Percolation in Laser Filamentation

Wahb Ettoumi

Author: Wahb Ettoumi
Affiliation: GAP-Biophotonics, University of Geneva, Switzerland.

Other coauthors of the PRL paper: Jérôme Kasparian (left) and Jean-Pierre Wolf.

The discovery of laser filamentation can be attributed to M. Hercher [1], who observed damage tracks along the laser path in crystals. Later, the filamentation phenomenon was shown for a laser propagating in air (For a review, see Ref.[2]). For the first time, the optical power at hand could allow one to witness a new type of light propagation based on the Kerr effect, a non-linear phenomenon which acts as a focusing lens and overcomes the beam natural diffraction. As a consequence, the propagation medium is ionized, and produces a plasma filament of tens of microns wide, which can be sustained over meters in air.

The beam collapse is eventually stopped by this newly created plasma, which acts as a defocusing lens, and counter-balances the Kerr effect. This subtile equilibrium is broken when the energy losses along the propagation cause the Kerr effect to be negligible again, and the beam finally diffracts.

Image 1

For powers largely exceeding the critical power needed for the observation of a single filament, the initial beam inhomogeneities seed the emergence of many single filaments, as if many small beamlets were each undergoing filamentation. In 2010, an experimental campaign in Dresden [3] was aimed at characterizing the number of filaments with respect to the initial power (Image 1). However, we only noticed until recently the similarity between the laser burns obtained there on photographic paper and the numerical simulations of systems relevant to the statistical physics community. More particularly, we decided to probe the resemblance of the experimental recordings with percolation patterns.

Initially, the laser beam exhibits a noisy profile, but with rather small fluctuations around an average fluence. As the laser propagates, the Kerr effect drives the light to concentrate more and more around the peaks of the highest amplitude, leading to the clustering of light into islands of different sizes, each one potentially holding one or multiple filaments.

Image 2

At larger distances, typically of several meters in usual experimental setups, the energy flux towards the inner cores of the multiple filaments causes the fluence islands to shrink in size, destroying the previously well held light clusters into smaller, disconnected parts (Image 2). At higher distances, the losses due to the medium's absorption eventually wipe out the smallest clusters.

Because of the lack of experimental data, we turned to the numerical simulation of the non-linear Schrödinger equation, well-known for its remarkable agreement with real filamentation experiments. We showed [4] that the precise way light clusters depending to each other is a phase transition: we measured a set of seven critical exponents governing the pattern dynamics at the vicinity of the transition between a fully connected state and a non-connected one. The similarity with the percolation universality class is striking, but the clusters' size distribution in the laser case exhibits a finite cut-off physically associated to fluence islands withholding a single filament (their area is approx. 2 mm²).

An interesting issue subsists, however. The finite-size scaling techniques we used are intrinsically equilibrium methods, so that we implicitely assumed that each slice during the laser propagation could be treated as a statistical equilibrium of a given system. But the laser obviously evolves in time, and is not trapped into a quasi-stationary state, nor a fluctuating equilibrium. A hand waving argument can be drawn by saying that the evolution is quasi-static, but a correct theoretical argument remains to be found.

References:
[1] M. Hercher, "Laser-induced damage in transparent media". Journal of Optical Society of America, 54, 563 (1964).
[2] A. Couairon, A. Mysyrowicz, "Femtosecond filamentation in transparent media". Physics Report, 441, 47-189 (2007). Abstract.
[3] S. Henin, Y. Petit, J. Kasparian, J.-P. Wolf, A. Jochmann, S. D. Kraft, S. Bock, U. Schramm, R. Sauerbrey, W. M. Nakaema, K. Stelmaszczyk, P. Rohwetter, L. Wöste, C.-L. Soulez, S. Mauger, L. Bergé, S. Skupin, "Saturation of the filament density of ultrashort intense laser pulses in air". Applied Physics B, 100, 77 (2010). Abstract.
[4] W. Ettoumi, J. Kasparian, J.-P. Wolf, "Laser Filamentation as a New Phase Transition Universality Class". Physical Review Letters, 114, 063903 (2015). Abstract.

Efficient Photon Collection from a Nitrogen Vacancy Center in a Circular Bullseye Grating in Diamond

[From left to right] Luozhou Li, Edward Chen and Dirk Englund.

Authors: Luozhou Li, Edward Chen, Dirk Englund

Affiliation: Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA.

Link to Quantum Photonics Laboratory >>

The nitrogen-vacancy center (NV) [1] behaves much like an atom trapped in the diamond lattice. Because of the high band gap and the mostly spin-free composition of the diamond host, the NV is well isolated from the environment, so it shows well-behaved atom-like properties. Most importantly, it’s possible to optically prepare and measure the long-lived states of the associated electron and nuclear spins. NVs are potentially promising building blocks for a large-scale quantum network where the optical addressability of the NV allows flying qubits, or photons, to connect nodes of this network together. One of the fundamental bottlenecks for this to be made into a reality is the flux of photons collected from an NV, which determines how quickly the NV’s spin state can be measured and compared: the more fluorescent photons that are collected, the faster new connections can be made. The same photon collection limitation is also true for using the NV as a highly sensitive quantum sensor, where the sensitivity to electric, magnetic and temperature fields increase with increased photon collection. Thus, higher photon detection of the NV’s photoluminescence is of central importance to many NV quantum technologies, such as communication, computing, and even sensing.

