Mesoscopic Interference and Light Trapping in Semiconductor Nanowire Mats

[From left to right clockwise] Claire Blejean, Otto Muskens, Tom Strudley, Tilman Zehender, Erik Bakkers

Authors: Tom Strudley¹, Claire Blejean¹, Tilman Zehender², Erik P.A.M. Bakkers^2,3, Otto L. Muskens¹,

Affiliation: 
¹Faculty of Physical and Applied Sciences, University of Southampton, UK
²Dept of Applied Physics, Eindhoven University of Technology, Netherlands
³Kavli Institute of Nanoscience, Delft University of Technology, Netherlands.

For many years the field of mesoscopic physics, defined as the interface between the microscopic and macroscopic worlds, has been the domain of solid state electronics. Amongst the most prominent of such mesoscopic effects are those of universal conductance fluctuations [1] and Anderson localization [2]. The case of localization, in which transport is completely halted due to interference effects in the presence of sufficiently strong disorder, has been of considerable interest over the years. Indeed it was one of the two pieces of work for which Anderson was jointly awarded a Nobel prize in 1977, and its complexity has prompted many to quote Anderson’s Nobel lecture: “Very few believed it at the time…among those who failed to fully understand it at first was certainly its author.” [3]

Past 2Physics articles by Erik Bakkers:
May 20, 2012: "Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices" by Vincent Mourik, Kun Zuo, Sergey Frolov, Sébastien Plissard, Erik Bakkers, Leo Kouwenhoven.

Due to the strong analogy between electron and wave transport, such phenomena should also occur for wave transport in random media. However this presents a significant challenge, as mesoscopic effects occur when the probability of a diffusion scattering back to the same point and interfering with itself becomes significant. Intuitively this break down of the traditional ‘random walk’ description requires scattering mean free paths significantly lower than the wavelength. As a consequence, demonstrations of Anderson localization of light in three dimensions have proved difficult, with most observations being for other systems such as microwaves in a waveguide [4], acoustic waves [5] and even cold atoms [6]. A couple of pioneering studies have reported localization of light in three dimensional media [7,8], however the interpretation of their results is complicated by absorption and fluorescence, which can mimic certain localization effects.

Figure 1: (left) The process of Vapour-liquid-solid growth starting from a gold nanoparticle catalyst is used to grow nanowires on a substrate. A lateral growth step increases the diameter of the wires, without affecting their length. (right) A typical high-density nanowire mat used in our experiments.

In our recent work published in Nature Photonics [9], we presented experimental results obtained using densely packed disordered mats of semiconductor nanowires. We demonstred strong mesoscopic effects using visible light in these layers. The nanowire mats were fabricated at the University of Eindhoven using the method of metallo-organic vapour phase epitaxy (MOVPE), see Fig. 1. By using a recipy of alternating cycles of vapour-liquid-solid (VLS) nanowire growth, followed by lateral growth to increase the wire diameter, precise control could be achieved over the length and diameters of the wire. A very high nanowire density of up to 50% area percentage was necessary to achieve the strong scattering strength required for observing the mesoscopic effects. These nanowire mats are remarkable as they have optical mean free paths as low as 0.2 micrometres, which along with their low intrinsic absorption make them ideal candidates for exploring Anderson localization.

Figure 2 [click on image to see higher resolution]: (left) typical intensity images of light transmitted through a nanowire mat, for a tight laser focus ('in focus') and for a laser illumination out of focus. Total image size ~20 μm. (middle) Intensity distribution normalized to ensemble average, showing the speckle fluctuations in space at the exit plane of the nanowire mat. (right) the total intensity fluctuations are enhanced for a tigthly focused laser, see Ref. [9].

By examining the intensity statistics of the transmitted light we found that it exhibited the large intensity fluctuations and long range correlations (both spatial and spectral) typical of mesoscopic interference (Fig. 2). Fitting these fluctuations with predictions from theory, we found an average of only 4 independent transmission channels through our sample, which is several orders of magnitude lower than previously reported values. These measurements unambiguously show for the first time that strong mesoscopic interference corrections can be achieved in three-dimensional nanomaterials and at optical wavelengths.

Mesoscopic transport corrections are a precursor of the strong or Anderson localization transition, where transport of light is halted by self-interference of many light paths returning to the same position in the medium. We are now in the exciting position where we can probe in detail the mesoscopic physics of light, as well as tuning our nanowire growth parameters further in a bid to observe localization itself. For practical applications, semiconductor nanowires have great potential in solar cell and light generation. A deep understanding of light transport in such materials is of great importance for further optimizing these applications. Ultimately, it may be possible for mesoscopic effects to be harnessed and turned into a new design tool for maximizing performance of real-world devices.

References:
[1] P.A. Lee and A. Douglas Stone, “Universal Conductance Fluctuations in Metals”, Physical Review Letters, 55, 1622-1625 (1985). Abstract.
[2] P.W. Anderson, “Absence of diffusion in certain random lattices”, Physical Review, 109, 1492-1505 (1958). Abstract.
[3] Philip W. Anderson, Nobel lecture (1977).
[4] A.A. Chabanov, M. Stoytchev, A.Z. Genack, “Statistical Signatures of Photon Localization”, Nature 404, 850-853 (2000). Abstract.
[5] Hefei Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, B. A. van Tiggelen, “Localization of Ultrasound in a Three-Dimensional Elastic Network”, Nature Physics, 4, 945-948 (2008). Abstract.
[6] Juliette Billy, Vincent Josse, Zhanchun Zuo, Alain Bernard, Ben Hambrecht, Pierre Lugan, David Clément, Laurent Sanchez-Palencia, Philippe Bouyer, Alain Aspect, “Direct Observation of Anderson localization of matter waves in a controlled disorder”, Nature, 453, 891-894 (2008). Abstract. 2Physics Article.
[7] Diederik S. Wiersma, Paolo Bartolini, Ad Lagendijk, Roberto Righini, “Localization of light in a disordered medium”, Nature 390, 671-673 (1997). Abstract.
[8] Martin Störzer, Peter Gross, Christof M. Aegerter, and Georg Maret, “Observation of the Critical Regime Near Anderson Localization of Light”, Physical Review Letters, 96, 063904 (2006). Abstract.
[9] Tom Strudley, Tilman Zehender, Claire Blejean, Erik P. A. M. Bakkers, Otto L. Muskens, “Mesoscopic Light Transport by Very Strong Collective Multiple Scattering in Nanowire Mats”, Nature Photonics, 7, 413-418 (2013). Abstract.

Edgy Photonics

[From Left to Right] Mordechai Segev, Julia M. Zeuner, Mikael C. Rechtsman, Yaakov Lumer, Yonatan Plotnik.

Authors: Mikael C. Rechtsman¹, Julia M. Zeuner², Yonatan Plotnik¹, Yaakov Lumer¹, Mordechai Segev¹ and Alexander Szameit²

Affiliation: 
¹Department of Physics and the Solid State Institute, Technion – Israel Institute of Technology, Haifa, Israel
²Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Germany

There is a topological revolution going on in solid-state physics. At its heart are ‘topological insulators’ (TIs), a class of materials that have electrical properties unlike anything else that has been seen before [1–4]. In TIs, electrical current flows only on the edges or surfaces and not through the bulk of the material: this is why the titles of many popular science articles on the topic are variants of “Physics on the edge.” The atoms making up these materials are, for example, Bismuth Selenide (for the three-dimensional case), and Mercury Telluride (for the two-dimensional case).

