Physics Nobel 2023: A Primer

Image Courtsey: NobelPrize.org

Author: Biplab Bhawal

In the early days of photography, pictures were all motionless. Those were either pictures of calm and quiet landscapes or pictures of families, in which -- not just the parents -- even the children were all very sober and sensible boys and girls. They never seemed to be running around.

But people could never live happily thereafter with whatever was achieved by then. They wanted something better.

They observed how the legs of a running baby or a horse were getting ghostly blurry when they tried taking pictures of such objects in motion. Photographing the 100m race at the Olympics posed a similar problem.

So, Now they started worrying about `Shutter Speed' or how quickly the shutter of the camera `opens and closes'. Things were getting blurry because the shutter speed could not catch up with the speed of the object in the photograph.

The minimum 'shutter speed' used these days is rough 'one-sixtieth of a second', depending on what the image is and how far away the focus is.

But, as usual, people could never live happily thereafter with whatever was achieved at any point in time. As usual, They wanted something even better.

They wanted to see every minute movement of the body of an athlete running 100 meters. They wanted to see how exactly hummingbird's wings flap up and down so quickly.

Thus began the era of photography when people wanted to see what they could not even see with their naked eyes.

The greatest achievement of humankind in the year 2020 was the quick development of the COVID-19 vaccine. So, most people could not pay enough attention to keep track of the news that in the same fateful year, a camera was developed at Caltech with a shutter speed of 140 trillionths of a second.

Again, people are not satisfied yet ....

Some thought they would want to get a better look at how electrons move around in atoms to understand how atoms and molecules interact with each other and how various chemical reactions happen.

Electrons, however, move very quickly within atoms. The speed is about 2200 km per second. At this speed, one can travel around the earth in just 18 seconds.

So researchers gradually developed such a unique pulse laser that is capable of generating an equivalent `shutter speed' of only 4000 trillionths of 1 second.

[Remember though we are now looking at what is happening inside atoms. The concept of `shutter speed' is no longer quite appropriate here. The act of `Looking' is no longer the same as `Looking with our eyes'. The size of an atom is about ten-millionth of a hair-width. So, `looking inside an atom' is governed by quantum mechanics. Newtonian Physics and intuition do not really apply here]

This year's Nobel Prize is a recognition of that success.

Ultrafast Quantum Simulator

Photos of some of the authors -- From Left to Right: (top row) Nobuyuki Takei,  Christian Sommer,  Claudiu Genes, Guido Pupillo; (bottom row)  Hisashi Chiba,  Matthias Weidemüller,  Kenji Ohmori.

Authors: Nobuyuki Takei^1,2, Christian Sommer^1,2,3, Claudiu Genes³, Guido Pupillo⁴, Haruka Goto¹, Kuniaki Koyasu^1,2, Hisashi Chiba^1,5, Matthias Weidemüller^6,7,8, Kenji Ohmori^1,2

Affiliation:
¹Department of Photo-Molecular Science, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Japan,
²SOKENDAI (The Graduate University for Advanced Studies), Okazaki, Japan,
³Max Planck Institute for the Science of Light, Erlangen, Germany,
⁴IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, Strasbourg, France,
⁵Faculty of Engineering, Iwate University, Morioka, Japan,
⁶Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany,
⁷Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, China,
⁸CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.

Link to Ohmori Group in Okazaki >>

The dynamics of interactions among large numbers of electrons govern a variety of important physical and chemical phenomena such as superconductivity, magnetism, and chemical reactions. An ensemble of many particles thus interacting with each other is referred to as a “strongly correlated system”. Understanding quantum mechanical behavior of a strongly correlated system is thus one of the central goals of modern sciences. It is extremely difficult, however, to predict theoretically the properties of a strongly correlated system even using the Japanese post-K supercomputer, which is expected to be one of the world’s fastest supercomputers planned to be completed by the year 2020. For example, the post-K cannot calculate even the ground-state energy by exact diagonalization, when the number of particles in the system is more than 30. It is in general more demanding to calculate the dynamics of the strongly correlated system.

Instead of calculating with a classical computer such as the post-K, an alternative concept has been proposed by Richard Feynman in 1980’s [1] and is now referred to as a “quantum simulator”, in which quantum mechanical particles such as atoms are assembled into an artificial strongly correlated system, whose properties are known and controllable [2,3]. It is then used to simulate and understand the properties of another strongly correlated system whose properties are not known. A quantum simulator could quickly simulate quantum mechanical behavior of a large number of particles that cannot be handled even by the post-K supercomputer, expected to become a next-generation simulation platform.

