korea (DPRK) in the 1990's serves as a stark reminder that providing reliable safeguards and timely warning of possible breaches is very difficult in a host country which is not deterred by international isolation. In the DPRK example the consequences were intermittent, but critically timed, denials of inspector access at the required level and ultimately, this allowed the DPRK to further its nuclear weapons capabilities while negotiating for an end of the plutonium program [5].

Antineutrino monitoring was proposed in the late 1970s by Borovoi and Mikaelyan [6]. The number of antineutrinos produced and their energy spectrum depends in a well-defined manner on the reactor power and on the relative contribution to fission from the various fissile isotopes. Thus a careful measurement of both the number of antineutrinos and their energy distribution allows, in principle, to infer the reactor power and the amount of plutonium in the core. Plutonium production is an inevitable result of reactor operation and thus in itself not indicative of any malfeasance. A quantitative indicator for a diversion of plutonium is a mismatch between the amount of plutonium produced by a reactor core and the amount of plutonium residing in the reactor core. Neither of these two quantities is easily measured directly and thus, suitable proxies are used: the reactor's power history provides a means to compute the amount of plutonium produced whereas a detailed history of reactor fueling allows to track the in-core plutonium content. Both indicators rely on a complete, uninterrupted data record -- should there be any loss of this so-called continuity of knowledge (CoK), the ability to determine any mismatch between produced and in-core plutonium is lost; any recovery is difficult and may be only partial. We argue that antineutrino monitoring could provide a robust and non-intrusive method to recover from a loss of the CoK.

Specifically, we consider a hypothetical IR-40 case which to some extent draws on the experience with the DPRK: There is full safeguards access for N-1 months. The reactor is shut down in the N^th month and at the same time the CoK is lost. The reasons for loss of the CoK can span a wide range from merely technical issues, to a diplomatic standoff, to an attempt at proliferation. The basic question arising in this scenario is: Was the reactor refueled or not? Obviously, finding an answer in a timely fashion would be of prime interest to the international community and in many cases also be in the best of Iran's interests.

In our earlier work [1] we demonstrated quantitatively that a measurement of the energy spectrum of antineutrinos emitted from a reactor makes it possible to determine the burn-up and, thus, the plutonium content with good accuracy and in a timely manner. Here, we make the same assumptions as in Refs.[1,2] about the detection system, we assume that product of efficiency and number of target protons is 4.3 X 10²⁹, which for a realistic detector translates to a detector mass in the 5-15 ton range. This is still light enough to envisage a detector system which fits inside a standard 20 feet intermodal shipping container. Furthermore, we assume sufficient background rejection capabilities to allow for surface operation.

For a long time this was considered not possible for antineutrino detectors, but recently a Japanese group succeeded in the detection of reactor antineutrinos from the back of a van [7]. Nonetheless, we have to point out that at this point in time no detector system with all the required characteristics exists. At the same time, there are about a dozen collaborations world-wide attempting to produce suitable detectors (for a different purpose) and it seems very likely that fully functional prototypes will demonstrate feasibility within 12 months. In our estimate, a detector inside its shipping container can be deployed outside the reactor containment building of the IR-40 at a distance of 19 m from the center of the reactor core.

Figure 1: In the upper panel, data points show the event rate spectrum obtained in a 90 day data taking period for a core of average age of 45 days. The error bars indicate the statistical error in each bin. The blue line indicates the corresponding expected event rate spectrum for a core of average age of 315 days. The lower panel shows the difference in event rates between the 45 day core and the 315 day core and the corresponding statistical error bars. Figure and caption from Ref.[2].

Our analysis of the IR-40 is using standard reactor physics calculations made using commercially available software and the details are given in Ref.[2]. This calculation establishes the relationship between the fission rates and the content of the fissile isotopes in the core. In Fig.1 we show the resulting event rate spectrum for a core of 45 day average age (data points with statistical error bars) and for comparison the expected event rates for a core of 315 days of age (blue line). It can be seen clearly, that the older core emits neutrinos with a lower mean energy corresponding to 7 kg of plutonium, whereas the fresh core has no plutonium. This difference remains statistically significant even in the presence of realistic systematic uncertainties.

