Observations of Short-Period Stars Orbiting the Supermassive Black Hole in our Galactic Center Are Probing the Gravitational Theory

From left to right: Aurelien Hees, Andrea M. Ghez, Tuan Do

Authors: Aurelien Hees, Andrea M. Ghez, Tuan Do

Affiliation:
Galactic Center Group, University of California Los Angeles, USA

Our current understanding of fundamental physics is based on four interactions: electromagnetism, the weak interaction, the strong interaction and gravitation. The first three ones are unified in a common framework, the Standard Model of particle physics based on a relativistic quantum field theory. On the other hand, Einstein’s theory of General Relativity, the gravitational theory, has not been successfully included in this quantum framework so far. The development of a quantum theory of gravity is important to understand phenomena that take place in very strong gravitational fields like for example in our very early universe or around black holes.

In addition, Dark Matter and Dark Energy are contributing to 26% and 69% to the mass-energy content of our Universe [1]. These two components of our Universe, essential to explain some cosmological and astrophysical observations, have not been directly observed so far and are also challenging General Relativity (see e.g. [2]).

For these reasons, in the last decades, theoreticians have developed many modified gravitational theories (see [3] and references therein). On the other hand, there has been a tremendous effort to confront General Relativity with different observations and to search for a deviation from General Relativity using a large number of experiments (see the review [4]). Historically, tests of gravitation have been first performed in the Solar System and in laboratories on Earth where extremely good accuracy in the measurements can be achieved. In these low gravitational fields, the agreement between General Relativity’s predictions and observations is extremely good. It is therefore highly interesting to perform such tests in other environments, such as in strong gravitational fields.

The motion of short-period stars orbiting around the supermassive black hole in the center of our Galaxy, the Milky Way, has been tracked since 1995 at the W. M. Keck Observatory in Hawaii by the UCLA Galactic Center Group. The stars observed close to the black hole have orbital periods of the orders of 10-50 years, allowing us to measure quasi-Keplerian motion (similar to
the motion of the planets around our Sun). These observations have led to many great discoveries, the most important one being the evidence for a supermassive black hole at the center of our Galaxy [5]. Two types of observations are made at the Keck observatory: (i) astrometric observations which give the 2-dimensional position of the stars in the plane of the sky and (ii) spectroscopic measurements which give the radial velocity of the stars. Nowadays, the typical accuracy of these measurements is at the level of 0.2 milliarcsecond for astrometry and of 30 km/s for radial velocity for a bright star. Recently, observations of two of these stars, S0-2 (period: 16 years) and S0-38 (period: 19 years), have been used to measure our distance to the Galactic Center and the mass of the central supermassive black hole with an accuracy of 5% [6] (Fig. 1 shows the orbit of these two stars).

Fig 1 : Orbital motion of two stars, S0-2 and S0-38, orbiting around the supermassive black hole at the center of our Galaxy. Observations of these two stars have been used to test the gravitational theory and to constrain the presence of a hypothetical 5th force.  Credit: S. Sakai and A. Ghez, W. M. Keck Observatory/UCLA Galactic Center Group.

In a recent work [7], we used these observations to perform a test of the gravitational theory using orbital dynamics in a strong gravitational field generated by a supermassive black hole. The main novelty in using these measurements to test General Relativity comes from the fact that we are probing the gravitational theory in a gravitational field much stronger than for example in the Solar System, around a central mass which is much more massive (the black hole mass is 4 x 10⁶ the mass of the Sun) and around an extremely interesting body: a black hole.

 More precisely, short-period stars are constraining the presence of a hypothetical fifth force in our Galactic Center. A fifth interaction is predicted by many modifications of General Relativity developed in order to unify it with the Standard Model of particle physics and by models of Dark Matter and Dark Energy. This fifth force is parametrized by a length of interaction λ and a strength of interaction  α, both of these parameters being constrained observationally by Solar System observations and by laboratory measurements (see e.g. [8]). We used observations of S0-2 and S0-38 to search for a fifth force in a strong gravitational field generated by a black hole [7]. No deviation from General Relativity has been observed and new constraint on this scenario has been derived (see Fig. 2).