Alexander Szameit of Friedrich-Schiller-Universität Jena

The two-dimensional TI has perhaps the most bizarre behavior: electrical current flowing on its edge does not get obstructed by imperfections of the lattice. Any kind of defect or disorder cannot scatter the electrons – allowing them to flow in a smooth and seamless way. Essentially because of this robustness, the condensed matter and solid-state physics community has been convinced that these are going to be the materials at the core of futuristic technologies like robust quantum computation and spintronic devices.

Just as electronics uses the flow of electrons to manipulate information, the field of photonics explores the use of light to do the same thing. Examples of photonic technologies are optical fibers (which transmit internet signals across oceans) and DVD players (think “optical drives”), among many, many others. Physicists in the 1980s realized that light could be manipulated with incredible control in “photonic crystals" [5,6], which are lattices made out of some transparent material (for example, glass, polystyrene, or even silicon). Photonic crystals are central in many emerging photonic technologies, and have the ability to manipulate light in much the same way that semiconductors can control and manipulate electrons in computer chips.

This begs the question: can photons be topologically protected from disorder the same way that electrons can in TIs? Can topological robustness be realized photonic crystals just as it was in solids? As Raghu and Haldane showed in a theoretical paper in 2008 [7], the answer is yes – all you need to do is make a photonic crystal out of a gyromagnetic material (like, for example, Yttrium Iron Garnet - YIG), and apply an external constant magnetic field. The external field acts to break “time-reversal symmetry,” meaning that if light is flowing forward, it could be prevented from being scattered (due to the unavailability of a backwards-propagating wave).

 Raghu and Haldane’s theory was proven correct by an experiment carried out in Marin Soljacic’s group in 2009 [8,9]. But there was a catch: because of the weakness of the gyromagnetic effect at optical wavelengths, their experiment could only be done at microwave frequencies. That meant that the photonic crystals involved could be (roughly) no smaller than the metallic grating you can find on the front cover of your microwave oven. Another scheme – in other words, different physics – would have to be found in order to scale down to micron scales and beyond.

There were quite a number of ideas put forward on how to exactly to scale down in order to make photonic topological insulators with light [10–12]. Our team of researchers (a collaboration between the Segev group at the Technion – Israel Institute of Technology in Haifa and the Szameit group at Friedrich-Schiller University in Jena, Germany) conceived of a new way of doing exactly this, and then implemented it in the lab [13]. The group used an array of waveguides made of fused silica – i.e., glass – to create a honeycomb lattice. The waveguides – which are essentially wires for light – were made to propagate in a helical fashion, rather than straight (see Fig. 1). The helicity is the key ingredient – it allows the light to differentiate between diffracting off to the left or to the right, and only thus can topological protection be achieved. An animation of a simulation in which light misses a defect and then goes around a corner is included below. Full experimental results are available in a recent publication in the journal Nature [13].

Figure 1: This is a schematic diagram of a photonic topological insulator realized in Ref. 13. Each helix represents a waveguide that guides light just as a wire guides electrical current. Each waveguide is about 6μm in diameter and the spacing between waveguides is 15μm.

Caption for Animation: This animation is a simulation of how light propagates through a photonic topological insulator. As light travels down the waveguides, it encounters a defect in the form of a missing waveguide and simply bypasses it without getting scattered. Then, light encounters the corner of the array and simply goes up along the edge because it cannot go back. The reason that the whole array is spinning in a circular way is due to the helicity of the waveguides.

The realization of topological protection of light will impact photonic crystal science and beyond – especially by making photonic devices more robust to disorder, and hence – hopefully – cheaper to manufacture. The optical setting will also enable probing new topological physics that may never have been accessed otherwise. Perhaps the most beautiful aspect of photonic TIs is that they are another example of “emergent physics” [14] – the idea that in complex systems, physics can be much more than the sum of its parts.

References:
[1] C. L. Kane and E. J. Mele. "Quantum Spin Hall Effect in Graphene". Physical Review Letters, 95, 226801 (2005). Abstract.
[2] Markus König, Steffen Wiedmann, Christoph Brüne, Andreas Roth, Hartmut Buhmann. "Quantum Spin Hall Insulator State in HgTe Quantum Wells". Science, 318, 766–770 (2007). Abstract.
[3] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, M. Z. Hasan. "A topological Dirac insulator in a quantum spin Hall phase". Nature, 452, 970–974 (2008). Abstract.
[4] M.Z. Hasan, C.L. Kane. "Colloquium: Topological insulators". Review of Modern Physics, 82, 3045–3067 (2010). Abstract.
[5] Eli Yablonovitch. "Inhibited Spontaneous Emission in Solid-State Physics and Electronics". Physical Review Letters, 58, 2059–2062 (1987). Abstract.
[6] Sajeev John. "Strong localization of photons in certain disordered dielectric superlattices". Physical Review Letters, 58, 2486–2489 (1987). Abstract.
[7] F.D.M. Haldane and S. Raghu. "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry". Physical Review Letters, 100, 013904 (2008). Abstract.
[8] Zheng Wang, Y. D. Chong, John D. Joannopoulos, Marin Soljačić. "Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal". Physical Review Letters, 100, 013905 (2008). Abstract.
[9] Zheng Wang, Yidong Chong, J. D. Joannopoulos, Marin Soljačić. "Observation of unidirectional backscattering-immune topological electromagnetic states". Nature, 461, 772–775 (2009). Abstract.
[10] Mohammad Hafezi, Eugene A. Demler, Mikhail D. Lukin, Jacob M. Taylor. "Robust optical delay lines with topological protection". Nature Physics, 7, 907–912 (2011). Abstract.
[11] Kejie Fang, Zongfu Yu, Shanhui Fan. "Realizing effective magnetic field for photons by controlling the phase of dynamic modulation". Nature Photonics, 6, 782–787 (2012). Abstract.
[12] Alexander B. Khanikaev, S. Hossein Mousavi, Wang-Kong Tse, Mehdi Kargarian, Allan H. MacDonald, Gennady Shvets. "Photonic topological insulators". Nature Materials, 12, 233–239 (2013). Abstract.
[13] Mikael C. Rechtsman, Julia M. Zeuner, Yonatan Plotnik, Yaakov Lumer, Daniel Podolsky, Felix Dreisow, Stefan Nolte, Mordechai Segev & Alexander Szameit. "Photonic Floquet topological insulators". Nature, 496, 196–200 (2013). Abstract.
[14] P.W. Anderson. "More Is Different". Science 177, 393–396 (1972). Abstract.

Precision Interferometry in a New Shape: Higher-order Laguerre-Gauss Modes for Gravitational Wave Detection

[Paul Fulda is the recipient of the 2012 GWIC (Gravitational Wave International Committee) Thesis Prize for his PhD thesis “Precision Interferometry in a New Shape: Higher-order Laguerre-Gauss Modes for Gravitational Wave Detection” (PDF). -- 2Physics.com]

Author: Paul Fulda

Affiliation:

Currently at Department of Physics, University of Florida, Gainesville, USA

PhD research performed at School of Physics and Astronomy, University of Birmingham, UK.


