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2Physics Quote:
"In analogy to their electronic counterparts, all-optical switches and transistors are required as basic building blocks for both classical and quantum optical information processing. Reaching the fundamental limit of such devices, where a single gate photon modifies the transmission or phase accumulation of multiple source photons, requires strong effective interaction between individual photons. Engineering sufficiently strong optical nonlinearities to facilitate photon-photon interaction is one of the key goals of modern optics."
-- Christoph Tresp, Ivan Mirgorodskiy, Hannes Gorniaczyk, Sebastian Hofferberth
(Read Full Article: "Single Photon Transistor Mediated by Rydberg Interaction" )

Sunday, October 26, 2014

Testing the Strong-Field Dynamics of General Relativity

Tjonnie G. F. Li

[Tjonnie G. F. Li is the recipient of the 2013 Stefano Braccini Thesis Prize administered by the Gravitational Wave International Committee (GWIC) for his PhD thesis “Extracting Physics from Gravitational Waves: Testing the Strong-field Dynamics of General Relativity and Inferring the Large-scale Structure of the Universe” (PDF). His thesis work was carried out at Nikhef - Dutch National Institute for Subatomic Physics, the Netherlands and the Ph.D was awarded by Vrije Universiteit, Amsterdam, the Netherlands.

The Stefano Braccini Thesis Prize was established to honor the memory of a talented gravitational wave physicist whose promising career was cut short. Stefano worked with the French-Italian Virgo project, and contributed to the superattentuator design, to the integration and commissioning of Virgo and to its data analysis efforts. -- 2Physics.com]

Author: Tjonnie G. F. Li

Affiliation: Rubicon Postdoctoral Fellow, LIGO Laboratory, California Institute of Technology, USA.

Motion of celestial objects

Humans have been watching the sky for thousands of years. In early times, humans tracked the motion of the Sun and the Moon to make calendars and to associate it with Earthly events such as tides and seasons. By tracking the motion of celestial objects, the early notion of the orbit of the Sun, the Moon and the planets started to form. Building on earlier work developed by Greek astronomers, Claudius Ptolemy (90–168) introduced an accurate model of the planetary orbits by including the notion of a smaller circular orbit (epicycle) augmenting the primary circular orbit.

During the Renaissance, our knowledge of the sky started to change. Johannes Kepler (1571–1630) introduced three laws that described the planetary orbits as ellipses with the Sun at the focus. Later, Isaac Newton (1642-1727) showed that Kepler’s laws of planetary motion can be derived from a law that not only describes the motion of planets, but also describes how all objects are attracted to each other. Newton’s law of universal gravitation states that all objects “pull” on each other through the gravitational force, and the strength of this force is determined by the masses of the two objects.

Despite the success of Newton’s law of universal gravitation, it could not account for the shift in Mercury’s perihelion, the point in Mercury’s orbit that is closest to the Sun. It was Albert Einstein (1879–1955) who refined Newton’s law of universal gravitation by introducing the general theory of relativity. Einstein’s general theory of relativity states that the curvature of spacetime dictates the way in which matter flows through it, and conversely, matter curves spacetime around it. Einstein’s theory explained the shift in Mercury’s perihelion, and so far seems to be the correct description of the motion of planets, stars and even galaxies.

Gravitational waves: a new window into the Universe

The general theory of relativity does more than just predicting the motion of objects. It also predicts a new type of radiation, known as gravitational radiation or gravitational waves. Gravitational waves are ripples in the curvature of spacetime, which propagate at the speed of light. The effect of gravitational waves is the periodic expansion and contraction of space and time (see Fig. 1).
Figure 1: Example of the distortion of spacetime due to a incident gravitational wave onto a ring of test particles. The top and bottom row represent the effects of the two polarisation states as a function of the phase of the gravitational wave.

The existence of gravitational waves has only been inferred indirectly through the motion of two stars orbiting each other. In particular, in 1974, Russell Hulse and Joseph Taylor found two pulsars (neutron stars that emit highly collimated beams of electromagnetic radiation) in a binary system that appeared to behave exactly as if the system was loosing energy and angular momentum in the form of gravitational waves (see Fig. 2). Today this discovery is regarded as the first indirect evidence of gravitational waves, and earned Hulse and Taylor the 1993 Nobel Prize in Physics [1].

Figure 2: Change in the time of the periastron of the binary pulsar “PSR B1913+16” as a function of time (red dots). These observation are compared to the prediction of general relativity (blue line). This data is considered as the first indirect evidence of gravitational waves.

Quest for strong gravity

So does this mean that general relativity has been fully verified? From a theoretical perspective, we might be inclined to say that general relativity cannot be the final answer, because of the current inability to describe it using a complete quantum theory. Therefore, it is currently not possible to unify gravity with the other forces of nature (electromagnetic, strong and weak force) into a grand unified theory, which some might argue is an indication that general relativity cannot be the final answer. In other words, a theory must exist that, in the low-energy regime, behaves like general relativity.

