.comment-link {margin-left:.6em;}


2Physics Quote:
"We consider that long-distance heat transport through transmission lines may be a useful tool for certain future applications in the quickly developing field of quantum technology. If the coupling of a quantum device to a low-temperature transmission line can be well controlled in situ, the device may be accurately initialized without disturbing its coherence properties when the coupling is turned off. The implementation of such in-situ-tunable environments opens an interesting avenue for the study of the detailed dynamics of open quantum systems and quantum fluctuation relations."
-- Matti Partanen and Mikko Möttönen (Read Full Article: "Efficient Long-Distance Heat Transport by Microwave Photons" )

Sunday, July 24, 2016

Relativistic Laser-Driven Table-top Intense Terahertz Transition Radiation Sources

From Left to Right: Guo-Qian Liao, Yu-Tong Li, Xiao-Hui Yuan

Authors: Guo-Qian Liao1, Yu-Tong Li1,4, Hao Liu1, Yi-Hang Zhang1, Xiao-Hui Yuan2,4, Xu-Lei Ge2, Su Yang2, Wen-Qing Wei2, Wei-Min Wang1,4, Zheng-Ming Sheng2,3,4, Jie Zhang2,4

1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
2Key Laboratory for Laser Plasmas (MoE) and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
3SUPA, Department of Physics, University of Strathclyde, Glasgow, United Kingdom,
4Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai, China.

Intense terahertz (THz) radiation sources, the frequency of which lies between far-infrared waves and microwaves in the electromagnetic spectrum, are significantly important for THz sciences and applications in many interdisciplinary fields [1]. Currently THz radiation with energies of >100 μJ/pulse is usually obtained with huge-sized accelerators [2]. Laser-plasma interactions provide a unique opportunity to achieve tabletop high-field THz radiation sources. With the relativistic electron beams accelerated by laser wakefields in gas targets, Leemans et al. have obtained ∼0.3 μJ THz pulses through transition radiation [3].

Strong THz radiation from laser-solid interactions has attracted much interest [4,5]. Compared with gas targets, fast electron beams from solid foil targets have much higher charge, up to nC or even near μC. Usually the bunch length of the electron beam accelerated by a femtosecond laser pulse is of the order of ~10 μm, which is smaller than the wavelength of THz radiation. Therefore, the forward fast electrons will induce coherent transition radiation (CTR) in the THz regime when crossing the rear surface-vacuum boundary (see Figure 1). This has so far not yet been verified experimentally.
Figure 1: Illustration of the THz generation due to the CTR of fast electron beams at the rear surface of a foil target irradiated by intense laser pulses.

In our recent work [6], we have experimentally demonstrated intense coherent THz transition radiation by laser-driven, relativistic electron beams crossing the rear surface of a thin solid foil. The experiment was carried out on the femtosecond laser system at the Laboratory for Laser Plasma, Shanghai Jiao Tong University. From the rear side of a 5 μm thick metal foil irradiated by a 2 J/ 30 fs laser pulse, we obtain an intense THz pulse with an energy of ~400 μJ, which is comparable to the energy level of the conventional accelerator based THz sources [2]. The measured THz radiation covers a bandwidth up to 30 THz [see Figure 2(a)], and has an asymmetric “double-wing-like” angular distribution [see Figure 2(b)]. Both CTR-based theoretical calculations and two-dimensional particle-in-cell simulations can well reproduce the experimental measurements.
Figure 2: [click on the image to view with higher resolution(a) Experimentally measured (blue circle dashed) and simulated (black solid) frequency spectra of the THz radiation from the metal foil. (b) Angular distributions of the THz radiation measured (blue circle), simulated (black dashed), and calculated with CTR model (red solid), all of which are normalized by the THz intensity at 75°.

The CTR model predicts that the THz radiation intensity is closely dependent on the target parameters, for example, the size and dielectric property of the target. To verify this, several types of targets are adopted to understand the THz generation. For the mass-limited metal targets, the observed dependence of THz intensity on the target sizes [see Figure 3(a)] can be explained by the CTR model modified by diffraction effect [7]. For the metal-PE double layered targets, we find that there exists an optimal PE thickness when increasing the thickness of the PE layer from 15 μm to 500 μm [see Figure 3(b)]. This can be explained by the CTR model considering the formation-zone effects [8]. Compared with the THz radiation from the PE targets, we find the THz intensity from the targets with a 5 μm thick metal coating at the target rear is dramatically enhanced by over 10 times [see Figure 3(c)]. This is a solid evidence for transition radiation.
Figure 3: [click on the image to view with higher resolution] (a) Experimentally measured THz intensity (blue circles) and theoretically calculated diffraction modification factor D (curves) as a function of target sizes. (b) Measured THz intensity at 75° (black square) and -75° (blue circle) from the metal-PE targets as a function of the thickness of the PE layer. (c) Comparison of the THz signals measured from the 40 μm thick PE targets with or without a 5 μm metal coating at the rear.

The laser-plasma-based THz transition radiation presented here could be a promising tabletop high-energy THz source. Moreover, it may provide a potential diagnostic to infer the spatiotemporal distribution of the high-flux fast electron beams generated in laser-solid interactions.