In our recent work [2], we introduce a circular “bullseye” grating in diamond (Figure 1), which enables record-high photon collection from the nitrogen-vacancy (NV) color center. The bullseye grating consists of concentric slits etched into a diamond membrane [3], which itself is about half of a wavelength in thickness. The grating period satisfies the second-order Bragg condition, giving rise to the scattering of light out of the membrane. The scattered light from each grating interferes constructively out of the plane and into the far field, thereby enabling significantly higher collection efficiency. With this circular grating, we have shown that it’s possible to collect about an order of magnitude more fluorescence than is possible from an NV in un-patterned diamond.

Figure 1: (a) Illustration of an array of diamond bullseye gratings adjacent to a microwave strip line. (b) Schematic of the circular grating. ‘a’ denotes the lattice constant and ‘gap’ the air spacing between circular gratings. (c) Simulated electric field intensity (log scale) in the x = 0 plane with air above and glass below the diamond. A dipole emitter was placed in the center of the bullseye grating, and was oriented along the horizontal direction.

Achieving higher collection efficiency from the NV impacts several applications such as improved sensing of static or dynamic electromagnetic fields just outside the diamond, higher luminosity room-temperature single photon sources, and better quantum memories for quantum computing and networking. For example, NV researchers [4] have recently shown that the NV is even sensitive to changes of single proton spins, paving the way for magnetic resonance imaging of individual molecules in liquid — and this application would be improved by better fluorescence collection from the NV.

The efficient photon collection should allow for a range of new measurements, such as non-demolition measurements of NV spins — i.e., you could make a measurement and then act back on the NV spin state. We’re also using the efficient collection for medium-scale quantum registers, which would contain on the order of tens of qubits each, and for quantum sensing.

References:
[1] Marcus W. Doherty, Neil B. Manson, Paul Delaney, Fedor Jelezko, Jörg Wrachtrup, Lloyd CL Hollenberg, "The nitrogen-vacancy colour centre in diamond." Physics Reports, 528, 1-45 (2013). Abstract.
[2] Luozhou Li, Edward H. Chen, Jiabao Zheng, Sara L. Mouradian, Florian Dolde, Tim Schröder, Sinan Karaveli, Matthew L. Markham, Daniel J. Twitchen, and Dirk Englund, "Efficient photon collection from a nitrogen vacancy center in a circular bullseye grating." Nano letters, 15, 1493 (2015). Abstract.
[3] Luozhou Li, Igal Bayn, Ming Lu, Chang-Yong Nam, Tim Schröder, Aaron Stein, Nicholas C. Harris, Dirk Englund. "Nanofabrication on unconventional substrates using transferred hard masks." Scientific reports, 5, Article number 7802 (2015). Article.
[4] A. O. Sushkov, I. Lovchinsky, N. Chisholm, R. L. Walsworth, H. Park, M. D. Lukin, "Magnetic resonance detection of individual proton spins using quantum reporters." Physical Review Letters, 113, 197601 (2014). Abstract.

Novel Electromagnetic Cavities: Bound States in the Continuum

Thomas Lepetit (left) and Boubacar Kanté (right)

Authors: Thomas Lepetit and Boubacar Kanté 

Affiliation: Department of Electrical and Computer Engineering, University of California San Diego, USA. 

In the last 10 years, an intense research effort has been devoted to bringing all-optical signal generation and processing on chip to realize true photonic integrated circuits (PICs). PICs are at their core made of waveguides, which transfer signals to different devices on the circuit, and cavities, which process signals for different functionalities [1]. First, linear devices such as couplers, splitters, and add-drop filters were developed and, more recently, nonlinear devices such as frequency combs, nanolasers, and optical rams have been demonstrated [2-4]. Overall, progress has resulted in devices with increased functionalities that work at lower power and are more compact.

Cavities are an essential building block of PICs because they provide enhanced light-matter interaction. Currently, the most mature technology is based on a silicon on insulator platform and ring resonators. Typically, these dielectric resonators are several microns in diameter [5]. However, due to the difficulty of integration with much smaller electronic components, other technologies such as plasmonics have started to be investigated. One of the main advantages of plasmonic devices, which are made of noble metals such as gold and silver, is that their size is not limited by the wavelength. For example, plasmonic ring resonators of only several hundred nanometers in diameter have been demonstrated [6]. Generally, cavities are characterized by their quality factor Q, which is a measure of their capacity to store signals for a long time. At present, dielectric cavities have reached quality factors of 10⁶, which are only limited by radiation losses coming from sidewall roughness, but typically have a footprint of 80 μm². In contrast, plasmonic cavities can have a footprint as low as 1.25 μm² but their quality factors are usually below 10², being limited by thermal losses coming from conduction electrons. Therefore, there is a need for novel cavity designs that can simultaneously achieve high quality factors and low footprints.

Figure 1: Cross-section of the electric field magnitude for the coupled resonators system (Half of it). Resonator 1, whose inner radius is zero, is on top and resonator 2, with a non-zero inner radius, is at the bottom. The symmetry plane on the right of each plot denotes the symmetry plane of interest. Odd modes are mostly confined in resonator 1 and even modes mostly in resonator 2.

