A Compact Gravimeter Based On An Atom Chip

From Left to Right: Martina Gebbe, Sven Abend, Matthias Gersemann, Holger Ahlers, Hauke Müntinga; (top right) Claus Lämmerzahl, (bottom right] Ernst M. Rasel.

Authors: Sven Abend¹, Martina Gebbe², Matthias Gersemann¹, Holger Ahlers¹, Hauke Müntinga², Enno Giese^3,4, Naceur Gaaloul¹, Christian Schubert¹, Claus Lämmerzahl², Wolfgang Ertmer¹, Wolfgang P. Schleich^3,5, Ernst M. Rasel¹

Affiliation:
¹Institut für Quantenoptik, Leibniz Universität Hannover, Germany,
²ZARM, Universität Bremen, Germany,
³Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Germany,
⁴Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, Canada,
⁵Texas A&M University Institute for Advanced Study (TIAS), Institute for Quantum Science and Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M University, College Station, Texas, USA,

Introduction to cold-atom gravimetry
The precise knowledge of gravity is important in the fields of geodesy, geophysics and metrology. Detecting small variations in the local gravitational force, for example, can provide information about the presence of mineral resources. Tectonic movements or volcanic activities can also be deduced by this method. Satellites allow the observation of the gravitational field of the whole planet yielding important parameters for climate studies such as sea-surface heights [1] or ice masses [2]. Moreover, gravity is a force that cannot be shielded and, thus, influences the measurement of other standard units.

Absolute classical gravimeters are based on tracing the free fall of macroscopic corner-cubes with laser interferometers, while the lab frame serves as inertial reference. Quantum inertial sensors operate similarly using freely falling atoms as test masses. They are based on the wave-particle duality stating that particles also have a wave nature and can therefore show diffraction and interference.

Prior to performing atom interferometry atoms have to be trapped and cooled close to absolute zero by a combination of magnetic fields and laser light. Room temperature atoms with velocities of hundreds of meters per second would almost immediately collide with the walls of the experimental chamber and leave no time to perform experiments. After release from the trap laser pulses direct the falling atoms along two different paths and let them recombine. The acceleration of free fall can then be read out from the interference pattern of the atomic wave functions.

Nowadays, commercially available quantum gravimeters feature an accuracy better than one part in 10⁸ of gravity [3,4] and are competitive to classical sensors. Their sensitivity could be improved by cooling the atoms further down until they reach an ultracold state of matter, called a Bose-Einstein condensate (BEC) where only a single quantum state is occupied. The size of a BEC is about 100 times smaller than typical millimeter-sized laser cooled clouds commonly used in atomic gravimeters. Such an ultracold cloud allows a more precise control of the atomic position and reduces the error due to spatially nonuniform laser pulse intensities.

In our paper [5] we have demonstrated an atom-chip fountain gravimeter, using a BEC source with an intrinsic sensitivity of one part in 107 of gravity, where all operations can be performed in a volume of less than a one centimeter cube.

Mach-Zehnder atom interferometer in free fall

In an atom interferometer beam splitting is based on the diffraction by an optical lattice generated by two counter-propagating laser beams. In our case, Bragg diffraction is employed, which can be described by the absorption and stimulated emission of a photon. During this process the atom receives an additional momentum kick. The duration and amplitude of the Bragg laser pulse determine the amount of atoms diffracted to another momentum state.

The Mach-Zehnder interferometer starts with a beam splitter pulse that gives a velocity kick with 50% probability resulting in an equal superposition of two atomic momentum states (see Figure 1(b)). After a free evolution time of T, the momentum states are inversed by a mirror pulse. At a time 2T a final pulse recombines the wave packets and an interferometer signal consisting of two output ports separated by a velocity difference is created. The atom number in each of these ports is detected via imaging with a CCD camera. An acceleration such as gravity leads to a path difference between the two interferometer arms and influences the population of the output ports. In principle, each atom participates independently in the interferometer. Large ensembles, however, are important to obtain detectable and statistically significant signals.

In such a free fall interferometer an important feature is the T square scaling of the phase shift, which directly links to the sensitivity. Hence, a gravitational sensor considerably benefits from an extension of the interferometer time. Unperturbed evolution times in the order of seconds can only be reached in very large devices [6], or on microgravity platforms [7]. In a compact, earth-bound device, however, the atom cloud can only fall a short distance, which limits T to the order of milliseconds.

Figure 1: (click on the image to view with higher resolution) Atom-chip-based gravimeter (a) and spacetime trajectories of an atom cloud in a Mach-Zehnder interferometer without (b) and with relaunch (c). Adapted from Reference [5]..

Measuring gravitation with a compact atom-chip setup

Figure 2: Centimeter-sized atom chip used for BEC generation.