We have developed a completely new quantum simulator that can simulate the quantum mechanical dynamics of a strongly correlated system of more than 40 atoms within one nanosecond [4-6]. This has been realized by introducing a novel approach in which an ultrashort laser pulse whose pulse width is only 10 picoseconds is employed to control a high-density ensemble of atoms cooled to temperatures close to absolute zero. Furthermore we have succeeded in simulating the motion of electrons of this strongly correlated system that is modulated by changing the strength of interactions among many atoms in the ensemble.

In order to generate a strongly correlated system in which a large number of particles interact simultaneously with each other, it should be effective to assemble a quantum simulator with particles whose forces could reach as far as possible. A “Rydberg atom” is expected as the most promising candidate for that [7,8]. An atom usually has a diameter of about sub-nanometer, but can be irradiated with laser light to bring an electron that moves near its atom core to a high-energy orbital called a “Rydberg orbital”, whose diameter could be more than hundreds of nanometers. The atom thus generated is referred to as a Rydberg atom. Due to its long distance between the atom core with a positive charge and the Rydberg electron with a negative charge, a Rydberg atom generates an electric field that reaches a long distance. If one could build up an ensemble of Rydberg atoms, it should become a strongly correlated system in which those many Rydberg atoms interact simultaneously with each other. However, the strong electric field induced by a Rydberg atom shifts the energies of the Rydberg orbitals of its surrounding atoms as shown schematically in Fig. 1, so that conventional laser light cannot bring electrons of those surrounding atoms to their Rydberg orbitals. Accordingly there can be only one Rydberg atom within a sphere of a certain radius. This phenomenon is referred to as “Rydberg blockade” [7,8] and needs to be circumvented to generate a strongly correlated system of Rydberg atoms.

Figure 1: Mechanism of Rydberg blockade

Moreover there is another problem to be solved to realize such a Rydberg quantum simulator. Even if one could generate a strongly correlated system, the strong interaction among the Rydberg atoms would induce the temporal evolution of their quantum states on the timescale of 100 picoseconds, which is faster by a factor of more than hundred thousand than the timescale of a quantum simulator that has so far been considered.

In order to create a Rydberg quantum simulator that can simulate a strongly correlated system, therefore, a totally new concept and technique have been needed to solve those two essential problems: (1) how to circumvent Rydberg blockade?; (2) how to observe the system on the timescale faster by a factor of hundred thousand than the one considered for a quantum simulator so far?

We have succeeded in solving those two essential problems for the first time. Figure 2a schematically shows a property of laser light that has so far been used typically for the development of a quantum simulator. It shines continuously as shown in Fig. 2(a-1) and is produced by a so-called “continuous wave laser”. This laser light has an extremely narrow range of wavelength (energy) as shown in Fig. 2(a-2). Therefore it cannot bring an electron to the Rydberg orbital that is shifted energetically in the surrounding atom as shown in Fig. 1. Instead of using this continuous wave laser, therefore, we has introduced a pulsed laser light that shines only during ~ 10 picoseconds as shown in Fig. 2(b-1). This pulsed laser light has its wavelength range broader than that of the continuous wave laser by a factor of more than one million as shown in Fig. 2(b-2). It can therefore bring an electron to the Rydberg orbital even if its energy is shifted in the surrounding atom. Moreover the temporal width of the laser pulse is one tenth of the timescale expected for the temporal evolution of the system, so that the evolution should be able to be observed in real time.

Figure 2: Properties of conventional laser light that has so far been used for the development of a quantum simulator (a-1, a-2) and of the one newly introduced in our work (b-1, b-2).

The experiment was performed with rubidium atoms. Figure 3 shows a schematic of the experiment. An ensemble of ~ 10⁶ rubidium atoms was cooled down to an ultralow temperature around 70 microK with laser cooling techniques and trapped in a laser tweezer. These atoms were irradiated with an “ultrashort laser pulse 1” whose pulse width was ~ 10 picoseconds, and its wavelength range was appropriately manipulated with a special technique. The temporal evolution of the atoms after laser pulse 1 was observed with another “ultrashort laser pulse 2”. The delay of laser pulse 2 from laser pulse 1 was controlled ultra-precisely on the 10 attosecond timescale with a special device, so that the evolution was observed on this timescale. It was then observed in real time that the electrons of many Rydberg atoms, which were generated with laser pulse 1 that circumvented Rydberg blockade, oscillated with a period of one femtosecond, and the timing of those oscillations was gradually shifted on the timescale of 10 attoseconds due to the simultaneous interactions among more than 40 Rydberg atoms. Furthermore this timing shift has successfully been accelerated by enlarging the Rydberg orbitals or by decreasing the distances among Rydberg atoms to increase the strength of the interactions.