From an experimental perspective, one can argue that all of the tests of general relativity have so far been done in the regime of weak gravity. A figure of merit which describes the strength of gravity is the quantity ϵ ~ GM∕(Rc2), where G is the gravitational constant, M is the total mass of the system, R is the characteristic length scale of the system and c is the speed of light. Near a black hole the strength is ϵ ~ 10-1, whereas for solar system tests, and for binary pulsar tests, this strength is about ϵ ~ 10-6 [2]. Therefore, there is a whole new regime of gravity to explore experimentally.

Scientists all over the world are working hard on the quest for strong gravity. Amongst many interesting questions, they also hope to uncover empirical insight into the quantisation of gravity, which could refine or guide new theories of gravity. One of the ways in which we could hope to probe the regime of strong gravity is through the direct measurement of gravitational waves. Such measurements could probe gravity close to black holes and other exotic astrophysical objects.

Advanced LIGO and Virgo

Large-scale physics experiments such as the USA-based LIGO (see Fig. 3) [3] and the Italy-based Virgo [4] aim to, for the first time in the history of mankind, detect the influences of gravitational waves directly. These experiments are set up to measure tiny changes in distances of about one thousandth of the diameter of a proton. These tiny perturbations of spacetime could lead us down a new path in our quest for strong gravity.

Figure 3: Aerial view of the LIGO-Hanford detector

The motion of the source closely dictates the characteristics of the gravitational waves emitted. So by mapping out the distortions caused by the incident gravitational wave, one could infer a wealth of information about its origins. In other words, where astronomers needed telescopes to determine the motion of planets, stars and galaxies, measurements of gravitational waves can provide an additional way to map the dynamics of celestial objects.

In particular, a promising class of candidates for the first detection of gravitational wave is the compact binary coalescence [5]. Compact binary coalescence typically refers to (especially in the context of LIGO/Virgo) the mergers of binary black holes or neutron stars (see Fig. 4). The components of such systems spiral toward each other as energy and momentum are radiated away through the emission of gravitational waves. Finally, when the objects are sufficiently close to each other, they merge to form a single black hole which then continues to ring down as it reaches a quiescence state. The dynamics of coalescence of a compact binary can be seen through simulations as in Ref. [6].
Figure 4: Image from a binary black hole simulation.

Testing strong-field gravity with compact binary coalescences

Compact binary coalescences are attractive systems to probe strong gravity, because close to black holes and neutron stars the effects of gravity can be considered strong. Moreover, these systems are relatively easy to understand theoretically, because they mainly involve the application of general relativity. In contrast, mechanisms behind, for example, supernovae, which are also candidates to be measured by Advanced LIGO/Virgo, involve a complicated interplay amongst many branches of physics. The direct measurement of gravitational waves emitted from a compact binary coalescence will therefore give us access to the motion of black holes in orbit around each other’s strong gravitational pull.

However, in order to extract this information, we need specialised algorithms to dig deep into the data. One of such algorithms is called Test Infrastructure for GEneral Relativity (TIGER). This algorithm tries to answer the question “is the signal consistent with general relativity?” through the application of Bayesian hypothesis testing [7]. This framework ensures the optimal use of available information, and allows one to combine information across multiple detections of compact binary coalescences. Using this algorithm in a simulation environment, we have shown that the Advanced LIGO-Virgo network is indeed capable of probing gravity in uncharted territories, to an accuracy never seen before.

Of course, many challenges have to be faced. Detection of gravitational waves is a major challenge by itself on which hundreds of scientist are currently working. Moreover, once the Advanced LIGO-Virgo network is making confident detections, we need to analyse the motion of black holes or neutron stars in the presence of noise that can be orders of magnitude louder than the signal. Nevertheless, we are on the brink of the first direct detection with Advanced LIGO coming online as early as 2015. A hundred years after the introduction of general relativity, Advanced LIGO/Virgo could either put the crown on Einstein’s work, or showcase its limitations.

To be continued…

[1] “The Nobel Prize in Physics 1993”. Link in: Nobelprize.org.
[2] C. M. Will. “The Confrontation between General Relativity and Experiment”. In: Living Reviews in Relativity 17.4 (2014). Link.
[3] http://www.ligo.org .
[4] http://wwwcascina.virgo.infn.it .
[5] B.S. Sathyaprakash and Bernard F. Schutz. “Physics, Astrophysics and Cosmology with Gravitational Waves”. In: Living Reviews in Relativity 12.2 (2009). Link.
[6] Download from: http://numarch.aei.mpg.de/numrel-webpages/movies/bbh08_small.mov .
[7] T. G. F. Li, W. Del Pozzo, S. Vitale, C. Van Den Broeck, M. Agathos, J. Veitch, K. Grover, T. Sidery, R. Sturani, A. Vecchio, “Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence”. Physical Review D, 85, 082003 (2012). Abstract.

