Comparing Matter Waves in Free Fall

[From Left to Right] J. Hartwig, D. Schlippert, E. M. Rasel

Authors: J. Hartwig, D. Schlippert, Ernst M. Rasel

Affiliation: Institut für Quantenoptik and Centre for Quantum Engineering and Space-Time Research (QUEST), Leibniz Universität Hannover, Germany

Introduction to Einstein’s Equivalence Principle

Einstein’s general relativity is based on three fundamental building blocks: local Lorentz invariance, the universality of the gravitational redshift and the universality of free fall. The enormous importance of general relativity in modern science and technology merits a continuous effort in improving experimental verification of these underlying principles.

The universality of free fall is one of the oldest mechanical theories originally proposed by Galileo. Testing can be done by so called free fall experiments, where two bodies with different composition are freely falling towards a third gravitating body.

Figure 1: Goddard Spaceflight Center Laser Ranging Facility. Source: NASA

Amongst the most sensitive measurements of this principle is the Lunar Laser Ranging experiment, which compares the free fall of earth and moon in the solar gravitational potential [1]. This measurement is only surpassed by torsion balance experiments based on the design of Eötvös [2]. In addition, exciting new insights are expected from the MICROSCOPE experiment [3] that is planned to launch in 2016.

Figure 2: Torsion balance experiment as used in the group of E. Adelberger, University of Washington. Source: Eöt-Wash-Group

The emergence of quantum physics and our improved understanding of the basic building blocks of matter increases the interest scientists have in the understanding of gravity. How do gravity and quantum mechanics interact? What`s the connection between different fundamental particles and their mass? Is there a deeper underlying principle combining our fundamental theories? To comprehensively approach these questions a wide array of parameters must be analyzed. The way how certain test materials may act under the influence of gravity can either be parametrized using a specific violation scenario, like the Dilaton scenario by T. Damour [4], or by using a test theory such as the extended Standard Model of particles (SME) [5]. Since the SME approach is not based on a specific mechanism of violating UFF it also does not predict a level to which a violation may occur. Instead, it delivers a model-independent approach to compare methodically different measurements and confine possible violation theories.

Table 1 states possible sensitivities for violations based on the SME framework for a variety of test masses and underlines the importance of complementary test mass choices are. Hence in comparison to classical tests, the use of atom interferometry opens up a new field of previously inaccessible test masses with perfect isotopic purity in a well-defined spin state. Quantum tests appear to differ from previous test also in a qualitative way. They allow to perform test with new states of matter, such as wave packets by Bose Einstein condensates being in a superposition state. The work presented here is just another early step in a quest to understand the deeper connections between the quantum and classical relativistic world.

Table 1: Sample violation strengths for different test masses linked to “Neutron excess” and the “total Baryon number” based on the Standard Model Extension formalism. The test mass pairs are chosen according to the best torsion balance experiment [6] and existing matter wave tests [7]. An anomalous acceleration would be proportional to the stated numerical coefficients. Source: D. Schlippert et al., Phys. Rev. Lett. 112, 203002 (2014).

Measuring accelerations with atom interferometry

Measuring accelerations with a free fall experiment is always achieved by tracking the movement of an inertial mass in free fall in comparison to the lab frame of reference. This is even true when the inertial mass in question needs to be described by a matter wave operating on quantum mechanics. Falling corner cube interferometers operating on this principle are among the most accurate measurements of gravity with classical bodies. They use a continuous laser beam to track the change of velocity of a corner cube reflector due to gravity in a Michelson interferometer with the corner cube changing one of the arm lengths. Acceleration sensors based on free falling matter waves use a similar principle.

Figure 3: A side view of the experimental setup with the two-dimensional (left side) and three-dimensional (right side) magneto-optical traps employed in [Phys. Rev. Lett. 112, 203002 (2014)].

The first demonstration of a true quantum test of gravity with matter waves was performed 1975 with neutrons in the Famous COW experiment [8]. We will focus on atom interferometers using alkaline atoms, since they are most commonly used for inertial sensing and are also employed in the discussed experiment. Experiments of this kind were first used for acceleration measurements in 1992 [9] and have improved in their performance ever since. The first test of the equivalence principle comparing two different isotopes was then performed in 2004 [10]. Research on quantum tests is for example proposed at LENS in Italy [11], in Stanford in an already existing large fountain [12] and in the scope of the French ICE mission in a zero-g plane [13]. All these initiatives show the high interest of testing gravity phenomena with quantum matters as opposed to classical tests.

In the case of atom interferometers, coherent beam splitting is performed by absorption and stimulated emission of photons. Which atomic transitions are used is dependent on the specific application but, in the case of alkaline atoms two photon transitions coupling either two hyperfine and respective momentum states (Raman transitions) or just momentum states (Bragg transitions) are employed. The point of reference for the measurement is then given by a mirror reflecting the laser beams used to coherently manipulate the atoms, since the electromagnetic field is vanishing at the mirror surface. This results in a reliable phase reference of the light fields and constitutes the laboratory frame. The role of the retroreflecting mirror is similar to the one of the mirror at rest in in the case of the falling corner cube experiment.

The atomic cloud acts as the test mass, which in an ideal case, is falling freely without any influence by the laboratory, except during interaction with the light fields employed as beam splitters or mirrors. During the interaction, the light fields drive Rabi-oscillations in the atoms between the two interferometer states |g> and |e> with a time 2τ needed for a full oscillation. This allows for the realization of beam splitters with a τ/2 pulse length resulting in an equal superposition of |g> and |e>. Mirrors can be realized the same way by applying the beam splitter light fields for a time of τ which leads to an inversion of the atomic state. These pulses are generally called π/2 (for the superposition) and π (for the inversion pulses) in accordance with the Rabi-oscillation phase. The simplest geometry used to measure acceleration is a Mach- Zehnder-like geometry. This is produced by applying a π/2-π-π/2 sequence with free evolution times T placed between pulses. The resulting geometry can be seen in Figure 4.

Figure 4: Space-time diagram of a Mach-Zehnder-like atom interferometer. An atomic ensemble is brought into a coherent superposition of two momentum states by a stimulated Raman transition (π/2 pulse). The two paths I+II propagate separated, are reflected by a pi-pulse after a time T and superimposed and brought to interference with a final π/2 pulse after time 2T. The phase difference is encoded in the population difference of the two output states.