Figure 3: Schematic of the experimental setup.

We have thus introduced ultrashort laser pulses into a quantum simulator for the first time and succeeded in developing a totally new quantum simulator. This ultrafast quantum simulator can simulate the dynamics of a large number of particles interacting with each other that cannot be handled by even a world’s fastest supercomputer such as the post-K. The simulation has been completed in 1 nanosecond.

It has been demonstrated that our ultrafast quantum simulator can quickly simulate the dynamics of a strongly correlated system of a large number of particles interacting with each other, which cannot be handled by even the post-K supercomputer. The ultrafast quantum simulator is expected to develop into a future simulation platform that could contribute to designing superconducting and magnetic materials and drug molecules, whose functionalities are governed by strongly correlated electrons. It is also expected to serve as a fundamental tool to investigate the origins of physical properties of matter such as superconductivity and magnetism as well as the mechanism of a chemical reaction that proceeds in a complex environment such as a liquid.

References:
[1] Richard P. Feynman, “Simulating physics with computers”, International Journal of Theoretical Physics 21, 467 (1982). Abstract.
[2] Immanuel Bloch, Jean Dalibard, Wilhelm Zwerger, “Many-body physics with ultracold gases”, Reviews of Modern Physics 80, 885 (2008). Abstract.
[3] I. M. Georgescu, S. Ashhab, Franco Nori, “Quantum simulation”, Reviews of Modern Physics 86, 153 (2014). Abstract.
[4] Nobuyuki Takei, Christian Sommer, Claudiu Genes, Guido Pupillo, Haruka Goto, Kuniaki Koyasu, Hisashi Chiba, Matthias Weidemüller,  Kenji Ohmori, “Direct observation of ultrafast many-body electron dynamics in an ultracold Rydberg gas”, Nature Communications 7, 13449 (2016). Abstract.
[5] Christian Sommer, Guido Pupillo, Nobuyuki Takei, Shuntaro Takeda, Akira Tanaka, Kenji Ohmori, Claudiu Genes, “Time-domain Ramsey interferometry with interacting Rydberg atoms”, Physical Review A 94, 053607 (2016). Abstract.
[6] Kenji Ohmori, “Optically Engineered Quantum States in Ultrafast and Ultracold Systems”, Foundations of Physics, 44, 813 (2014). Abstract.
[7] M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms”, Reviews of Modern Physics, 82, 2313 (2010). Abstract.
[8] Daniel Comparat, Pierre Pillet, “Dipole blockade in a cold Rydberg atomic sample”, Journal of the Optical Society of America, B 27, A208 (2010). Abstract.

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.

Quantum Tunneling of Water in Ultra-Confinement

From Left to Right: (top row) Alexander I. Kolesnikov, George F. Reiter, Narayani Choudhury, Timothy R. Prisk, Eugene Mamontov; (bottom row) Andrey Podlesnyak, George Ehlers,  David J. Wesolowski, Lawrence M. Anovitz.

Authors: Alexander I. Kolesnikov¹, George F. Reiter², Narayani Choudhury³, Timothy R. Prisk⁴, Eugene Mamontov¹, Andrey Podlesnyak⁵, George Ehlers⁵, Andrew G. Seel⁶, David J. Wesolowski⁴, Lawrence M. Anovitz⁴

Affiliation:
¹Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
²Physics Department, University of Houston, Texas, USA,
³Math and Science Division, Lake Washington Institute of Technology, Kirkland, Washington, USA; School of Science, Technology, Engineering and Math, University of Washington, Bothell, Washington, USA,
⁴Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
⁵Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
⁶ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, United Kingdom.

The quantum-mechanical behavior of light atoms plays an important role in shaping the physical and chemical properties of hydrogen-bonded liquids, such as water [1,2]. Tunneling is a classic quantum effect in which a particle moves through a potential barrier despite classically lacking sufficient energy to transverse it. The tunneling of hydrogen atoms in condensed matter systems has been observed for translational motions through metals, anomalous proton diffusion in water phases, and in the rotation of methyl and ammonia groups, and Gorshunov et al. inferred on the basis of terahertz spectroscopy measurements that water molecules inside the mineral beryl may undergo rotational tunneling [3, 4].