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Saturday, October 18, 2014

Optomechanical Coupling between a Multilayer Graphene Mechanical Resonator and a Superconducting Microwave Cavity

Left to Right: (top row) V. Singh, S. J. Bosman, B. H. Schneider, (bottom row) Y. M. Blanter, A. Castellanos-Gomez, G. A. Steele.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, 
G. A. Steele

Kavli Institute of NanoScience, Delft University of Technology, The Netherlands.


Mechanical resonators made from two dimensional exfoliated crystals offer very low mass, low stress, and high quality factor due to their crystalline structure [1]. These properties make them very attractive for application in mass sensing, force sensing, and exploring the quantum regime of motion by providing large quantum zero-point fluctuations over a small bandwidth. The most studied exfoliated crystal so far is graphene, where a considerable progress has been made in exploring its properties for mass sensing, study of nonlinear mechanics, and voltage tunable oscillators [2-9]. These properties also make graphene attractive for exploring the quantum regime of motion.

Past 2Physics articles by Andres Castellanos-Gomez and Gary A. Steele:

July 20, 2014: "Few-layer Black Phosphorus Phototransistors for Fast and Broadband Photodetection" by Michele Buscema, Dirk J. Groenendijk, Sofya I. Blanter, Gary A. Steele, Herre S.J. van der Zant, Andres Castellanos-Gomez.

A possible route towards exploring the quantum regime of graphene motion is cavity optomechanics [10]. It has shown exquisite position sensitivity, enabled the preparation and detection of mechanical systems in the quantum ground state with conventional top-down superconducting mechanical resonators [11-18]. Therefore, a natural candidate for implementing cavity optomechanics with graphene resonator is to couple it to a high Q superconducting microwave cavity. However, coupling graphene resonators with superconducting cavities in such a way that both retain their excellent properties (such as their high quality factors) is technologically challenging. Using a deterministic dry transfer technique [19], we combine a multilayer graphene resonator to a high quality factor microwave cavity [20]. Although multilayer graphene has a higher mass than a mono-layer, it could be advantageous for coupling to a superconducting cavity because of its lower electrical resistance.



To fabricate the superconducting cavities in coplanar waveguide geometry, we use an alloy of molybdenum and rhenium with superconducting transition temperature of 8.1 K. Using the dry transfer technique, we place a few layer thick graphene mechanical resonator near the coupler forming coupling capacitor for the cavity. Figure 1(a) shows a false color scanning electron microscope image of a device with a 10 nm thick multilayer graphene resonator coupled to a superconducting cavity. Figure 1(b) shows an equivalent schematic diagram with graphene resonator acting as a capacitor (C) between the superconducting cavity (formed by Lsc and Csc ) and the external microwave source. By cooling these cavities to very low temperatures (14 mK), we measured internal quality factor as high as 107,000.
FIG. 1: Coupling of a multilayer graphene mechanical resonator to a superconducting cavity. (a) A tilted angle scanning electron micrograph (false color) near the coupler showing 4 μm diameter multilayer (10 nm thick) graphene resonator (cyan) suspended 150 nm above the gate. (b) Schematic lumped element representation of the device with the equivalent lumped parameters as Csc ≈ 415 fF and Lsc ≈ 1.75 nH.

Mechanical motion readout sensitivity

To the first order, the superconducting microwave cavity can be thought simply as motional transducer for the graphene resonator. To readout the motion of the graphene resonator, we inject a microwave near the cavity frequency given by
The motion of graphene resonator modulates the cavity frequency and hence its displacement gets imprinted on the phase of the reflected microwave signal from the cavity. By measuring the phase of the reflected signal (technically known as the homodyne detection), one can directly read the mechanical motion of the resonator [11]. The large quality factor of our cavity and its ability to sustain superconductivity with large number of the microwave photons enable us to measure the thermo-mechanical motion of the graphene resonator down to temperatures of 96 mK and a displacement sensitivity as low as 17 fm/√Hz.

Optomechanical coupling

In addition to detecting the motion of the graphene drum, we can also exert a force on the mechanical drum by using the radiation pressure of microwave photons trapped in the superconducting cavity. This force comes from the fact that light carries momentum: shining light from a flashlight at a piece of paper would in principle apply a force to it, pushing it away from the light source. The radiation pressure force that light exerts, however, is usually far too small to detect. Due to the tiny mass of the graphene sheet and the ability to detect small displacement, we could see the graphene sheet shaking in response to a "beat" set by the microwave light sent into the cavity.