 Two main factors are expected to improve such an analysis in the future. First, in 2018, the star S0-2 will experience its closest approach to the supermassive black hole. At that time, the gravitational effects experienced by the star are the strongest and the possibility to measure relativistic effects and to test General Relativity is enhanced. Observations during S0-2’s closest approach in 2018 will be the most sensitive to a hypothetical deviation from General Relativity. The UCLA Galactic Center Group is currently actively preparing this wonderful event. On the other hand, the development of the next generation of extremely large telescope, such as the Thirty Meter Telescope, will allow us to detect and to track stars that are even closer to the black hole. On the long-term, this will improve significantly tests of General Relativity.

Fig 2: (click on the image to view with higher resolution) Constraints on a hypothetical fifth interaction. In green are constraints coming from Earth observations or from the LAGEOS satellites, in blue the constraints coming from Lunar Laser Ranging observations, in orange constraints from planetary ephemerides and in red the new constraint obtained using observations of stars around our Galactic Center. Our current analysis probed the 5th interaction in a strong gravity field as emphasized in the right panel (red region).

References:
[1] Planck Collaboration, “Planck 2015 results. XIII. Cosmological parameters”. Astronomy & Astrophysics, 594, A13 (2016). Abstract.
[2] Ivan Debono, George F. Smoot, “General Relativity and Cosmology: Unsolved Questions and Future Directions”. Universe, 2, 23 (2016). Abstract.
[3] Timothy Clifton, Pedro G. Ferreira, Antonio Padilla, Constantinos Skordis, “Modified gravity and cosmology”. Physics Reports, 513, 1 (2012). Abstract.
[4] Clifford M. Will, “The Confrontation between General Relativity and Experiment”. Living Review in Relativity, 17, 4 (2014). Abstract.
[5] A. M. Ghez, B. L. Klein, M. Morris, E. E. Becklin, “High Proper-Motion Stars in the Vicinity of  
Sagittarius A*: Evidence for a Supermassive Black Hole at the Center of Our Galaxy”.  Astrophysical Journal, 509, 678 (1998). Abstract.
[6] A. Boehle, A. M. Ghez, R. Schödel, L. Meyer, S. Yelda, S. Albers, G. D. Martinez, E. E. Becklin, T. Do, J. R. Lu, K. Matthews, M. R. Morris, B. Sitarski, G. Witzel, “An Improved Distance and Mass Estimate for Sgr A* from a Multistar Orbit Analysis”. Astrophysical Journal, 830, 17 (2016). Abstract.
[7] A. Hees, T. Do, A. M. Ghez, G. D. Martinez, S. Naoz, E. E. Becklin, A. Boehle, S. Chappell, D. Chu, A. Dehghanfar, K. Kosmo, J. R. Lu, K. Matthews, M. R. Morris, S. Sakai, R. Schödel, G. Witzel, “Testing General Relativity with stellar orbits around the supermassive black hole in our Galactic center”. Physical. Review Letters, 118, 211101 (2017). Abstract.
[8] E.G. Adelberger, J.H. Gundlach, B.R. Heckel, S. Hoedl, S. Schlamminger, “Torsion balance experiments: A low-energy frontier of particle physics”. Progress in Particle and Nuclear Physics 62, 102 (2009). 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.

A New Way To Weigh A Star

Nils Andersson (left) and Wynn Ho 

Authors: Nils Andersson, Wynn Ho

Affiliation: Mathematical Sciences and STAG Research Centre, University of Southampton, UK. 

You probably have a pretty good idea of your own weight. And if you need an exact answer it is relatively easy to find out. Get the bathroom scales out, step up and read off the result. But have you ever asked yourself what was actually involved in that measurement? Have you considered that what actually happened was that gravity’s pull was countered by the electromagnetic interaction of the atoms that make up the surface of the scale, and what you actually measured was how hard the atoms had to work to push back on your feet? Possibly not, and the chances are that you have never really considered how one would weigh a distant star, either.