BEC-based inertial sensors have usually been large, laboratory-sized experiments [9]. Our apparatus features a compact setup, provided amongst others by the use of a centimeter-wide atom chip [9,10], which allows a fast, robust and efficient generation of BECs (Figure 2). Inside a small vacuum chamber we repeatedly produce up to 15,000 condensed Rubidium-87 atoms at a temperature of 50nK [8, 11]. Each experimental cycle consisting of BEC generation and performing atom interferometry takes about 15 seconds.

The atom chip is not only used for the whole state preparation of the BEC but also acts as a reference mirror inside the chip gravimeter (see Figure 1(a)). It is oriented horizontally and retroreflects the light pulses coming from an upwards-pointing laser. The interferometer region extends about 1 cm below the atom chip. Since the atoms are freely falling along the optical lattice, its velocity has to be constantly increased in order to match the gravitational acceleration of the atoms. If lattice and atomic acceleration are identical, only one state entering the interferometer is detected at the output. This means, our interference signal, the normalized population assumes a minimum independent of the pulse interval T. Local gravity is than deduced from the optical lattice acceleration which can be measured very precisely.

Figure 3(a) shows interference signals in dependence of the lattice acceleration for pulse intervals of T=1,3 and 5ms in a dropped interferometer. The acceleration of free fall was determined to be g = (9.8134 ± 0.0006) m/s². After repeating the measurements with the maximal interrogation time T=5ms over 8h we achieved a relative precision of one part in 10⁵ of gravity (see Figure 3(b)).

Figure 3: (click on the image to view with higher resolution) Measuring gravitational acceleration in a single fall interferometer. (a) Normalized atom number in one output port of the MZI for T = 1, 3, 5 ms depending on the acceleration of the Bragg lattice. (b) Allan deviation of the acceleration improves with the square root (black line) of the integration time t reaching a precision of 1 part in 10⁵ of gravity after 8 hours. Source: Reference [5].

In order to improve the sensitivity of our interferometer we developed a simple and efficient fountain sequence illustrated in Figure 1(c). At the bottom of the detection zone the atoms are caught and tossed upwards with an optical lattice generated by the same laser light beams that are used for interferometry. This way, we are able to enhance the total free evolution time by a factor of three, without increasing the free-fall baseline of the experiment.

The interferometer starts directly after the relaunch and can be extended to T=25ms. Its intrinsic sensitivity equals one part in 10⁷ which represents a 20-fold increase in comparison to the simple fall setup. Due to the environmental conditions and the absence of any vibrational isolation we were not able to observe fringes any more. However, we did a statistical analysis of the data and determined a high interferometric contrast of 80%.

Conclusion and outlook

In conclusion, we demonstrated the first miniaturized atom-chip fountain gravimeter without and with relaunch. The new fountain scheme leads to extended interferometer times without changing the compact volume of a one centimeter cube. The sensor is currently limited by the large vibrations in our system, which we aim to suppress in the future.

The current sensitivity of 1 part in 10⁷ of gravity is about two orders of magnitude lower compared to state-of-the-art sensors. However, with an advanced apparatus [12], which produces 10⁵ atoms in a BEC per second, and small improvements in the measurement scheme, we believe an intrinsic sensitivity of one part in 10⁹ is feasible. At the same time, further miniaturization can be done by using for example a pyramidal-shaped retroreflector [13] that reduces the size of the laser system. All these improvements open up the route to a backpack-sized device for high-precision absolute gravimetry utilized in remote locations.