The crystal structure of beryl, shown in Figure 1, contains hexagonally shaped nanochannels just wide enough to contain single water molecules. In a recently published paper [5], we presented evidence from inelastic neutron scattering experiments and ab initio computational modeling that these water molecules do, in fact, undergo rotational tunneling at low temperatures. In their quantum-mechanical ground state, the hydrogen atoms are delocalized among the six symmetrically-equivalent positions about the channels so that the water molecule on average assumes a double-top like shape.

Figure 1: The crystal structure of beryl

The first set of inelastic neutron scattering experiments was performed using the CNCS and SEQUOIA spectrometers located at Oak Ridge National Laboratory's Spallation Neutron Source. A number of transitions are observed in the energy spectrum that can only be attributed to quantum-mechanical tunneling. Alternative origins for these transitions, such as vibrational modes or crystal field effects of magnetic impurities, are inconsistent with the temperature and wavevector dependence of the energy spectrum. However, they are consistent with an effective one-dimensional orientational potential obtained from Density Functional Theory and Path Integral Molecular Dynamics calculations.

To confirm these results we performed neutron Compton scattering of experiments on beryl single-crystals using the VESUVIO spectrometer at the Rutherford Appleton Laboratory. In this technique, a high-energy incident neutron delivers an impulsive blow to a single atom in the sample, transferring a sufficiently large amount of kinetic energy to the target atom that it recoils freely from the impact. The momentum distribution n(p) of the hydrogen atoms may then be inferred from the observed dynamic structure factor S(Q, E) in this high-energy limit, providing a direct probe of the momentum-space wavefunction of the water hydrogens in beryl.

Figure 2: the measured momentum distribution n(p) in neutron Compton scattering experiments.

The tunneling behavior of the water protons is revealed in our neutron Compton scattering experiments by the measured momentum distribution n(p), illustrated as a color contour plot in Figure 2. The variation of n(p) with angle is due to vibrations of the O—H covalent bond. If it is true that water molecules undergo rotational tunneling between the six available orientations, then n(p) will include oscillations or interference fringes as a function of angle. On the other hand, if the water molecules are incoherently and randomly arranged among the possible positions, then no such interference fringes will be observed. As marked by the yellow line in Figure 2, the interference fringes were clearly observed in our experiment! The water molecule is, therefore, in a coherent superposition of states over the six available orientational positions.

Taken together, these results show that water molecules confined in the channels in the beryl structure undergo rotational tunneling, one of the hallmark features of quantum mechanics.

References:
[1] Michele Ceriotti, Wei Fang, Peter G. Kusalik, Ross H. McKenzie, Angelos Michaelides, Miguel A. Morales, Thomas E. Markland, "Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges", Chemical Reviews, 116, 7529 (2016). Abstract.
[2] Xin-Zheng Li, Brent Walker, Angelos Michaelides, "Quantum nature of the hydrogen bond", Proceedings of the national Academy of Sciences of the United States of America, 108, 6369 (2011). Abstract.
[3] Boris P. Gorshunov, Elena S. Zhukova, Victor I. Torgashev, Vladimir V. Lebedev, Gil’man S. Shakurov, Reinhard K. Kremer, Efim V. Pestrjakov, Victor G. Thomas, Dimitry A. Fursenko, Martin Dressel, "Quantum Behavior of Water Molecules Confined to Nanocavities in Gemstones", The Journal of Physical Chemistry Letters, 4, 2015 (2013). Abstract.
[4] Boris P. Gorshunov, Elena S. Zhukova, Victor I. Torgashev, Elizaveta A. Motovilova, Vladimir V. Lebedev, Anatoly S. Prokhorov, Gil’man S. Shakurov, Reinhard K. Kremer, Vladimir V. Uskov, Efim V. Pestrjakov, Victor G. Thomas, Dimitri A. Fursenko, Christelle Kadlec, Filip Kadlec, Martin Dressel, "THz–IR spectroscopy of single H₂O molecules confined in nanocage of beryl crystal lattice", Phase Transitions, 87, 966 (2014). Abstract.
[5] Alexander I. Kolesnikov, George F. Reiter, Narayani Choudhury, Timothy R. Prisk, Eugene Mamontov, Andrey Podlesnyak, George Ehlers, Andrew G. Seel, David J. Wesolowski, Lawrence M. Anovitz, "Quantum Tunneling of Water in Beryl: A New State of the Water Molecule", Physical Review Letters, 116, 167802 (2016). Abstract.