With the approach of advanced detector science runs, the field of gravitational wave detection stands on the brink of finally making the much sought after first direct detection of gravitational waves. Never a bunch to rest on our laurels, however, we are always trying to think of ways to push the sensitivity of these kilometer-scale interferometers ever higher. A single detection, with its ramifications in the areas of astrophysics, cosmology and General Relativity, would be an incredible achievement for a scientific field long in the making.

However, since the observable astrophysical event rate scales as the cube of the observable event distance (and hence roughly as the cube of the broadband sensitivity), any sensitivity increase we can make will bring with it an ever greater number of detected gravitational wave events. The more events we have, the better statistics we can do with them, and the better we can refine our model of the universe itself. With that in mind, in this article I will focus on one of many ideas for improving the sensitivity of gravitational wave detectors beyond the 'advanced' generation; the idea of using higher-order Laguerre-Gauss modes to reduce the thermal noise of the test-masses of the interferometers.

2Physics articles by past winners of the GWIC Thesis Prize:

Rutger van Haasteren (2011): "Pulsar Timing Arrays: Gravitational-wave detectors as big as the Galaxy"
Haixing Miao (2010): "Exploring Macroscopic Quantum Mechanics with Gravitational-wave Detectors"
Holger J. Pletsch (2009): "Deepest All-Sky Surveys for Continuous Gravitational Waves"
Henning Vahlbruch (2008): "Squeezed Light – the first real application starts now"
Keisuke Goda (2007): "Beating the Quantum Limit in Gravitational Wave Detectors"
Yoichi Aso (2006): "Novel Low-Frequency Vibration Isolation Technique for Interferometric Gravitational Wave Detectors"
Rana Adhikari (2003-5)*: "Interferometric Detection of Gravitational Waves : 5 Needed Breakthroughs"
*Note, the gravitational wave thesis prize was started initially by LIGO as a biannual prize, limited to students of the LIGO Scientific Collaboration (LSC). The first award covered the period from 1 July 2003 to 30 June 2005. In 2006, the thesis prize was adopted by GWIC, renamed, converted to an annual prize, and opened to the broader international community.

The rest of this article won't make a lot of sense if I don't first explain what a higher-order laser mode is, but in order to understand this concept we also need to know a little bit about optical cavities. An optical cavity exists wherever there is an arrangement of mirrors that form a closed optical path. Perhaps the simplest case is a linear cavity, which consists of two partially transmissive mirrors, one flat and one curved, orientated with the reflective surfaces parallel to each other (see Fig. 1). When the length of the cavity is tuned just right relative to the frequency of the light, light entering through one partially transmissive mirror creates a standing wave inside the cavity. This condition is known as a resonance of the cavity, and it creates a higher circulating light power inside the cavity than the light power entering. The light is 'stored' inside the cavity for some time before it leaks out again.

Fig 1: A cartoon picture of an optical cavity. Light enters the cavity through the input mirror from the left, and resonates inside the cavity if the cavity length is divisible by an integer number of half wavelengths.

There is another condition on top of the length/frequency condition in order for light to resonate in an optical cavity; the amplitude cross-section of the light (i.e. the beam shape) must be unchanged after several reflections from the mirrors that make up the cavity. If this is not the case, the light will not properly add up after each reflection to make a standing wave. For a cavity made up of spherically curved mirrors, this condition is satisfied by sets of so-called "spatial modes". There are two main families of these spatial modes - Hermite-Gauss (HG) modes and Laguerre-Gauss (LG) modes (see Fig. 2). In a well designed optical cavity, each higher mode order (the order being n+m for HG modes and 2p+l for LG modes) is resonant at a different cavity tuning. These modes are mathematical solutions to the wave equation in the beam-like or 'paraxial' limit. However, far from being purely abstract mathematical constructs, they really exist and show up in interferometers all the time, as we shall soon see!

Fig 2: [click on the image to see better resolution] Intensity patterns for ideal higher-order HG (top left) and LG (top right) modes. The lower half of the image shows the higher-order LG modes generated in the lab using an SLM (in negative to show detail).

Advanced interferometric gravitational wave detectors make use of optical cavities in many places. Advanced LIGO for example has a pre- mode-cleaner cavity, an input mode cleaner cavity and an output mode cleaner cavity, in addition to the 4 coupled cavities of the central interferometer (see Fig. 3) [1]. These optical cavities are used outside the central interferometer as 'mode cleaners' for their ability to filter the frequency and spatial properties of light, and inside the central interferometer in order to increase the circulating light power and the interaction time between the light and passing gravitational waves. LIGO would not have been able to achieve the unprecedented strain sensitivity it did without using these crucial interferometric tools.

Fig 3: [click on the image to see better resolution] The optical layout of an Advanced LIGO interferometer, showing the input and output mode cleaner cavities, the two 4km long arm cavities and the two recycling cavities.

Usually one aims to use only the lowest order 'fundamental' mode (the HG00/LG00 mode), for precision interferometric metrology. The presence of any of the higher-order modes commonly signifies an imperfection in the optical setup, for example a misalignment or a discrepancy in the characteristic size of two interfering beams. As a result, there are several activities directed towards reducing the presence of these modes in interferometers [2, 3].

Recently, however, it was shown that by using one of the higher-order Laguerre-Gauss modes instead of the funamental mode it may be possible to reduce the effects of mirror thermal noise, which is expected to be one of the limiting noise sources in gravitational wave detectors [4]. Mirror thermal noise appears as random fluctations of the reflecting surfaces, which can mask any gravitational wave passing through the interferometer. Higher-order LG modes are able to reduce the effect of this noise by averaging better over the mirror surface, effectively smoothing out the fluctuations. Higher-order LG modes also have the interesting property of having spiral phasefronts, thereby carrying angular momentum - a property which has made them useful in the fields of cold atoms and bio-photonics [5].

Could it then be a case of "from villain to hero" for higher-order modes? This is the question we sought to answer with a program of research into the application of LG modes in precision interferometry. Although the thermal noise benefits of using LG modes made them seem like an attractive option, it was crucial to test their compatibility with all of the other technologies that are used in gravitational wave detectors. At the University of Birmingham we started this investigation using simulations of advanced interferometer where the main fundamental mode beam was exchanged for a LG33 beam (top right in each panel of Fig. 1) [6]. The LG33 beam performed very favorably in the simulations, giving us the motivation to move forward to table-top lab experiments.

We used a device called a spatial light modulator (SLM) to generate the higher-order LG modes in the lab. This device works somewhat like an LCD screen, except that each pixel can change the phase of the light reflected from it instead of the intensity. By displaying a specific phase pattern on the SLM, we were able to convert a fundamental mode beam into almost any higher-order LG mode we wanted (see the lower half of Fig. 2). We confirmed the spiral phase front of the beams by interfering them with a fundamental mode beam, creating the spiral intensity patterns shown in Fig. 4. However, the mode purity we could achieve with the SLM alone was not high enough for use with gravitational wave detectors.