As it turns out, this question has a fairly straightforward answer, which also involves gravity, electromagnetism… and a bit of luck. If you want to figure out how heavy a particular star is, and you are lucky enough that this star has a close companion, then all you need to do is track the star’s motion. The orbital motion of a double-star system is dictated by gravity and you can figure out how much the stars weigh using the same arguments that we use to figure out the mass of the moon (going around the Earth) and the Earth (circling the Sun). If you want to be a bit more precise you should use Einstein’s curved spacetime theory for gravity rather than Newton’s inverse square-law, but this may be a luxury in this exercise.

Using this technique, astronomers have weighed many stars with great precision and they have also managed to work out the masses of a number of pulsars [1]. This is particularly exciting as these systems stretch our understanding of several aspects of fundamental physics.

A pulsar is a highly magnetised rotating neutron star formed when a massive star runs out of nuclear fuel. At this point it can no longer hold itself up against gravity and it starts falling in on itself. This leads to a spectacular explosion – a supernova – the remains of which may be either a neutron star or a black hole. Neutron stars are nature’s own counterparts to the Large Hadron Collider [2]. In essence, they provide a link between astronomy and laboratory work in both high-energy and low-temperature physics. By weighing these stars we gain insight into physics under extreme conditions [3].

Pulsars are named for their rotating beam of electromagnetic radiation, which is observed by telescopes as it sweeps past the Earth, just like the familiar beam of a lighthouse [4]. They are renowned for their incredibly stable rate of rotation [5], but young pulsars occasionally experience so-called glitches where they are found to speed up for a very brief period of time [6]. The prevailing idea is that these glitches provide evidence of exotic states of matter in the star’s interior [3]. The glitches arise when a rapidly spinning superfluid within the star transfers rotational energy to the star's crust, a solid outer layer like a bowl containing a mysterious soup; the component that is tracked by observations. Imagine the bowl spinning at one speed and the soup spinning faster. Friction between the inside of the bowl and its contents, the soup, can cause the bowl to speed up. Whenever this happens, the more soup there is, the faster the bowl will be made to rotate.

Interestingly, it seems that the superfluid soup provides us with a new way of weighing these stars. This new technique is very different from the usual approach as it is not based on gravity, but nuclear physics, and it can also be used for stars in isolation. The star does not have to have a companion.

In a recent paper in Science Advances [7], we have developed this exciting new idea, which relies on a detailed understanding of neutron star superfluidity and the dynamics of the quantum vortices - a kind of ultra-slim tornadoes - by means of which these systems mimic large-scale rotation. Our results are promising and have important implications for the generation of revolutionary radio telescopes, like the Square Kilometre Array (SKA [8]) and the Low Frequency Array (LOFAR [9]), that are being developed by large international collaborations. The discovery and monitoring of many more pulsars is one of the key scientific goals of these projects. We now have a set of scales that may allow us to figure out how much these stars weigh, as well.

References: 
[1] See, for example, the list maintained at stellarcollapse.org. 
[2] See Large Hadron Collider. 
[3] J.M. Lattimer, M. Prakash, "The Physics of Neutron Stars", Science, 304, 536-542 (2004). Abstract. 
[4] The discovery of pulsars was recognized with the Nobel prize in physics in 1974. 
[5] Gravity tests using the stability of the timing of pulsars was recognized with the Nobel prize in physics in 1993. 
[6] A catalog of glitches is maintained by Jodrell Bank Centre for Astrophysics. 
[7] W.C.G. Ho, C.M. Espinoza, D. Antonopoulou, N. Andersson, "Pinning down the superfluid and measuring masses using pulsar glitches," Science Advances, 1, e1500578 (2015). Full Article. 
[8] See Square Kilometre Array.  
[9] See LOFAR. 