References:
[1] B. D. Tapley, D. P. Chambers, S. Bettadpur, J. C. Ries, "Large scale ocean circulation from the GRACE GGM01 Geoid". Geophysical Review Letters, 30(22) (2003). Full Article.
[2] Isabella Velicogna, John Wahr. "Measurements of Time-Variable Gravity Show Mass Loss in Antarctica“. Science, 311, 1754 (2006). Abstract.
[3] Muquans, http://www.muquans.com/.
[4] AOSense, http://www.aosense.com/.
[5] S. Abend, M. Gebbe, M. Gersemann, H. Ahlers, H. Müntinga, E.Giese, N. Gaaloul, C. Schubert, C. Lämmerzahl, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Atom-chip fountain gravimeter”, Physical Review Letters, 117, 203003 (2016). Abstract.
[6] T. Kovachy, P. Asenbaum, C. Overstreet, C. A. Donnelly, S. M. Dickerson, A. Sugarbaker, J. M. Hogan, M. A. Kasevich, "Quantum superposition at the half-metre scale", Nature, 528, 530 (2015). Abstract.
[7] H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, E. M. Rasel, "Interferometry with Bose–Einstein Condensates in Microgravity", Physical Review Letters, 110, 093602 (2013). Abstract.
[8] J. E. Debs, P. A. Altin, T. H. Barter, D. Döring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, N. P. Robins, "Cold-atom gravimetry with a Bose–Einstein condensate", Physical Review A 84, 033610 (2011). Abstract.
[9] József Fortágh, Claus Zimmermann, “Magnetic Microtraps for Ultracold Atoms”, Reviews of Modern Physics, 79, 235 (2007). Abstract.
[10] Mark Keil, Omer Amit, Shuyu Zhou, David Groswasser, Yonathan Japha, Ron Folman, “Fifteen Years of Cold Matter on the Atom Chip: Promise, Realizations, and Prospects”, Jornal of Modern Optics, 63, 1840 (2016). Abstract.
[11] T. van Zoest, N. Gaaloul, Y. Singh, H. Ahlers, W. Herr, S. T. Seidel, W. Ertmer, E. Rasel, M. Eckart, E. Kajari, S. Arnold, G. Nandi, W. P. Schleich, R. Walser, A. Vogel, K. Sengstock, K. Bongs, W. Lewoczko-Adamczyk, M. Schiemangk, T. Schuldt, A. Peters, T. Könemann, H. Müntinga, C. Lämmerzahl, H. Dittus, T. Steinmetz, T. W. Hänsch, J. Reichel, "Bose–Einstein condensation in microgravity", Science, 328, 1540 (2010). Abstract.
[12] Jan Rudolph, Waldemar Herr, Christoph Grzeschik, Tammo Sternke, Alexander Grote, Manuel Popp, Dennis Becker, Hauke Müntinga, Holger Ahlers, Achim Peters, Claus Lämmerzahl, Klaus Sengstock, Naceur Gaaloul, Wolfgang Ertmer, Ernst M Rasel, "A high-flux BEC source for mobile atom interferometers", New Journal of Physics, 17, 065001 (2015). Abstract.
[13] Q. Bodart, S. Merlet, N. Malossi, F. Pereira Dos Santos, P. Bouyer, and A. Landragin, "A cold atom pyramidal gravimeter with a single laser beam", Applied Physics Letters, 96, 134101 (2010). Abstract.

The Real-Space Collapse of a Two Dimensional Polariton Gas

Photos of some of the authors -- From left to right: (top row) Lorenzo Dominici, Dario Ballarini, Milena De Giorgi; (bottom row) Blanca Silva Fernández, Fabrice Laussy, Daniele Sanvitto.

Authors:
Lorenzo Dominici¹, Mikhail Petrov², Michal Matuszewski³, Dario Ballarini¹, Milena De Giorgi¹, David Colas⁴, Emiliano Cancellieri^5,6, Blanca Silva Fernández^1,4, Alberto Bramati⁶, Giuseppe Gigli^1,7, Alexei Kavokin^2,8,9, Fabrice Laussy^4,10, Daniele Sanvitto¹.

Affiliation:
¹CNR NANOTEC—Istituto di Nanotecnologia, Lecce, Italy,
²Spin Optics Laboratory, Saint Petersburg State University, Russia,
³Institute of Physics, Polish Academy of Sciences, Warsaw, Poland,
⁴Física Teorica de la Materia Condensada, Universidad Autónoma de Madrid, Spain,
⁵Department of Physics and Astronomy, University of Sheffield, UK,
⁶Laboratoire Kastler Brossel, UPMC-Paris 6, ÉNS et CNRS, France,
⁷Università del Salento, Dipartimento di Matematica e Fisica “Ennio de Giorgi”,  Lecce, Italy,
⁸CNR-SPIN, Tor Vergata, Rome, Italy,
⁹Physics and Astronomy, University of Southampton, UK,
¹⁰Russian Quantum Center, Moscow Region, Skolkovo, Russia.

Can photons in vacuum interact?
The answer is not, since the vacuum is a linear medium where electromagnetic excitations and waves simply sum up, crossing themselves with no interaction. There exist a plenty of nonlinear media where the propagation features depend on the concentration of the waves or particles themselves. For example travelling photons in a nonlinear optical medium modify their structures during the propagation, attracting or repelling each other depending on the focusing or defocusing properties of the medium, and giving rise to self-sustained preserving profiles such as space and time solitons [1,2] or rapidly rising fronts such as shock waves [3,4].

One of the highest nonlinear effects can be shown by photonic microcavity (MC) embedding quantum wells (QWs), which are very thin (few tens of atomic distances) planar layers supporting electronic dipolar oscillations (excitons). What happens when a drop of photons, like a laser pulse, is trapped in a MC between two high reflectivity mirrors, and let to interact during this time with the electromagnetic oscillations of the QWs? If the two modes, photons and excitons, are tuned in energy each with the other, they cannot exist independently anymore and the result is the creation of a mixed, hybrid fluid of light and matter, which are known as the polaritons [5].