Fig. 4: Images of the interference pattern between various SLM generated higher-order LG beams and a fundamental mode beam. The spiral pattern indicates the presence of a spiral phasefront in the LG beams. From left: LG22, LG33, LG44, LG55.

The positive aspect of this was that it gave us the perfect opportunity to make one of the most crucial compatibility tests for the LG33 mode - if the LG33 mode was to be effective in gravitational wave detectors, it would have to be compatible with mode cleaner optical cavities and the control schemes that are commonly used with them. If it worked, we would have the added bonus of a `cleaned' LG33 mode after the mode cleaner. As predicted by the earlier simulations, the LG33 mode was compatible with a mode cleaner cavity, and we achieved mode purity in excess of 99%. Figure 5 shows images of two kinds of LG33 mode before and after the mode cleaner cavity [7].

Fig. 5: Images of the SLM generated LG33 mode before (top) and after (bottom) transmission through a linear optical cavity.

With these positive results we decided to move on to the next level of compatibility testing: using LG modes with a suspended 10m prototype interferometer in Glasgow. The specific aim here was to address a tricky problem with LG modes that was identified through simulations; with larger beam sizes, the imperfections in the mirrors that form an optical cavity can cause a significant reduction in the mode purity [8,9].

We set up an LG mode conversion path on the Glasgow prototype input bench (see Fig. 6), and directed the beam into the vacuum tank towards a 10m long optical cavity. We employed a sophisticated method to precisely tune the length of the cavity, while observing the transmitted light power with a high-speed infra-red camera. Since different modes are resonant in the cavity at different tunings, the high-speed camera measurements gave us a good picture of the higher-order mode content in the cavity.

Fig. 6: [click on the image to see better resolution] The LG mode conversion path for the Glasgow 10m prototype interferometer experiment. The red line shows the LG33 conversion path, the green line shows the fundamental mode 'control' path, and the purple line shows the original laser path.

We saw that even when we injected a LG33 mode, we could only observe the rectangular shaped HG modes resonating in the cavity (see Fig. 7). The work reported in [8] and [9] suggested that this behavior might be expected in a cavity where the mirrors are astigmatically curved, rather than the spherically curved ideal case. This was a setback for the use of LG modes in gravitational wave interferometers, as it was the first experimental evidence that mirror surface imperfections might have a stronger impact on mode purity for the LG33 mode than for the fundamental mode. The cavity mirrors were taken out of the prototype and independent measurements of the surface figures were made. The measured astigmatism values were used as inputs for a simulation of the 10m cavity, which reproduced the resonance structures seen in Fig. 7 very well. This was the confirmation that was needed to show that the LG33 mode really was more sensitive to mirror surface imperfections that the fundamental mode [10].

Fig. 7: [click on the image to see better resolution] A trace showing reflected power from the 10m cavity as a function of time as the cavity is swept across a resonance with the LG33 input beam. The resonance is split into several peaks, as predicted in [8] and [9]. Images from the high-speed camera in transmission of the cavity show the resonant mode shape around several of the separate resonance peaks.

From here it was possible to derive tolerances on the mirror imperfections that would be allowable if the LG33 mode was to be used as the readout beam in a real gravitational wave detector. The requirements that the LG33 mode puts on the quality of the mirror surfaces are beyond what is achievable with the current technology, and as such they do look very tough to meet. However, coating and polishing technology is always moving forward with the demands of ever more precise experiments, so at some time in the future we may yet see the LG33 mode flashing on the projector screens in a gravitational wave detector installation.

Those of us who work in the business of laser interferometry become quite accustomed to the sight of higher-order spatial laser modes. It can be easy to take their aesthetic qualities for granted, especially when a lot of our efforts are directed towards minimizing their presence. I still remember the first time I aligned an optical cavity though, and how I was mesmerized by the small CCTV camera picture showing the strange and beautiful patterns in the cavity transmitted light. I'm very glad that my PhD research took me in the direction of studying a particular one of these higher-order laser modes in great detail. By the end of my studies, the higher-order modes weren't just obscure patterns of light to me any more; rather they seemed like cryptic hieroglyphs which when translated could provide a wealth of knowledge about the state of an optical system.

References:
[1] Gregory M. Harry and the LIGO Scientific Collaboration. "Advanced LIGO: the next generation of gravitational wave detectors". Classical and Quantum Gravity, 27(8):084006 (2010). Abstract.
[2] Euan Morrison, Brian J. Meers, David I. Robertson, and Henry Ward. "Automatic alignment of optical interferometers". Applied Optics, 33:5041–5049 (1994). Abstract.
[3] Guido Mueller, Qi-ze Shu, Rana Adhikari, D. B. Tanner, David Reitze, Daniel Sigg, Nergis Mavalvala, and Jordan Camp. "Determination and optimization of mode matching into optical cavities by heterodyne detection". Optics letters, 25(4):266-268 (2000). Abstract.
[4] Benoît Mours, Edwige Tournefier and Jean-Yves Vinet. "Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes". Classical and Quantum Gravity, 23:5777-5784 (2006). Abstract.
[5] H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity". Physical Review Letters, 75(5):826–829 (1995). Abstract.
[6] Simon Chelkowski, Stefan Hild, and Andreas Freise. "Prospects of higher- order Laguerre-Gauss modes in future gravitational wave detectors". Physical Review D, 79(12):122002 (2009). Abstract.
[7] Paul Fulda, Keiko Kokeyama, Simon Chelkowski, and Andreas Freise. "Experimental demonstration of higher-order Laguerre-Gauss mode interferometry". Physical Review D, 82(1):012002 (2010). Abstract.
[8] Charlotte Bond, Paul Fulda, Ludovico Carbone, Keiko Kokeyama, and Andreas Freise. "Higher order Laguerre-Gauss mode degeneracy in realistic, high finesse cavities". Physical Review D, 84(10):102002 (2011). Abstract.
[9] T. Hong, J. Miller, H. Yamamoto, Y.Chen, R. Adhikari. "Effects of mirror aberrations on Laguerre-Gaussian beams in interferometric gravitational wave detectors". Physical Review D, 84(10):102001 (2011). Abstract.
[10] B. Sorazu, P. Fulda, B.W. Barr, A.S. Bell, C. Bond, L. Carbone, A. Freise, S.H. Huttner, J. Macarthur, K.A. Strain. "Experimental test of higher-order Laguerre–Gauss modes in the 10m Glasgow prototype interferometer". Classical and Quantum Gravity, 30(3):035004 (2013). Abstract.

Storage and Control of Optical Photons

Authors of the paper in Physical Review Letters (reference [1] ).
Left to Right: 
(top row) D. Maxwell, D. J. Szwer, D. Paredes-Barato, 
(middle row) H. Busche, J. D. Pritchard, A. Gauguet, 
(bottom row) K. J. Weatherill, M. P. A. Jones, C. S. Adams.



Authors: 
David Szwer and Hannes Busche

Affiliation:
Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, UK.





