The Real-Space Collapse of a Two Dimensional Polariton Gas

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

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

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

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

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

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

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

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

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

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

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

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



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

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

Recent Supernova Debris on the Moon

Thomas Faestermann (left) and Gunther Korschinek.

Authors: Thomas Faestermann, Gunther Korschinek

Affiliation: Technische Universität München, 85748 Garching, Germany.

Stars with a mass of more than about 8 times the solar mass usually end in a supernova explosion (SN). Before and during this explosion new elements, stable and radioactive, are formed by nuclear reactions and a large fraction of their mass is ejected with high velocities into the surrounding space. Most of the new elements are in the mass range until Fe, because there the nuclear binding energies are the largest. If such an explosion happens close to the sun it can be expected that part of the debris might enter the solar system and therefore should leave a signature on the planets and their moons. The interstellar space is not empty but contains dust and atomic particles, of course in minuscule densities.

A SN is cleaning up the surrounding space such that empty bubbles (around 0.06 atoms per cm³) are formed surrounded by denser space (around 10 atoms per cm3). The sun is embedded in a so called local bubble [1], indicating that one or even more SNe should have happened near the solar system in the past. Considering these ideas we have started already in the past to search for SN traces on our Earth. The best suited isotope for such a signature is ⁶⁰Fe. It has a half-life of 2.6 Myr [2] and it is not produced naturally on Earth, however it is also formed in small amounts by cosmic rays in interplanetary dust particles.

To detect and measure such extremely tiny amounts of ⁶⁰Fe an ultrasensitive method is needed. Accelerator mass spectrometry (AMS) is the only choice in this case. We have developed this method for many years using the Munich tandem accelerator, and achieve, besides a facility in Australia, the highest sensitivity worldwide [3]. The principle is the following: negative ions are formed in an ion source, acceleration with a voltage of a few kV and then pass a combination of electric and magnetic fields as in a conventional mass spectrometer. Subsequently they are accelerated in the tandem accelerator to a high velocity on the order of 7% of the speed of light. In the tandem the negative ions traverse a thin carbon foil where they lose a certain number of electrons to become multiply charged positive ions.

This process is so effective that absolutely no interfering molecules can survive. Thus a typical limitation in conventional mass spectrometry, molecular background, vanishes. In addition, because of the high energy of the ions, nuclear physics techniques are applied to reduce drastically possible interferences of stable isobars. In our case it is ⁶⁰Ni in our iron samples which is suppressed that much that an isotopic ratio ⁶⁰Fe/Fe of a few times 10^-17 can still be measured.

Our first studies in the past were focused on deep sea ferromanganese crusts. These depositions are very slowly growing, around 2 to 3 mm/Myr, on the bottom of the oceans, and accumulate elements present in the ocean water. As they collect also ¹⁰Be, a radioactive isotope with a half-life of 1.387 Myr, formed by cosmic rays on Nitrogen and Oxygen in our atmosphere, samples taken from different depths in the crust can be dated via the decreasing concentration of ¹⁰Be in deeper layers. The results of the most conclusive studies [4,5] are shown in fig.1.

Figure 1: (click on figure to view with higher resolution) The ⁶⁰Fe/Fe concentrations as measured in different depths of the ferromanganese crust 237KD (red points). The peak of an enhanced ⁶⁰Fe/Fe concentration at an age of around 2-3 Myr is due to the flux of SN-formed ⁶⁰Fe which has entered the solar system at that time. The blue triangles are from a separate measurement series where we have carefully leached out iron from crust samples and then analyzed. The vertical bars indicate 68% uncertainties, the horizontal ones the age range covered by the sample.

From the measured concentrations we had deduced the ⁶⁰Fe flux at that time and also the distance of one or more SNe. The critical point was however, the transport of the ⁶⁰Fe from the upper atmosphere through all atmospheric processes towards the biosphere in the ocean until the final deposition in the ferromanganese crust. To circumvent this difficulty we considered [6] to search for ⁶⁰Fe in lunar samples collected by US Astronauts between 1969 and 1972 and brought to earth. Together with colleagues from the Rutgers University, New Jersey (USA), we applied successfully for selected sample material from the astronomical laboratory of the Johnson space center (NASA).

An enhanced ⁶⁰Fe concentration in lunar material would be a clear proof of our previous measurements and the conclusions drawn. It must have been deposited everywhere in our solar system, on all the planets and their moons. In addition, the total amount of ⁶⁰Fe would provide solid data for the fluence and also the distance of the SNe because the ⁶⁰Fe has been collected directly on the surface of the Moon.