[1] M. Tonouchi, “Cutting-edge terahertz technology”, Nature Photonics, 1, 97 (2007). Abstract.
[2] Ziran Wu, Alan S. Fisher, John Goodfellow, Matthias Fuchs, Dan Daranciang, Mark Hogan, Henrik Loos, Aaron Lindenberg, “Intense terahertz pulses from SLAC electron beams using coherent transition radiation”, Review of Scientific Instruments, 84, 022701 (2013). Abstract.
[3] W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, M. C. Martin, “Observation of terahertz emission from a laser-plasma accelerated electron bunch crossing a plasma-vacuum boundary”, Physical Review Letters, 91, 074802 (2003). Abstract.
[4] G. Q. Liao, Y. T. Li, C. Li, L. N. Su, Y. Zheng, M. Liu, W. M. Wang, Z. D. Hu, W. C. Yan, J. Dunn, J. Nilsen, J. Hunter, Y. Liu, X. Wang, L. M. Chen, J. L. Ma, X. Lu, Z. Jin, R. Kodama, Z. M. Sheng, J. Zhang, “Bursts of terahertz radiation from large-scale plasmas irradiated by relativistic picosecond laser pulses”, Physical Review Letters, 114, 255001 (2015). Abstract.
[5] A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H-G. Meyer, G. G. Paulus, “Observation of Gigawatt-class THz pulses from a compact laser-driven particle accelerator”, Physical Review Letters, 111, 074802 (2013). Abstract.
[6] Guo-Qian Liao, Yu-Tong Li, Yi-Hang Zhang, Hao Liu, Xu-Lei Ge, Su Yang, Wen-Qing Wei, Xiao-Hui Yuan, Yan-Qing Deng, Bao-Jun Zhu, Zhe Zhang, Wei-Min Wang, Zheng-Ming Sheng, Li-Ming Chen, Xin Lu, Jing-Long Ma, Xuan Wang, Jie Zhang, “Demonstration of coherent terahertz transition radiation from relativistic laser-solid interactions”, Physical Review Letters, 116, 205003 (2016). Abstract.
[7] C. B. Schroeder, E. Esarey, J. van Tilborg, W. P. Leemans, “Theory of coherent transition radiation generated at a plasma-vacuum interface”, Physical Review E, 69, 016501 (2004). Abstract.
[8] Luke C. L. Yuan, C. L. Wang, H. Uto, “Formation-zone effect in transition radiation due to ultrarelativistic particles”, Physical Review Letters, 25, 1513 (1970). Abstract.

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Sunday, July 17, 2016

Demonstrating Quantum Advantage with the Simplest Quantum System -- Qubit

From left to right: Xiao Yuan, Ke Liu, Xiongfeng Ma, Luyan Sun.

Authors: Xiao Yuan, Ke Liu, Luyan Sun, Xiongfeng Ma

Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China.

Along the search for quantum algorithms, the sophisticated quantum speed-up generally arises with delicately designed quantum circuits by manipulating quantum states that contain intricate multipartite correlations. While the essence of quantum correlation originates from coherent superposition of different states, it is natural to expect the essence of quantum advantage to also originate from coherence. This raises a fundamental question: Can quantum advantage be obtained even with the simplest quantum state system, qubit, i.e., superposition of a two level system. The question was answered affirmatively in our recent work published in Physical Review Letters on June 29th [1].

In our everyday life, a classical coin is called p-coin if it outputs a head and a tail with probability p and 1-p respectively. Given an unknown p-coin, a simple yet interesting problem is to construct an f (o)-coin, where f (p) is a given function of p and f(p)∈[0,1]. For example, when f (p)=1/2, a rather simple but heuristic strategy is given by Von Neumann [2]. Flip the p-coin (p ≠ 0) twice. If the outcomes are the same, start over; otherwise, output the second coin value as the 1/2-coin output. In general, such construction processing is called a Bernoulli factory. Solved by Keane and O’Brien [3], it says that not all functions can be constructed classically. Generally speaking, a necessary condition for f(p) being constructible is that f(p) ≠ 0 or 1 when p ∈ (0,1). A simple example is f (p) = 4p (1-p), where we have f (1/2)=1.
Figure 1: Classical and quantum coin.

As shown in Fig.1, a p-coin corresponds to a machine that outputs identically mixed qubit states, ρ= p|0⟩⟨0| + (1-p)|1⟩⟨1|, where p∈[0,1]. In general, such unknown p can also be encoded in a quantum way, |p⟩ = √p |0⟩ + √(1-p) |1⟩, which is called by a quoin. As classical coins can always be constructed via a quoin, a natural question is whether the set of quantum constructible functions (via a quantum Bernoulli factory) is strictly larger than the classical set.

Remarkably, Dale et al. [4] have theoretically proved the necessary and sufficient conditions for quantum Bernoulli factory. Especially for the function f(p) = 4 p (1-p), they proposed a method to construct it by simultaneously measuring two p-quoins. Essentially, entanglement is not necessary for constructing quantum Bernoulli factory. Therefore, we focus on the function f(p) = 4p (1-p) and show the quantum advantage in both theory and experiment with the simplest quantum system.

In practice, we cannot realize exact f(p)-coin due to imperfections, which may cause the realized function classically constructible. However, the number of classical coins N required to construct f(p) generally scales poorly to the inverse of the deviation. Thus, we need to implement high-fidelity state preparation and measurement to reduce the deviation as small as possible in order to faithfully demonstrate the quantum advantage. Superconducting quantum systems have made tremendous progress in the last decade, including a realization of long coherence times, showing great stability with fast and precise qubit manipulations, and demonstrating high-fidelity quantum non-demolition (QND) qubit measurement. Thus, it serves as a perfect candidate for our test.
Figure 2: Experimental setup. (a) Optical image of a transmon qubit located in a trench, which dispersively couples to two 3D Al cavities. (b) Optical image of the single-junction transmon qubit. (c) Scanning electron microscope image of the Josephson junction. (d) Schematic of the device with the main parameters.