By sending two microwave signals, a probe signal ωp (near the cavity resonance frequency ω) and another signal at ωd (detuned by mechanical frequency ω, such that ωd = ω+ω), one can apply a a radiation pressure force on the mechanical resonator. This radiation pressure force beats at the mechanical resonance frequency, leading to coherent driven motion of the mechanical resonator, as shown schematically by process 1 in Figure 2(a). In presence of the significant optomechanical coupling, this coherent drive of the mechanical resonator down-converts the detuned drive photons exactly at the probe frequency (pink arrow) shown by process 2 in Figure 2(a). These two signals at probe frequency interfere with each other leading to a transmission window, appearing as a sharp peak in the cavity response, shown in Figure 2(b). This phenomena is known as "optomechanically induced transparency" (OMIT) and is a signature of the optomechanical coupling between the graphene mechanical resonator and the superconducting cavity [21-23]. As this effect rely on the coherent driven motion of the graphene mechanical resonator, the width of the transparency window is set by the mechanical resonator's linewidth as shown in the inset of Figure 2(b). Using the radiation pressure force driving, we measure the quality factor of the graphene resonator as high as 220,000.
FIG. 2: Optomechanically induced transparency (OMIT). (a) Schematic illustrate OMIT features in terms of the interference of the probe field (black arrow) with the microwave photons that are cyclically down- and then up- converted by the optomechanical interaction (pink arrow). (b) Measurement of the cavity reflection |S11| in presence of sideband detuned drive tone. A detuned drive at ωc+ωm results in a window of optomechanically induced reflection (OMIR) in the cavity response. Inset: Zoom of the OMIR window. (c) Measurement of the cavity reflection |S11| with a stronger detuned drive. At the center of the cavity response, the reflection coefficient exceeds 1, corresponding to mechanical microwave amplification of 17 dB by the graphene resonator.

By increasing the drive signal amplitude further, one can increase the strength of the optomechanical coupling. Using this, we make an amplifier in which microwave signals are amplified by the mechanical motion of the graphene resonator [16]. With a stronger detuned drive, we observed a microwave gain of 17 dB (equivalent to a photon gain of 50) as shown in Figure 2(c), before the nonlinear effects from the mechanical resonators come into play. Similarly, a different "beat" of the microwave photons (having ωd = ωc - ω) allows one to store microwave photons into the mechanical motion of the resonator [24]. To this end we show a storage time up to 10 millisecond, which is equivalent to delay from a few hundreds of kilometer long coaxial cable.

The phenomena of OMIT also allow one to directly extract a quantity called "cooperativity" C without any fi t parameters. The quantity C is an important fi gure of merit in characterizing the optomechanical systems. For example, in sideband resolved limit (when mechanical frequency exceeds the cavity linewidth), the criteria for quantum-coherent regime can be simply written as C + 1 > nth , where nth is the average number of thermal phonon in the mechanical resonator. In our experiment, we have been able to achieve C = 8 close to the expected number of thermal phonon in the mechanical resonator at 14 mK, bringing this system close to the quantum coherent regime.

Summary and outlook:

In our work, we demonstrated the potential of exfoliated graphene crystal applied to form an optomechanical device, which so far have been realized using top-down technology. This opens up a new dimension to explore exfoliated two-dimensional crystals in optomechanical systems, and harnessing their unique properties such as extremely low mass and high quality factors. For future devices, two-dimensional superconducting exfoliated flakes could be of great interest for such applications. Superconducting cavity in our work is a very good detector for mechanical displacement with a bandwidth three orders of magnitude larger than the mechanical line-width. This would provide a new tool to study nonlinear restoring forces, nonlinear damping, and mode coupling in mechanical resonators from twodimensional crystals. The characterization of our device shows that in future by making little larger area mechanical resonators, devices operating in quantum regime can be easily realized, which can possibly be used as a memory element in a quantum computer. As many of the 2D crystals can be grown by chemical processes in large areas, they also hold the promise of scalability.