Recently, we have demonstrated the possibility of making electromagnetic cavities using a different concept, namely bound states in the continuum (BICs) [7]. BICs were first proposed in 1929 in the context of quantum mechanics by Von Neumann and Wigner [8]. They surprisingly showed that bound states can exist above the continuum threshold, i.e., there are states that do not decay even in the presence of open decay channels. However, due to the theoretical nature of the first proposal, BICs did not become fully appreciated until 1985 when Friedrich and Wintgen showed that they could be interpreted as resulting from the interference of two distinct resonances [9]. In this picture, one resonance traps the other and thus one quality factor decreases while the other one tends to infinity. Since BICs are essentially a wave phenomenon they also appear in electromagnetics where they translate for lossless dielectrics into an infinite quality factor. As a proof of concept, we have designed and measured a BIC in the microwave range using a periodic metasurface [10-11].

BICs are intrinsically sensitive to perturbations as they only exist at a single point in phase space. This is very useful for sensing applications but detrimental for most others. To obtain an extended BIC, we designed a system with two quasi-degenerate BICs. We achieved this by considering a unit cell with two resonators, a disk and a ring (see Figure 1). Odd modes of the disk resonator interfere and lead to one BIC and even modes of the ring resonator interfere and lead to another BIC. We use ceramic resonators of high-permittivity (ε_r=43±0.75) and they are thus only slightly coupled. Experimentally, to limit the fabrication dispersion inherent to a large array, we made the measurements in a rectangular metallic waveguide (X-band, 8.2-12.4 GHz). It is possible because such a guided setup is equivalent to an infinite array at oblique incidence as shown by image theory.

Figure 2: Modes of two dielectric resonators (ε_r=43) in a rectangular metallic waveguide (X-band). Both resonators are cylindrical (r=3.5 mm, h₁=2.25 mm, h₂=3.0 mm) and the second has a non-zero inner radius. a) Resonance frequencies vs. inner radius for even and odd modes. b) Quality factor vs. inner radius for even and odd modes for lossless and lossy resonators.

We explored phase space along a line, by varying the inner radius of the ring resonator, and showed the presence of two avoided resonance crossings (see Figure 2a), which are typical of BICs [12]. As a result, there is an extended region of phase space where the quality factor tends to infinity (see Figure 2b). BICs only serve to cancel radiation losses and in the presence of thermal losses these are the limiting factor. At present, this scheme is therefore practical only for dielectrics but it could be extended to plasmonics by introducing gain materials to achieve loss-compensation.

Beyond the fundamental interest on the limit of quality-factors given a certain volume, there is a sustained interest in reducing the footprint of many cavity-based devices for future PICs. Tailoring the optical potential further, for example by moving away from perfectly periodic structures [13], opens the possibility improving the field confinement and thus shrink devices. Our work is a first step in this promising direction.

References:
[1] L. A. Coldren, S. W. Corzine, and M. Mašanović, “Diode Lasers and Photonic Integrated Circuits”, 2nd edition, Wiley (2012).
[2] Fahmida Ferdous, Houxun Miao, Daniel E. Leaird, Kartik Srinivasan, Jian Wang, Lei Chen, Leo Tom Varghese, Andrew M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs”, Nature Photonics, 5, 770 (2011). Abstract.
[3] M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, Y. Fainman, “Thresholdless nanoscale coaxial lasers”, Nature 482, 204 (2012). Abstract.
[4] Eiichi Kuramochi, Kengo Nozaki, Akihiko Shinya, Koji Takeda, Tomonari Sato, Shinji Matsuo, Hideaki Taniyama, Hisashi Sumikura, Masaya Notomi, “Large-scale integration of wavelength-addressable all-optical memories on a photonic crystal chip”, Nature Photonics 8, 474 (2014). Abstract.
[5] W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators”, Laser Photonics Review 6, 47 (2012). Abstract.
[6] Hong-Son Chu, Yuriy Akimov, Ping Bai, Er-Ping Li, “Submicrometer radius and highly confined plasmonic ring resonator filters nased on hybrid metal-oxide-semiconductor waveguide”, Optics Letters, 37, 4564 (2012). Abstract.
[7] Thomas Lepetit, Boubacar Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum”, Physical Review B Rapid Communications, 90, 241103 (2014). Abstract.
[8] J. von Neumann and E. Wigner, “On unusual discrete eigenvalues”, Zeitschrift für Physik 30, 465 (1929).
[9] H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum”, Physical Review A, 32, 3231 (1985). Abstract.
[10] Boubacar Kanté, Jean-Michel Lourtioz, André de Lustrac, “Infrared metafilms on a dielectric substrate”, Physical Review B, 80, 205120 (2009). Abstract.
[11] Boubacar Kanté, André de Lustrac, Jean Michel Lourtioz, “In-plane coupling and field enhancement in infrared metamaterial surfaces”, Physical Review B, 80, 035108 (2009). Abstract.
[12] Chia Wei Hsu, Bo Zhen, Jeongwon Lee, Song-Liang Chua, Steven G. Johnson, John D. Joannopoulos, Marin Soljačić, “Observation of trapped light within the radiation continuum”, Nature, 499, 188 (2013). Abstract.
[13] Yi Yang, Chao Peng, Yong Liang, Zhengbin Li, Susumu Noda, “Analytical perspective for Bound States in the Continuum in Photonic Crystal Slabs”, Physical Review Letters, 113, 037401 (2014). Abstract.