During the interaction with the light fields, the lattice formed by the two light fields imprints its local phase onto the atoms. This results in an overall phase scaling with the relative movement between the atomic cloud and the lattice. Calculating the overall phase imprinted on the atoms results in first order term, Φ=a*T²*k_eff, where k_eff is the effective wave vector of the lattice and a is the relative acceleration between lattice and atoms. This immediately shows the main feature of free fall atom interferometry: the T² scaling of the resulting phase. This is of particular interest for future experiments aiming for much higher free evolution times than currently possible. The phase Φ also shows another key feature. As the acceleration between atoms and lattice approaches zero, the phase also goes to zero, independently of the interferometry time T. This yields a simple way to determine the absolute acceleration of the atomic sample by accelerating the lattice until the lattice motion is in the same inertial reference frame as the freely falling atoms.

Lattice acceleration is achieved by chirping the frequency difference between the two laser beams used for the two photon transition. This transforms the measurement of a relatively large phase, spanning many thousand radians, to a null measurement. The signal produced is the population difference between the interferometer states |g> and |e> as a function of lattice acceleration and thus frequency sweep rate, α. The sweep rate corresponding to a vanishing phase directly leads to the acceleration experienced by the atoms according to lattice acceleration formula a=α/k_eff. Taking into account Earth’s gravitational field and a lattice wavelength of 780/2 nm (the factor of ½ is introduced due to the use of a two-photon transition) this leads to a sweep rate of around 25 MHz/s. The advantage of this method is that the acceleration measurement is now directly coupled to measurement of the wavelength of the light fields and frequencies in the microwave regime, which are easily accessible.

Our data

Figure 5: Determination of the differential acceleration of rubidium and potassium. The main systematic bias contributions do not change their sign when changing the direction of momentum transfer. Hence, the mean acceleration of upward and downward momentum transfer direction greatly suppresses the aforementioned biases. Source: D. Schlippert et al., Phys. Rev. Lett. 112, 203002 (2014)

Figure 6:  the wave nature of ⁸⁷Rb and ³⁹K 
atoms and their interference are exploited 
to measure the gravitational acceleration.

In order to test the universality of free fall, we simultaneously chirp the Raman frequencies to compensate for the accelerations a(Rb,±)(g) and a(K,±)(g) experienced by rubidium and potassium that were previously identified (Figure 6). Here, the observed phase shift exhibits contributions due to additional perturbations, such as magnetic field gradients. We make use of a measurement protocol based on reversing the transferred momentum (upward and downward directions ±). This technique makes use of the fact that many crucial perturbations do not depend on the direction of momentum transfer. Thus, by computing the half-difference of the phase differences determined in a single momentum direction, phase shifts induced by, e.g., the AC-Stark effect or Zeeman effect, can be strongly suppressed [14].

Figure 7: Allan deviations of the single species interferometer signals and the derived Eötvös ratio. Source: D. Schlippert et al., Phys. Rev. Lett. 112, 203002 (2014)

The data presented in this work [15] was acquired in a data run that was ~4 hours long. By acquiring 10 data points per direction of momentum transfer, and species and then switching to the opposite direction, we were able to determine the Eötvös ratio of rubidium and potassium to a statistical uncertainty of 5.4 x 10^-7 after 4096s; the technical noise affecting the potassium interferometer is the dominant noise source.

Taking into account all systematic effects, our measurement yields η(Rb,K)=(0.3 ± 5.4) x 10^-7.

Outlook

In our measurement, the performance was limited both by technical noise and the limited free evolution time T. In order to improve these parameters, we are currently extending the free fall time in our experiment. Furthermore, in an attempt to increase the contrast of our interferometers and thus the signal-to-noise ratio, we are working on implementing state preparation schemes for both species.

We expect to constrain our uncertainty budget (which currently is on the 10 ppb level for the Eötvös ratio) on the ppb level and below through the use of a common optical dipole trap applied to both species. By using Bose-Einstein-condensed atoms, we gain the ability to precisely calculate the ensembles, as well as carefully control the input state. This technique will also be able to reduce uncertainty factors linked to the transverse motion of the cloud, in addition to spatial magnetic field and gravitational field gradients.

Improving the precision of a true quantum test into the sub-ppb regime is the focus of current research. For example we are currently planning a 10m very long baseline atom interferometer (VLBAI) in Hannover [16]. In the framework of projects funded by the German Space Agency (DLR), we moreover develop experiments that are suitable for microgravity operation in the ZARM drop tower in Bremen and on sounding rocket missions [17].

Parallel to the development done in the LUH and at a national level, we are also involved in projects on an international level looking into extending the frontier of atom interferometry and especially the test of the equivalence principle. A major project investigating the feasibility of a space borne mission is the STE-Quest Satellite Mission proposed by a European consortium including nearly all major research institutions working in the field of inertial sensing with atom interferometry, as well as a variety of specialist of other fields [18]. This mission is aimed towards doing a simultaneous test of the equivalence principle with two rubidium isotopes and a clock comparison with several ground based optical clocks, pushing the sensitivity to the Eötvös ratio into the 10^-15 regime.