More specifically, we study the two-dimensional fluids of microcavity exciton polaritons, which can be enumerated among quantum or bosonic gases, and their hydrodynamics effects. Things become pretty nice since these polaritons behave partially as photons, in their light effective masses and fast speeds, and partially as excitons, with strong nonlinear interactions which can be exploited, for example, in all-optical transistors and logic gates [6]. Moreover, some photons continuously leak-out of the microcavity, bringing with them the information on the internal polariton fluid which can be on the one hand more straightforwardly studied with respect, for example, to atomic Bose-Einstein condensates, on the other hand making them out-of-equilibrium bosonic fluids.

Figure 1 (click on the image to view with higher resolution): Snapshots of the polariton fluid density and phase at significant instants. The amplitude and phase maps (the dashed circles depict the initial pump spot FWHM) have been taken at time frames of 0 ps, 2.8 ps and 10.4 ps, which correspond, respectively, to the pulse arrival, the ignition of the dynamical peak and its maximum centre density. The Figure has been extracted from Ref. [7].

In a recent study [7], we point out a very intriguing and unexpected effect, the dynamical concentration of the initial photonic pulse, upon its conversion into a polariton drop of high density. The accumulation of the field in a robust bright peak at the centre, as represented in Figure 1, is indeed surprising because it is at odds with the repulsive interactions of polaritons, which are expected to lead only to the expansion of the polariton cloud. The global phenomenology is spectacular because it is accompanied with the initial Rabi oscillations of the fluid [8,9] on a sub-picosecond scale, the formation of stable ring dark solitons [10,11], and the irradiation of planar ring waves on the external regions. Given the circular symmetry of the system, all these features can be represented in the time-space charts of Figure 2, where a central cross cut of the polariton cloud is represented during time.

Figure 2 (click on the image to view with higher resolution): Time-space charts of the polariton redistribution during time, for both the amplitude (a) and phase (b). The y-axis represents a central cross-cut of the circular-symmetry of the system and the x-axis represents time with a sample stepof 50 fs. Initially the polariton fluid oscillates with a Rabi period of about 800 fs (vertical stripes in the map), while the central density rapidly decays to zero before starting to rise as a bright peak. The two solid lines in both charts mark the phase disturbance delimiting the expanding region with large radial phase-gradient. The Figure has been extracted from Ref. [7].

From an application-oriented perspective we can devise features such as the enhancement ratio of the centre density with respect to the initial one (up to ten times in some experiments), the localization or shrinking factor of the original size (up to ten times as well), and the response speed (few picosecond rise time) and stability time (few tens of picosecond, well beyond the initial pulse length). These features can be tuned continuously with the intensity of the source laser pulse. Figure 3 reports the time dependence of the total population and of the relative centre density in one exemplificative case. The experiments have been reported in Nature Communications [7] and deserve, at least in a divulgative context, its own definition, which effect we like to refer to as the 'polariton backjet'. Indeed, its features are such to intuitively resemble the backjet of a water drop upon a liquid surface, while we devised the physics at the core as a collective polaron effect. This consists in the heating of the semiconductor lattice, resulting in the dynamical redshift of the exciton resonance. It is an interesting case of retarded nonlinearity inversion, leading to the self-sustained localization of the polariton condensate.

Figure 3. Total population and centre density versus time. Blue line are the experimental data of the area-integrated emission intensity, and the black line is a fit based on a model of coupled and damped oscillators. The red curve to be plotted on the right axis is the centre density versus time relative to that at the time of pulse arrival. The real enhancement factor obtained here in the centre density is 1.5, reached in a rise time of t = 10 ps. The Figure has been extracted from Ref. [7] Supplementary information.

The results have been obtained on a very high-quality QW-MC sample (quality factor of 14000) and upon implementing a state-of-the-art real-time digital holography setup. This latter is based on the coherence characteristics of the resonant polariton fluid and the possibility of retrieving its amplitude and phase distribution during ultrafast times upon the interference of the device emission with the laser pulse itself. Indeed this allowed also to prepare other interesting experiments dedicated to peculiar phenomena, such as the Rabi oscillations and their coherent [8] or polarization control [9] and the integer and half-integer quantum vortices [12] which can be excited on the polariton fluid. For most of these cases we could retrieve the complex wavefunction (which is given by an amplitude and phase) of the polariton fluid, with time steps of 0.1 or 0.5 ps and space steps as small as 0.16 micrometers. Fundamentally it is like making a movie on the micrometer scale with a 1.000.000.000.000 slow-motion ratio, as in the following video:



The fabrication and use of high quality microcavity polariton devices coupled to the most advanced characterization technique is opening a deep insight on fundamental properties of the coupling between light and matter and into exotic phenomena linked to condensation, topological states and many-body coherent and nonlinear fluids. Applications can be expected on the front of new polariton lasers, sub-resolution pixels, optical storage and clocks, data elaboration and multiplexing, sensitive gyroscopes, polarization and angular momentum shaping for optical tweezers and advanced structured femtochemistry.