Quantum communication and information processing rely on robust carriers of quantum information (qubits), and optical photons are prime candidates. Light can easily be transmitted using optical technologies such as fibre cables, and barely interact with other photons or the environment. To process the information they carry however, controllable interactions between the single photons are needed. Physicists at Durham University in the UK have combined two advanced techniques of quantum optics with a microwave synthesiser, to control the interactions between individual photons [1,2]. The photons were stored in a cloud of rubidium atoms as so-called Rydberg polaritons. Due to long-ranged interactions between them, only a single photon may be stored in a volume of a few micrometres, limiting the number of stored photons to about three. The microwaves manipulated the photons while they were stored, forcing them to interact in ways whose details are still not fully understood. The ability to not only induce interactions on the level of single optical photons, but also to control them using microwave fields, could be an important new angle for future quantum technologies.

A beam of light is one of the least substantial things you'll ever encounter. It is the very essence of something fast and untrappable - so much so that Einstein invented relativity specifically because he couldn't imagine what light would be like if it was stationary. And although light reflects off mirrors and scatters off other objects, we never consider that two light beams could bounce off each other.

However, in specially tuned systems physicists can not only stop light, but make light interact with light. Our work achieves both these effects, making the interaction work at the single-photon level and even controlling it with microwaves.

The loophole that allows us to do these things is that light isn't always the pure electromagnetic wave that it is in vacuum. When light travels through matter, like glass or water, the electric field of the light slightly distorts the atoms in the matter, and they tug back on the light. This slows the light down (to half-speed or slower), and is ultimately responsible for lenses, optical fibres, rainbows and other phenomena.

Almost always, matter responds linearly to light so that the distortion from one beam does not affect another. At very high intensities, nonlinear effects can appear that do allow light to affect light. However, the dependence is so weak that it only manifests at very high powers. We care about the quantum nature of light, which only becomes apparent at the level of single photons. Photons carry a tiny amount of energy: a normal red laser pointer (emitting 1mW of power) produces over 3 million billion photons every second. Hence photons almost never interact.

To slow photons to a crawl, bring them to a full stop and make them interact, we therefore need to deliberately engineer our own medium. We start from an extremely thin and cold gas of the element rubidium (it’s normally a solid metal) created by laser cooling and trapping techniques [3]. The gas is about a million times more dilute than normal air (number of atoms per unit volume), so the experiment is done in a vacuum chamber. The gas needs to be extremely cold, just 100 μK (a ten-thousandth of a degree above absolute zero), because if the gas atoms move too fast they’ll mix up the light they’re storing.

Figure 1: Relevant energy levels of rubidium, showing the 780 nm (red, signal) and 480 nm (blue, control) spectral lines, and the Rydberg-Rydberg microwaves. 

 Gases like rubidium are useful because they have strong resonance lines – specific frequencies of light they interact with strongly and correspond to transitions between the discrete energy levels of the atom. We use two lines in rubidium, of wavelength 780 nm (less than a thousandth of a millimetre, a dim red colour) and 480 nm (bright blue). The red light is the signal we store – it excites normal, ground-state atoms to a particular excited energy level. The blue light takes atoms from that excited state to an even higher level called a Rydberg state. It affects how the rubidium atoms respond to the red light, not only preventing them from scattering the signal, but also slowing it down greatly because it is mixed so strongly with atomic distortion. If we turn the blue light off while signal is travelling through the cloud, the red photons are stopped and transformed completely into atomic distortion: a specific pattern of Rydberg excitations called a polariton.

Unlike photons, Rydberg states do interact with each other extremely strongly, causing shifts in the resonance frequencies needed to excite nearby atoms to Rydberg states. As a single Rydberg excitation shifts the remaining atoms out of resonance with our blue light, a blockade effect occurs preventing multiple Rydberg excitations within a volume of a few micrometres. If photons are mixed with Rydberg states, like in our cloud, the photons gain this ability to interact strongly and the blockade applies to them, imposing a minimum separation between photons. Photons that are too close together are scattered out of the cloud. If the cloud is dense enough, this leads to a continuous laser beam being filtered into a series of individual photons, as demonstrated recently by a group at MIT [4]. Alternatively we can stop light in the cloud, and allow the blockade to work while the photons are stored – this was done not only in our experiment, but also by a group at Georgia Tech where a single photon source was implemented [5]. Reliable single-photon sources like this are important for many other quantum experiments, as well as for quantum cryptography [6].

Our cloud is large enough for about three polaritons to sit in a line, each containing a single photon shared among many atoms. Due to the blockade, they are separated by a distance called the blockade radius, which measures the strength of interaction between two Rydberg atoms. This interaction is called the Van der Waals interaction, and it’s the same force that sticks molecules to each other in most solids around you.

Once we have some photons stored, our next step is to beam microwaves at the cloud, tuned to a transition between two different Rydberg states. One of these is the state we stored a photon in (called “S”), and the other state was previously empty (called “P”). Our blue light is only tuned to interact with the S state, not the P, so it will only release a stored photon if the polariton is in S. In an isolated Rydberg polariton, this would drive regular sine-wave “Rabi” oscillations between the two states. So if we apply microwaves for just long enough to transfer to P, and then turn the blue beam on, we don’t retrieve the photon.

Figure 2: Diagram of the experiment, showing the cloud of atoms with three stored polaritons. The two single-photon detectors shown are used to prove that the number of stored photons is limited, via a Hanbury Brown & Twiss experiment [7.8].

Instead of a single polariton, we’re most interested in what happens when the polaritons aren’t isolated, but have neighbours to interact with. The microwaves make them oscillate at the same rate. For a start, photons are only retrieved from the cloud when all polaritons are in S. This leads to the Rabi oscillations (shown in Figure 3) having flattened bottoms and sharper peaks when we scan the microwaves, and the exact shape helps us estimate the number of polaritons we have. Also, while the polaritons are half-way between S and P, they have large electric dipole moments – (the static electricity equivalent of a tiny bar magnet). The original van der Waals interaction is replaced with resonant dipole-dipole interactions – this makes them interact much more strongly than before, and at longer distances. Blockade was caused by the atoms within a polariton interacting – but now the polaritons interact with each other. We see that at low microwave powers, these interactions completely prevent the stored photons being retrieved, scattering them out of the cloud in other directions. But stronger microwaves can overwhelm the dipole-dipole interactions, and we see oscillations again.

Figure 3: The microwave-induced Rabi oscillations between two Rydberg states. Microwave power increases from left to right. The dashed line shows the transition from low power (dominated by Rydberg-Rydberg interactions) to high power (dominated by the microwaves).

This is a subtle system, and not yet fully understood. There is plenty more experimental and theoretical work to do. But we can already imagine applications. By controlling strong interactions between individual photons, it may be possible to build quantum logic gates that could be used in super-fast quantum computers, or super-secure quantum cryptography. There are also similarities between the way that specific Rydberg states can “hop” between polaritons, and the hopping of excitations along light harvesting complexes in plants. Experiments like these may help model photosynthesis, perhaps even helping scientists design more efficient solar cells.