References:
[1] James G. Williams, Slava G. Turyshev, Dale H. Boggs, "Progress in Lunar Laser Ranging Tests of Relativistic Gravity". Physical Review Letters, 93, 261101 (2004). Abstract.
[2] S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, E. G. Adelberger, "Test of the Equivalence Principle Using a Rotating Torsion Balance". Physical Review Letters, 100, 041101 (2008). Abstract.
[3] P. Touboul, G. Métris, V. Lebat, A Robert, "The MICROSCOPE experiment, ready for the in-orbit test of the equivalence principle". Classical and Quantum Gravity, 29, 184010 (2012). Abstract.
[4] Thibault Damour, "Theoretical aspects of the equivalence principle". Classical Quantum Gravity, 29, 184001 (2012). Abstract.
[5] M.A. Hohensee, H. Müller, R.B. Wiringa, "Equivalence Principle and Bound Kinetic Energy". Physical Review Letters, 111, 151102 (2013). Abstract.
[6] S. Schlamminger, K.-Y. Choi, T.A. Wagner, J.H. Gundlach, E.G. Adelberger, "Test of the Equivalence Principle Using a Rotating Torsion Balance". Physical Review Letters, 100, 041101 (2008). Abstract.
[7] A. Bonnin, N. Zahzam, Y. Bidel, A. Bresson, "Simultaneous dual-species matter-wave accelerometer". Physical Review A, 88, 043615 (2013). Abstract ; S. Fray, C. Alvarez Diez, T. W. Hänsch, M. Weitz, "Atomic Interferometer with Amplitude Gratings of Light and Its Applications to Atom Based Tests of the Equivalence Principle". Physical Review Letters, 93, 240404 (2004). Abstract ; M. G. Tarallo, T. Mazzoni, N. Poli, D. V. Sutyrin, X. Zhang, G. M. Tino, "Test of Einstein Equivalence Principle for 0-Spin and Half-Integer-Spin Atoms: Search for Spin-Gravity Coupling Effects". Physical Review Letters, 113, 023005 (2014). Abstract.
[8] R. Colella, A. W. Overhauser, S. A. Werner, "Observation of Gravitationally Induced Quantum Interference". Physical Review Letters, 34, 1472 (1975). Abstract.
[9] M. Kasevich, S. Chu, "Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer". Applied Physics B, 54, 321–332 (1992). Abstract.
[10] Sebastian Fray, Cristina Alvarez Diez, Theodor W. Hänsch, Martin Weitz, "Atomic Interferometer with Amplitude Gratings of Light and Its Applications to Atom Based Tests of the Equivalence Principle". Physical Review Letters, 93, 240404 (2004). Abstract.
[11] M. G. Tarallo, T. Mazzoni, N. Poli, D. V. Sutyrin, X. Zhang, G. M. Tino, "Test of Einstein Equivalence Principle for 0-Spin and Half-Integer-Spin Atoms: Search for Spin-Gravity Coupling Effects". Physical Review Letters, 113, 023005 (2014). Abstract.
[12] Susannah M. Dickerson, Jason M. Hogan, Alex Sugarbaker, David M. S. Johnson, Mark A. Kasevich, "Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry". Physical Review Letters, 111, 083001 (2013). Abstract. 2Physics Article.
[13] G Varoquaux, R A Nyman, R Geiger, P Cheinet, A Landragin, P Bouyer, "How to estimate the differential acceleration in a two-species atom interferometer to test the equivalence principle". New Journal of Physics, 11, 113010 (2009). Full Article.
[14] J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and,M. A. Kasevich, "Sensitive absolute-gravity gradiometry using atom interferometry". Physical Review A, 65, 033608 (2002). Abstract; Anne Louchet-Chauvet, Tristan Farah, Quentin Bodart, André Clairon, Arnaud Landragin, Sébastien Merlet, Franck Pereira Dos Santos, "The influence of transverse motion within an atomic gravimeter". New Journal of Physics, 13, 065025 (2011). Full Article.
[15] D. Schlippert, J. Hartwig, H. Albers, L. L. Richardson, C. Schubert, A. Roura, W. P. Schleich, W. Ertmer, E. M. Rasel, "Quantum Test of the Universality of Free Fall". Physical Review Letters, 112, 203002 (2014). Abstract.
[16] http://www.geoq.uni-hannover.de/350.html
[17] http://www.iqo.uni-hannover.de/quantus.html
[18] D N Aguilera, H Ahlers, B Battelier, A Bawamia, A Bertoldi, R Bondarescu, K Bongs, P Bouyer, C Braxmaier, L Cacciapuoti, C Chaloner, M Chwalla, W Ertmer, M Franz, N Gaalou, M Gehler, D Gerardi, L Gesa, N Gürlebeck, J Hartwig, M Hauth, O Hellmig, W Herr, S Herrmann, A Heske, A Hinton, P Ireland, P Jetzer, U Johann, M Krutzik, A Kubelka, C Lämmerzah, A Landragin, I Lloro, D Massonnet, I Mateos, A Milke, M Nofrarias, M Oswald, A Peters, K Posso-Trujillo, E Rase, E Rocco, A Roura, J Rudolph, W Schleich, C Schubert, T Schuldt, S Seide, K Sengstock, C F Sopuerta, F Sorrentino, D Summers, G M Tino, C Trenkel, N Uzunoglu, W von Klitzing, R Walser, T Wendrich, A Wenzlawski, P Weßels, A Wicht, E Wille, M Williams, P Windpassinger, N Zahzam,"STE-QUEST—test of the universality of free fall using cold atom interferometry". Classical Quantum Gravity, 31, 115010 (2014), Abstract.

Excited Efimov State Observed

Rudolf Grimm (Photo by: C. Lackner)

Author: Rudolf Grimm

Affiliations:
Institute of Experimental Physics, University of Innsbruck, Austria,
and
Institute of Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Innsbruck, Austria.



Introduction:

In 1970, the Russian physicist Vitaly Efimov made a prediction that today represents one of the most bizarre and fascinating results of quantum mechanics [1]. In the context of nuclear physics, he considered the elementary situation of three bosons with pairwise interactions near a scattering resonance. He found an infinite ladder of three-body bound states, even existing under conditions where the interaction is too weak to support two-bound bound states. Until 2006, these Efimov trimer states have remained a theoretical curiosity without any experimental confirmation. Then the situation changed with the first observations in ultracold atomic systems, and Efimov’s scenario turned into a hot topic with many experimental investigations [2].

Efimov’s factor 22.7 :

Inherent to Efimov’s scenario is a discrete scaling law, expressing the self-similarity of all these trimer states. Discrete scaling means that, if a three-body state exists, then another state must also exist, being just a factor of 22.7 larger. Similarly the binding energy is by factor 22.7² smaller. This leads to an infinite series of states, as illustrated in Fig. 1. In practice, by the usual standards of molecular physics, already the first state is a very large quantum object (a so-called “halo state”), as it is a hundred times larger than conventional trimers and it is extremely weakly bound. In our earlier experiments on cesium atoms [3], we found the first Efimov state with a size of roughly 50 nm.

The second state in the series, also referred to as the first excited Efimov trimer, is expected to be 22.7 larger and about 500 times more weakly bound than the lowest Efimov state. This makes it an extreme molecular quantum object, 1 µm in size and exceptionally weakly bound.

Fig. 1: Efimov’s scenario for three interacting particles. The energy of the Efimov states (green solid lines) is plotted versus the inverse scattering length. In the grey-shaded region (E>0), the system consists of unbound atoms. In the blue-shaded region, atoms coexist with dimers. In the green-shaded region, the trimer states occur. For illustration purposes, the discrete scaling factor is artificially reduced from 22.7 to 2.

Ultracold atomic gases:

In our experiments, an ultracold atomic gas of cesium atoms is prepared by methods of laser cooling and subsequent evaporative cooling. The ensemble of a few ten thousand atoms is then kept by the weak attractive forces of an infrared laser beam in a volume of about 50µm diameter. They atoms collide with each other in the trap and the ensemble is observed over a few seconds.