Figure 2: Shown is the 1σ accuracy for the determination of the plutonium content of the reactor as a function of time in the reactor cycle. The data-taking period is 90 days each. Dashed error bars indicate the accuracy from a fit to the plutonium fission rate f_Pu, whereas the solid error bars show the result of a fit constrained by a burn-up model. The blue line indicates operation without refueling and the orange line indicates operation with a refueling after 270 days. Figure and caption from Ref.[2].

The quantitative sensitivity to the plutonium content is shown in Fig.2, where the vertical axis shows the amount of plutonium in the reactor core as a function of time. The blue curve shows the change of plutonium content for the case of no refueling, whereas the orange curve assumes that the irradiated core, containing 8\,kg of plutonium, was replaced with a fresh core after 270 days of irradiation. 270 days is the time at which the isotopic content of plutonium-239 [8] drops to 93% of all plutonium and thus formally ceases to be considered weapons-grade. Within the first 90 days after the IR-40 shutdown (shown as gray vertical band) the two cases can be clearly distinguished by the antineutrino monitoring data. Even partial core refuelings corresponding to as little as 2 kg of removed plutonium could be detected at 90% confidence level. Alternatively, a full core refueling would be detected within about 9 days at 90% confidence level.

To summarize, in this note, based on the results of Ref.[2] we demonstrate that antineutrino monitoring of the IR-40 would provide a high-level tool to assess the amount of in-core plutonium as well as the amount of produced plutonium. Both tasks can be accomplished withing the 90 day period set by the International Atomic Energy Agency (IAEA) and with a quantitative accuracy greatly exceeding 1 significant quantity (8 kg) as required by the IAEA. This technique is non-intrusive and independent from any other safeguards information, in particular the CoK is not required. This combination of features appears to be a considerable and practically valuable characteristic not offered by any other known method. Needless to say, these advantages would not only arise for antineutrino monitoring of the IR-40 but for any reactor with a power output in the 20-250 MW_th range, which are the most likely candidates for being an entry point for a plutonium-based nuclear weapons program. Antineutrino reactor monitoring would not replace other techniques but in combination with those techniques can enhance the overall effectiveness and reliability of non-proliferation safeguards. A practical system appears feasible on a timescale of 1-2 years and the next step would be an actual antineutrino reactor monitoring experiment.

This work was supported by the U.S. Department of Energy under contract DE-SC0003915 and by a Global Issues Initiative grant by the Institute for Society, Culture and Environment at Virginia Tech.

References:
[1] Eric Christensen, Patrick Huber, Patrick Jaffke, "Antineutrino reactor safeguards - a case study". arXiv:1312.1959v2 [physics.ins-det] (2013).
[2] Eric Christensen, Patrick Huber, Patrick Jaffke, Thomas E. Shea, "Antineutrino Monitoring for Heavy Water Reactors". Physical Review Letters, 113, 042503 (2014). Abstract.
[3] T. B. Cochran and C. E. Paine, Technical Report, Natural Resources Defense Council, Inc. (1995).
[4] O. Heinonen, "Can the Nuclear Talks With Iran Be Saved?" Foreign Policy, 1 (January 27, 2011). Full Article.
[5] J. S. Wit, D. Poneman, and R. L. Gallucci, "Going Critical: The First North Korean Nuclear Crisis" (Brookings Institution Press, 2007).
[6] A. A. Borovoi, L. A. Mikaélyan, "Possibilities of the practical use of neutrinos". Soviet Atomic Energy, 44, 589 (1978). Link.
[7] S. Oguri, Y. Kuroda, Y. Kato, R. Nakata, Y. Inoue, C. Ito, M. Minowa, "Reactor antineutrino monitoring with a plastic scintillator array as a new safeguards method". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 757, 33 (2014). Abstract.
[8] Thomas Mo Willig, Cecilia Futsaether, Halvor Kippe, "Converting the Iranian Heavy Water Reactor IR-40 to a More Proliferation-Resistant Reactor". Science and Global Security, 20, 97 (2012). Full Article.