Bibliography
[1] D. Maxwell, D. J. Szwer, D. Paredes-Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, C. S. Adams, "Storage and Control of Optical Photons Using Rydberg Polaritons". Physical Review Letters , 110, 103001 (2013). Abstract.
[2] Antoine Browaeys, "Viewpoint: Catch and Release of Photons". Physics , 6, 25 (2013). Article.
[3] Nobel Prize in Physics 1997: Link.
[4] Thibault Peyronel, Ofer Firstenberg, Qi-Yu Liang, Sebastian Hofferberth, Alexey V. Gorshkov, Thomas Pohl, Mikhail D. Lukin, Vladan Vuletić, "Quantum nonlinear optics with single photons enabled by strongly interacting atoms". Nature, 488, 57-60 (2012). Abstract.
[5] Y.O. Dudin,  A. Kuzmich, "Strongly Interacting Rydberg Excitations of a Cold Atomic Gas. Science". 336, 887-889 (2012). Abstract.
[6] Alexios Beveratos, Rosa Brouri, Thierry Gacoin, André Villing, Jean-Philippe Poizat, and Philippe Grangier, "Single Photon Quantum Cryptography". Physical Review Letters, 89, 187901 (2002). Abstract.
[7] Michel Orrit, "Photon Statistics in Single Molecule Experiments". Single Molecules, 3, 255-265 (2002). Abstract.
[8] R. Hanbury Brown, R.Q.  Twiss, "Correlation between Photons in two Coherent Beams of Light". Nature, 177, 27-29 (1956). Abstract.

Seeing People Moving Behind Smoke and Flames by Lensless Digital Holography at Long Infrared Wavelength

The working group of National Institute of Optics (INO-CNR), Italy. From left to right: Vittorio Bianco (behind), Pasquale Poggi (ahead), Lisa Miccio (behind), Melania Paturzo, Pietro Ferraro, Riccardo Meucci, Massimiliano Locatelli, Anna Pelagotti, Eugenio Pugliese.

Authors:
V. Bianco¹, M. Paturzo¹, M. Locatelli², E. Pugliese², A. Finizio¹, A. Pelagotti², P. Poggi², L. Miccio¹, R. Meucci², P. Ferraro¹.

Affiliations:
¹National Institute of Optics (INO-CNR), Pozzuoli (Naples), Italy.
²National Institute of Optics (INO-CNR), Florence, Italy.

Fire accidents are responsible every year for thousands of deaths, damages and permanent burn injuries, the most of them regarding home fires (3000 deaths occurring each year due to home fires according to the U.S. Fire Administration [1]). In such situations, firefighters and first responders are called to operate in hostile environments, where their skills are often strained to the limit by the reduced visibility due to the presence on the field of curtains of smoke and walls of flames. In these cases, the rescue operations can slow down and be more dangerous, depending on the fire and smoke spread which impair the naked-eye view as well as the vision obtainable with white-light detectors, hiding any target behind the “obstacle.”

Many efforts have been spent to try to extend the human eye capabilities in hostile environments. In order to cope with this problem many fire departments make use of the last generation of Infrared (IR) bolometers, now commercially available at contained costs, which operate in the range 7-14μm of the electromagnetic spectrum and, hence, they are much less affected by the scattering of smoke particles, or incandescent soot. However, if a flame is present on the line of sight between the detector and the target, the flame emission tends to saturate the detector elements, unavoidably resulting in blind areas in the image. This problem is more severe in presence of extended flames, as the whole fire scene becomes not observable. For example, in case of a room invaded by smoke and flames, the thermographic cameras return images with blind areas in correspondence with incandescent or burning objects, or the flame source itself, and also the mere detection of the presence of people trapped inside is not achievable with enough reliability.

On the contrary, we have proved that Digital Holography [2] at far Infrared radiation (IRDH) is a promising technique to substitute, in a forthcoming future, the existing thermographic devices, allowing to get a clear and sharp imaging of small objects as well as moving humans hidden behind smoke and flames. In principle this is possible exploiting some unique features of IRDH [3-5]. First of all, thanks to the IR radiation, the wavefront propagation is just slightly scattered by incandescent soot and smoke particles, making IRDH competitive with respect to the existing IR cameras. Moreover, employing a long wavelength (10.6µm in our experiments), the acquisition system is much less affected by seismic noise and vibrations, so that it can be brought outside the lab, to be exploited on the field. Thanks to the long wavelength, one of the most binding requirements of Digital Holography (DH) have been overcome for the first time. In fact, DH at visible radiation has been deeply employed so far in quantitative phase microscopy and, in general, to image small size objects. On the contrary, the IR wavelength allows to increase of about 20 times the maximum size of the target detectable, as this size is proportional to the wavelength employed [5]. However, the key feature of IRDH, which enables to overcome the limits of thermographic imaging, is the possibility to discard the flame emitted radiation and to recover the only useful information content behind it.

In fact, since in conventional IR imaging a zoom lens is employed, the radiating contributions emitted in several different directions and matching the numerical aperture of the lens are all conveyed on a few detector elements, and the focused energy causes their saturation. In turn, this results in blind areas in the retrieved image and the useful information of the targets beyond the flames is lost. On the contrary, IRDH in lensless configuration allows to perform the data capture by placing the detector out of the focus plane and the numerical focusing can be performed by means of numerical techniques simulating the diffraction integral, i.e. reproducing the propagation of the complex wavefield from the recording plane to the focus one. In this way, the disturbing radiation is distributed on the whole camera array and saturation is avoided. Taking advantage of the combination of all these features, we obtained the first holographic recording of a moving man standing behind a flame generated by a portable mini-stove [5].

To demonstrate the IRDH capabilities, in our first experiment we placed a bronze statuette 10cm high into a plexiglass box where smoke has been injected in controlled way, as shown in Fig.1a, and both thermographic and holographic acquisitions have been performed. From Fig.1b and Fig.1c it is apparent that both the investigated techniques are able to offer a clear view of the object inside the chamber, despite the presence of the dense curtain of smoke.

In our second experiment digital holograms of objects hidden by the flame of a candle have been acquired. The candle was placed on the path of the object wave so that it constitute an obstacle for thermographic cameras. The illustration of Fig. 2 shows the working principle of lensless IRDH which directly gets rid of the flame emission as previously described. As a result, in Fig. 2a the thermographic image of the bronze statuette placed behind the candles shows a blind area in the middle, impairing the vision of a part of the target. On the contrary, no information is lost by employing the lensless IRDH set-up, as shown in the holographic reconstruction of Fig. 2b.

Finally, in the last experiment we recorded holograms of a moving person behind a curtain of flames generated by a portable mini-stove. Figure 3a shows the result obtainable simply employing a thermographic sensor. The man shaking his hands is just barely visible through the extended blind area in the middle of the image and only his arms are appreciable. With such a sensor, a more extended flame would completely impair the detection of the target. In Fig. 3b the holographic reconstruction of the eye-glassed man imaged behind the same kind of flame is shown. No sensor saturation occurs, so that the reconstruction does not show blind areas and also details of the arm are appreciable in the region where the flame emission is stronger, thus demonstrating the capability of IRDH of rejecting it.

Thanks to these unique features of IRDH technique we believe that this work can open the route for the development, in the next future, of a new generation of portable holographic sensors to be exploited by firefighters and first responders in order to coordinate the rescue operations and work safely in hostile environments.