A key feature is the possibility to tune the quantum-mechanical interaction between pairs of atoms in a well-controlled way. Experimentalists take advantage of so-called Feshbach resonances [4], which arise as a consequence of the coupling of two colliding atoms to a molecular state. The collision sensitively depends on a magnetic field and -- at specific field strengths -- resonances occur. Very accurate knowledge of these resonances is an essential prerequisite for the experiments.

The experimental signature of the formation of an Efimov state is the loss of atoms from the trap [5]. At specific magnetic fields, loss is observed to be much faster than usual. This marks the situation when three atoms couple to an Efimov state. The Efimov state here is an object that can live for a few milliseconds, before it undergoes a fragmentation into a deeply bound molecule and a free atom, with the energetic fragments leaving the trap.

Three challenges:

For observing the excited Efimov trimer [6] we were confronted with three major challenges: (1) We needed an extremely cold gas, colder than everything else we had prepared in our lab before. We extended our previous methods with an additional stage, where we expanded the ultracold ample into an ultraweak electromagnetic trap made of a combination of magnetic and optical fields. In this way we reached a temperature as low as 7 nK. (2) We had to control the interaction properties near a resonance at an unprecedented accuracy level. Here we benefitted from the special properties of cesium and our long-standing expertise with this particular species [7]. (3) We had to understand the role of the finite temperatures in our sample, as even the 7nK reached is a relatively high temperature on the energy scale of the excited Efimov state. Thanks to a theoretical model developed by a group at the École Normale Supérieure, Paris [8], this was finally possible.

Observing the long-sought second Efimov resonance:

We show the main result of our experiments in Fig. 2. The loss of atoms out of the trap is quantified by a rate coefficient L3, which is plotted as a function of the inverse scattering length 1/a. In the center, where 1/a is zero, the strongest interaction is realized. The strongest loss does not occur there, but somewhat shifted away from this center. From a detailed analysis of this peak we could obtain the exact position where the Efimov state couples to three atoms colliding in the limit of zero energy. It appears when the scattering length has a value 20000(000) larger than Bohr’s radius (size of a hydrogen atom in the ground state). This result also characterizes the size of the Efimov state.

Fig. 2: The resonance that results from the excited Efimov state. The loss rate coefficient L3 is plotted as a function of the inverse scattering length. Two data sets have been recorded under similar conditions (sets A and B). The vertical dashed line indicates the expected position in the limit of zero temperature. The resonance is slightly upshifted because of the finite temperature of the sample. The solid line is a theoretical prediction based on the properties of the ground-state Efimov resonance, characterized in earlier work, with the grey-shaded region indicating the uncertainty range.

The final result for the Efimov period:

We can finally compare our observation for the first excited Efimov state to earlier measurements on the Efimov ground state in the same system [9]. The final result is that the second state is by a factor of 21.0 (with an uncertainty of ±1.3) larger than the first Efimov state. With some probability this result may still be consistent with the ideal factor of 22.7. However, we believe that the small deviation is due to the fact that the lowest Efimov state deviates somewhat from Efimov’s idealized case. This is theoretically expected, but not fully understood.

Future trends:

This exactly points to the intriguing question: How Efimov states appear in real systems and in how far the ideal scenario holds predictive power to describe the real situation. Many theoretical and experimental investigations currently pursue research along these lines.

The Efimov scenario is a paradigm for few-body physics, and it is just a tip of an iceberg of many more phenomena related to a few interacting particles in the quantum world. Many more phenomena will be discovered (see Ref. [10] for a recent example from the world of fermions). A particularly interesting question is how few-body interactions will affect the properties of macroscopic many-body quantum states, like in new superconducting materials.

Team and funding:

Bo Huang (graduate student) and Leonid Sidorenkov (postdoctoral researcher) carried out the work in the laboratory of the author at the University of Innsbruck. Theoretical support came from Jeremy M. Hutson, professor of physics and chemistry at the Univ. of Durham, United Kingdom. The experiment was funded by the Austrian Science Fund FWF.

The team: The main picture (photo M. Knabl/IQOQI) shows the experimental team Leonid Sidorenkov, Rudolf Grimm and Bo Huang on the background of the mountains Patscherkofel (right) and Glungezer (left) near Innsbruck, Austria. The inset shows Jeremy M. Hutson from the University of Durham, United Kingdom.

References
[1] V. Efimov, "Energy levels arising from resonant two-body forces in a three-body system". Physics Letters B, 33, 563 (1970). Abstract.
[2] Francesca Ferlaino, Rudolf Grimm, "Trend: Forty years of Efimov physics: How a bizarre prediction turned into a hot topic". Physics, 3, 9 (2010). Full Article.
[3] T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch, A. Jaakkola, H.-C. Nägerl, R. Grimm, "Evidence for Efimov quantum states in an ultracold gas of caesium atoms". Nature, 440, 315 (2006). Abstract.
[4] Cheng Chin, Rudolf Grimm, Paul Julienne, Eite Tiesinga, "Feshbach resonances in ultracold gases". Review of Modern Physics, 82, 1225 (2010). Abstract.
[5] B. D. Esry, Chris H. Greene, and James P. Burke, Jr., "Recombination of Three Atoms in the Ultracold Limit". Physical Review Letters, 83, 1751 (1999). Abstract.
[6] Bo Huang, Leonid A. Sidorenkov, Rudolf Grimm, Jeremy M. Hutson, "Observation of the Second Triatomic Resonance in Efimov’s Scenario". Physical Review Letters, 112, 190401 (2014). Abstract.
[7] Martin Berninger, Alessandro Zenesini, Bo Huang, Walter Harm, Hanns-Christoph Nägerl, Francesca Ferlaino, Rudolf Grimm, Paul S. Julienne, and Jeremy M. Hutson, "Feshbach resonances, weakly bound molecular states, and coupled-channel potentials for cesium at high magnetic fields". Physical Review, A 87, 032517 (2013). Abstract.
[8] B. S. Rem, A. T. Grier, I. Ferrier-Barbut, U. Eismann, T. Langen, N. Navon, L. Khaykovich, F. Werner, D. S. Petrov, F. Chevy, C. Salomon, "Lifetime of the Bose Gas with Resonant Interactions". Physical Review Letters, 110, 163202 (2013). Abstract.
[9] M. Berninger, A. Zenesini, B. Huang, W. Harm, H.-C. Nägerl, F. Ferlaino, R. Grimm, P. S. Julienne, J. M. Hutson, "Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium". Physical Review Letters, 107, 120401 (2011). Abstract.
[10] Michael Jag, Matteo Zaccanti, Marko Cetina, Rianne S. Lous, Florian Schreck, Rudolf Grimm, Dmitry S. Petrov, Jesper Levinsen, "Observation of a Strong Atom-Dimer Attraction in a Mass-Imbalanced Fermi-Fermi Mixture". Physical Review Letters, 112, 075302 (2014). Abstract.