The experiment setup is shown in Fig. 2. The necessary high fidelity (~99.6%) and QND qubit detection can be realized with the help of a near-quantum-limited Josephson parametric amplifier [4,5]. A randomized benchmark calibration shows that the single-qubit gate fidelity is about 99.8%, allowing for a highly precise qubit manipulation. Therefore, with the high fidelity state preparation, manipulation and measurement, we are able to achieve fexp (1/2)=0.965. For a special model of the experiment data, we show that more than 105 classical coins are needed for simulating this model, while the average number of quoins for our protocol is about 20.

Our experimental verification sheds light on a fundamental question about what the essential resource for quantum information processing is, which may stimulate the search for more protocols that show quantum advantages without multipartite correlations. Considering the conversion from coherence to multipartite correlation, investigating the power of coherence may also be helpful in understanding the power of multipartite correlation and universal quantum computation.

[1] Xiao Yuan, Ke Liu, Yuan Xu, Weiting Wang, Yuwei Ma, Fang Zhang, Zhaopeng Yan, R. Vijay, Luyan Sun, Xiongfeng Ma, "Experimental Quantum Randomness Processing Using Superconducting Qubits", Physical Review Letters, 117, 010502 (2016). Abstract.
[2] J. Von Neumann, "Various Techniques used in connection with random digits", Journal of Research of the National Bureau of Standards -- Applied Mathematics Series, 12, 36 (1951). PDF File.
[3] M. S. Keane, George L. O’Brien, "A Bernoulli factory", ACM Transactions on Modeling and Computer Simulation, 4, 213 (1994). Abstract.
[4] Howard Dale, David Jennings, Terry Rudolph, Nature Communications, 6, 8203 (2015). Abstract.
[5] M. Hatridge, R. Vijay, D.H. Slichter, John Clarke, I. Siddiqi, "Dispersive magnetometry with a quantum limited SQUID parametric amplifier", Physical Review B, 83, 134501 (2011). Abstract.


Sunday, July 10, 2016

Nonlinear Medium for Efficient Steady-State Directional White-Light Generation

From Left to Right: (top row) Nils W. Rosemann, Jens P. Eußner, Andreas Beyer, Stephan W. Koch; (bottom row) Kerstin Volz, Stefanie Dehnen, Sangam Chatterjee 
(credit for Sangam's picture: Tim van de Bovenkamp)

Authors: Nils W. Rosemann1,2, Jens P. Eußner2,3, Andreas Beyer1,2, Stephan W. Koch1,2, Kerstin Volz1,2, Stefanie Dehnen2,3, Sangam Chatterjee1,2,4

1Fachbereich Physik, Philipps-Universität Marburg, Marburg, Germany.
2Wissenschaftliches Zentrum für Materialwissenschaften, Philipps-Universität Marburg, Marburg, Germany.
3Fachbereich Chemie, Philipps-Universität Marburg, Marburg, Germany.
4Institute of Experimental Physics I, Justus-Liebig-University, Giessen, Germany.

Tailored light sources have greatly advanced over the past decades. In particular, the development of light-emitting diodes[1] (LED) was the last milestone in the field of illumination. This includes the virtually omnipresent white LEDs where ultraviolet emitting gallium nitride (GaN) LEDs [2] excite light converting phosphors to cover the visible spectrum. They are reasonably priced and are starting to replace incandescent or compact fluorescent sources for lighting and display applications [3,4].

For many scientific uses, the development of the laser was a comparable milestone [5]. Lasers are light sources with well-defined and well-manageable properties, making them an ideal tool for scientific research. Nevertheless, at some points the inherent (quasi-)monochromaticity of lasers is a drawback. Using a convenient converting phosphor can produce a broad spectrum but also results in a loss of the desired laser properties, in particular the high degree of directionality. To generate true white light while retaining this directionality, one can resort to nonlinear effects like soliton formation [6]. Unfortunately, nonlinear effects usually require large field-strength, thus large-scale, expensive pulsed or high-power lasers. On the route towards a more favorable solution, we recently presented an amorphous cluster compound that converts the infrared (IR) light of a reasonably priced laser diode into a broad visible spectrum while retaining the desired laser properties [7].

The compound contains clusters with a tin-sulfur based core and four organic ligands per formula unit. The core is composed of an adamantane-like scaffold, [Sn4S6]. It has a tetrahedral shape and is thus lacking inversion symmetry. This is accompanied by a random orientation of the four ligands R = 4-(CH2=CH)-C6H4 (Fig. 1a). The ligands consolidate the structure of the core [8,9] and prevent crystallization of the compound, hence prevent any long-range order. As a result, the compound is obtained as an amorphous white powder (Fig. 1b).
Figure 1: (a) Molecular structure of the adamantane-like cluster molecule, with tin and sulfur atoms drawn as blue and yellow spheres, respectively; carbon (grey) and hydrogen (white) atoms are given as wires. (b) Photograph of the as prepared powder.

Upon irradiation with infrared laser light, the compound emits a warm white-light (Fig. 2a). Its spectrum is virtually independent of the excitation wavelength in the range from 725 to 1050 nm. Variation of the laser intensity, however, results in a slight shift of the spectral weight towards higher energies for higher intensities (Fig. 2b). This common impression of a dimming tungsten-halogen light bulb could lead to the assumption that the novel light-emission is also thermal. However, the input-output characteristic of the white-light process scales highly nonlinear. Additionally, the emitted intensity depending on the color temperature of the observed spectra differs vastly from the Stefan-Boltzmann law. These two points exclude a thermal process to be the source of the observed white light. Furthermore, spontaneous emission can be ruled out: exciting the compound above the absorption edge, i.e., with photon energies above 3.0 eV, changes the emitted spectrum drastically.
Figure 2: (a) Photograph of the cluster compound embedded in a polymer and sandwiched between two glass slips. The compound is excited in the bright center spot, using 800nm laser. (b) White-light spectra for different pump intensities, from low (grey) to high intensity (black). For reference, the emission of a black-body emitter at 2856K is shown.