The drawback is however that the moon does not deliver the chronological information like the crust samples. The lunar surface (regolith) is constantly stirred and mixed by the impact of micrometeorites (a process called gardening) and also sporadic impacts by full-sized meteorites, thus losing any precise time information. A further drawback is that ⁶⁰Fe is also formed by the much higher cosmic ray flux via nuclear reactions on Ni which is present in lunar regolith, albeit only in tiny concentrations. To quantify this contribution we compared the lunar data with data from iron meteorites, which have been exposed for many millions of years to cosmic rays, and which we investigated as well. We know that cosmogenic ⁶⁰Fe is formed by nuclear reactions only on the heaviest stable nickel isotope ⁶⁴Ni. We know also that another long-lived radioisotope ⁵³Mn (T_1/2 = 3.7 Myr) is formed by cosmic rays on stable iron. In the case of additional SN produced ⁶⁰Fe the concentration ratios of ⁶⁰Fe/Ni to ⁵³Mn/Fe should be higher in the lunar samples than in the meteoritic data.

Fig. 2 shows the comparison of 11 lunar samples (red points) with meteoritic samples (green points). Instead of concentrations we plot by convention their activity (disintegrations per minute) relative to the amount of the target element Ni and Fe. The meteoritic data follow, as expected, a proportionality (the range between the green lines), indicating that ⁶⁰Fe like ⁵³Mn is produced by cosmic rays; the scatter of the activities is mainly due to differences in the meteoroid geometry. Most of the lunar samples have ⁶⁰Fe activities well above the expected relationship of the meteorite samples because of the SN contribution. Only three of the lunar samples have activities comparable to cosmic ray origin; they are from greater depth or have a complicated history; e.g. sample 3 is eroded material from the surface of a rock thus has no SN contribution.

Figure 2: (click on figure to view with higher resolution) The measured activities of ⁶⁰Fe versus ⁵³Mn in meteoritic and lunar samples. Units are disintegrations per minute per kg Fe and Ni, for ⁵³Mn and ⁶⁰Fe, respectively. Samples 1 through 11 (red) are lunar samples; the other values (green) are for iron meteorites. The area between the green straight lines indicates the 68% error band for cosmic ray produced ⁵³Mn and ⁶⁰Fe activities in meteorites.

Any ⁶⁰Fe signal is expected to be distributed downward due to gardening of the lunar surface [7]. In Fig. 3 we show the SN produced ⁶⁰Fe concentration (cosmic ray contribution subtracted) as a function of the depth (areal density) of the samples. The deposition of the ⁶⁰Fe on the lunar surface must have happened on a time scale of Myr, since already considerable gardening has happened and, on the other hand, cannot have happened more than some 3 half-lives, i.e. 8 Myr, ago to be still detectable. Thus it is very likely that it coincides with the ⁶⁰Fe surplus in the ferromanganese crust, which was collected between 1.7 and 2.6 Myr ago. In a time period of around 2.2 Myr, gardening is expected down to a few g/cm². It is reasonable, therefore, to integrate the measured ⁶⁰Fe concentration over this range, in order to estimate the local fluence of ⁶⁰Fe. Nevertheless we found also elevated concentrations of ⁶⁰Fe down to a depth of 20 g/cm² (Fig. 3), indicating possible excavations by meteorites and/or down-slope movements.

Figure 3: (click on figure to view with higher resolution) Depth dependence of the SN produced ⁶⁰Fe concentration and estimation of the local fluence of  ⁶⁰Fe on the Moon’s surface. The dashed curves represent two different integration scenarios. They symbolize a lower and an upper limit. The error bars indicate a 68% confidence level.

Thus, an inclusion of these deep samples yields an upper limit of ⁶⁰Fe for the integration to obtain a local interstellar fluence of ⁶⁰Fe. As the lower limit (smallest depth) we adopted that of sample 4. From the data we can estimate a range for ⁶⁰Fe/kg soil. Including corrections for the decay, and assuming a uniform spread over the lunar surface we end up with a fluence between 0.8 x 10⁸ atoms/cm² and 4 x 10⁸ atoms/cm² which was deposited during the past about 4 Myr. If we assume that this fluence came from a single SN and that the (typical) theoretical ⁶⁰Fe mass of 2x10^-5 solar masses has been ejected and formed dust to penetrate the solar system, then the SN would have happened 300 to 600 light years away.

In conclusion, our results show for the first time that the SN-formed ⁶⁰Fe has been also collected by the Moon, thus confirming the SN origin of previous measurements of ⁶⁰Fe on Earth. It delivers also more solid data for the fluence of ⁶⁰Fe which allow better theoretical estimation of other long-lived radioisotopes released by the SNe around 2 Myr ago. Theoretical considerations interpret our findings as SN activity in an association of young stars. They even seem to find good candidates like the Sco-Cen association [8] where the exploding stars could have been 2 Myr ago at a distance of around 300 light years or the Tuc-Hor association at about 150 light years [9].