Direct Detection of the 229Th Nuclear Clock Transition

From left to right: Peter G. Thirolf, Lars v.d. Wense, Benedict Seiferle.

Authors: Lars von der Wense¹, Benedict Seiferle¹, Mustapha Laatiaoui^2,3, Jürgen B. Neumayr¹, Hans-Jörg Maier¹, Hans-Friedrich Wirth¹, Christoph Mokry^3,4, Jörg Runke^2,4, Klaus Eberhardt^3,4, Christoph E. Düllmann^2,3,4, Norbert G. Trautmann⁴, Peter G. Thirolf¹

Affiliations:
¹Ludwig-Maximilians-Universität München, 85748 Garching, Germany.
²GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany.
³Helmholtz Institut Mainz, 55099 Mainz, Germany.
⁴Johannes Gutenberg Universität, 55099 Mainz, Germany.

The measurement of time has always been an important tool in science and society [1]. Today’s most precise time measurements are performed with optical atomic clocks, which achieve a precision of about 10^-18, corresponding to 1 second uncertainty in more than 15 billion years, a time span which is longer than the age of the universe [2]. By comparing two of such clocks, which are shifted in height by just a few centimetres, also the time dilation due to general relativistic effects becomes measurable [3].

Despite such stunning precision, these clocks could be outperformed by a different type of clock, the so called “nuclear clock” [4]. The nuclear clock makes use of a nuclear transition instead of an atomic shell transition as so far applied. The expected factor of improvement in precision of such a new type of clock has been estimated to be up to 100, in this way pushing the ability of time measurement to the next level [5]. The reason for the expected improvement is the size of the nucleus, which is orders of magnitude smaller than the size of the atom, thus leading to significantly improved resilience against external influences.

Many potential applications for a nuclear clock are currently under discussion. These include practical applications such as improved satellite-based navigational systems, data transfer, gravity detectors [6] as well as fundamental physical applications like gravitational wave detection [7] and testing for potential changes in fundamental constants [8].

Using existing technology, there is only one nuclear state known, which could serve for a nuclear clock. This is the first excited nuclear isomeric state of ²²⁹Th. Among all known (more than 175,000) nuclear excitations, this isomeric state exhibits a unique standing due to its extremely low excitation energy of only a few electronvolts [9]. The energy is that low, that it would allow for a direct laser excitation of the nuclear transition, which is the prerequisite for the development of a nuclear clock.

The existence of this isomeric state was shown in 1976, based on indirect measurements [10]. However, despite significant efforts, the direct detection of the isomeric decay could not be achieved within the past 40 years [11]. In the recently presented work [12], our group was able to solve this long-standing problem, leading to the first direct detection of the ²²⁹Th nuclear clock transition. This direct detection is important, as it paves the way for the determination of all decay parameters relevant for optical excitation of the isomeric state. It is thus a breakthrough step towards the development of a nuclear clock.

Figure 1: (click on the image to view with higher resolution) Experimental setup used for the production of a purified ²²⁹Th ion beam and the direct detection of the isomeric state. For details we refer the reader to the text and to Ref. [12].

The detection was achieved by producing a low energy, pure ²²⁹Th ion beam, with a fractional content of ²²⁹Th in the isomeric state. The isomer was produced by making use of a 2% decay branch of the alpha-decay of ²³³U into the isomeric state. The setup used for ion beam production is shown in Fig. 1 and will be described in the following section. The ions were collected with low kinetic energy onto the surface of a micro-channel-plate (MCP) detector, triggering the isomer’s decay and leading to its detection at the same time. The obtained signal is shown in Fig. 2. A high signal-to-background ratio could be achieved owing to the concept of spatial separation of the ²³³U source and the point of isomer detection. Many comparative investigations were performed in order to unambiguously show that the detected signal originates from the ²²⁹Th isomeric decay [12].

Figure 2: ²²⁹Th isomeric decay signal as observed during 2000 second integration time on the MCP detector allowing for spatially resolved signal read out.