Orbital Fluctuations of Electron Distributions: A New Path to Superconductivity

Brookhaven Lab scientists (from left) Lijun Wu, Yimei Zhu, Chris Homes, and Weiguo Yin stand by the electron microscope used to reveal the multi-orbital distributions with a technique called quantitative convergent beam electron diffraction (CBED).

Armed with just the right atomic arrangements, superconductors allow electricity to flow without loss and radically enhance energy generation, delivery, and storage. Scientists tweak these superconductor recipes by swapping out elements or manipulating the valence electrons in an atom's outermost orbital shell to strike the perfect conductive balance. Most high-temperature superconductors contain atoms with only one orbital impacting performance—but what about mixing those elements with more complex configurations?

Now, researchers at the U.S. Department of Energy's Brookhaven National Laboratory have combined atoms with multiple orbitals and precisely pinned down their electron distributions. Using advanced electron diffraction techniques, the scientists discovered that orbital fluctuations in iron-based compounds induce strongly coupled polarizations that can enhance electron pairing—the essential mechanism behind superconductivity. The study, published in the journal Physical Review Letters [1], provides a breakthrough method for exploring and improving superconductivity in a wide range of new materials.

"For the first time, we obtained direct experimental evidence of the subtle changes in electron orbitals by comparing an unaltered, non-superconducting material with its doped, superconducting twin," said Brookhaven Lab physicist and project leader Yimei Zhu.

While the effect of doping the multi-orbital barium iron arsenic—customizing its crucial outer electron count by adding cobalt—mirrors the emergence of high-temperature superconductivity in simpler systems, the mechanism itself may be entirely different.

"Now superconductor theory can incorporate proof of strong coupling between iron and arsenic in these dense electron cloud interactions," said Brookhaven Lab physicist and study coauthor Weiguo Yin. "This unexpected discovery brings together both orbital fluctuation theory and the 50-year-old 'excitonic' theory for high-temperature superconductivity, opening a new frontier for condensed matter physics."

Atomic Jungle Gym :

Imagine a child playing inside a jungle gym, weaving through holes in the multicolored metal matrix in much the same way that electricity flows through materials. This particular kid happens to be wearing a powerful magnetic belt that repels the metal bars as she climbs. This causes the jungle gym's grid-like structure to transform into an open tunnel, allowing the child to slide along effortlessly. The real bonus, however, is that this action attracts any nearby belt-wearing children, who can then blaze through that perfect path.

Flowing electricity can have a similar effect on the atomic lattices of superconductors, repelling the negatively charged valence electrons in the surrounding atoms. In the right material, that repulsion actually creates a positively charged pocket, drawing in other electrons as part of the pairing mechanism that enables the loss-free flow of current—the so-called excitonic mechanism. To design an atomic jungle gym that warps just enough to form a channel, scientists audition different combinations of elements and tweak their quantum properties.

"High-temperature copper-oxide superconductors, or cuprates, contain in effect a single orbital and lack the degree of freedom to accommodate strong enough interactions between electricity and the lattice," Yin said. "But the barium iron arsenic we tested has multi-orbital electrons that push and pull the lattice in much more flexible and complex ways, for example by inter-orbital electron redistribution. This feature is especially promising because electricity can shift arsenic's electron cloud much more easily than oxygen's."

In the case of the atomic jungle gym, this complexity demands new theoretical models and experimental data, considering that even a simple lattice made of north-south bar magnets can become a multidimensional dance of attraction and repulsion. To control the doping effects and flow of electricity, scientists needed a window into the orbital interactions.

Tracking Orbits :

"Consider measuring waves crashing across the ocean's surface," Zhu said. "We needed to pinpoint those complex fluctuations without having the data obscured by the deep water underneath. The waves represent the all-important electrons in the outer orbital shells, which are barely distinguishable from the layers of inner electrons. For example, each barium atom alone has 56 electrons, but we're only concerned with the two in the outermost layer."

The Brookhaven researchers used a technique called quantitative convergent beam electron diffraction (CBED) to reveal the orbital clouds with subatomic precision. After an electron beam strikes the sample, it bounces off the charged particles to reveal the configuration of the atomic lattice, or the exact arrays of nuclei orbited by electrons. The scientists took thousands of these measurements, subtracted the inner electrons, and converted the data into probabilities—balloon-shaped areas where the valence electrons were most likely to be found.

Shape-Shifting Atoms :

The researchers first examined the electron clouds of non-superconducting samples of barium iron arsenic. The CBED data revealed that the arsenic atoms—placed above and below the iron in a sandwich-like shape (see Figure 1) exhibited little shift or polarization of valence electrons. However, when the scientists transformed the compound into a superconductor by doping it with cobalt, the electron distribution radically changed.

Figure 1: These images show the distribution of the valence electrons in the samples explored by the Brookhaven Lab collaboration—both feature a central iron layer sandwiched between arsenic atoms. The tiny red clouds (more electrons) in the undoped sample on the left (BaFe₂As₂) reveal the weak charge quadrupole of the iron atom, while the blue clouds (fewer electrons) around the outer arsenic ions show weak polarization. The superconducting sample on the right (doped with cobalt atoms), however, exhibits a strong quadrupole in the center and the pronounced polarization of the arsenic atoms, as evidenced by the large, red balloons.

"Cobalt doping pushed the orbital electrons in the arsenic outward, concentrating the negative charge on the outside of the 'sandwich' and creating a positively charged pocket closer to the central layer of iron," Zhu said. "We created very precise electronic and atomic displacement that might actually drive the critical temperature of these superconductors higher."

Added Yin, "What's really exciting is that this electron polarization exhibits strong coupling. The quadrupole polarization of the iron, which indicates the orbital fluctuation, couples intimately with the arsenic dipole polarization—this mechanism may be key to the emergence of high-temperature superconductivity in these iron-based compounds. And our results may guide the design of new materials."

This study explored the orbital fluctuations at room temperature under static conditions, but future experiments will apply dynamic diffraction methods to super-cold samples and explore alternative material compositions.