[1] Andres Castellanos-Gomez, Vibhor Singh, Herre S.J. van der Zant, Gary A. Steele, "Mechanics of freely-suspended ultrathin layered materials". arXiv:1409.1173 [cond-mat] (2014).
[2] J. Scott Bunch, Arend M. van der Zande, Scott S. Verbridge, Ian W. Frank, David M. Tanenbaum, Jeevak M. Parpia, Harold G. Craighead, Paul L. McEuen, "Electromechanical resonators from graphene sheets". Science, 315, 490-493 (2007). Abstract.
[3] Changyao Chen, Sami Rosenblatt, Kirill I. Bolotin, William Kalb, Philip Kim, Ioannis Kymissis, Horst L. Stormer, Tony F. Heinz, James Hone, "Performance of monolayer graphene nanomechanical resonators with electrical readout". Nature Nanotechnology, 4, 861-867 (2009). Abstract.
[4] Vibhor Singh, Shamashis Sengupta, Hari S Solanki, Rohan Dhall, Adrien Allain, Sajal Dhara, Prita Pant, Mandar M Deshmukh, "Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators". Nanotechnology, 21, 165204 (2010). Abstract.
[5] Robert A. Barton, B. Ilic, Arend M. van der Zande, William S. Whitney, Paul L. McEuen, Jeevak M. Parpia, Harold G. Craighead, "High, size-dependent quality factor in an array of graphene mechanical resonators". Nano Letters, 11, 1232{1236 (2011). Abstract.
[6] A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, "Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene". Nature Nanotechnology, 6, 339-342 (2011). Abstract.
[7] Xuefeng Song, Mika Oksanen, Mika A. Sillanpää, H. G. Craighead, J. M. Parpia, Pertti J. Hakonen, "Stamp transferred suspended graphene mechanical resonators for radio frequency electrical readout". Nano Letters, 12, 198-202 (2012). Abstract.
[8] Robert A. Barton, Isaac R. Storch, Vivekananda P. Adiga, Reyu Sakakibara, Benjamin R. Cipriany, B. Ilic, Si Ping Wang, Peijie Ong, Paul L. McEuen, Jeevak M. Parpia, Harold G. Craighead, "Photothermal self-oscillation and laser cooling of graphene optomechanical systems". Nano Letters, 12, 4681-4686 (2012). Abstract.
[9] Changyao Chen, Sunwoo Lee, Vikram V. Deshpande, Gwan-Hyoung Lee, Michael Lekas, Kenneth Shepard, James Hone, "Graphene mechanical oscillators with tunable frequency". Nature Nanotechnology 8, 923{927 (2013). Abstract.
[10] Markus Aspelmeyer, Tobias J. Kippenberg, Florian Marquardt, "Cavity optomechanics". arXiv:1303.0733 [cond-mat.mes-hall] (2013).
[11] C. A. Regal, J. D. Teufel, K. W. Lehnert, "Measuring nanomechanical motion with a mi- crowave cavity interferometer". Nature Physics, 4, 555-560 (2008). Abstract.
[12] J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, K. W. Lehnert, "Nanomechanical motion measured with an imprecision below that at the standard quantum limit". Nature Nanotechnology 4, 820-823 (2009). Abstract.
[13] T. Rocheleau, T. Ndukum, C. Macklin, J. B. Hertzberg, A. A. Clerk, K. C. Schwab, "Preparation and detection of a mechanical resonator near the ground state of motion". Nature, 463, 72-75 (2010). Abstract.
[14] J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, R. W. Simmonds, "Circuit cavity electromechanics in the strong-coupling regime". Nature, 471, 204-208 (2011). Abstract.
[15] J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, R. W. Simmonds, "Sideband cooling of micromechanical motion to the quantum ground state". Nature, 475, 359-363 (2011). Abstract.
[16] F. Massel, T.T. Heikkilä, J.-M. Pirkkalainen, S.U. Cho, H. Saloniemi, P.J. Hakonen, M.A. Sillanpää, "Microwave ampli fication with nanomechanical resonators". Nature, 480, 351-354 (2011). Abstract.
[17] Fredrik Hocke, Xiaoqing Zhou, Albert Schliesser, Tobias J Kippenberg, Hans Huebl, Rudolf Gross, "Electromechanically induced absorption in a circuit nano-electromechanical system". New Journal of Physics, 14, 123037 (2012). Abstract.
[18] T. A. Palomaki, J. D. Teufel, R. W. Simmonds, K. W. Lehnert, "Entangling mechanical motion with microwave fields". Science, 342, 710-713 (2013). Abstract.
[19] Andres Castellanos-Gomez, Michele Buscema, Rianda Molenaar, Vibhor Singh, Laurens Janssen, Herre S J van der Zant, Gary A Steele, "Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping". 2D Materials, 1, 011002 (2014). Abstract.
[20] V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, G. A. Steele, "Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity". Nature Nanotechnology 9, 820–824 (2014). Abstract.
[21] G. S. Agarwal, Sumei Huang, "Electromagnetically induced transparency in mechanical eff ects of light". Physical Review A, 81, 041803 (2010). Abstract.
[22] Stefan Weis, Rémi Rivière, Samuel Deléglise, Emanuel Gavartin, Olivier Arcizet, Albert Schliesser, Tobias J. Kippenberg, "Optomechanically induced transparency". Science, 330, 1520-1523 (2010). Abstract.
[23] A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, O. Painter, "Electromagnetically induced transparency and slow light with optomechanics". Nature, 472, 69-73 (2011). Abstract.
[24] X. Zhou, F. Hocke, A. Schliesser, A. Marx, H. Huebl, R. Gross, T. J. Kippenberg, "Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics". Nature Physics, 9, 179-184 (2013). Abstract.

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Sunday, October 12, 2014

Atoms Under the Magnifying Glass: Direct Observation of the Nodal Structures of Electronic States

Aneta Stodolna (left) and Marc J.J. Vrakking

Authors: Aneta Stodolna1, Marc J.J. Vrakking2  

1FOM Institute AMOLF, Amsterdam, Netherlands,
2Max-Born-Institut, Berlin, Germany.