References
[1] U.S. Fire Administration, http://www.usfa.fema.gov/statistics.
[2] T. Kreis, “Handbook of holographic interferometry: optical and digital methods,” (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005).
[3] Melania Paturzo, Anna Pelagotti, Andrea Finizio, Lisa Miccio, Massimiliano Locatelli, Andrea Gertrude, Pasquale Poggi, Riccardo Meucci, and Pietro Ferraro “Optical reconstruction of digital holograms recorded at 10.6 μm: route for 3D imaging at long infrared wavelengths,” Opt. Lett. 35, 2112-2114 (2010). Abstract.
[4] Anna Pelagotti, Massimiliano Locatelli, Andrea Giovanni Geltrude, Pasquale Poggi, Riccardo Meucci, Melania Paturzo, Lisa Miccio, and Pietro Ferraro, “Reliability of 3D imaging by digital holography at long IR wavelength,” Journal of Display Technology, 6, 465-471 (2010). Abstract.
[5] M. Locatelli, E. Pugliese, M. Paturzo, V. Bianco, A. Finizio, A. Pelagotti, P. Poggi, L. Miccio, R. Meucci, and P. Ferraro, “Imaging live humans through smoke and flames using far-infrared digital holography,” Optics Express, 21, 5379-5390 (2013). Abstract.

Role of Statistics in Two-Particle Anderson Localization

Roberto Osellame (left)  and Fabio Sciarrino (right)

Authors: Roberto Osellame¹ and Fabio Sciarrino²

Affiliations:
¹Istituto di Fotonica e Nanotecnologie (IFN) – CNR, Milan, Italy.
Link to the Femtosecond Laser Micromachining group >>
²Dipartimento di Fisica – Sapienza Università di Roma, Rome, Italy.
Link to the Quantum Optics group >>

3D QUEST >>

Disorder in our daily life typically has a negative connotation. Also in science it has been normally considered as a source of noise or imperfection. However, disorder is ubiquitous in nature: indeed it plays, on the one hand, a crucial role in understanding the behavior of complex physical phenomena [1] and, on the other hand, it can turn into an advantageous property for developing completely new devices [2]. One of the most striking effects of disorder is the suppression of transport of electrons in a disordered crystal. This phenomenon, known as Anderson localization after the 1958 paper by P.W. Anderson [3], is due to coherent scattering of the electron wavefunction in the disordered crystal and is general to any wave propagating in a disordered media [4]. Being a coherent effect, Anderson localization can be directly observed with photons, due to their little interaction with the environment and long coherence time. In addition, photonic structures, e.g. waveguide lattices, can be manufactured with a very high level of control of the structure parameters and are therefore prone to implementing and investigating different kinds of disorder.

Fig. 1 Femtosecond laser writing of optical waveguides. The glass sample is translated with respect to the writing laser beam. The bright spot in the glass comes from electron plasma generated by the focused laser; the energy transferred to the glass matrix after plasma relaxation is responsible for the local increase of refractive index.

A very recent technique (Fig. 1) that allows the accurate fabrication of photonic lattices is femtosecond laser waveguide writing [5]. With respect to standard microfabrication techniques it enables rapid prototyping of devices, being a direct write method, and extreme flexibility in the layout reconfiguration, being a maskless process [6]. In addition, it has the unique capability of exploiting the third dimension in the fabrication of the photonic circuits, which opens the possibility for completely new architectures [7,8].

The simplest way of observing Anderson localization is the study of a single particle in a 1D periodic crystal with static disorder (i.e. disorder that is spatially uncorrelated, but does not vary with time)[9]. This is analogous to observing the quantum walk of a single photon in a disordered waveguide array. If the observation in time is not continuous, but periodical, we are studying a discrete quantum walk. Femtosecond laser waveguide writing can be effectively exploited to produce matrices of integrated optical interferometers constituting a discrete quantum walk for photons [10]. The same technology enables a straightforward implementation of arbitrary phases in the different optical paths, thus introducing disorder in the structure. In our recent paper, published on Nature Photonics [11] in collaboration with Scuola Normale di Pisa, we implemented random phase maps representing static disorder, as in the chip depicted in Fig. 2a.

Anderson localization is essentially a single particle process, however in this work we experimentally investigated for the first time the role of particle statistics in the localization of two non-interacting photons. In order to mimick bosonic and fermionic statistics we exploited the symmetric and antisymmetric wavefunction of polarization entangled photons [10]. We observed Anderson localization for the two particles obeying both statistics, however when two bosonic particles were propagating they tended to localize on the same site, while the fermionic ones localized on adjacent sites but not on the same one, as expected from the Pauli exclusion principle (Fig. 2b). We also observed that the mean position between the two particles has a stronger localization for fermions than for bosons, while the relative distance has a smaller expectation value for bosons than for fermions [11].

Fig. 2 (a) Scheme of the device implementing a discrete quantum walk with static disorder. The m ports represents the sites of the 1D crystal, the n steps represents the discrete observation times. The colors of the phase shifters represent different implemented phases, which are constant along n to implement a static disorder. (b) Experimental correlation maps representing the joint probability of finding one photon in output port i and the other in output port j; with respect to the case without disorder (where ballistic propagation is observed), a clear localization is observed when static disorder is introduced [11] (Click on the image to view a version of better resolution).

These results demonstrate that even without interaction, particle statistics is capable of influencing the way two particles localize in a disordered media. In addition they show the potential of femtosecond laser waveguide writing for implementing arbitrary quantum walks with controlled disorder. The capability of our technology to implement arbitrary phase maps in quantum walks will enable the experimental quantum simulation of the quantum dynamics of multiparticle correlated systems and its ramifications towards the implementation of realistic universal quantum computation with quantum walks.

References
[1] Liad Levi, Yevgeny Krivolapov, Shmuel Fishman & Mordechai Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder”, Nature Physics, 8, 912-917 (2012). Abstract.
[2] Diederik S. Wiersma, “Disordered photonics”, Nature Photonics, 7, 188-196 (2013). Abstract.
[3] P.W. Anderson, “Absence of diffusion in certain random lattices”, Physical Review, 109, 1492-1505 (1958). Abstract.
[4] Mordechai Segev, Yaron Silberberg & Demetrios N. Christodoulides, “Anderson localization of light”, Nature Photonics, 7, 197–204 (2013). Abstract.
[5] Rafael R. Gattass, Eric Mazur, “Femtosecond laser micromachining in transparent materials”, Nature Photonics, 2, 219 - 225 (2008). Abstract.
[6] G. Della Valle, R. Osellame, P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses”, J. Opt. A 11, 013001(2009). Abstract.
[7] Nicolò Spagnolo, Chiara Vitelli, Lorenzo Aparo, Paolo Mataloni, Fabio Sciarrino, Andrea Crespi, Roberta Ramponi & Roberto Osellame, “Three-photon bosonic coalescence in an integrated tritter”, Nature Communications, doi:10.1038/ncomms2616 (Published March 19, 2013). Abstract.
[8] Mikael C. Rechtsman, Julia M. Zeuner, Andreas Tünnermann, Stefan Nolte, Mordechai Segev & Alexander Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures”, Nature Photonics, 7, 153-158 (2013). Abstract.
[9] Yoav Lahini, Assaf Avidan, Francesca Pozzi, Marc Sorel, Roberto Morandotti, Demetrios N. Christodoulides and Yaron Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices”, Physical Review Letters, 100, 013906 (2008). Abstract.
[10] Linda Sansoni, Fabio Sciarrino, Giuseppe Vallone, Paolo Mataloni, Andrea Crespi, Roberta Ramponi and Roberto Osellame, “Two-particle bosonic–fermionic quantum walk via integrated photonics”, Physical Review Letters, 108, 010502 (2012). Abstract.
[11] Andrea Crespi, Roberto Osellame, Roberta Ramponi, Vittorio Giovannetti, Rosario Fazio, Linda Sansoni, Francesco De Nicola, Fabio Sciarrino & Paolo Mataloni, “Anderson localization of entangled photons in an integrated quantum walk”, Nature Photonics, doi:10.1038/nphoton.2013.26 (Published online March 3, 2013). Abstract.