The experimental work at Brookhaven Lab was supported by the Office of Science at Department of Energy (DOE). The materials synthesis was carried out at the Chinese Academy of Sciences' Institute of Physics.

References:
[1] Chao Ma, Lijun Wu, Wei-Guo Yin, Huaixin Yang, Honglong Shi, Zhiwei Wang, Jianqi Li, C. C. Homes, Yimei Zhu, "Strong Coupling of the Iron-Quadrupole and Anion-Dipole Polarizations in Ba(Fe_1−xCo_x)₂As₂". Physical Review Letters, 112, 077001 (published on February 20th, 2014). Abstract.

Stopping Molecules with a Centrifuge

From Left to Right: (top row) Sotir Chervenkov, Xing Wu, Josef Bayerl, Andreas Rohlfes, (bottom row) Thomas Gantner, Martin Zeppenfled, Gerhard Rempe

Authors: Sotir Chervenkov, Xing Wu, Josef Bayerl, Andreas Rohlfes, Thomas Gantner, Martin Zeppenfled, Gerhard Rempe

Affiliation: Max-Planck-Institut für Quantenoptik, Garching, Germany

A novel deceleration technique brings fast continuous beams of polyatomic polar molecules almost to a halt.

The fast-growing research of cold polar molecules holds promise for delivering answers to many long-standing questions in fundamental physics, e.g., the existence of electric dipole moment of the electron, and for diverse future applications ranging from quantum simulations through quantum computation to controlled chemistry [1,2]. Producing abundant samples of cold polyatomic molecules from thermal ensembles, however, is a formidable challenge. A key step for obtaining cold molecules is the deceleration of molecular beams in analogy to atoms.

Indeed, the stunning advances in atomic physics and quantum optics over the past three decades ensued to a great extend from the development of efficient laser cooling and deceleration techniques [3]. Those methods heavily rely on closed cycling transitions between the electronic states in atoms, making possible multiple scattering of photons (~10⁴) from a single atom, whereupon each scattered photon carries away a certain fraction of the atom’s kinetic energy, and this is how atoms are eventually decelerated and cooled. Compared to atoms, molecules are more complex objects and possess a more involved internal-energy structure: in addition to the electronic states, molecules have also vibrational and rotational states. For this reason, in general, closed cycling transitions are not possible for molecules, in particular for polyatomic ones, and hence the laser cooling and deceleration methods, which are the workhorses in atomic physics, are not applicable to molecules.

A natural way to decelerate a molecule (as any other object) is to make it climb up a potential hill, thereby transforming its kinetic energy into a potential one. Such a hill can be provided through the interaction of a molecule with an external field, be it electric, magnetic or gravitational. For instance, the application of electric fields makes use of the dipole moment that a large number of molecules (unlike atoms) possess because of an uneven charge distribution within the molecule. The dipole moment interacts with the external electric fields, and by making the molecules move from a region with a weaker field to a region with a stronger field they lose kinetic energy. In a similar fashion magnetic molecules can be decelerated with external magnetic fields.

The disadvantage of these two methods is that for most molecules of interest the typical height of electric or magnetic hills is of the order of 1 K, whereas molecules from typical sources, e.g., a liquid-nitrogen-cooled source [4], have initial kinetic energies of the order of 100 K. Hence, the molecules have to climb up a sequence of about hundred hills. This implicates that one has to apply this process many times in succession, which leads to operation in the pulsed regime. That is why molecules have been decelerated so far only in the pulsed mode, with a very low duty cycle. Thus the hitherto-implemented techniques [5-9] cannot make use of the intrinsically high flux delivered by the available continuous molecular sources. To utilize the full potential of such sources, a continuous deceleration is warranted.

To achieve this, one has to provide a sufficiently high potential (~100 K) in order to decelerate molecules in one stretch. Such a high potential is provided by the gravitational field of the Earth, for instance. Simple calculations, however, show that for a molecule to be decelerated from around 200 ms^-1 down to a trappable velocity of around 20 ms^-1 it has to fly upwards in the gravitational field of the Earth for 2000 m, which renders such an experiment impossible or at least very demanding. The alternative is to artificially create an analogue of a gravitational field in the laboratory.

In our group we exploit this concept: everyone who has been on a merry-go-round has experienced the outward force, which exists in a rotating frame. This force can be much larger than the gravitational force of the Earth, and is employed in centrifuges for a multitude of biological, chemical, medical and industrial applications. Now we employ a rotating frame for a conceptually different purpose, namely to decelerate a gas of neutral molecules from about 200 ms^-1 to almost a standstill.

Figure 1: Design of the centrifuge decelerator. Molecules are guided from the periphery to the centre of a rotating spiral-shaped quadrupole guide. As the molecules propagate they climb up a centrifugal potential hill and get slowed down, eventually approaching the exit of the centrifuge at a close-to-zero velocity.

The 3D image in Fig. 1 shows the design of the centrifuge decelerator. The molecules are delivered from the source to the centrifuge through an electrostatic quadrupole guide (injector) composed of four parallel 2-mm-in-diameter electrodes with alternating polarity spaced one millimetre apart and arranged at the apices of a square (left lower corner of Fig. 1). The electric field of the quadrupole guide (Fig. 2) provides a transverse confinement for the guided molecules, which are trapped in the minimum of the electric field in the centre of the guide. The molecules are, however, free to move in the longitudinal direction and thus follow the guide. Once launched into the decelerator, the molecules propagate first around the periphery of the centrifuge in a stationary storage ring with a diameter of 40 cm composed of two static (Fig. 1, beige and green) and two rotating (Fig. 1, maroon and blue) electrodes. The electric field in the storage ring is the same as the one in the injector (see Fig. 2).

Figure 2: Transverse electric field in a quadrupole guide. The x and y axes show the transverse dimensions of the guide. L and H on the right of the colour bar stand for low and high electric filed, respectively.

Then, those of the molecules that move fast enough catch up with the entrance of a rotating spiral-shaped electrostatic quadrupole guide, and at this point they transit from the static into the rotating frame. The entrance of the rotating quadrupole guide is designed such that the outer two rotating electrodes are tapered and approach very closely, almost glide over at a distance of around 200 µm, the static electrodes of the stationary storage ring. The small gap between the tapered rotating electrodes and the static electrodes ensures a continuous electrostatic guiding potential, and hence a smooth transition for the molecules. The passage of the molecules from the laboratory into the rotating frame can take place almost at any point around the periphery of the centrifuge, which enables its operation in the continuous regime. Thus the centrifuge deceleration is a two-step process: the velocity of the molecules decreases first upon their transition from the laboratory into the rotating frame (because of the subtraction of the peripheral velocity of the centrifuge), and further, while propagating in the rotating guide, as they are forced to climb up a huge centrifugal potential hill, whereupon they are continuously slowed down by converting their initial kinetic energy into a centrifugal potential one, thus eventually reaching the rotation axis at a close-to-zero velocity. The decelerated molecules exit the centrifuge along its rotation axis through an exit bent quadrupole guide with a radius of curvature of 5 cm (see Fig. 1).