Atoms Under the Magnifying Glass: Direct Observation of the Nodal Structures of Electronic States

Aneta Stodolna (left) and Marc J.J. Vrakking

Authors: Aneta Stodolna¹, Marc J.J. Vrakking²  

Affiliation:
¹FOM Institute AMOLF, Amsterdam, Netherlands,
²Max-Born-Institut, Berlin, Germany.

To describe the microscopic properties of matter and its interaction with the external world, quantum mechanics uses wave functions, whose structure and time dependence is governed by the Schrödinger equation. In atoms, electronic wave functions describe - among other things - charge distributions existing on length-scales that are many orders of magnitude removed from our daily experience. In physics laboratories, experimental observations of charge distributions are usually precluded by the fact that the process of taking a measurement changes a wave function and selects one of its many possible realizations. For this reason, physicists usually know the shape of charge distributions through calculations that are shown in textbooks. But in the last few years, this has started to change. Recent experiments have visualized the nodal structure of electronic states of hydrogen and helium on two-dimensional detectors.

The development of quantum mechanics in the early part of the last century had a profound influence on the way that scientists understand the world. Central to quantum mechanics is the concept of a wave function that satisfies the time-dependent Schrödinger equation. According to the Copenhagen interpretation, this wave function describes the probability of observing the outcome of measurements that are performed on a quantum mechanical system, such as measurements of the energy of the system or the position or momenta of its constituents. This allows reconciling the occurrence of non-classical phenomena on the micro-scale with manifestations and observations made on the macro-scale, which correspond to viewing one or more of countless realizations described by the wave function.

Despite the overwhelming impact on modern electronics and photonics, grasping quantum mechanics and the many possibilities that it describes continues to be intellectually challenging, and has motivated numerous experiments illustrating the intriguing predictions contained in the theory. For example, the 2012 Nobel Prize in Physics was awarded to Haroche and Wineland for their work on measurement and control of individual quantum systems in quantum non-demolition experiments, paving the way to more accurate optical clocks and, potentially, future quantum computers.

About thirty years ago, Russian theoreticians proposed an intriguing method for measuring properties of wave functions. They suggested studying atomic ionization in a static electric field that projects the electrons onto a two-dimensional detector and predicted interference patterns, with one of two possible origins. First of all, interference patterns result from path length differences between different trajectories that the electron can take between the atom and the detector. As clearly shown in the famous double-slit experiment on interference of single electrons (voted "the most beautiful physics experiment", in a poll conducted by Physicsworld about a decade ago) electrons exhibit both particle- and wave-like behavior.

The wave-like behavior derives from the de Broglie wavelength that quantum mechanics associates with any moving particle. The lower the kinetic energy of the electron, the larger the de Broglie wavelength is. Correspondingly, for low enough kinetic energies, the de Broglie wavelength becomes observable on macroscopic length scales. Secondly, in the case of hydrogen, the interference patterns can directly reflect the nodal structure of the electronic wave function. The fact that this is so, is due to the special status of hydrogen as nature´s only single-electron atom. Due to this circumstance, the hydrogen wave function can be written as the product of two functions that describe how the wave function changes as a function of two, so-called “parabolic coordinates”, which are linear combinations of the distance of the electron from the H+ nucleus “r”, and the displacement of the electron along the electric field axis “z”. Importantly, the shape of the two parabolic wave functions is independent of the strength of the static electric field, and therefore stays the same as the electron travels from the place where the ionization takes place to the two-dimensional detector.

Last year we published a paper, where we reported experiments for hydrogen atoms [1]. Ground state hydrogen atoms were optically excited to electronic states of interest, using two precisely tunable laser sources, and a delicate electrostatic lens was used to magnify the imprint of the electrons on the two-dimensional detector to millimeter-scale dimensions, so the nodal patterns of the wave functions could be observed with the naked eye. The main result is shown in Figure 1. This figure shows raw camera data for four measurements, where the hydrogen atoms were excited to states with 0, 1, 2 and 3 nodes in the wave function for the ξ = r+z parabolic coordinate. The nodes can be easily recognized. The experimental arrangement served as a microscope, allowing us to look deep inside the hydrogen atom, with a magnification of approximately a factor twenty-thousand.