Experimental Boson Sampling

[From left to right] Part of the Oxford integrated quantum optics team: Steve Kolthammer,
Ben Metcalf, Merritt Moore, Peter Humphreys, Justin Spring, and Ian Walmsley

Authors: Steve Kolthammer, Justin Spring, Ian Walmsley

Affiliation: Department of Physics, University of Oxford, UK

A long-term ambition of many quantum physicists these days is to construct and understand large and complex quantum systems. This goal is driven in part by the notion that such systems have the potential to reveal interesting phenomena that cannot be studied by classical simulation. Such phenomena occur widely across the natural sciences, from biochemistry to condensed matter physics. The notion of complexity itself, however, is perhaps on firmest ground within the framework of computation. Here complexity refers to how the physical resources needed to achieve a particular task depend on the size of the task. Dramatic cases in which a quantum algorithm provides an exponential advantage over the best known classical algorithm make clear the potential for a quantum system to process information in ways that would eclipse even the most fantastically advanced classical machines.

Past 2Physics articles by this Group:
December 25, 2011: "Entang-bling" by Ian Walmsley and Joshua Nunn
August 07, 2011: "Building a Quantum Internet" by Joshua Nunn

Despite steady progress in manipulating and measuring simple quantum systems, a gulf remains between the theoretical promise of quantum computation and what has been shown in the laboratory. Bridging this divide requires not only further experimental advances but also the development of models of computation which are easier to test. In 2010, Scott Aaronson and Alex Arkhipov reported important progress toward the latter in a study of the computational power inherent in the quantum interference of indistinguishable, non-interacting bosons [1]. The specific problem they posed, termed boson sampling, is appealing due to its relatively straight-forward implementation with linear optical elements, such as beam splitters and phase shifters, sources of indistinguishable single photons, and single-photon detectors.

Importantly, this scheme does not require on-demand entanglement and feed-forward control, which are required for other approaches to linear-optical quantum computing and difficult to achieve in the laboratory. From a computational perspective, the key advance by Aaronson and Arkhipov was to show strong evidence that boson sampling is in fact interesting – that is, it cannot be solved efficiently by classical computation.

The essence of the boson sampling problem can be readily understood by examining the quantum machine which solves it. Our machine begins by injecting indistinguishable single photons into a linear optical network of single-mode waveguides. Due to quantum interference as the photons traverse the network, the photons emerge in a complicated entangled state. The positions of the photons are then measured by single-photon detectors. The machine bears some resemblance to the classical Galton board, illustrated below, in which balls randomly fall through an array of pegs. However, while these distinguishable classical balls take familiar, distinct paths down the board, rolling either left or right off of each peg they encounter, the photons in some sense collectively take all possible paths through their network.

Surprisingly, the interference of these paths makes it hard for a classical computer to predict where the photons tend to emerge! In the quantum case, the probability for a particular measurement outcome after N photons are injected into a network described by a unitary matrix U, is related to the permanent of a specific N x N submatrix of U. The permanent, a function of a matrix similar to the determinant, is noteworthy since its computation is hard. Aaronson and Arkhipov showed that an efficient classical algorithm that samples from a distribution of matrix permanents, precisely the task accomplished by the quantum machine, is very unlikely to exist.

Classical Galton board (left) and quantum boson sampling machine (right).

Last month, our group was one of two teams to report initial boson sampling experiments in Science [2, 3]. In fact, a remarkable interest in boson sampling became apparent last December when four groups - with experiments undertaken in Oxford, Brisbane, Vienna, and Rome - presented results on arXiv.org within the same week [2-5]. In our measurements, the principles of boson sampling were verified with three and four photons in a photonic chip. The photons were generated by degenerate parametric down-conversion, a nonlinear optical three-wave-mixing process, in a pair of crystals and coupled into a silica-on-silicon waveguide chip fabricated by our collaborators at the University of Southampton. The output from the chip was measured with single-photon avalanche photodiodes.

How closely did our quantum machine match an ideal boson sampling device? To address this issue we compared our measurements to the predictions of a classical computer, which is able to handle small boson sampling tasks. By extending the model of our machine to include a number of small, independently measured imperfections, such as rare multi-pair photon emission from a source, we verified that the machine ran as expected. In terms of quantum optics, our findings extend the well-studied Hong-Ou-Mandel quantum interference of two photons to processes with three and four photons. In terms of computation, we demonstrated the feasibility of running small-scale boson sampling tasks with the current experimental state of the art.

A striking feature of the boson sampling problem is that it appears to be amenable to the tools of complexity theorists as well as those of quantum experimenters. Meeting these disparate requirements is the crucial challenge to achieving a direct test of quantum computational power. Future work on boson sampling will benefit from an on-going effort to understand how unavoidable experimental imperfections relate to computational complexity. Meanwhile quantum optics labs, including our own, will continue to work towards experiments with increasing numbers of single photons. Extending our initial studies to ten photons should provide clear evidence for the computational power of this simple quantum machine, and a calculation with tens of photons could reach the frontier of quantum complexity which is inaccessible by classical computation.

References
[1] Scott Aaronson and Alex Arkhipov. “The Computational Complexity of Linear Optics”. Proceedings of the ACM Symposium on the Theory of Computing (ACM, New York, 2011), pp. 333-342. Download.
[2] Justin B. Spring, Benjamin J. Metcalf, Peter C. Humphreys, W. Steven Kolthammer, Xian-Min Jin, Marco Barbieri, Animesh Datta, Nicholas Thomas-Peter, Nathan K. Langford, Dmytro Kundys, James C. Gates, Brian J. Smith, Peter G. R. Smith, Ian A. Walmsley. “Boson Sampling on a Photonic Chip”. Science, 339, 798 (2013). Abstract.
[3] Matthew A. Broome, Alessandro Fedrizzi, Saleh Rahimi-Keshari, Justin Dove, Scott Aaronson, Timothy C. Ralph, Andrew G. White. “Photonic Boson Sampling in a Tunable Circuit”. Science, 339, 794 (2013). Abstract.
[4] Max Tillmann, Borivoje Dakić, René Heilmann, Stefan nolte, Alexander Szameit, Philip Walther. “Experimental Boson Sampling”. ArXiv:1212.2240 [quant-ph] (2012).
[5] Andrea Crespi, Roberto Oselame, Roberta Ramponi, Daniel J. Brod, Ernesto Galvão, Nicolò Spagnolo, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Fabio Sciarrino. “Experimental Boson Sampling in Arbitrary Integrated Photonic Circuits”. ArXiv:1212.2783 [quant-ph] (2012).