For the production of a low-energy ²²⁹Th ion beam, a ²³³U source was used, which was placed inside of a buffer-gas stopping cell, filled with 40 mbar of ultra-pure helium. ²²⁹Th isotopes, as produced in the alpha-decay of ²³³U, are leaving this source due to their kinetic recoil energy of 84 kiloelectronvolts. These recoil isotopes were stopped in the helium buffer-gas, thereby staying charged due to the large ionization potential of helium. The low-energy ²²⁹Th ions, produced in this way, were guided through the helium background towards the exit of the stopping cell by electric fields, provided by a radio-frequency funnel system. The exit of the stopping cell consists of a Laval-nozzle system, leading to the formation of a supersonic gas jet. This gas jet injects the ions into a radio-frequency quadrupole (RFQ) ion-guide, leading to the formation of an ion beam. This ion beam is further purified with the help of a quadrupole mass-separator (QMS). In this way, a low-energy, pure ²²⁹Th ion beam was produced, possessing a fractional isomeric content of about 2%.

The next envisaged steps towards the development of a nuclear clock will be performed within the framework of the EU-funded Horizon 2020 collaboration named “NuClock” (www.nuclock.eu). Experiments will be carried out that aim for a precise determination of the isomer’s energy and half-life as being the basis for the first direct laser excitation of a nuclear transition.

References:
[1] David Landes, "Revolution in Time: Clocks and the Making of the Modern World" (Harvard University Press, Cambridge, 2000).
[2] T.L. Nicholson, S.L. Campbell, R.B. Hutson, G.E. Marti, B.J. Bloom, R.L. McNally, W. Zhang, M.D. Barrett, M.S. Safronova, G.F. Strouse, W.L. Tew, J. Ye, "Systematic evaluation of an atomic clock at 2 X 10^-18 total uncertainty", Nature Communications, 6, 6896 (2015). Abstract.
[3] Andrew D. Ludlow, Martin M. Boyd, Jun Ye, E. Peik, P. O. Schmidt, "Optical atomic clocks", Review Modern Physics, 87, 637-701 (2015). Abstract.
[4] E. Peik, Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in ²²⁹Th", Europhysics Letters, 61, 181-186 (2003). Abstract.
[5] C. J. Campbell, A. G. Radnaev, A. Kuzmich, V. A. Dzuba, V. V. Flambaum, A. Derevianko, "Single-Ion nuclear clock for metrology at the 19th decimal place", Physical Review Letters, 108, 120802 (2012). Abstract.
[6] Marianna Safronova, "Nuclear physics: Elusive transition spotted in thorium", Nature, 533, 44-45 (2016). Abstract.
[7] Shimon Kolkowitz, Igor Pikovski, Nicholas Langellier, Mikhail D. Lukin, Ronald L. Walsworth, Jun Ye, "Gravitational wave detection with optical lattice atomic clocks", arXiv:1606.01859 [physics.atom-ph] (2016).
[8] V.V. Flambaum, "Enhanced effect of temporal variation of the fine structure constant and the strong interaction in ²²⁹Th", Physical Review Letters, 97, 092502 (2006). Abstract.
[9] B.R. Beck, J.A. Becker, P. Beiersdorfer, G.V. Brown, K.J. Moody, J.B. Wilhelmy, F.S. Porter, C.A. Kilbourne, R.L. Kelley, "Energy splitting of the ground-state doublet in the nucleus ²²⁹Th", Physical Review Letters, 98, 142501 (2007). Abstract.
[10] L.A. Kroger, C.W. Reich, "Features of the low energy level scheme of ²²⁹Th as observed in the alpha decay of ²³³U", Nuclear Physics A, 259, 29-60 (1976). Abstract.
[11] Ekkehard Peik, Maxim Okhapkin, "Nuclear clocks based on resonant excitation of gamma-transitions", Comptes Rendus Physique, 16, 516-523 (2015). Abstract.
[12] Lars von der Wense, Benedict Seiferle, Mustapha Laatiaoui, Jürgen B. Neumayr, Hans-Jörg Maier, Hans-Friedrich Wirth, Christoph Mokry, Jörg Runke, Klaus Eberhardt, Christoph E. Düllmann, Norbert G. Trautmann, Peter G. Thirolf, "Direct detection of the ²²⁹Th nuclear clock transition", Nature, 533, 47 (2016). Abstract.