To describe the microscopic properties of matter and its interaction with the external world, quantum mechanics uses wave functions, whose structure and time dependence is governed by the Schrödinger equation. In atoms, electronic wave functions describe - among other things - charge distributions existing on length-scales that are many orders of magnitude removed from our daily experience. In physics laboratories, experimental observations of charge distributions are usually precluded by the fact that the process of taking a measurement changes a wave function and selects one of its many possible realizations. For this reason, physicists usually know the shape of charge distributions through calculations that are shown in textbooks. But in the last few years, this has started to change. Recent experiments have visualized the nodal structure of electronic states of hydrogen and helium on two-dimensional detectors.

The development of quantum mechanics in the early part of the last century had a profound influence on the way that scientists understand the world. Central to quantum mechanics is the concept of a wave function that satisfies the time-dependent Schrödinger equation. According to the Copenhagen interpretation, this wave function describes the probability of observing the outcome of measurements that are performed on a quantum mechanical system, such as measurements of the energy of the system or the position or momenta of its constituents. This allows reconciling the occurrence of non-classical phenomena on the micro-scale with manifestations and observations made on the macro-scale, which correspond to viewing one or more of countless realizations described by the wave function.

Despite the overwhelming impact on modern electronics and photonics, grasping quantum mechanics and the many possibilities that it describes continues to be intellectually challenging, and has motivated numerous experiments illustrating the intriguing predictions contained in the theory. For example, the 2012 Nobel Prize in Physics was awarded to Haroche and Wineland for their work on measurement and control of individual quantum systems in quantum non-demolition experiments, paving the way to more accurate optical clocks and, potentially, future quantum computers.

About thirty years ago, Russian theoreticians proposed an intriguing method for measuring properties of wave functions. They suggested studying atomic ionization in a static electric field that projects the electrons onto a two-dimensional detector and predicted interference patterns, with one of two possible origins. First of all, interference patterns result from path length differences between different trajectories that the electron can take between the atom and the detector. As clearly shown in the famous double-slit experiment on interference of single electrons (voted "the most beautiful physics experiment", in a poll conducted by Physicsworld about a decade ago) electrons exhibit both particle- and wave-like behavior.

The wave-like behavior derives from the de Broglie wavelength that quantum mechanics associates with any moving particle. The lower the kinetic energy of the electron, the larger the de Broglie wavelength is. Correspondingly, for low enough kinetic energies, the de Broglie wavelength becomes observable on macroscopic length scales. Secondly, in the case of hydrogen, the interference patterns can directly reflect the nodal structure of the electronic wave function. The fact that this is so, is due to the special status of hydrogen as nature´s only single-electron atom. Due to this circumstance, the hydrogen wave function can be written as the product of two functions that describe how the wave function changes as a function of two, so-called “parabolic coordinates”, which are linear combinations of the distance of the electron from the H+ nucleus “r”, and the displacement of the electron along the electric field axis “z”. Importantly, the shape of the two parabolic wave functions is independent of the strength of the static electric field, and therefore stays the same as the electron travels from the place where the ionization takes place to the two-dimensional detector.

Last year we published a paper, where we reported experiments for hydrogen atoms [1]. Ground state hydrogen atoms were optically excited to electronic states of interest, using two precisely tunable laser sources, and a delicate electrostatic lens was used to magnify the imprint of the electrons on the two-dimensional detector to millimeter-scale dimensions, so the nodal patterns of the wave functions could be observed with the naked eye. The main result is shown in Figure 1. This figure shows raw camera data for four measurements, where the hydrogen atoms were excited to states with 0, 1, 2 and 3 nodes in the wave function for the ξ = r+z parabolic coordinate. The nodes can be easily recognized. The experimental arrangement served as a microscope, allowing us to look deep inside the hydrogen atom, with a magnification of approximately a factor twenty-thousand.
Figure 1: (left) two-dimensional projection of electrons resulting from excitation of hydrogen atoms to four electronic states labeled with a set of quantum numbers (n1,n2,m) and having (from top to bottom) 0, 1, 2 and 3 nodes in the wave function for the ξ = r+z parabolic coordinate; (right) comparison of the experimentally measured radial distributions (solid lines) with results from quantum mechanical calculations (dashed lines), illustrating that the experiment has measured the nodal structure of the quantum mechanical wave function (copyright: American Physical Society).

More recently, we have performed similar experiments for the helium atom [2]. After the hydrogen atom, the helium atom is nature´s simplest atom, consisting of a doubly-charged nucleus surrounded by two electrons. The presence of two electrons in the atom introduces the concept of electron correlation. Remarkably, we saw that we could turn the electron correlation in helium on or off at will.

In the experiment, helium atoms were ionized by the absorption of an ultra-violet (UV) photon. Like in the hydrogen experiment, the photon energy of the UV light was tuned in such a manner that it was only just sufficient for ionization of the atom, thus producing very slow photoelectrons that were accelerated by an electric field towards a two-dimensional detector. At most of the UV photon energies, interference patterns were measured that could be explained by considering differences in the lengths of possible paths of the electron on the way to the detector (see Figure 2). Here, two paths differing by an integral number of de Broglie wavelengths interfere constructively, whereas two paths differing by a half-integer number of de Broglie wavelengths interfere destructively.
Figure 2: Sample images recorded for ionization of helium atoms. The four images contain interference patterns that result from path length differences along trajectories that the electron can take between the atom and the detector. The labels contained in the figures indicate the energy of the states used in the experiment defined with respect to the field-free ionization limit (copyright: American Physical Society).