The largest advantage application-wise is found in its directionality, i.e., the angular emission characteristics. When the sample is excited in a transmission like geometry, the spatial distribution of the white-light is found to be very close to that of the driving laser. In combination with the very low threshold of the nonlinear process, this enables the use of this light source for many applications where a broad spectrum and low-etendue are required, e.g., in microscopes or optical coherence tomography systems.

To explain the white-light emitting process, we developed a semi-classical model. This model ascribes the white-light emission to the driven movement of an electron in the clusters ground state potential. During this process, the electron gets accelerated by the IR-laser and subsequent deceleration of the electron leads to the emission of radiation just like Bremsstrahlung. Implementing this process numerically leads to an excellent agreement of theory and experiment. While such anharmonic oscillator models are commonly applied for nonlinear optical phenomena, here, the shape of the simulated ground state potential is completely based on experimentally verified parameters and results from first-principle calculations. This model does not yield the observed directionality that only could be ascribed to a phased-array effect caused by the driving continuous wave-laser.

Finally, we find that the compound can be used to coat semiconductor substrates like gallium arsenide or silicon. This enables the possibility of functionalization of well established III/V semiconductor laser diodes.

[1] H. J. Round, “A note on carborundum”,  Electrical World, 49.6, 309 (1907). Abstract.
[2] Shuji Nakamura, Takashi Mukai, Masayuki Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes”, Applied Physics Letters, 64, 1687 (1994). Abstract.
[3] Fred Schubert, Jong Kyu Kim, “Light-emitting diodes hit the centenary milestone”, Compound Semiconductor, pages 20-22 (October, 2007). Article.
[4] Siddha Pimputkar, James S. Speck, Steven P. DenBaars, Shuji Nakamura, “Prospects for LED lighting”, Nature Photonics, 3, 180–182 (2009). Abstract.
[5] T. H. Maiman, “Stimulated optical radiation in ruby”, Nature, 187, 493–494 (1960). Abstract.
[6] Robert R. Alfano, "The Supercontinuum Laser Source" (Springer, 2013).
[7] Nils W. Rosemann, Jens P. Eußner, Andreas Beyer, Stephan W. Koch, Kerstin Volz, Stefanie Dehnen, Sangam Chatterjee, “A highly efficient directional molecular white-light emitter driven by a continuous-wave laser diode”, Science, 352, 1301–1304, (2016). Abstract.
[8] Hermann Berwe, Alois Haas, “Thiastannacyclohexane (R2SnS)3 und -adamantane (RSn)4S6 Synthesen, Eigenschaften und Strukturen”, Chemische Berichte, 120, 1175–1182 (1987). Abstract.
[9] Jens P. Eußnera, Stefanie Dehnen, “Bronze, silver and gold: functionalized group 11 organotin sulfide clusters”, Chemical Communications, 50, 11385–8 (2014). Abstract.

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Sunday, June 26, 2016

Direct Detection of the 229Th Nuclear Clock Transition

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

Authors: Lars von der Wense1, Benedict Seiferle1, Mustapha Laatiaoui2,3, Jürgen B. Neumayr1, Hans-Jörg Maier1, Hans-Friedrich Wirth1, Christoph Mokry3,4, Jörg Runke2,4, Klaus Eberhardt3,4, Christoph E. Düllmann2,3,4, Norbert G. Trautmann4, Peter G. Thirolf1

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

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

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

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

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

The existence of this isomeric state was shown in 1976, based on indirect measurements [10]. However, despite significant efforts, the direct detection of the isomeric decay could not be achieved within the past 40 years [11]. In the recently presented work [12], our group was able to solve this long-standing problem, leading to the first direct detection of the 229Th nuclear clock transition. This direct detection is important, as it paves the way for the determination of all decay parameters relevant for optical excitation of the isomeric state. It is thus a breakthrough step towards the development of a nuclear clock.
Figure 1: (click on the image to view with higher resolution) Experimental setup used for the production of a purified 229Th ion beam and the direct detection of the isomeric state. For details we refer the reader to the text and to Ref. [12].

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

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

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

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

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

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Sunday, June 12, 2016

Demonstration of Light Induced Conical Intersections in Diatomic Molecules

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

Authors: Adi Natan1, Matthew R Ware1,4, Vaibhav S. Prabhudesai2, Uri Lev3, Barry D. Bruner3, Oded Heber3, Philip H Bucksbaum1,4

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

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

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

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

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

The simplest place to start is H2+ in its ground rotational state, interacting with a strong laser field that couples resonantly the two electronic states. The spherical symmetry of the ground state field-free nuclear probability density, changes rapidly when a strong field is turned on. We can follow how this probability density evolves in the dressed state framework. In the dressed picture, the LICI is a local maximum in the two-dimensional (R,θ) potential energy landscape, while in other angles, the population dissociates adiabatically on the unbound part of the light induced potential curve. This causes the part of the population to accumulate around the LICI and then scatter from it, similar to waves scattering from a cone shape potential barrier. However, unlike scattering of a free particle around a barrier, the scattering described here is of bound nuclear wave packet, which scatters into a multitude of rovibrational states on the ground electronic surface, similar to the non-adiabatic dynamics around a natural CI. The scattering from the LICI leads to dissociation, but imposes a scattering time delay. The coherent addition of all the scattering trajectories creates an interference pattern at various angles and kinetic energy releases (Fig 1 (b), and Fig 1(c)). These quantum interferences are a universal signature for LICIs because they arise from the nature of coherent scattering interference near a point of degeneracy.
Figure 1: [Click on the image to view with higher resolution] (a) The dressed potential energy surfaces of H2+ featuring LICIs. (b) The calculated instantaneous probability of dissociation P(θ,t)diss from a given vibrational state (for example, v=9) during the interaction with the laser pulse reveals the interference. (c) Experimental (top) and calculated (bottom) angular distributions of H2+ dissociation at kinetic energy releases that correspond to specific initial vibrations states.