A Magnetic Wormhole

(From left to right) Carles Navau, Alvaro Sanchez, Jordi Prat-Camps

Authors: Jordi Prat-Camps, Carles Navau, Alvaro Sanchez 

Affiliation: Departament de Física, Universitat Autònoma de Barcelona, Spain.

Link to Superconductivity Group UAB >>

Is it possible to build a wormhole in a lab? Taking into account that large amounts of gravitional energy would be required [1], this seems an impossible task. However, redefining a wormhole into a path between two points in space that is completely undetectable, Greenleaf and colleagues [2] suggested in 2007 a (theoretical) way of realizing an electromagnetic wormhole capable of guiding light through an invisible path. They demonstrated that this is topologically equivalent as if the light had been sent through another spatial dimension. However, such a wormhole required metamaterials with extreme properties, which prevented its construction.

In our work, we have constructed an actual 3D wormhole working for magnetostatic fields. It allows the passage of magnetic field between distant regions while the region of propagation remains magnetically invisible. Our wormhole takes advantage of the possibilities that magnetic metamaterials offer for shaping static magnetic fields [3]. These metamaterials can be constructed using existing magnetic materials that can provide extreme magnetic permeability values ranging from zero - superconductors - to effectively infinity - ferromagnets.

Figure 1: (Left) 3D sketch of the magnetic wormhole, showing how the magnetic field lines (in red) of a small magnet at the right are transferred through it. (Right) From a magnetic point of view the wormhole is magnetically undetectable so that the field of the magnet seems to disappear at the right and reappear at the left in the form of a magnetic monopole. (Image credit: Jordi Prat-Camps and Universitat Autònoma de Barcelona).

The magnetic wormhole requires three properties: (i) to magnetically decouple a given volume from the surrounding 3D space, (ii) to have the whole object magnetically undetectable, and (iii) to have magnetic fields propagating through its interior. The first two properties are achieved by constructing a 3D magnetic cloak. Based on previous ideas [4] such a cloak could be made by surrounding a superconducting sphere with a specially created ferromagnetic (meta)surface, such that the magnetic signature of the superconductor was cancelled by the ferromagnet. For the third property, we use magnetic hoses, also made by magnetic metamaterials, as developed in [5].

The parts composing the magnetic wormhole are shown in fig. 2: a central magnetic hose to guide the magnetic field from one end of the hose to the opposite one, and a magnetic cloak composed of a superconducting-ferromagnetic bilayer to make the hose magnetically invisible.

Figure 2: (a) 3D image of the magnetic wormhole, formed by concentric shells: from outside inwards, an external metasurface made of ferromagnetic pieces (b), an internal superconducting shell made of coated conductor pieces (c), and a magnetic hose made of ferromagnetic foil (d). (e) Cross-section view of the wormhole, including the plastic formers (in green and red) used to hold the different parts. (Image credit: Jordi Prat-Camps and Universitat Autònoma de Barcelona).

Experimental results clearly demonstrate [6] the two desired properties for the wormhole: (i) magnetic field from a source at one end of the wormhole appear at the opposite end (actually as a kind of isolated magnetic monopole), (ii) the overall device is magnetically undetectable (it does not noticeably distort an applied magnetic field, even a non-uniform one).

Besides the scientific interest per se in the realization of an object with properties of a wormhole, our device may have applications in practical situations where magnetic fields have to be transferred without distorting a given field distribution, as in magnetic resonance imaging.

Acknowledgements: We thank Spanish project MAT2012-35370 and Catalan 2014-SGR-150 for financial support. A.S. acknowledges a grant from ICREA Academia, funded by the Generalitat de Catalunya. J. P.-C. acknowledges a FPU grant form Spanish Government (AP2010-2556).