References:
[1] S. Barland, M. Giudici, G. Tissoni, J. R. Tredicce, M. Brambilla, L. Lugiato, F. Prati, S. Barbay, R. Kuszelewicz, T. Ackemann, W. J. Firth, G.-L. Oppo, "Solitons in semiconductor microcavities", Nature Photonics, 6, 204–204 (2012). Abstract.
[2] Stephane Barland, Jorge R. Tredicce, Massimo Brambilla, Luigi A. Lugiato, Salvador Balle, Massimo Giudici, Tommaso Maggipinto, Lorenzo Spinelli, Giovanna Tissoni, Thomas Knödl, Michael Miller, Roland Jäger, "Cavity solitons as pixels in semiconductor microcavities", Nature, 419, 699–702 (2002)  Abstract.
[3] Wenjie Wan, Shu Jia, Jason W. Fleischer, "Dispersive superfluid-like shock waves in nonlinear optics", Nature Physics, 3, 46–51 (2006). Abstract.
[4] N. Ghofraniha, S. Gentilini, V. Folli, E. DelRe, C. Conti, "Shock waves in disordered media", Physical Review Letters, 109, 243902 (2012). Abstract.
[5] Daniele Sanvitto, Stéphane Kéna-Cohen, "The road towards polaritonic devices", Nature Materials (2016). Abstract.
[6] D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, D. Sanvitto, "All-optical polariton transistor", Nature Communications, 4, 1778 (2013). Abstract.
[7] L. Dominici, M. Petrov, M. Matuszewski, D. Ballarini, M. De Giorgi, D. Colas, E. Cancellieri, B. Silva Fernández, A. Bramati, G. Gigli, A. Kavokin, F. Laussy,  D. Sanvitto, "Real-space collapse of a polariton condensate", Nature Communications, 6, 8993 (2015). Abstract.
[8] L. Dominici, D. Colas, S. Donati, J. P. Restrepo Cuartas, M. De Giorgi, D. Ballarini, G. Guirales, J. C. López Carreño, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, D. Sanvitto, "Ultrafast Control and Rabi Oscillations of Polaritons", Physical Review Letters, 113, 226401 (2014). Abstract.
[9] David Colas, Lorenzo Dominici, Stefano Donati, Anastasiia A Pervishko, Timothy CH Liew, Ivan A Shelykh, Dario Ballarini, Milena de Giorgi, Alberto Bramati, Giuseppe Gigli, Elena del Valle, Fabrice P Laussy, Alexey V Kavokin, Daniele Sanvitto "Polarization shaping of Poincaré beams by polariton oscillations", Light: Science & Applications, 4, e350 (2015). Abstract.
[10] Yuri S. Kivshar, Xiaoping Yang, "Ring dark solitons", Physical Review E, 50, R40–R43 (1994). Abstract.
[11] A S Rodrigues, P G Kevrekidis, R Carretero-González, J Cuevas-Maraver, D J Frantzeskakis, F Palmero, "From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates", Journal of Physics: Condensed Matter, 26, 155801 (2014). Abstract.
[12] Lorenzo Dominici, Galbadrakh Dagvadorj, Jonathan M. Fellows, Dario Ballarini, Milena De Giorgi, Francesca M. Marchetti, Bruno Piccirillo, Lorenzo Marrucci, Alberto Bramati, Giuseppe Gigli, Marzena H. Szymańska, Daniele Sanvitto, "Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid", Science Advances, 1, e1500807 (2015). Abstract.

A Continuously Pumped Reservoir of Ultracold Atoms

From Left to Right: (top row) Jan Mahnke, Ilka Kruse, Andreas Hüper, (bottom row) Wolfgang Ertmer, Jan Arlt, Carsten Klempt.