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

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

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

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Sunday, May 22, 2016

Two dimensional Superconducting Quantum Interference Filter (SQIF) arrays using 20,000 YBCO Josephson Junctions

From Left to Right: (top row) Emma Mitchell, Jeina Lazar, Keith Leslie, Chris Lewis,
(bottom row) Alex Grancea, Shane Keenan, Simon Lam, Cathy Foley.

Emma Mitchell1, Kirsty Hannam1, Jeina Lazar1, Keith Leslie1, Chris Lewis1
Alex Grancea2, Shane Keenan1, Simon Lam1, Cathy Foley1

1CSIRO Manufacturing, Lindfield, NSW, Australia,
2CSIRO Data61, Epping, NSW, Australia.

Josephson junctions form the essential magnetic sensing element at the heart of most superconducting electronics. A Josephson junction consists of two superconducting electrodes separated by a thin barrier [1]. Provided the barrier width is less than the superconducting coherence length, Cooper pairs can tunnel quantum mechanically from one electrode to the other coherently when the temperature is below the critical temperature of the two electrodes. Due to the macroscopic quantum coherence of the Cooper pairs in the superconducting state, Josephson junctions not only detect magnetic fields and RF radiation over an extremely wide frequency band, but can also emit radiation. The highly sensitive response of the Josephson junction current to magnetic fields is the key to many of its applications, including magnetometers, absolute magnetic field detectors and low noise amplifiers. More recent applications also include small RF antennas which utilize the Josephson junction’s broadband (dc- THz) detection abilities.

The dc SQUID, or Superconducting Quantum Interference Device, consists of two Josephson junctions connected together in parallel via a superconducting loop. The SQUID is an extremely sensitive flux-to voltage transducer, but despite this simplicity, an exact solution of this problem can only be given in the case of negligible inductance of the loop containing the two junctions. When the SQUID is biased with a current and an external magnetic field is applied, the voltage response oscillates periodically with applied magnetic field (Figure 1a). The period of the oscillation is inversely proportional to the loop area. SQUIDs have been connected together into arrays of increasing size and complexity to improve device sensitivity.

Figure 1: Voltage responses for a (a) dc SQUID with two step-edge junctions (b) two dimensional SQIF with 20,000 step-edge junctions.

Feynman et al. (1966) first predicted [2] an enhancement in the SQUID interference effect by having multiple (identical) junctions in parallel, analogous to a multi-slit diffraction grating. This enhancement was originally observed using superconducting point contact junctions [3] and has been further developed using series arrays of low temperature superconducting (LTS) Nb SQUIDs. More recently 1D arrays of SQUIDs with incommensurate loop areas (non-identical and variable spread) with a non-periodic voltage response were suggested [4]. The voltage response of these superconducting quantum interference filters (SQIFs) is then analogous to a non-conventional optical grating where different periodic responses from individual SQUIDs with different loop areas are summed. This results in a voltage response to a magnetic field in which a dominant anti-peak develops at zero applied field due to constructive interference of the individual SQUID responses. Weaker non-periodic oscillations occur at non-zero fields where the individual SQUID responses destructively interfere. The magnitude and width of the anti-peak for a SQIF is governed by the range and distribution of SQUID loop areas and inductances.

In our recent work [5] we demonstrate high temperature superconducting (HTS) two dimensional SQIF arrays based on 20,000 YBCO step-edge Josephson junctions connected together in series and parallel (Figure 1b). The maximum SQIF response we measured had a peak-to-peak voltage of ~ 1mV and a sensitivity of (1530 V/T) using a SQIF design with twenty sub-arrays connected in series with each sub-array consisting of 50 junctions in parallel connected to 20 such rows in series. The variation in loop areas within each subarray had a pseudo- random distribution with a mean loop area designed to have an inductance factor βL = 2LIc0 ~1 [6]. Figure 2a shows part of our array with four whole sub-arrays visible. At higher magnification the variation of individual loop areas is evident (Figure 2b) with the rows of step-edge junctions indicated by arrows.
Figure 2: (a) Part of the 20,000 YBCO step-edge junction SQIF array showing four complete sub-arrays of 1,000 junctions each (b) one sub-array at higher magnification showing rows of junctions (arrows) and variable loop areas (darker material is the YBCO).

The Josephson junctions in our samples are step-edge junctions formed when a grain boundary develops between the YBCO electrodes that grow epitaxially when a thin film is deposited over a small step approximately 400nm high with an angle of ~38o, etched into the supporting MgO substrate [7, 8]. It is well documented that HTS Josephson junctions are difficult to fabricate in large numbers across a substrate. However, step-edge junctions have the advantage of being relatively simple and inexpensive to fabricate and can be placed, at high surface density almost anywhere on a substrate. To date, we have made 2D arrays showing a SQIF response with 20,000 up to 67,000 step-edge junctions on a 1cm2 substrate.

Two dimensional SQIF arrays allow for large numbers of junctions to be placed in high density across a chip, enabling increases in the output voltage and sensitivity of the device. 2D arrays also allow for impedance matching of the array to external electronics by varying the ratio of junctions in parallel to those in series, by virtue of the junction normal resistance, Rn.