The Plasmoelectric Effect: A New Strategy for Converting Optical Energy into Electricity

Matthew Sheldon

Author: Matthew Sheldon

Affiliation: Department of Chemistry, Texas A&M University, USA.

Link to Sheldon Research Group >>

A plasmon resonance is a remarkable optical phenomenon that occurs in metallic nanostructures and other nanoscale materials that have high electrical conductivity. As reported in 'Science' on October 30 [1], we have demonstrated a new way to use plasmon resonances to generate electrical potentials during optical excitation. Our work could lead to new ways of converting optical energy into electrical energy, and may guide new opportunities in the very active research areas of plasmonics and nanophotonics.

A plasmon resonance results from the oscillations of electrons (or other electrical carriers) lining up with the oscillating electric field of incident radiation. This resonance causes significant concentration of light energy within the small sub-wavelength volume defined by the nanostructure. Because the resonant frequency can be tailored by controlling the nanoscale geometry, plasmonic materials have been the subject of considerable scientific activity for a host of applications that benefit from the ability to tune and concentrate radiation, such as Raman spectroscopy, cell labeling, sub-wavelength optical communication, or enhanced light trapping in solar cells, to list a few examples [2]. However, much of the confined optical energy is quickly absorbed by the metal and converted to heat. This heating is generally regarded as a limitation for optical applications.

Despite this loss of optical energy as heat, we questioned whether the strong plasmonic concentration of energy could still be utilized to perform electrical work. Electrical work can be understood as the movement of electrons through a circuit load, so it seemed natural to wonder if the plasmon resonance, which fundamentally results from the coupling of light to the motion of electrons, could also move electrons through a circuit. As reported in Science on October 30th [1], we discovered a mechanism by which optical absorption in plasmonic resonances indeed produces an electrical potential, a necessary first step towards performing useful electrical work. We have labeled this phenomenon the ‘plasmoelectric effect’. In conjunction with a thermodynamic model we developed, our analysis shows how a plasmonic resonance can act as a heat engine that uses thermal energy from the absorption of light to move electrons and produce static electric potentials.

Currently, the photovoltaic effect is the primary mechanism used in technology for the production of electrical potentials from the absorption of light, i.e. photo-voltages. The photovoltaic effect is the generation of excess electrical carriers in semiconductors during optical excitation with energy greater than the band gap energy. Our discovery, the plasmoelectric effect, is a fundamentally different mechanism for generating an electrical potential, and instead results from the dependence of the plasmon resonance frequency on electron density in conductors.

Recent works from other researchers studying plasmonic systems [3-5] have demonstrated that it is possible to tune the plasmon resonance frequency of a nanostructure by modulating electron density. Specifically, these researchers applied a static electric potential to inject or remove electrons from resonant structures, and they observed a shift to higher or lower frequency, respectively, of the plasmonic absorption resonance. In essence, the electrical state of the conductor, whether it is charged positively, negatively, or neutral, is coupled with the frequency of the plasmonic absorption. This behavior is analogous to how the resonant pitch of a musical instrument, such as a flute, would change if you modify the density of the air in the acoustic cavity.

Inspired by these experiments, we considered the extent to which the optical absorption, the plasmon resonance frequency, and the charge state are linked in this way, and if the reverse of this behavior would also occur. That is, can optical excitation with off-resonant light cause a change in the electron density of a plasmonic structure that shifts the plasmonic absorption into resonance with the illumination, and thereby induce an electrical potential? Considering the acoustic analogy above, this would be like the chamber of a flute adopting a slightly modified air density in order to become resonant with a loud pitch playing nearby that would otherwise be slightly out of tune.

To probe this possibility experimentally, we monitored the electric potential of a conductive surface coated with plasmonic Au nanoparticles using Kelvin probe force microscopy (KPFM). For KPFM a conductive atomic force microscope (AFM) tip is maintained a few nanometers above a sample surface, and the electrical potential between the tip and sample is measured. During KPFM experiments we also illuminated the nanoparticles with a tunable laser, varying the output from higher frequency to lower frequency through the plasmon resonance. We observed that higher frequency light caused negative surface potentials and that lower frequency light caused positive surface potentials, but there was no potential measured when the incident light was the same frequency as the plasmon resonance. This is the exact behavior expected if the nanoparticles are adjusting charge density so that the plasmon resonance is better matched with the frequency of the optical excitation.

Our report also details a thermodynamic model that anticipates this behavior for plasmonic materials. We show how the condition of minimum free energy, the preferred thermodynamic state of a system, corresponds to a configuration of charge density that modulates the plasmon resonance frequency in order to maximize the amount of heat produced via optical absorption. However, the energy required to electrically charge the structure moderates how much the plasmon resonance can shift. Therefore, for a given optical intensity, single frequency light induces a specific charge state that balances these counteracting effects. In general, during illumination a plasmonic structure will only remain neutral if incident light is the same frequency as the plasmon resonance of the neutral structure.

To show that the behavior is general to plasmonic systems, we also measured the optical response of periodic arrays of nanoscale holes in thin gold films that have strong, tunable plasmonic resonances across the visible spectrum based on the hole pitch. These fabricated hole arrays also displayed electrical potential trends consistent with our description of the plasmoelectric effect, as summarized in Fig. 1.