Authors: Jan Mahnke¹, Ilka Kruse¹, Andreas Hüper¹, Stefan Jöllenbeck¹, Wolfgang Ertmer¹, Jan Arlt², Carsten Klempt¹

Affiliation:
¹Institut für Quantenoptik, Gottfried Wilhelm Leibniz Universität Hannover, Germany
²Institut for Fysik og Astronomi, Aarhus Universitet, Aarhus C, Denmark

During the last decades, the quantum regime could be accessed through very different systems, including trapped ions, micromechanical oscillators, superconducting circuits and dilute ultracold gases. Mostly, these systems show the desired quantum-mechanical features at ultra-low temperatures only. The lowest temperatures [1] to date are reached in dilute atomic gases by a combination of laser cooling and evaporative cooling. This approach has two disadvantages: It relies on the internal structure of the atoms due to the laser cooling and it can only cool discrete samples instead of continuous beams due to the evaporative cooling.

However, many applications would greatly benefit from a continuous source of cold atoms, for example sympathetic cooling [2] of molecules. Here, the molecules are brought into contact with a bath of cold atoms to redistribute the thermal energy through collisions. Ideally, such a cold bath is realized in absence of disturbing laser light as the rich internal structure of the molecules results in a broad absorption spectrum and any photon can potentially harm the cooling process. Another application of a continuous beam of cold atoms is continuous matter interferometry. Atom interferometry is already in use for the precise measurement of many observables, including time [3], gravity [4] and rotation [5]. These measurements could greatly benefit from a continuous observation instead of the sequential interrogation of discrete samples. Even though continuous sources are highly desired, no continuous sources without the application of laser light have been demonstrated in the microkelvin regime yet.

One possible realization of an ultracold continuous sample was proposed theoretically [6], where a conservative and static trap is loaded by an atomic beam. In this scheme, pre-cooled atoms are guided towards the entrance barrier of an elongated trap with a finite trap depth (see figure 1). If the atoms pass the entrance barrier, they follow the elongated potential until they are reflected by the end of the trap. The strong confinement in the radial direction ensures that most atoms collide with another atom before they reach the entrance barrier again. These collisions allow for a redistribution of the kinetic energy. Consequently, some atoms acquire a kinetic energy larger than the trap depth and escape the trap. Other atoms lose energy and stay trapped. If the trap parameters are chosen well, an equilibrium condition with a surprisingly large phase-space density may be reached.

Figure 1: 3D plot of the static trapping potential in the x–z-plane through the point of the trap minimum.

In our recent publication [7], we demonstrate the first experimental implementation of such a continuous loading of a conservative trap. Our realization is based on a mesoscopic atom chip (see figure 2 and Ref. [8]), a planar structure of millimeter-sized wires. The mesoscopic chip generates the magnetic fields for a three-dimensional magneto-optical trap, a magnetic waveguide and the static trapping potential described above. The three-dimensional magneto-optical trap is periodically loaded with an ensemble of atoms. These ensembles are launched into the magnetic waveguide, where they overlap and produce a continuous atom beam with varying intensity. This beam traverses an aperture which optically isolates the loading region from the static trapping region. In this trapping region, the atom beam is directed onto the elongated magnetic trap, where the atoms accumulate.

Figure 2: Photograph of the mesoscopic atom chip with millimeter-scale wires. The magneto-optical trap is in the lower left area and the static trap is generated in the top right area. The bend wires create a guide connecting the two regions.

With this loading scheme, we create and maintain an atomic reservoir with a total number of 3.8 × 10⁷ trapped atoms at a temperature of 102 µK, corresponding to a peak phase-space density of 9 × 10^-8 h^-3. This is the first continuously loaded cloud in the microkelvin regime without the application of laser light. Such a continuously replenished ensemble of ultracold atoms presents a new tool for metrological tasks and for the sympathetic cooling of other atomic species, molecules or nanoscopic solid state systems. The scheme is also very versatile in creating cold samples of atoms and molecules directly, as it does not rely on any internal level structure.

Figure 3 Photograph of the experimental setup. The atom chip is visible outside of the vacuum chamber at the top. In the front is the glass cell and the optics for the two-dimensional magneto-optical trap, which is used to load the three dimensional magneto-optical trap on the chip.