Demonstration of Light Induced Conical Intersections in Diatomic Molecules

Left to right: Adi Natan, Matt Ware, Phil Bucksbaum

Authors: Adi Natan¹, Matthew R Ware^1,4, Vaibhav S. Prabhudesai², Uri Lev³, Barry D. Bruner³, Oded Heber³, Philip H Bucksbaum^1,4

Affiliation:
¹Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
²Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai, India
³Faculty of Physics, the Weizmann Institute of Science, Rehovot, Israel
⁴Departments of Physics, Applied Physics, and Photon Science, Stanford University, Stanford, CA, USA

About 200 femtoseconds after you started reading this line, the first step in actually seeing it took place. In the very first step of vision, the retinal chromophores in the rhodopsin proteins in your eyes were photo-excited and then driven through a conical intersection to form a trans isomer [1]. The conical intersection is the crucial part of the machinery that allows such ultrafast energy flow. Conical intersections (CIs) are the crossing points between two or more potential energy surfaces. These tend to repel when they approach each other, but cannot stay separated everywhere in the multidimensional geometry landscape of a molecule. CIs are ubiquitous in photo-processes in polyatomic molecules and govern key phenomena such as DNA photostability [2], but they are difficult to locate, measure and control, since their positions and features depend on specific molecular system under study. It is therefore of great interest to simulate their effects.

The case for diatomic molecules is different because naturally occurring CIs cannot exist for them: Energy levels are repelled when they approach each other, and there are not enough degrees of freedom for a true crossing. However a strong laser field applied to a diatomic molecule adds one additional degree of freedom, which gives rise to a light-induced artificial CI (LICI) that is predicted to have several features in common with the poly-atomic “wild-type” CI [3-5]. More recent theoretical studies have examined various aspects of this LICI phenomenon [6-9].

The molecular dynamics in the vicinity of a LICI can be explored in the simplest laser-illuminated molecular system, the ground state of the hydrogen molecular ion, H₂⁺ [10]. An infrared laser will induce interactions between the two lowest nuclear potential energy curves, named 1sσ_g and 2pσ_u. The interaction of strong fields with H₂⁺ can be expressed by shifting one of the potential curves by the energy of one photon. The now ”dressed” potential curve crosses at some internuclear separation R where the two states are resonantly coupled by the laser field, the analog of the curve crossings at CIs in polyatomic molecules, as seen in Fig 1(a) . We define the LICI as this crossing point, when the polarization of the laser is perpendicular to the molecular axis. For other angles, there is no crossing, and the dynamics is “adiabatic”, that is, a nuclear wavepacket will travel only on one of the dressed potential curves.

Consider for a moment what it means to have a point of crossing where the field is perpendicular to the molecular axis of a diatomic molecule: This molecule effectively “feels” zero laser field only at this specific angle, so the potential curves assume their field free R-dependence only here. The key to the dynamics induced by the LICI is the special behavior of the molecule as it rotates through this special point, from an angle on one side where it experiences the field, to an angle on the other side where the field is once again felt.

The simplest place to start is H₂⁺ in its ground rotational state, interacting with a strong laser field that couples resonantly the two electronic states. The spherical symmetry of the ground state field-free nuclear probability density, changes rapidly when a strong field is turned on. We can follow how this probability density evolves in the dressed state framework. In the dressed picture, the LICI is a local maximum in the two-dimensional (R,θ) potential energy landscape, while in other angles, the population dissociates adiabatically on the unbound part of the light induced potential curve. This causes the part of the population to accumulate around the LICI and then scatter from it, similar to waves scattering from a cone shape potential barrier. However, unlike scattering of a free particle around a barrier, the scattering described here is of bound nuclear wave packet, which scatters into a multitude of rovibrational states on the ground electronic surface, similar to the non-adiabatic dynamics around a natural CI. The scattering from the LICI leads to dissociation, but imposes a scattering time delay. The coherent addition of all the scattering trajectories creates an interference pattern at various angles and kinetic energy releases (Fig 1 (b), and Fig 1(c)). These quantum interferences are a universal signature for LICIs because they arise from the nature of coherent scattering interference near a point of degeneracy.

Figure 1: [Click on the image to view with higher resolution] (a) The dressed potential energy surfaces of H₂⁺ featuring LICIs. (b) The calculated instantaneous probability of dissociation P(θ,t)_diss from a given vibrational state (for example, v=9) during the interaction with the laser pulse reveals the interference. (c) Experimental (top) and calculated (bottom) angular distributions of H₂⁺ dissociation at kinetic energy releases that correspond to specific initial vibrations states.