Figure 1: Plasmoelectric effect (a) Schematic of a metal nanoparticle that becomes electrically charged by illumination. (b) Electron microscopy image of the metal nanocircuit, composed of an array of nanoscale holes in a 20-nm-thin gold film. The scale bar is 500 nanometer. (c) Measured optical absorption spectra for metal nanocircuits with different spacings between the holes (175, 225, 250, and 300 nm). (d) Electrical potential of the nanocircuits in (c) as a function of wavelength of the incident light. The measured potentials range from -100 mV to +100 mV as the wavelength of the incident light is tuned from high frequency blue light to low frequency red light.

We believe our results are exciting for two fundamental reasons: First, we have demonstrated a new way to generate an electrical potential by the absorption of radiation. There is general interest in materials that can convert light to electrical potentials for sensing and for optical power conversion, for example, and our report lays the groundwork for these possible applications. Second, we believe our analysis provides more insight into the basic thermodynamic behavior of plasmonic materials. Given the very active research in this area by scientists from many different disciplines, these insights may open new opportunities in plasmonics research.

References:
[1] Matthew T. Sheldon, Jorik van de Groep, Ana M. Brown, Albert Polman, Harry A. Atwater, "Plasmoelectric potentials in metal nanostructures". Science, 346, 828–831 (2014). Abstract.
[2] Albert Polman, "Plasmonics Applied". Science, 322, 868–869 (2008). Abstract.
[3] Carolina Novo, Alison M. Funston, Ann K. Gooding, Paul Mulvaney, "Electrochemical Charging of Single Gold Nanorods". Journal of the American Chemical Society, 131, 14664–14666 (2009). Abstract.
[4] S. K. Dondapati, M. Ludemann, R. Müller, S. Schwieger, A. Schwemer, B. Händel, D. Kwiatkowski, M. Djiango, E. Runge, T. A. Klar, "Voltage-Induced Adsorbate Damping of Single Gold Nanorod Plasmons in Aqueous Solution". Nano Letters, 12, 1247–1252 (2012). Abstract.
[5] Guillermo Garcia, Raffaella Buonsanti, Evan L. Runnerstrom, Rueben J. Mendelsberg, Anna Llordes, Andre Anders, Thomas J. Richardson, Delia J. Milliron, "Dynamically Modulating the Surface Plasmon Resonance of Doped Semiconductor Nanocrystals". Nano Letters, 11(10), 4415–4420 (2011). Abstract.

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

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

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

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

Introduction:

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

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

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

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

Results:

Device

To fabricate the superconducting cavities in coplanar waveguide geometry, we use an alloy of molybdenum and rhenium with superconducting transition temperature of 8.1 K. Using the dry transfer technique, we place a few layer thick graphene mechanical resonator near the coupler forming coupling capacitor for the cavity. Figure 1(a) shows a false color scanning electron microscope image of a device with a 10 nm thick multilayer graphene resonator coupled to a superconducting cavity. Figure 1(b) shows an equivalent schematic diagram with graphene resonator acting as a capacitor (C_g ) between the superconducting cavity (formed by L_sc and C_sc ) and the external microwave source. By cooling these cavities to very low temperatures (14 mK), we measured internal quality factor as high as 107,000.

FIG. 1: Coupling of a multilayer graphene mechanical resonator to a superconducting cavity. (a) A tilted angle scanning electron micrograph (false color) near the coupler showing 4 μm diameter multilayer (10 nm thick) graphene resonator (cyan) suspended 150 nm above the gate. (b) Schematic lumped element representation of the device with the equivalent lumped parameters as C_sc ≈ 415 fF and L_sc ≈ 1.75 nH.

Mechanical motion readout sensitivity

To the first order, the superconducting microwave cavity can be thought simply as motional transducer for the graphene resonator. To readout the motion of the graphene resonator, we inject a microwave near the cavity frequency given by

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

Optomechanical coupling

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

By sending two microwave signals, a probe signal ω_p (near the cavity resonance frequency ω_c ) and another signal at ω_d (detuned by mechanical frequency ω_m , such that ω_d = ω_c +ω_m ), one can apply a a radiation pressure force on the mechanical resonator. This radiation pressure force beats at the mechanical resonance frequency, leading to coherent driven motion of the mechanical resonator, as shown schematically by process 1 in Figure 2(a). In presence of the significant optomechanical coupling, this coherent drive of the mechanical resonator down-converts the detuned drive photons exactly at the probe frequency (pink arrow) shown by process 2 in Figure 2(a). These two signals at probe frequency interfere with each other leading to a transmission window, appearing as a sharp peak in the cavity response, shown in Figure 2(b). This phenomena is known as "optomechanically induced transparency" (OMIT) and is a signature of the optomechanical coupling between the graphene mechanical resonator and the superconducting cavity [21-23]. As this effect rely on the coherent driven motion of the graphene mechanical resonator, the width of the transparency window is set by the mechanical resonator's linewidth as shown in the inset of Figure 2(b). Using the radiation pressure force driving, we measure the quality factor of the graphene resonator as high as 220,000.