Our group has demonstrated the capabilities and the universality of the new technique by deceleration of three species with different masses and a dipole moment of the order of 1.5 Dy, CH₃F, CF₃H, and CF₃CCH. Fig. 3 shows the velocity distributions of the output molecular beams of CF₃H for different rotation speeds of the centrifuge, and consequently, different centrifugal potentials. The deceleration effect clearly manifests itself in the shift of the velocity distributions to lower velocities with increasing the centrifuge rotation speed. In our experiments we can vary both the rotation speed of the spiral guide and the voltage at the quadrupole guide. For optimal conditions we achieved continuous output beams with intensities of several 109 mm^-2s^-1 for molecules with kinetic energies below 1 K (shaded area in Fig. 3). Combining the centrifuge decelerator with a hydrodynamically enhanced buffer-gas source [10,11] is expected to deliver even higher fluxes of slow and, in addition to that, internally cold molecules.

Figure 3:  Velocity distributions of the continuous output beam of CF₃H molecules at a guide voltage of ±5 kV for different centrifuge rotation speeds. The range of velocities trappable in a 1-K-deep trap is shaded.

Novel features of the centrifuge decelerator are its continuous operation, high output beam intensity, applicability to a large set of molecules, and ease of operation. Therefore it has the potential to become an extremely valuable method in the cold-molecule research. The universality of the centrifugal force might also enable one to slow down atoms that cannot be laser-cooled, and possibly even cold neutrons [12]. Accumulation of centrifuge-decelerated molecules in an electric trap [13] and further cooling them via the recently demonstrated technique of Sisyphus cooling developed in our group at the MPQ [14] might allow for a dramatic increase of the phase-space density for controlled collision experiments with polyatomic molecules and pave the way to achieving quantum degenerate regimes with polar molecules.

References
[1] Lincoln D. Carr, David DeMille, Roman V. Krems, Jun Ye, “Cold and ultracold molecules: science, technology and applications”. New Journal of Physics, 11, 055049 (2009). Abstract.
[2] Debora S. Jin, Jun Ye (eds.), “Introduction to ultracold molecules: New frontiers in quantum and chemical physics". Chemical Reviews, Special Issue, 112, 4801–4802 (2012). Abstract.
[3] Harold J. Metcalf, Peter van der Straten, “Laser Cooling and Trapping”. Springer, New York (1999).
[4] Tobias Junglen, Thomas Rieger, Sadiq A. Rangwala, Pepijn W. H. Pinkse, Gerherd Rempe, “Two-Dimensional Trapping of Dipolar Molecules in Time-Varying Electric Fields”. Physical Review Letters, 92, 223001 (2004). Abstract.
[5] Manish Gupta, Dudley Herschbach, “A Mechanical Means to Produce Intense Beams of Slow Molecules,” Journal of Physical Chemistry A, 103, 10670–10673 (1999). Abstract.
[6] Hendrick L. Bethlem, Giel Berden, Gerard Meijer, “Decelerating Neutral Dipolar Molecules”. Physical Review Letters, 83, 1558-1561 (1999). Abstract.
[7] R. Fulton, A. I. Bishop, P. F. Barker, “Optical Stark Decelerator for Molecules”. Physical Review Letters, 93, 243004 (2004). Abstract.
[8] Edvardas Narevicius, Adam Libson, Christian G. Parthey, Isaac Chavez, Julia Narevicius, Uzi Even, Mark G. Raizen, “Stopping Supersonic Beams with a Series of Pulsed Electromagnetic Coils: An Atomic Coilgun”. Physical Review Letters, 100, 093003 (2008). Abstract.
[9] S. D. Hogan, C. Seiler, F. Merkt, “Rydberg-state-enabled deceleration and trapping of cold molecules”. Physical Review Letters, 103, 123001 (2009). Abstract.
[10] Christian Sommer, Laurens D. van Buuren, Michael Motsch, Sebastian Pohle, Josef Bayerl, Pepijn W. H. Pinkse, Gerhard Rempe, “Continuous guided beams of slow and internally cold polar molecules”. Faraday Discussions, 142, 203 (2009). Abstract.
[11] Nicholas R. Hutzler, Maxwell F. Parsons, Yulia V. Gurevich, Paul W. Hess, Elizabeth Petrik, Ben Spaun, Amar C. Vutha, David DeMille, Gerald Gabrielse, John M. Doyle, “A cryogenic beam of refractory, chemically reactive molecules with expansion cooling”. Physical Chemistry Chemical Physics, 13, 18976–18985 (2011). Abstract.
[12] C. M. Lavelle, C.-Y. Liu, W. Fox, G. Manus, P. M. McChesney, D. J. Salvat, Y. Shin, M. Makela, C. Morris, A. Saunders, A. Couture, A. R. Young, “Ultracold-neutron production in a pulsed-neutron beam line”. Physical Review C, 82, 015502 (2010). Abstract.
[13] B. G. U. Englert, M. Mielenz, C. Sommer, J. Bayerl, M. Motsch, P. W. H. Pinkse, G. Rempe, M. Zeppenfeld, “Storage and adiabatic cooling of polar molecules in a microstructured trap”. Physical Review Letters, 107, 263003 (2011). Abstract.
[14] Martin Zeppenfeld, Barbara G. U. Englert, Rosa Glöckner, Alexander Prehn, Manuel Mielenz, Christian Sommer, Laurens D. van Buuren, Michael Motsch, Gerherd Rempe, “Sisyphus cooling of electrically trapped polyatomic molecules”. Nature, 491, 570–573 (2012). 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.