References:
[1] A. E. Leanhardt, T. A. Pasquini, M. Saba, A. Schirotzek, Y. Shin, D. Kielpinski, D. E. Pritchard,  W. Ketterle. “Cooling Bose-Einstein condensates below 500 picokelvin”, Science, 301, 1513 (2003). Abstract.
[2] Wade G. Rellergert, Scott T. Sullivan, Svetlana Kotochigova, Alexander Petrov, Kuang Chen, Steven J. Schowalter, Eric R. Hudson, “Measurement of a large chemical reaction rate between ultracold closed-shell ⁴⁰Ca atoms and open-shell ¹⁷⁴Yb⁺ ions held in a hybrid atom-ion trap”, Physical Review Letters, 107, 243201 (2011). Abstract.
[3] R. Wynands and S. Weyers. “Atomic fountain clocks”, Metrologia, 42 (3), S64 (2005). Abstract.
[4] A. Louchet-Chauvet, S. Merlet, Q. Bodart, A. Landragin, F. Pereira Dos Santos, H. Baumann, G. D'Agostino, C. Origlia, “Comparison of 3 absolute gravimeters based on different methods for the e-MASS project”, Instrumentation and Measurement, IEEE Transactions on, 60(7), 2527-2532 (2011). Abstract.
[5] J. K. Stockton, K. Takase, and M. A. Kasevich. “Absolute geodetic rotation measurement using atom interferometry”, Physical Review Letters, 107, 133001 (2011). Abstract.
[6] C. F. Roos, P. Cren, D. Guéry-Odelin, and J. Dalibard. “Continuous loading of a non-dissipative atom trap”, Europhysics Letters, 61, 187 (2003). Abstract.
[7] J. Mahnke, I. Kruse, A. Hüper, S. Jöllenbeck, W. Ertmer, J. Arlt, C. Klempt. “A continuously pumped reservoir of ultracold atoms”, Journal of Physics B: Atomic Molecular and Optical Physics, 48, 165301 (2015). Abstract.
[8] S. Jöllenbeck, J. Mahnke, R. Randoll, W. Ertmer, J. Arlt, C. Klempt. “Hexapole-compensated magneto-optical trap on a mesoscopic atom chip”, Physical Review A, 83, 043406 (2011). Abstract.

Evidence for Pre-formed Pairs in an Oxide Superconductor

From left to right: Mengcheng Huang, Shicheng Lu, Jeremy Levy, Guanglei Cheng, Michelle Tomczyk, Patrick Irvin. 

Authors: Guanglei Cheng, Michelle Tomczyk, Jeremy Levy

Affiliation:
Department of Physics and Astronomy, University of Pittsburgh, USA.
Pittsburgh Quantum Institute, Pittsburgh, Pennsylvania, USA.

Link to Levy Research Group >>

Strontium titanate (SrTiO₃ or simply STO) is the first and best-known superconducting semiconductor. Its many fascinating properties, especially superconductivity, motivated Georg Bednorz and Alex Müller to search for high-temperature (high-T_c) superconductors in perovskite oxides [1]. STO shares many features related to the cuprate high-T_c superconductors, including a dome-shaped phase diagram and a pseudogap phase [2]. However, STO has much lower temperature and carrier density than the high-T_c compounds. A longstanding question surrounds the nature of the pseudogap state: ‘To pair or not to pair?’ – Does the existence of a pseudogap indicate electron pairing in the absence of superconductivity?

In 1969, long before high-T_c superconductivity was discovered, D.M. Eagles predicted [3] that electrons could remain paired outside of the superconducting state in STO. Eagles predicted that electrons can form a dilute gas so that the size of pairs is very small compared to the inter-electron distance. Namely, electrons pair in real space and the superconductivity is a result of Bose-Einstein condensation (BEC), contrasting the weak pairing in momentum space described by Bardeen-Schrieffer-Cooper (BCS) theory, which is highly successful in explaining conventional superconductors. Eagles was the first to propose the concept of BEC-BCS crossover, which was later independently developed by Nobel laureate Anthony Leggett [4] and experimentally realized in an ultracold atomic gas [5]. The discovery of BEC-type superconductivity in solid state systems has been challenging.

The LaAlO₃/SrTiO₃ (LAO/STO) interface [6] has attracted numerous interests in the last decade. It hosts a two-dimensional conducting interface that possesses a wealth of strongly correlated phenomena including superconductivity, magnetism, metal-insulator transition (MIT) and spin-orbit interaction [7]. A few years ago, we developed a lithography technique that allows us to ‘write’ and ‘erase’ nanostructures at the LAO/STO interface by using a sharp conductive atomic force microscope (c-AFM) tip, thus effectively programming all the novel properties at the nanoscale [8,9]. The writing mechanism relies critically on the MIT, in which the interface becomes conducting above the critical 3 unit cell (uc) LAO thickness. While the 3uc LAO/STO interface is insulating, it is switchable by a voltage-biased c-AFM tip. Under the c-AFM tip, a series of nanoscale devices have been made available. The resulting nanowires are only a few nanometers wide, exhibit anomalously high mobility [10] and show potential for the development of new types of nanoelectronics.

To investigate electron pairing, we use a superconducting single-electron transistor (Figure 1a). The device consists of a main superconducting nanowire channel intersected with voltage leads. Two tunnel potential barriers are engineered through c-AFM ‘cutting’ procedures so that a nanoscale island is defined. Due to the nanoscale confinement, the energy levels inside the island are quantized, and carrier transport is only possible when the chemical levels of external electrodes (source and drain) are aligned with an island energy level, which is dependent on the side gate voltages.