FIG. 2: Optomechanically induced transparency (OMIT). (a) Schematic illustrate OMIT features in terms of the interference of the probe field (black arrow) with the microwave photons that are cyclically down- and then up- converted by the optomechanical interaction (pink arrow). (b) Measurement of the cavity reflection |S₁₁| in presence of sideband detuned drive tone. A detuned drive at ω_c+ω_m results in a window of optomechanically induced reflection (OMIR) in the cavity response. Inset: Zoom of the OMIR window. (c) Measurement of the cavity reflection |S₁₁| with a stronger detuned drive. At the center of the cavity response, the reflection coefficient exceeds 1, corresponding to mechanical microwave amplification of 17 dB by the graphene resonator.

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

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

Summary and outlook:

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

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

Physics Nobel Prize 2014: Blue LED

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

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

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

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

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

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

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

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

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

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

When Magnetism Meets Optics

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

Authors: 

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

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

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

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

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

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

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

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

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


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

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

Bio-inspired Plasmonic Structures Built on Virus Capsids and DNA Origami Tiles

Debin Wang (left) and James J. De Yoreo

Authors: Debin Wang^1,2, James J. De Yoreo^1,2

Affiliation:
¹Materials Sciences Division and the Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California, USA.
²Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington, USA.

The use of biomolecular scaffolds to direct the organization of inorganic or organic nanomaterials addresses the grand challenge of assembling multiple functional units with precise control over their spatial arrangement at the molecular level [1-3]. Biomolecules, such as peptides, proteins, and nucleic acids have all been used as building blocks for bottom-up assembly of intricate structures thanks to their inherent chemical and biological addressability, structural precision, and efficiency of synthesis [4].

In photosynthetic bacteria, light-harvesting units are organized with molecular-level precision around the photochemical units [5-6]. In this way, they generate antenna complexes that ensure efficient photon absorption and energy transfer. In a similar way, biomimetic assembly of plasmonic nanostructures can provide molecular-level spatial precision, creating potential improvements in efficiency of light-harvesting platforms, light-emitting devices, and optical sensors [7-8].

Recently, we reported the bottom-up assembly of hierarchical plasmonic nanostructures using DNA origami tiles and MS2 virus capsids [9]. These bio-inspired structures serve as programmable scaffolds that provide molecular level control over the distribution of fluorescent dye molecules and nanometer-scale control over their distance from a gold nanoparticle antenna (Fig. 1). While previous studies on DNA origami assembly of plasmonic nanostructures focused on the distance-dependent response of single fluorescent dye molecules [10-11], these hybrid structures allowed us to investigate the plasmonic response of an entire ensemble of fluorescent molecules.

Figure 1. Bio-inspired assembly of plasmonic nanostructures using DNA origami and MS2 virus capsids. TEM imaging and profile analysis confirmed tight control over the distance between fluorophore labelled virus capsids and gold nanoparticle antennae. Correlated Raman-AFM imaging provided direct single-particle measurements of fluorescence intensities. Adapted with permission from ACS Nano 2014, 8, 7896-7904. Copyright 2014 American Chemical Society.

We studied the collective plasmon-coupled response of fluorophore-labeled capsids to the presence of an AuNP as a function of their separation distance. We demonstrated tight control over this distance by exploiting the programmable nature of DNA origami templates and the ability to site-specifically modify MS2 virus capsids (Fig.1). Using finite-difference time-domain (FDTD) numerical simulations in conjunction with atomic force microscopy (AFM) and correlated scanning confocal fluorescence microscopy, we then showed that the utilizing a 3D ensemble of dye molecules can effectively suppress the fluorescence quenching in the single molecule quenching regime, presumably due to the size effect of the capsid scaffold (Fig. 1). FDTD simulations also showed that increasing the size of the AuNPs to be commensurate with that of the capsids optimizes the fluorescence enhancement (Fig.2).

Figure 2. Finite-difference-time-domain (FDTD) numerical simulations predict the plasmon-coupled response of the bio-inspired nanostructures. Adapted with permission from ACS Nano 2014, 8, 7896-7904. Copyright 2014 American Chemical Society.

Looking forward, we plan to use this bio-inspired light harvesting platform to explore the effect of variations in nanoparticle size, choice of fluorophore, arrangement of fluorophores, and even the capsid shape on device performance. More generally, our assembly strategy establishes the possibility of using biological scaffolds to build hierarchical plasmonic nanostructures to address the need for energy harvesting in solar energy applications.