References:
[1] Michael S. Morris, Kip S. Thorne, Ulvi Yurtsever, "Wormholes, Time Machines, and the Weak Energy Condition", Physical Review Letters, 61, 1446 (1998). Abstract.
[2] Allan Greenleaf, Yaroslav Kurylev, Matti Lassas, Gunther Uhlmann, "Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials", Physical Review Letters, 99, 183901 (2007). Abstract.
[3] Steven M. Anlage, "Magnetic Hose Keeps Fields from Spreading", Physics, 7, 67 (2014). Full Article.
[4] Fedor Gömöry, Mykola Solovyov, Ján Šouc, Carles Navau, Jordi Prat-Camps, Alvaro Sanchez, "Experimental realization of a magnetic cloak", Science, 335, 1466 (2012). Abstract.
[5] C. Navau, J. Prat-Camps, O. Romero-Isart, J. I. Cirac, A. Sanchez. "Long-Distance Transfer and Routing of Static Magnetic Fields", Physical Review Letters, 112, 253901 (2014). Abstract.
[6] Jordi Prat-Camps, Carles Navau, Alvaro Sanchez. "A Magnetic Wormhole", Scientific Reports 5, 12488 (2015). Full Article.

How Time Dilation Affects Quantum Superpositions

(From left to right) Igor Pikovski, Magdalena Zych, Fabio Costa, Časlav Brukner
(Click on the image to see their faces with better resolution)

Authors: Igor Pikovski^1,2,3,4, Magdalena Zych^1,2,5, Fabio Costa^1,2,5, Caslav Brukner^1,2

Affiliation:
¹Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Austria,
²Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Vienna, Austria,
³ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USA,
⁴Department of Physics, Harvard University, Cambridge, Massachusetts, USA,
⁵Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland, Australia.

Can gravity affect quantum systems? Quantum theory and gravity seem to apply to very different physical regimes. It is often argued that gravity is irrelevant on very small scales, where typical quantum phenomena are observed. A well-known argument compares the forces between an electron and a proton: gravity is roughly 10³⁹ times weaker than electromagnetism. But this is not the full story. As has been shown in numerous experiments, gravity can indeed influence a quantum wave function of the smallest particles. Newtonian gravity from Earth can induce a quantum phase-shift for a particle that is in a superposition between two different heights. This was first demonstrated with Neutrons in the famous COW (Colella-Overhauser-Werner) experiment in 1975 [1].

Past 2Physics article by this group:
January 15, 2012: "Quantum Complementarity Meets Gravitational Redshift" by Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner.

What about Einstein’s gravity? If the Newtonian potential can influence a quantum wave function, what can one expect from post-Newtonian effects stemming from general relativity? It turns out that novel phenomena arise, with no classical analogue. A few years ago, we studied how time dilation affects a single clock in superposition [2] (see also 2Physics article “Quantum Complementarity Meets Gravitational Redshift”). Classically, two clocks placed at different heights will experience different proper times, and thus will be time dilated with respect to each other. But in quantum theory, an additional effect arises: If a single clock is brought into superposition of two heights, its internal degrees of freedom (or clock states) get entangled with its position. This entanglement affects the superposition of heights. If the two amplitudes are brought together to interfere, the interference pattern will be affected due to quantum complementarity: As the internal clock states record time, they gain “which-way information” and thus destroy the quantum coherence. This interplay has been recently demonstrated in an experiment with a BEC, where the time delay of spin precession was simulated by inhomogeneous magnetic fields [3] (see also 2Physics article “One Clock in Two Places Simultaneously”).

Figure 1: The gravitational field causes time dilation, clocks closer to Earth run slower than clocks further away. For a quantum superposition of a single clock at two heights, the clock states and its position become entangled.