Figure 1: (left) two-dimensional projection of electrons resulting from excitation of hydrogen atoms to four electronic states labeled with a set of quantum numbers (n1,n2,m) and having (from top to bottom) 0, 1, 2 and 3 nodes in the wave function for the ξ = r+z parabolic coordinate; (right) comparison of the experimentally measured radial distributions (solid lines) with results from quantum mechanical calculations (dashed lines), illustrating that the experiment has measured the nodal structure of the quantum mechanical wave function (copyright: American Physical Society).

More recently, we have performed similar experiments for the helium atom [2]. After the hydrogen atom, the helium atom is nature´s simplest atom, consisting of a doubly-charged nucleus surrounded by two electrons. The presence of two electrons in the atom introduces the concept of electron correlation. Remarkably, we saw that we could turn the electron correlation in helium on or off at will.

In the experiment, helium atoms were ionized by the absorption of an ultra-violet (UV) photon. Like in the hydrogen experiment, the photon energy of the UV light was tuned in such a manner that it was only just sufficient for ionization of the atom, thus producing very slow photoelectrons that were accelerated by an electric field towards a two-dimensional detector. At most of the UV photon energies, interference patterns were measured that could be explained by considering differences in the lengths of possible paths of the electron on the way to the detector (see Figure 2). Here, two paths differing by an integral number of de Broglie wavelengths interfere constructively, whereas two paths differing by a half-integer number of de Broglie wavelengths interfere destructively.

Figure 2: Sample images recorded for ionization of helium atoms. The four images contain interference patterns that result from path length differences along trajectories that the electron can take between the atom and the detector. The labels contained in the figures indicate the energy of the states used in the experiment defined with respect to the field-free ionization limit (copyright: American Physical Society).

However, at a number of UV photon energies the interference patterns looked markedly different, extending out to a much larger radius and containing a different number of nodes compared to measurements at slightly lower or higher photon energy (see Figure 3). A theoretical analysis revealed that at these energies the effect of electron correlation was momentarily suppressed. The suppression occurs when two electronic states, whose precise energies depend on the strength of the electric field, accidentally occur at almost identical energies. These two states then interact with each other, and for a particular value of the electric field, the energy exchange between the two parabolic coordinates is almost completely turned off. In other words, the atom becomes hydrogenic.

Figure 3: Sometimes helium behaves like a hydrogen atom, and interference patterns are measured that reveal the nodal structure of the electronic wave function that is excited (middle image). These cases stand out because the nodal pattern of these images is very different from those recorded at nearby excitation energies (left and right image), and the images extends farther radially. The labels contained in the figures indicate the energy of the states used in the experiment defined with respect to the field-free ionization limit (copyright: American Physical Society).

Correspondingly, the nodal pattern measured on the detector is once again the nodal pattern of the electronic state that is optically excited. The effect was found to be very subtle: tiny changes (<< 1%) in the strength of the electric field are sufficient to convert an atom that reveals the nodal pattern of its wave function in a hydrogen-like manner, into an atom where electron correlation removes the observability of this nodal pattern, and where the observed interference patterns are completely determined by path length differences between the atom and the detector.

In this manner, the hydrogen and helium atom constitute a wonderful nano-scale laboratory for studies of fundamental quantum mechanics, providing text-book images of nodal patterns in the case of hydrogen, and revealing the onset of electron correlation in the case of helium.

References:
[1] Aneta Stodolna, Ymkje Huismans, Arnaud Rouzée, Frank Lépine, Marc J. J. Vrakking, "Photoelectron holography in strong optical and dc electric fields". Journal of Physics: Conference Series 488, 012007 (2014). Full Article.
[2] A. S. Stodolna, F. Lépine, T. Bergeman, F. Robicheaux, A. Gijsbertsen, J. H. Jungmann, C. Bordas, M. J. J. Vrakking, "Visualizing the Coupling between Red and Blue Stark States Using Photoionization Microscopy". Physical Review Letters, 113, 103002 (2014). Abstract.