In addition, we demonstrated that the sensitivity of the SQIF depends strongly on the mean junction critical current, Ic, in the array, and the inductance (area) of the average loop in the array. In both cases keeping these parameters small such that βL < 1 is necessary for improving the SQIF sensitivity, but can be difficult to achieve with HTS junctions in which the typical spread in Ic can be 30%. The SQIF response also depends on the number of junctions; a linear increase in the SQIF sensitivity with junction number was measured for our SQIF designs.

We were also able to demonstrate RF detection at 30 MHz using our HTS SQIFs at 77 K [5]. More recently a broadband SQIF response from DC to 140 MHz was demonstrated following improvements to our SQIF sensitivity (unpublished). This follows on from reports of near field RF detection to 180 MHz using 1000 low temperature superconducting (LTS) junctions [9], where more complex and expensive cryogenic requirements limit the LTS array applications outside the laboratory.

[1] B.D. Josephson,  "Possible new effects in superconductive tunneling". Physics Letters, 1, 251 (1962). Abstract.
[2] Richard P. Feynman, Robert B. Leighton, Matthew Sands, “The Feynman lectures on Physics, Vol III” (Addison-Wesley, 1966).
[3] J.E. Zimmerman, A.H. Silver, "Macroscopic quantum interference effects through superconducting point contacts", Physical Review, 141, 367 (1966). Abstract.
[4] J. Oppenländer, Ch. Häussler, N. Schopohl, "Non-Φo periodic macroscopic quantum interference in one-dimensional parallel Josephson junction arrays with unconventional grating structures", Physical Review B, 63, 024511 (2000). Abstract.
[5] E.E. Mitchell, K.E. Hannam, J. Lazar, K.E. Leslie, C.J. Lewis, A. Grancea, S.T. Keenan, S.K.H. Lam, C.P. Foley, “2D SQIF arrays using 20,000 YBCO high RN Josephson junctions”, Superconductor Science and Technology, 29, 06LT01 (2016). Abstract.
[6] “The SQUID Handbook, Vol. I Fundamentals and technology of SQUIDs and SQUID systems", eds. John Clarke and Alex I. Braginski (Wiley, 2004).
[7] C.P. Foley, E.E. Mitchell, S.K.H. Lam, B. Sankrithyan, Y.M. Wilson, D.L. Tilbrook, S.J. Morris, "Fabrication and characterisation of YBCO single grain boundary step edge junctions", IEEE Transactions on Applied Superconductivity, 9, 4281 (1999). Abstract.
[8] E.E. Mitchell, C.P. Foley, “YBCO step-edge junctions with high IcRn”, Superconductivity Science and Technology, 23, 065007 (2010). Abstract.
[9] G.V. Prokopenko, O.A. Mukhanov, A. Leese de Escobar, B. Taylor, M.C. de Andrade, S. Berggren, P. Longhini, A. Palacios, M. Nisenoff, R. L. Fagaly, “DC and RF measurements of serial bi-SQUID arrays”, IEEE Transactions on Applied Superconductivity, 23, 1400607 (2013). Abstract.

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Sunday, May 15, 2016

Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering

From Left to Right: Sabine Wollmann, Howard Wiseman, Geoff Pryde.

Sabine Wollmann1, Nathan Walk1,2, Adam J. Bennet1, Howard M. Wiseman1, Geoff J. Pryde1

1Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland, Australia.
2Department of Computer Science, University of Oxford, United Kingdom.

Quantum entanglement, a nonlocal phenomenon, is a key resource for foundational quantum information and communication tasks, such as teleportation, entanglement swapping and quantum key distribution. The idea of this widely investigated feature was first discussed by Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) in 1935 [1]. In their famous thought experiment they consider a maximally-entangled state shared between two observers, Alice and Bob. Alice makes a measurement on her system and controls Bob’s measurement outcomes by her choice of measurement setting. They concluded from this counterintuitive effect, which Einstein later called ‘spooky action at a distance’, that quantum theory must be incomplete and an underlying hidden variable model must exist. It took another 29 years until it was proven by Bell that there exist predictions of quantum mechanics for which no possible local hidden variable model could account for [2].

Figure 1: Illustration of one-way EPR steering. Alice and Bob share a state which only allows Alice to demonstrate steering.

It was not until recently that the class of nonlocality described by EPR, being intermediate to entanglement witness tests and Bell inequality violations, was formalized by Wiseman et al. [3]. While the previous classes are a symmetric feature - in the sense that, the effects persist under exchange of the parties - this does not necessarily hold for EPR steering. The asymmetry arises because one of the parties is trusted (i.e. their measurements are assumed to be faithfully described by quantum mechanics) and the other is not. In this distinctive class of nonlocality we usually consider a shared state between the two parties Alice and Bob. The question which arises is whether sharing an asymmetric state can result in one-way EPR steering, where Alice can steer Bob, for example, but not the other way around.

This foundational question was first experimentally addressed by Haendchen et al. in 2012, who demonstrated experimentally Gaussian one-way EPR steering with two-mode squeezed states [4]. However their experimental investigation was in a limited context: Gaussian measurements on Gaussian states. As we have shown [5] there exist explicit examples of supposedly one-way steerable Gaussian states actually being two-way steerable for a broader class of measurements. So one could ask, do states exist which are one-way steerable for arbitrary measurements? And the answer is yes. Two independent groups, Nicolas Brunner’s in Geneva and Howard Wiseman’s in Brisbane, proved the existence of such states. Brunner’s approach holds for arbitrary measurements with infinite settings, so called infinite-setting positive-operator-valued measures (POVM), with the cost of using an exotic family of states to demonstrate the effect over an extremely small parameter range, which is unsuitable for experimental observation [6]. David Evans and Howard Wiseman showed one-way steerability exists for projective measurements of more practical, singlet states with symmetric noise - so called Werner states – and loss [7].
Figure 2: Creation of a one-way steerable state (see text for details). One half of a Werner state ρW is sent directly to Alice, whose measurements are described by {Ma|k}, while the other is transmitted to Bob through a loss channel, which replaces a qubit with the vacuum state and is parametrized by probability p. Bob’s measurements are described by {Mb|j}. For differing values of p the final state is unsteerable by Bob for arbitrary projective measurements or arbitrary POVMs. For the same range of p values, Alice can explicitly demonstrate steering via a finite number of Pauli measurements on both sides. She does this by steering Bob’s measurement outcomes so that their shared correlations exceed the upper bound Cn allowed in an optimal local hidden state model.