However, at a number of UV photon energies the interference patterns looked markedly different, extending out to a much larger radius and containing a different number of nodes compared to measurements at slightly lower or higher photon energy (see Figure 3). A theoretical analysis revealed that at these energies the effect of electron correlation was momentarily suppressed. The suppression occurs when two electronic states, whose precise energies depend on the strength of the electric field, accidentally occur at almost identical energies. These two states then interact with each other, and for a particular value of the electric field, the energy exchange between the two parabolic coordinates is almost completely turned off. In other words, the atom becomes hydrogenic.
Figure 3: Sometimes helium behaves like a hydrogen atom, and interference patterns are measured that reveal the nodal structure of the electronic wave function that is excited (middle image). These cases stand out because the nodal pattern of these images is very different from those recorded at nearby excitation energies (left and right image), and the images extends farther radially. The labels contained in the figures indicate the energy of the states used in the experiment defined with respect to the field-free ionization limit (copyright: American Physical Society).

Correspondingly, the nodal pattern measured on the detector is once again the nodal pattern of the electronic state that is optically excited. The effect was found to be very subtle: tiny changes (<< 1%) in the strength of the electric field are sufficient to convert an atom that reveals the nodal pattern of its wave function in a hydrogen-like manner, into an atom where electron correlation removes the observability of this nodal pattern, and where the observed interference patterns are completely determined by path length differences between the atom and the detector.

In this manner, the hydrogen and helium atom constitute a wonderful nano-scale laboratory for studies of fundamental quantum mechanics, providing text-book images of nodal patterns in the case of hydrogen, and revealing the onset of electron correlation in the case of helium.

[1] Aneta Stodolna, Ymkje Huismans, Arnaud Rouzée, Frank Lépine, Marc J. J. Vrakking, "Photoelectron holography in strong optical and dc electric fields". Journal of Physics: Conference Series 488, 012007 (2014). Full Article.
[2] A. S. Stodolna, F. Lépine, T. Bergeman, F. Robicheaux, A. Gijsbertsen, J. H. Jungmann, C. Bordas, M. J. J. Vrakking, "Visualizing the Coupling between Red and Blue Stark States Using Photoionization Microscopy". Physical Review Letters, 113, 103002 (2014). Abstract.  

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Tuesday, October 07, 2014

Physics Nobel Prize 2014: Blue LED

(From Left to Right) Isamu Akasaki, Hiroshi Amano and Shuji Nakamura

The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2014 to Isamu Akasaki (Meijo University, Nagoya, Japan and Nagoya University, Japan), Hiroshi Amano (Nagoya University, Japan) and Shuji Nakamura (University of California, Santa Barbara, CA, USA) “for the invention of efficient blue light-emitting diodes which has enabled bright and energy-saving white light sources”.

This year’s Nobel Laureates are rewarded for having invented a new energy-efficient and environment-friendly light source – the blue light-emitting diode (LED). In the spirit of Alfred Nobel the Prize rewards an invention of greatest benefit to mankind; using blue LEDs, white light can be created in a new way. With the advent of LED lamps we now have more long-lasting and more efficient alternatives to older light sources.

When Isamu Akasaki, Hiroshi Amano and Shuji Nakamura produced bright blue light beams from their semi-conductors in the early 1990s, they triggered a fundamental transformation of lighting technology. Red and green diodes had been around for a long time but without blue light, white lamps could not be created. Despite considerable efforts, both in the scientific community and in industry, the blue LED had remained a challenge for three decades.

They succeeded where everyone else had failed. Akasaki worked together with Amano at the University of Nagoya, while Nakamura was employed at Nichia Chemicals, a small company in Tokushima. Their inventions were revolutionary. Incandescent light bulbs lit the 20th century; the 21st century will be lit by LED lamps.

White LED lamps emit a bright white light, are long-lasting and energy-efficient. They are constantly improved, getting more efficient with higher luminous flux (measured in lumen) per unit electrical input power (measured in watt). The most recent record is just over 300 lm/W, which can be compared to 16 for regular light bulbs and close to 70 for fluorescent lamps. As about one fourth of world electricity consumption is used for lighting purposes, the LEDs contribute to saving the Earth’s resources. Materials consumption is also diminished as LEDs last up to 100,000 hours, compared to 1,000 for incandescent bulbs and 10,000 hours for fluorescent lights.

Blue light has a shorter wavelength than other colors such as red and green, and therefore can be used to read and write smaller and smaller bits of information. Creating blue LEDs and lasers was a technologically difficult feat. While compact disc players were on the scene since 1982, Blu-Ray players and the Playstation 3, introduced in late 2006, were among the first consumer electronics devices to use these shorter-wavelength diode lasers. (Fun fact: Even though they're called Blu-Ray, the lasers in the players and Playstation are actually violet, an even shorter-wavelength color.)