References:
[1] Trevor Douglas, Mark Young, "Viruses: Making Friends with Old Foes". Science, 312, 873-875 (2006). Abstract.
[2] James J. Storhoff, Chad A. Mirkin, "Programmed Materials Synthesis with DNA". Chemical Reviews, 99, 1849-1862 (1999). Abstract.
[3] Andre V. Pinheiro, Dongran Han, William M. Shih, Hao Yan, "Challenges and Opportunities for Structural DNA Nanotechnology". Nature Nanotechnology, 6, 763-772 (2011). Abstract.
[4] Shuguang Zhang, "Fabrication of Novel Biomaterials through Molecular Self-Assembly". Nature Biotechnology, 21, 1171-1178 (2003). Abstract.
[5] Svetlana Bahatyrova, Raoul N. Frese, C. Alistair Siebert, John D. Olsen, Kees O. van der Werf, Rienk van Grondelle, Robert A. Niederman, Per A. Bullough, Cees Otto, C. Neil Hunter, "The Native Architecture of a Photosynthetic Membrane". Nature, 430, 1058-1062 (2004). Abstract.
[6] Pascal Anger, Palash Bharadwaj, Lukas Novotny, "Enhancement and Quenching of Single-Molecule Fluorescence". Physical Review Letters, 96, 113002 (2006). Abstract.
[7] Stephan Link, Mostafa A. El-Sayed, "Size and Temperature Dependence of the Plasmon Absorption of Colloidal Gold Nanoparticles". Journal of Physical Chemistry B, 103, 4212-4217 (1999). Abstract.
[8] Joanna Malicka, Ignacy Gryczynski, Zygmunt Gryczynski, Joseph R Lakowicz, "Effects of Fluorophore-to-Silver Distance on The Emission of Cyanine-Dye-Labeled Oligonucleotides". Analytical Biochemistry, 315, 57-66 (2003). Abstract.
[9] Debin Wang, Stacy L. Capehart, Suchetan Pal, Minghui Liu, Lei Zhang, P. James Schuck, Yan Liu, Hao Yan, Matthew B. Francis, James J. De Yoreo, "Hierarchical Assembly of Plasmonic Nanostructures Using Virus Capsid Scaffolds on DNA Origami Templates". ACS Nano, 8, 7896-7904 (2014). Abstract.
[10] G. P. Acuna, F. M. Möller, P. Holzmeister, S. Beater, B. Lalkens, P. Tinnefeld, "Fluorescence Enhancement at Docking Sites of DNA-Directed Self-Assembled Nanoantennas". Science, 338, 506-510 (2012). Abstract.
[11] Guillermo P. Acuna, Martina Bucher, Ingo H. Stein, Christian Steinhauer, Anton Kuzyk, Phil Holzmeister, Robert Schreiber, Alexander Moroz, Fernando D. Stefani, Tim Liedl, Friedrich C. Simmel, Philip Tinnefeld, "Distance Dependence of Single-Fluorophore Quenching by Gold Nanoparticles Studied on DNA Origami". ACS Nano, 6, 3189-3195 (2012). Abstract.

Single Photon Transistor Mediated by Rydberg Interaction

From Left to Right: Hannes Gorniaczyk, Christoph Tresp, Johannes Schmidt, Ivan Mirgorodskiy, Sebastian Hofferberth

Authors: Christoph Tresp, Ivan Mirgorodskiy, Hannes Gorniaczyk, Sebastian Hofferberth 

Affiliation:
Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Germany.

Link to Rydberg Quantum Optics, Emmy Noether Group >>

Introduction:

In analogy to their electronic counterparts, all-optical switches and transistors are required as basic building blocks for both classical and quantum optical information processing [1,2]. Reaching the fundamental limit of such devices, where a single gate photon modifies the transmission or phase accumulation of multiple source photons, requires strong effective interaction between individual photons. Engineering sufficiently strong optical nonlinearities to facilitate photon-photon interaction is one of the key goals of modern optics. Immense progress towards this goal has been made in a variety of systems in recent years. Most prominent so far are cavity QED experiments where a high finesse resonator enhances the interaction between light and atoms [3,4] or artificial atoms [5,6].

In this work, we demonstrate a free-space all-optical transistor operating on the single photon level using a novel approach to realize effective photon-photon interaction [7], which is based on mapping the strong interaction of Rydberg atoms [8] onto slowly travelling photons using electromagnetically induced transparency [9]. This technique has already been used to demonstrate highly efficient single-photon generation [10], attractive interaction between single photons [11], entanglement generation between light and atomic excitations [12], and most recently single-photon all-optical switching [13].

However, demonstration of amplification, that is, controlling many photons with a single one, has so far only been achieved in a cavity QED setup [14]. Gain > 1 is one of the key properties of the electric transistor that lies at the heart of its countless applications. In our experiment, we demonstrate an all-optical transistor with optical gain G > 10 [15]. Similar results have been obtained by the group of G. Rempe, their results have been published in parallel to ours [16].

Experiment:

The level scheme and geometry of our transistor are illustrated in Fig. 1 (a, b). Photons in the weak gate pulse are stored as Rydberg excitations in an atomic ensemble by coupling the ground state |g> to the Rydberg state |r_g> via the strong gate control field. After this storage process, a second weak pulse, the source pulse, is sent through the medium at reduced velocity due to EIT provided by the source control laser coupling to the Rydberg state |r_s>.

FIG. 1: (a) Level scheme, (b) simplified schematic, and (c) pulse sequence of our all-optical transistor. (d) The absorption spectrum for the source field (dots) over the full intermediate state absorption valley shows the EIT window on resonance; the gate field spectrum (circles) is taken around the two-photon resonance at Δ = 40 MHz. The solid lines are fits to the EIT spectra.

In the absence of the gate pulse, source photons travel through the transparent medium (Fig. 1d). If a gate photon has been stored, the strong interaction between the two Rydberg states destroys the EIT condition for the source photons in the medium, resulting in absorption. To observe this conditional switching, we record the number of transmitted source photons in a time interval tint after the gate excitation pulse, cf. Fig. 1 (c). For the experimental realization of this scheme, we prepare 2.5 X 10^{4 87}Rb atoms at a temperature of T = 40 µK in an optical dipole trap. All four lasers required for the transistor scheme are focused into this medium along a single direction (Fig. 1b). The weak gate and source pulses are recorded on single photon counters.