Figure 1: (click on the figure to view with higher resolution) Device schematic and transport characteristics. (a), Device schematic written by c-AFM lithography. The nanowires are typically 5 nm wide, and the length between 2 barriers is 1 μm. (b) and (c) Differential conductance dependent on the source-drain bias and side gate voltages at B=0 T (b) and B=4 T (c). The number of diamonds is doubled in (c). Color scales are 0-80 µS. (d) Magnetic field dependence of the conductance peaks. The bifurcation of conductance peaks above B_p suggest electron pairing without superconductivity. Color scale: 0-40 µS.

Indeed, bias spectroscopy reveals [11] a series of conductance diamonds (Fig. 1b), reminiscent of so-called ‘Coulomb diamonds’ in conventional blockade physics. In the latter case, each sequential Coulomb diamond corresponds to the stability of one additional electron, and applying an external magnetic field merely changes the size of diamonds due to Zeeman Effect. Remarkably, when we increase the magnetic field, the diamonds initially remain insensitive to field, then bifurcate above a critical magnetic field B_p~2 T (Fig. 1b,c). Such behavior is clearly revealed when we track the magnetic field dependence of the zero-bias conductance peaks. We find that all of the peaks bifurcate above a ‘pairing field’ B_p (Fig. 1d), suggesting transport is dominated by electron pairs rather than single electrons below B_p. Electron pairing persists far above the critical temperature (T_c~0.3 K) and for magnetic fields far above the upper critical field (H_c2~0.2 T) for superconductivity in bulk STO.

The observed electron pairing without superconductivity is difficult to explain using BCS theory. Pair fluctuations in disordered BCS superconductor films may give signatures of pairing above T_c which is greatly suppressed by disorder. However, the corresponding pairing temperature will not exceed T_c in the clean limit. Here the pairing temperature we have observed is around several kelvin, one order of magnitude higher than the T_c in the bulk. These experimental signatures are captured by a phenomenological model that favors BEC pairing, consistent with D. M. Eagles’s theory proposed 46 years back.

References:
[1] J. Georg Bednorz and K. Alex Müller, "Perovskite-type oxides - the new approach to High Tc superconductivity", Nobel Lecture (1987).
[2] C. Richter, H. Boschker, W. Dietsche, E. Fillis-Tsirakis, R. Jany, F. Loder, L. F. Kourkoutis, D. A. Muller, J. R. Kirtley, C. W. Schneider, J. Mannhart, "Interface superconductor with gap behaviour like a high-temperature superconductor", Nature, 502, 528 (2013). Abstract.
[3] D.M. Eagles, "Possible pairing without superconductivity at low carrier concentrations in bulk and thin-film superconducting semiconductors", Physical Review, 186, 456 (1969). Abstract.
[4] Anthony J. Leggett, "A theoretical description of the new phases of liquid ³He", Reviews of Modern Physics,  47, 331 (1975). Abstract.
[5] M. W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle, "Vortices and superfluidity in a strongly interacting Fermi gas",  Nature, 435, 1047 (2005). Abstract.
[6] A. Ohtomo,  H.Y. Hwang, "A high-mobility electron gas at the LaAlO₃/SrTiO₃ heterointerface", Nature, 427, 423 (2004). Abstract.
[7] Joseph A. Sulpizio, Shahal Ilani, Patrick Irvin, Jeremy Levy, "Nanoscale Phenomena in Oxide Heterostructures", Annual Review of Materials Research, 44, 117 (2014). Abstract.
[8] C. Cen, S. Thiel, G. Hammerl, C. W. Schneider, K. E. Andersen, C. S. Hellberg, J. Mannhart, and J. Levy, "Nanoscale control of an interfacial metal-insulator transition at room temperature", Nature Materials, 7, 298 (2008). Abstract.
[9] Cheng Cen, Stefan Thiel, Jochen Mannhart, Jeremy Levy, "Oxide nanoelectronics on demand", Science, 323, 1026 (2009). Abstract.
[10] Patrick Irvin, Joshua P. Veazey, Guanglei Cheng, Shicheng Lu, Chung-Wung Bark, Sangwoo Ryu, Chang-Beom Eom, Jeremy Levy, "Anomalous High Mobility in LaAlO₃/SrTiO₃ Nanowires", Nano Letters, 13, 364 (2013). Abstract.
[11] Guanglei Cheng, Michelle Tomczyk, Shicheng Lu, Joshua P. Veazey, Mengchen Huang, Patrick Irvin, Sangwoo Ryu, Hyungwoo Lee, Chang-Beom Eom, C. Stephen Hellberg, Jeremy Levy, "Electron pairing without superconductivity", Nature 521, 196 (2015). 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).

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.