In our work, recently published in [5], we ask if we can extend the result in Ref. [6] to find a simple state which is steerable in one direction but cannot be steered in the other direction even for the case of arbitrary measurements and infinite settings. For that we consider a shared Werner state
between our observers Alice and Bob. This is a probabilistic mixture of a maximally entangled singlet state with a symmetric noise state parametrised by the mixing probability, or Werner parameter, µ. Using the theorem of Quintino et al. [5] allowed us to construct a state
where the probability p of a vacuum state represents adding asymmetric loss in Bob’s arm. This state is one-way steerable for arbitrary measurements, if we can fulfil the condition
for loss .
Figure 3: In the experimental scheme, Alice and Bob are represented by black and green boxes, respectively. Both are in control of their line and their detectors. The party that is steering is additionally in control of the source. Entangled photon pairs at 820 nm were produced via SPDC in a Sagnac interferometer. Different measurement settings are realized by rotating half- and quarter-wave plates (HWP and QWP) relative to the polarizing beam splitters. A gradient neutral density (ND) filter is mounted in front of Bob’s line to control the fraction of photon qubits passing through. Long pass (LP) filters remove 410 nm pump photons copropagating with the 820 nm photons before the latter are coupled into single-mode fibers and detected by single photon counting modules and counting electronics.

In our experiment we generate an one-way steerable state for projective measurements with a fidelity of (99.6±0.01)% with a Werner state of µ = 0.991±0.003 and insert a filter into Bob’s line to generate the loss = (87±3)%. To demonstrate that Alice remains able to steer Bob’s state, it is necessary to violate the EPR steering inequality. That means measuring a correlation function – the so called steering parameter Sn – which exceeds the classically allowed value. We observe that Alice’s steering parameter of S16 = 0.970±0.004 is 7.3 standard deviations above the classical bound at an heralding efficiency of η = (17.11±0.07)%. The loss of information in Bob’s arm makes him unable to steer the other party. We observe a steering parameter of S16 = 0.963±0.006. In this case, this S value would not have violated a steering inequality even with an infinite number of measurements.

The second one-way steerable regime which we investigate, does still allow Alice to steer Bob’s state but he remains unable to steer hers even by using POVMs. To demonstrate this case, we produce a state with a fidelity of (99.1±0.3)% with a Werner state of µ = 0.978±0.008 and applied a loss p =(99.5±0.3)%. Alice remains able to steer Bob with a steering parameter S16 = 0.951±0.005, being 6.6 standard deviations above the classical bound, at an heralding efficiency of η = (17.17±0.04)%. Bob’s steering parameter S16 = 0.951±0.006 does not violate the inequality and there is no kind of measurement he could choose, even in principle, to be able to steer Alice. We note that the shared state is not exactly a Werner state, but the extremely high fidelities imply, with low probability of error, that the state is only one-way steerable.

Thus, we observe genuine one-way EPR steering for the first time. We note that an independent demonstration was realised in Ref.[8]. While their result is restricted to two measurement settings, our experimental demonstration holds for an arbitrary number of measurements.

[1] A. Einstein, B. Podolsky, N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?", Physical Review, 47, 777 (1935). Abstract.
[2] John S. Bell, “On the Einstein Podolsky Rosen paradox”, Physics, 1, 195 (1964). Full Text.
[3] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox”, Physical Review Letters, 98, 140402 (2007). Abstract.
[4] Vitus Händchen, Tobias Eberle, Sebastian Steinlechner, Aiko Samblowski, Torsten Franz, Reinhard F. Werner, and Roman Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering”, Nature Photonics, 6, 596 (2012). Abstract.
[5] Sabine Wollmann, Nathan Walk, Adam J. Bennet, Howard M. Wiseman, and Geoff J. Pryde, "Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering", Physical Review Letters, 116, 160403 (2016). Abstract.
[6] Marco Túlio Quintino, Tamás Vértesi, Daniel Cavalcanti, Remigiusz Augusiak, Maciej Demianowicz, Antonio Acín, Nicolas Brunner, "Inequivalence of entanglement, steering, and Bell nonlocality for general measurements", Physical Review A, 92, 032107 (2015). Abstract.
[7] D. A. Evans, H. M. Wiseman, "Optimal measurements for tests of Einstein-Podolsky-Rosen steering with no detection loophole using two-qubit Werner states", Physical Review A, 90, 012114 (2014). Abstract.
[8] Kai Sun, Xiang-Jun Ye, Jin-Shi Xu, Xiao-Ye Xu, Jian-Shun Tang, Yu-Chun Wu, Jing-Ling Chen, Chuan-Feng Li, and Guang-Can Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering”, Physical Review Letters, 116, 160404 (2016). Abstract. 2Physics Article.


Sunday, April 24, 2016

Demonstrating One-Way Einstein-Podolsky-Rosen Steering in Two Qubits

Some authors of the PRL paper (Reference 6) published on Thursday. From Left to Right: (top row) Kai Sun, Xiang-Jun Ye, Jin-Shi Xu, (bottom row) Jing-Ling Chen, Chuan-Feng Li, Guang-Can Guo.