In addition, further evidence for the SN activity has been added recently. An enhancement of ⁶⁰Fe has been found in ocean sediments at an Australian laboratory [10] and by our group [11]. This gives us a much better timing information than the crust and shows that the SN activity lasted for about 1 Myr and started about 2.7 Myr ago. Even in cosmic rays 15 nuclei of ⁶⁰Fe have been detected with the spectrometer CRIS aboard NASA’s satellite ACE (Advanced Composition Explorer) [12]. The authors conclude that at least two SNs must have occurred within 3000 light years from the sun during the last few Myr. Analysis of the spectra of high-energy cosmic rays leads to similar conclusions [13].

References:
[1] T. W. Berghöfer, D. Breitschwerdt, "The origin of the young stellar population in the solar neighborhood - A link to the formation of the Local Bubble?”, Astronomy & Astrophysics, 390, 299 (2002). Abstract.
[2] K. Knie, T. Faestermann, G. Korschinek, G. Rugel, W. Rühm, C. Wallner, "High-sensitivity AMS for heavy nuclides at the Munich Tandem accelerator”, Nuclear Instruments and Methods in Physics Research B, 172, 717 (2000). Abstract.
[3] G. Rugel, T. Faestermann, K. Knie, G. Korschinek, M. Poutivtsev, D. Schumann, N. Kivel, I. Günther-Leopold, R. Weinreich, M. Wohlmuther, “New Measurement of the ⁶⁰Fe Half-Life”, Physical Review Letters, 103, 072502 (2009). Abstract.
[4] K. Knie, G. Korschinek, T. Faestermann, E. A. Dorfi, G. Rugel, A. Wallner, "⁶⁰Fe Anomaly in a Deep-Sea Manganese Crust and Implications for a Nearby Supernova Source”, Physical Review Letters, 93, 171103 (2004). Abstract.
[5] C. Fitoussi, G. M. Raisbeck, K. Knie, G. Korschinek, T. Faestermann, S. Goriely, D. Lunney, M. Poutivtsev, G. Rugel, C. Waelbroeck, A. Wallner, “Search for Supernova-Produced ⁶⁰Fe in a Marine Sediment”, Physical Review Letters, 101, 121101 (2008). Abstract.
[6] L. Fimiani, D. L. Cook, T. Faestermann, J. M. Gómez-Guzmán, K. Hain, G. Herzog, K. Knie, G. Korschinek, P. Ludwig, J. Park, R. C. Reedy, G. Rugel, “Interstellar ⁶⁰Fe on the Surface of the Moon", Physical Review Letters, 116, 151104 (2016). Abstract.
[7] D.E.Gault, F. Hoerz, D.E. Brownlee, J.B. Hartung, "Mixing of the lunar regolith”, Proc. 5th Lunar Science Conference, Vol. 3, 2365 (1974). Abstract.
[8] D. Breitschwerdt, J. Feige, M. M. Schulreich, M. A. de. Avillez, C. Dettbarn, B. Fuchs,  “The locations of recent supernovae near the Sun from modelling ⁶⁰Fe transport”, Nature, 532, 73 (2016). Abstract.
[9] Brian J. Fry, Brian D. Fields, John R. Ellis, “Radioactive Iron Rain: Transporting ⁶⁰Fe in Supernova Dust to the Ocean Floor”,  Astrophysical Journal, 827, 48 (2016). Abstract.       
[10] A. Wallner, J. Feige, N. Kinoshita, M. Paul, L. K. Fifield, R. Golser, M. Honda, U. Linnemann, H. Matsuzaki, S. Merchel, G. Rugel, S. G. Tims, P. Steier, T. Yamagata, S. R. Winkler “Recent near-Earth supernovae probed by global deposition of interstellar radioactive ⁶⁰Fe”. Nature, 532, 69 (2016). Abstract.
[11] Peter Ludwig, Shawn Bishop, Ramon Egli, Valentyna Chernenko, Boyana Deneva, Thomas Faestermann, Nicolai Famulok, Leticia Fimiani, José Manuel Gómez-Guzmán, Karin Hain, Gunther Korschinek, Marianne Hanzlik, Silke Merchel, Georg Rugel, “Time-resolved 2-million-year-old supernova activity discovered in Earth’s microfossil record”, PNAS, 113, 9123 (2016). Abstract.
[12] W. R. Binns, M. H. Israel, E. R. Christian, A. C. Cummings, G. A. de Nolfo, K. A. Lave, R. A. Leske, R. A. Mewaldt, E. C. Stone, T. T. von Rosenvinge, M. E. Wiedenbeck, "Observation of the ⁶⁰Fe nucleosynthesis-clock isotope in galactic cosmic rays", Science, 352, 677 (2016). Abstract.
[13] M. Kachelrieß, A. Neronov, D. V. Semikoz “Signatures of a Two Million Year Old Supernova in the Spectra of Cosmic Ray Protons, Antiprotons, and Positrons”, Physical Review Letters, 115, 181103 (2016). 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.