The LED lamp holds great promise for increasing the quality of life for over 1.5 billion people around the world who lack access to electricity grids: due to low power requirements it can be powered by cheap local solar power.

The invention of the blue LED is just twenty years old, but it has already contributed to create white light in an entirely new manner to the benefit of us all.

Homepage of Isamu Akasaki >>
Homepage of Hiroshi Amano >>
Homepage of Shuji Nakamura >>

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Sunday, September 28, 2014

When Magnetism Meets Optics

S. Mangin (Left) and E. E. Fullerton


C.H. Lambert, M. Salah, N. Bergeard, G. Malinowski, M. Hehn, S. Mangin,
Equipe Nanomagnetisme et Electronique de Spin de l’Institut Jean Lamour UMR CNRS 7198, Université de Lorraine, France

Y. Fainman, E. E. Fullerton,
Center For Magnetic Recording Research, University of California San Diego (UCSD), USA 

M. Cinchetti, M. Aeschlimann, 
Department of Physics and Research Center OPTIMAS, University of Kaiserlautern- Allemagne, Germany 

B. Varaprasad, Y. Takahashi, K. Hono, 
National Institute for Materials Science, Japan

With the fast development of mass storage units all around the world (clouds, data centers…) the pressure to increase the density, speed and energy efficiency of conventional hard disk drives is becoming stronger and stronger. The discovery of “All-optical control of ferromagnetic thin films and nanostructures” might open up new technological horizons in magnetic recording. This work is the results of a collaboration between scientists and engineers from University of California San Diego, Universite de Lorraine, Kaiserlauter Universitat and National Institute for Materials Science in Tsukuba, Japan published in Science on September 14th 2014 [1].

 The authors found that they could control the final state of the magnetization of a broad range of magnetic materials using laser pulses of circularly polarized light instead of an applied magnetic fields. In particular these researchers find out that the magnetization of some magnetic material similar to those used in the recording industry can be manipulated directly with a laser beam. The ability to optically control magnetic materials the density and access time of data on hard drives could be increased dramatically.

Image: Writing with a laser on a magnetic thin film.

The first observation of “all optical switching” of magnetic materials was performed in 2007 by the group from T. Rasing in Nijmegen on a very particular ferrimagnetic alloy GdFeCo [2]. Since this discovery there has been extensive studies of optical switching of this material class including detailed studies of the magnetic response to optical excitations of both the rare-earth (Gd) and transition metal (Fe and Co) elements. Based on these studies a detailed understanding has emerged of the ultra-fast physics of rare-earth-transition-metal alloys [3,4]. However, the extent of the practical impact of this research is limited by the materials that are not compatible with many modern technologies. By extending these exciting studies to new classes of materials such as ferromagnets, the “all-optical” magnetization switching has made a significant step to demonstrate its potential for technological impact.

These results further show that theoretical understanding of all-optical switching needs to be re-examined. Most recent theories predicted that the all-optical reversal should only occur in ferrimagnetic materials, where the overall magnetization is the result of the competition between two magnetic sub-lattices that are antiferromagnetically coupled. Our results show that all-optical switching is not exclusive to ferrimagnetic materials and therefore antiferromagnetic exchange coupling between two magnetic sublattices is not required. The results do suggest that heating near the Curie point is important for the all-optical switching in ferromagnetic materials. Near the Curie point then a small symmetry-breaking from circularly polarized light (e.g. the inverse Faraday effect or transfer of angular momentum from the light to the magnetic system) can deterministically determine the magnetization direction. However details of this process still need to be determined.

Video: Writing with a laser on a magnetic thin film : Micrometer size "Etch A Sketch".

[1] C-H. Lambert, S. Mangin, B. S. D. Ch. S. Varaprasad, Y. K. Takahashi, M. Hehn, M. Cinchetti, G. Malinowski, K. Hono, Y. Fainman, M. Aeschlimann, E. E. Fullerton, "All-optical control of ferromagnetic thin films and nanostructures".  Science, 345, 1337-1340 (2014). Abstract.
[2] C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, Th. Rasing, "All-optical magnetic recording with circularly polarized light". Physical Review Letters, 99, 047601 (2007). Abstract.
[3] Andrei Kirilyuk, Alexey V Kimel, Theo Rasing, "Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys". Reports on Progress in Physics, 76, 026501 
(2013). Abstract.
[4] S. Mangin, M. Gottwald, C-H. Lambert, D. Steil, V. Uhlíř, L. Pang, M. Hehn, S. Alebrand, M. Cinchetti, G. Malinowski, Y. Fainman, M. Aeschlimann, E.E. Fullerton, "Engineered materials for all-optical helicity-dependent magnetic switching".  Nature Materials, 13, 286–292 (2014). Abstract.


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