Authors: Kai Sun1, Xiang-Jun Ye1, Jin-Shi Xu1, Jing-Ling Chen2, Chuan-Feng Li1, Guang-Can Guo1

1Key Laboratory of Quantum Information, CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.
2Chern Institute of Mathematics, Nankai University, Tianjin, China.

Asymmetric Einstein-Podolsky-Rosen (EPR) steering is an important “open question” proposed when EPR steering is reformulated in 2007 [1]. Suppose Alice and Bob share a pair of two-qubit states; it is easy to imagine that if Alice entangles with Bob, then Bob must also entangle with Alice. Such a symmetric feature holds for both entanglement and Bell nonlocality [2]. However, the situation is dramatically changed when one turns to a novel kind of quantum nonlocality, the EPR steering, which stands between entanglement and Bell nonlocality. It may happen that for some asymmetric bipartite quantum states, Alice can steer Bob but Bob cannot steer Alice. This distinguished feature would be useful for the one-way quantum tasks. The first experimental verification of one-way EPR steering was performed by using two entangled continuous variable systems in 2012 [3]. However, the experiments demonstrating one-way EPR steering [3,4] are restricted to Gaussian measurements, and for more general measurements, like projective measurements, there is no experiment realizing the asymmetric feature of EPR steering, even though the theoretical analysis has been proposed [5].

Figure 1: Illustration of one-way EPR steering. In one direction (red), EPR steering is realized and this direction is safe for quantum information. In the other direction (blue), steering task fails and this direction is not safe.

Recently, we for the first time quantified the steerability and demonstrated one-way EPR steering in the simplest entangled system (two qubits) using two-setting projective measurements [6]. The asymmetric two-qubit states in the form of ρAB = η |Ψ(θ)⟩⟨Ψ(θ)| + (1-η) |Φ(θ)⟩⟨Φ(θ)|, where 0 ≤ η≤ 1, |Ψ(θ)⟩ = cos ⁡θ |0A 0B⟩ + sin⁡θ |1A 1B⟩, |Φ(θ)⟩ = cos⁡θ |1A 0B⟩ + sin⁡θ |0A 1B⟩, are prepared in this experiment (see Figure 2(a) ). Based on the steering robustness [7], an intuitive criterion R called as “steering radius” is defined to quantify the steerability (see Figure 2 (c) ). The different values of R on two sides clearly illustrate the asymmetric feature of EPR steering. Furthermore, the one-way steering is demonstrated when R > 1 on one side and R < 1 on the other side (see Figure 2 (b)).
Figure 2:  (click on the figure to view with higher resolution)  Experimental results for asymmetric EPR steering. (a) The distribution of the experimental states. The right column shows the entangled states we prepared, and the left column is a magnification of the corresponding region in the right column. The states located in the yellow (grey) regions are predicted to realize one-way (two-way) steering theoretically in the case of two-setting measurements. The blue points and red squares represent the states realizing one-way and two-way EPR steering, respectively. The black triangles represent the states for which EPR steering task fails for both observers. (b) The values of R for the states are labeled in the left column in (a). The red squares represent the situation where Alice steers Bob's system, and the blue points represent the case where Bob steers Alice's system. (c) Geometric illustration of the strategy for local hidden states (black points) to construct the four normalized conditional states (red points) obtained from the maximally entangled state.

For the failing EPR steering process, the local hidden state model, which provides a direct and convinced contradiction between the nonlocal EPR steering and classical physics, is prepared experimentally to reconstruct the conditional states obtained in the steering process (see Figure 3).
Figure 3. (click on the figure to view with higher resolution) The experimental results of the normalized conditional states and local hidden states shown in the Bloch sphere. The theoretical and experimental results of the normalized conditional states are marked by the black and red points (hollow), respectively. The blue and green points represent the results of the four local hidden states in theory and experiment, respectively. The normalized conditional states constructed by the local hidden states are shown by the brown points. Spheres (a) and (c) are for the case in which Alice steers Bob's system, whereas (b) and (d) show the case in which Bob steers Alice's system. The parameters of the shared state in (a) and (b) are θ = 0.442 and η = 0.658; the parameters of the shared state in (c) and (d) are θ = 0.429 and η = 0.819. The spheres (a), (b) and (d) show that the local hidden state models exist, and the steering tasks fail. The sphere (c) Shows that no local hidden state model exists for the steering process with the constructed hidden states located beyond the Bloch sphere and R = 1.076.

The quantification of EPR steering provides an intuitional and fundamental way to understand the EPR steering and the asymmetric nonlocality. The demonstrated asymmetric EPR steering is significant within quantum foundations and quantum information, and shows the applications in the tasks of one-way quantum key distribution [8] and the quantum sub-channel discrimination [7], even within the frame of two-setting measurements.

[1] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox”, Physical Review Letters, 98, 140402 (2007). Abstract.
[2] John S. Bell, “On the Einstein Podolsky Rosen paradox”, Physics, 1, 195 (1964). Full Text.
[3] Vitus Händchen, Tobias Eberle, Sebastian Steinlechner, Aiko Samblowski, Torsten Franz, Reinhard F. Werner, and Roman Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering”, Nature Photonics, 6, 596 (2012). Abstract.
[4] Seiji Armstrong, Meng Wang, Run Yan Teh, Qihuang Gong, Qiongyi He, Jiri Janousek, Hans-Albert Bachor, Margaret D. Reid, and Ping Koy Lam, “Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks”, Nature Physics, 11, 167 (2015). Abstract.
[5] Joseph Bowles, Tamás Vértesi, Marco Túlio Quintino, and Nicolas Brunner, “One-way Einstein-Podolsky-Rosen steering”, Physical Review Letters, 112, 200402 (2014). Abstract.
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