Entanglement-enhanced Atom Interferometer with High Spatial Resolution

(From left to right) Philipp Treutlein, Roman Schmied, and Caspar Ockeloen

Authors: Caspar Ockeloen, Roman Schmied, Max F. Riedel, Philipp Treutlein

Affiliation: Department of Physics, University of Basel, Switzerland

Link to Quantum Atom Optics Lab, Treutlein Group >>

Interferometry is the cornerstone of most modern precision measurements. Atom interferometers, making use of the wave-like nature of matter, allow for ultraprecise measurements of gravitation, inertial forces, fundamental constants, electromagnetic fields, and time [1,2]. A well-known application of atom interferometry is found in atomic clocks, which provide the definition of the second. Most current atom interferometers operate with a large number of particles, which provides high precision but limited spatial resolution. Using a small atomic cloud as a scanning probe interferometer would enable new applications in electromagnetic field sensing, surface science, and the search for fundamental short-range interactions [2].

Past 2Physics article by Philipp Treutlein:
May 09, 2010: "Interface Between Two Worlds -- Ultracold atoms coupled to a micromechanical oscillator"
by Philipp Treutlein, David Hunger, Stephan Camerer.

In an atom interferometer, the external (motional) or internal (spin) state of atoms is coherently split and allowed to follow two different pathways. During the interrogation time T, a phase difference between the paths is accumulated, which depends on the quantity to be measured. When the paths are recombined, the wave-character of the atoms gives rise to an interference pattern, from which the phase can be determined. To measure this interference, the number of atoms in each output state is counted. Here the particle-character of the atoms is revealed, as the measurement process randomly projects the wave function of each atom into a definite state. When operating with an ensemble of N uncorrelated (non-entangled) atoms, the binomial counting statistics limits the phase uncertainty of the interferometer to 1/√N, the standard quantum limit (SQL) of interferometric measurement.

It is possible to overcome the SQL by making use of entanglement between the atoms [3]. Using such quantum correlations, the measurement outcome of each atom can depend on that of the other atoms. If used in a clever way, the phase uncertainty of an interferometer can be reduced below the SQL, in theory down to the ultimate Heisenberg limit of 1/N. Such entanglement-enhanced interferometry is in particular useful in situations where the number of atoms is limited by a physical process and the sensitivity can no longer be improved by simply increasing N. One such scenario is when high spatial resolution is desired. The number of atoms in a small probe volume is fundamentally limited by density-dependent losses due to collisions. As more atoms are added to this volume, the collision rate increases, and eventually any additional atoms are simply lost from the trap before the interferometer sequence has completed. This sets a tight limit on both the phase uncertainty and the maximum interrogation time T.

Fig. 1. Experimental setup. a) Central region of the atom chip showing the atomic probe (blue, size to scale) and the scanning trajectory we use. The probe is used to measure the magnetic near-field potential generated by an on-chip microwave guide (microwave currents indicated by arrows). A simulation of the potential is shown in red/yellow. b) Photograph of the atom chip, mounted on its ultra-high vacuum chamber.

In a recent paper [4] we have demonstrated a scanning-probe atom interferometer that overcomes the SQL using entanglement. Our interferometer probe is a Bose-Einstein condensate (BEC) on an atom chip, a micro-fabricated device with current-carrying wires that allow magnetic trapping and accurate positioning of neutral atoms close to the chip surface [5]. A schematic view of the experiment is shown in figure 1. We use N=1400 Rubidium-87 atoms, trapped in a cloud of 1.1 x 1.1 x 4.0 micrometers radius, 16 to 40 micrometers from the surface. Two internal states of the atoms are used as interferometric pathways, and the pathways are split and recombined using two-photon microwave and radio frequency pulses. At the end of the interferometer sequence, we count the atoms in each output state with sensitive absorption imaging, with a precision of about 5 atoms.

We create entanglement between the atoms by making use of collisions naturally present in our system. When two atoms collide, both atoms obtain a phase shift depending on the state of the other atom, thus creating quantum correlations between the two. Normally, the effect of these collisions is negligible in our experiment, as the phase shift due to collisions between atoms in the same state are almost completely canceled out by collisions where each atom is in a different state. We can turn on the effect of collisions by spatially separating the two states, such that collisions between states do not occur. When, after some time, we recombine the two states, collisional phase shifts are effectively turned off during the subsequent interrogation time of the interferometer.

The performance of our interferometer is shown in figure 2, measured at 40 micrometer from the chip surface. It has a sensitivity of 4 dB in variance below to SQL, and improved sensitivity is maintained for up to T = 10 ms of interrogation time, longer than in previous experiments [6,7,8]. We demonstrate the scanning probe interferometer by transporting the entangled atoms between 40 and 16 micrometer from the atom chip surface, and measuring a microwave near field potential at each location. The microwave potential is created by wires on our atom chip, and is also used for generation of the entangled state. As shown in figure 3, our scanning probe interferometer operates on average 2.2 dB below the SQL, demonstrating that the entanglement partially survives being transported close to the chip surface, which takes 20 ms of transport time.

Fig. 2. Interferometer performance operating at a single position for different interrogation times. Plotted is the variance relative to the standard quantum limit (SQL). The entanglement-enhanced interferometer (blue diamonds) operates about 4 dB below the SQL, whereas the non-entangled interferometer (red, coherent state) operates close to the SQL. For T > 10 ms, both experiments are limited by technical noise. The inset shows a typical interference fringe, with a fringe contrast of (98.1 ± 0.2)%.

The scanning probe measurement presented here corresponds to a microwave magnetic field sensitivity of 2.4 µT in a single shot of the experiment (cycle time ~ 11 s). The sensitivity shown in figure 2 corresponds to 23 pT for an interrogation time of 10 ms. This sensitivity is obtained with a probe volume of only 20 µm³. Our interferometer bridges the gap between vapor cell magnetometers, which achieve subfemtotesla sensitivity at the millimeter to centimeter scale [9,10] but do not have the spatial resolution needed to resolve near-field structures on microfabricated devices, and nitrogen vacancy centers in diamond, which are excellent magnetometers at the nanometer scale but currently offer lower precision in the micrometer regime [11].

Fig. 3. Scanning probe interferometer. a) Phase shift due to the microwave near-field potential measured at different positions. The dashed line is a simulation of the potential. b) Interferometer performance for the same measurement. At all positions, the interferometer operates below the SQL. These measurements were done with an interrogation time of T = 100 µs, during which the microwave near-field was pulsed on for 80 µs.

In conclusion, we have experimentally demonstrated a scanning-probe atom interferometer operating beyond the standard quantum limit, and used it for the measurement of a microwave near-field. High-resolution measurements of microwave near-fields are relevant for the design of new microwave circuits for use in communication technology [12]. This is the first demonstration of entanglement-enhanced atom interferometry with a high spatial resolution scanning probe, and promises further high-resolution sensing and measurement applications.

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