In our latest work, we showed that the effect of time dilation on quantum systems is very general and affects the quantum coherence of any composite quantum system [4]. Time dilation is universal: it affects any system regardless of its structure or composition. Clocks are affected by time dilation as much as the heart beat or the half-life of a decaying particle. Also composite quantum systems are affected, as they usually have a finite temperature: It means that there is always some internal dynamics present within the system, which can be affected by time dilation. If such a composite system is brought into superposition between different heights above Earth, as in the above example with a clock, time dilation will correlate all internal dynamics with the height of the system. And this causes decoherence of the center-of-mass, just as in the case with an actual clock. In practice, any system is affected that has some internal energy spread. If the center-of-mass of such a system is brought into superposition and a sufficient difference in proper times is accumulated along the superposed paths, quantum coherence will be lost because of the relative time delay of the internal dynamics of the system. Needless to say, time dilation can be caused by a gravitational field but also by any acceleration or by velocities. There is no “external” environment, only the presence of time dilation causes the system’s center-of-mass to decohere due to the dynamics of its own composition.

Figure 2: A complex molecule in superposition in a gravitational field. Because of time dilation, the frequencies of the individual atoms depend on the height of the molecule. This causes decoherence of quantum superpositions of the center-of-mass of the molecule.

One may expect this effect to be vanishingly small. After all, it is very hard to detect time dilation on Earth. But it turns out that already on mesoscopic scales, the effect is strong: If a gram-scale object at room temperature is put into a superposition of height difference of 1µm, then time dilation will cause decoherence after about 1ms. This is because many internal degrees of freedom contribute to the effect. Each individually is affected by time dilation only a tiny bit, but for a larger composite system, the effect can become significant. For quantum systems, it is of course very challenging to prepare such large superpositions, and other decoherence effects will also be of importance. But there is a parameter range at superfluid temperatures, where experiments with very large molecules or microspheres could in principle observe the predicted phenomena in the future. But importantly, the effect is universal and any internal dynamics will contribute to decoherence. Thus one can think of other possible experiments with internal dynamics other than thermal, such as nuclear dynamics or some fast chemical processes.

All of these will contribute to the rate of decoherence; one can be creative in designing a clever experiment. In fact, one could also use such setups to reverse the logic: observing coherence of the center-of-mass might be a key to shed light on unknown internal dynamics. Maybe the best possible way for experimental verification will turn out to take an actual clock and put it in superposition -- as we proposed in [2] and which has recently been shown to work in an analogue experiment [3]. Future experiments should be able to verify decoherence due to time dilation, which follows only from quantum theory and general relativity as we know them.

Finally, what do we actually learn from this study? In our work, we do not treat the gravitational field quantum-mechanically, thus there is no direct connection to “quantum gravity”. Yet, we study how quantum mechanical test systems behave on a background space-time, as opposed to classical test particles, and new effects arise. We discovered a new decoherence mechanism, but the most exciting aspect of the work is that the interplay between quantum theory and gravity has novel phenomena to offer. Our work shows one example, but this research direction is still widely unexplored: Many more possible effects and experiments on the interplay between these two great theories are waiting to be discovered!

References:
[1] Roberto Colella, Albert W. Overhauser, Samuel A. Werner. “Observation of Gravitationally Induced Quantum Interference”, Physical Review Letters, 34, 1472 (1975). Abstract.
[2] Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner. “Quantum interferometric visibility as a witness of general relativistic proper time”, Nature Communications, 2, 505 (2011). Abstract. 2Physics Article.
[3] Yair Margalit, Zhifan Zhou, Shimon Machluf, Daniel Rohrlich, Yonathan Japha, Ron Folman. “A self-interfering clock as a 'which path' witness”, published online in 'Science Express' (August 6, 2015). Abstract. 2Physics Article.
[4] Igor Pikovski, Magdalena Zych, Fabio Costa, Časlav Brukner, “Universal decoherence due to gravitational time dilation”, Nature Physics ,11, 668-672 (2015). Abstract.

One Clock in Two Places Simultaneously

Ron Folman (photo credit: Naomi Weisman)

Author: Ron Folman

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

Link to atom chip group >>

Introduction:

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

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

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

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

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

The experiment :

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

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

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

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

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

The Team :

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

Additional Thoughts :

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

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

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

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