We have experimentally demonstrated the effects of LICIs on strong-field photodissociation of H₂⁺ by means of quantum interferences that modify the angular distributions of the dissociating fragments [10]. The interferences depend strongly on the energy difference between the initial state and the LICI. The larger the overlap between the initial state and the LICI, the larger the effective duration of interaction and the more developed the interferences. For example, we can compare the effect among different initial states, starting from an initial state that is nearly resonant, hence has a large overlap with the LICI, such as the vibrational level v = 9 in H₂⁺, to a state that is non-resonant such as v = 7. We observe in both calculation and experiment how these initial states indeed capture the different effective duration of the interaction with the LICI (Fig 1(c)).

LICIs are particularly attractive for future quantum control experiments due to their high degree of controllability using the polarization and frequency of the laser. The interaction is not limited to just a single LICI, and allows control of the timing of its appearance as well. Understanding the dynamics induced by LICIs will facilitate understanding and applicability to systems of higher complexity. Implementing and understanding LICIs in more complex systems will open the way to novel spectroscopy techniques in physics and chemistry.

References:
[1] Dario Polli, Piero Altoè, Oliver Weingart, Katelyn M. Spillane, Cristian Manzoni, Daniele Brida, Gaia Tomasello, Giorgio Orlandi, Philipp Kukura, Richard A. Mathies, Marco Garavelli, Giulio Cerullo, "Conical intersection dynamics of the primary photoisomerization event in vision", Nature, 467, 440 (2010). Abstract.
[2] B. K. McFarland, J. P. Farrell, S. Miyabe, F. Tarantelli, A. Aguilar, N. Berrah, C. Bostedt, J. D. Bozek, P. H. Bucksbaum, J. C. Castagna, R. N. Coffee, J. P. Cryan, L. Fang, R. Feifel, K. J. Gaffney, J. M. Glownia, T. J. Martinez, M. Mucke, B. Murphy, A. Natan, T. Osipov, V. S. Petrović, S. Schorb, Th. Schultz, L. S. Spector, M. Swiggers, I. Tenney, S. Wang, J. L. White, W. White, M. Gühr, "Ultrafast X-ray Auger probing of photoexcited molecular dynamics", Nature Communications, 5, 4235 (2014). Abstract.
[3] Nimrod Moiseyev, Milan Šindelka, Lorentz S. Cederbaum, "Laser-induced conical intersections in molecular optical lattices", Journal of Physics B,  41, 221001 (2008). Full Article.
[4] Milan Šindelka, Nimrod Moiseyev, Lorentz S. Cederbaum, "Strong impact of light-induced conical intersections on the spectrum of diatomic molecules", Journal of Physics B, 44, 045603 (2011). Abstract.
[5] Nimrod Moiseyev, Milan Šindelka, "The effect of polarization on the light-induced conical intersection phenomenon", Journal of Physics B, 44, 111002 (2011). Abstract.
[6] Gábor J. Halász, Ágnes Vibók, Nimrod Moiseyev, Lorenz S. Cederbaum, "Nuclear-wave-packet quantum interference in the intense laser dissociation of the D₂⁺ molecule", Physical Review A, 88, 043413 (2013). Abstract.
[7] Gábor J Halász, Ágnes Vibók, Nimrod Moiseyev, Lorenz S Cederbaum, "Light-induced conical intersections for short and long laser pulses: Floquet and rotating wave approximations versus numerical exact results", Journal of Physics B, 45, 135101 (2012). Abstract.
[8] Gábor J. Halász, Ágnes Vibók, Milan Šindelka, Lorenz S. Cederbaum, Nimrod Moiseyev, "The effect of light-induced conical intersections on the alignment of diatomic molecules", Chemical Physics, 399, 146 (2012). Abstract.
[9] G.J. Halász, A. Vibók, L.S. Cederbaum, "Direct Signature of Light-Induced Conical Intersections in Diatomics", Journal of Physical Chemistry Letters, 6, 348 (2015). Abstract.
[10] Adi Natan, Matthew R. Ware, Vaibhav S. Prabhudesai, Uri Lev, Barry D. Bruner, Oded Heber, Philip H. Bucksbaum, "Observation of Quantum Interferences via Light-Induced Conical Intersections in Diatomic Molecules", Physical Review Letters, 116, 143004 (2016). 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.