Results:

We first investigate the relative attenuation of a weak source pulse as a function of mean incident gate photons. In Fig. 2 (a) we plot the switch contrast in the source beam transmission as a function of the mean incoming gate photon number. For an average gate photon number of N_g,in = 1.04(3), we observe a switch contrast C_coh = 0.39(4). The switch contrast is mainly determined by the Poissonian statistics of our coherent gate photons, which sets a fundamental upper bound. In other words, a perfect switch with coherent gate photons has a switch contrast C_coh = 1 - exp(-N_g,in) (dashed line in Fig. 2 (a)). How close our switch approaches this fundamental limit depends on the gate photon storage efficiency and the source attenuation caused by a single gate excitation. In Fig. 2 (b) we plot the switch contrast versus the mean number of stored gate photons, which is smaller than the mean incident gate photon number due to not perfect gate photon storage. Finally, by again taking the Poissonian statistics of the input light into account, we extrapolate the switch contrast caused by a single stored excitation to be C_exc = 0.9.

FIG. 2: Switch contrast (red) as function of (a) mean number of incident gate photons and (b) mean number of stored photons. The dashed line indicates the fundamental limit set by the photon statistics of the coherent gate input. Black data points represent the calculated switch contrast expected for (a) one-, two- and three-photon Fock input states or (b) deterministic single and two stored gate excitations.

Next, we investigate how many source photons can be switched by our system. To quantify the gate-induced change in source transmission, we consider the optical gain
G = N_s,out^{no gate} - N_s,out^{with gate}. In Fig. 3 (a), we plot the measured optical gain for an average input of gate photons N_g,in = 0.75(3). For this gate input, we observe a maximum optical gain G(N_g,in = 0.75) = 10(1). Further increase of the optical gain at fixed gate input is limited by the self-blockade of the source beam, which results in nonlinear source transmission even in the absence of gate photons [7, 17]. The red (blue) data points in Fig. 3 (b) show the source photon transfer function when N_g,in = 0 (N_g,in = 0.75(3)). For the given integration time the source transmission saturates at 46 photons, which limits the maximum gain we can observe. On the other hand, the self-nonlinearity of the source light does not affect the transistor performance, we observe a constant switch contrast of C = 0.22(3), consistent with the mean gate input, even for incoming source photons up to ~250. Based on this robustness, we can again extrapolate the transistor performance for a true single photon gate input (Fig. 3 green line) and a single stored excitation (grey line). For a single excitation, we calculate the maximally achievable optical gain of our current system as G_st = 28(2).

FIG. 3: (a) Optical gain of our transistor, measured for coherent gate input N_g,in = 0.75(3) (blue data), and extrapolated to single photon Fock state input (green line), and single stored excitation (black line). (b) Source photon transfer function without (red) and with coherent gate input N_g,in = 0.75(3) (blue). We observe a constant switch contrast between the two data sets over the whole source input range. The green (black) solid line are again the estimated behavior of the system for a single-photon Fock input state (a single stored excitation). Shaded regions are error estimates.

Discussion and outlook:

In summary, we have demonstrated a free-space single photon transistor based on two-color Rydberg interaction. Further improvements of our system could enable a high optical gain, high efficiency optical transistor, so far only realized in a cavity QED setup [14]. One approach to overcome the self-nonlinearity of the source photons has already been demonstrated by the Rempe group, who employ a two-color Förster resonance in their transistor scheme [16].

A key step towards turning our transistor into device which can perform quantum operations on single or few photons is the retrieval of gate photon(s) after the switch process, which could enable multi-photon entanglement protocols and creation of non-classical light-states with large photon numbers. Finally, our system is a highly sensitive probe for studying Rydberg interaction on the few-particle level [18]. In particular, the combination of two independently controlled Rydberg-EIT schemes enables novel fields of study, such as the interplay between slow light propagation and Rydberg exchange interaction [19], or realization of a two-photon phase gate based on Rydberg-polariton collision [20].

References:
[1] H. John Caulfield and Shlomi Dolev, "Why future supercomputing requires optics". Nature Photonics, 4, 261 (2010). Abstract.
[2] Jeremy L. O'Brien, Akira Furusawa, Jelena Vuckovic, "Photonic quantum technologies". Nature Photonics, 3, 687 (2009). Abstract.
[3] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, H. J. Kimble, "Photon blockade in an optical cavity with one trapped atom". Nature, 436, 87 (2005). Abstract.
[4] Tatjana Wilk, Simon C. Webster, Axel Kuhn, Gerhard Rempe, "Single-Atom Single-Photon Quantum Interface". Science, 317, 488 (2007). Abstract.
[5] P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, A. Imamoglu, "A Quantum Dot Single-Photon Turnstile Device". Science, 290, 2282 (2000). Abstract.
[6] Dirk Englund, Andrei Faraon, Ilya Fushman, Nick Stoltz, Pierre Petroff, Jelena Vuckovic, "Controlling cavity reflectivity with a single quantum dot". Nature, 450, 857 (2007). Abstract.
[7] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, C. S. Adams, "Cooperative Atom-Light Interaction in a Blockaded Rydberg Ensemble". Physical Review Letters, 105, 193603 (2010). Abstract.
[8] M. Saffman, T. G. Walker, K. Mølmer, "Quantum information with Rydberg atoms". Review of Modern Physics, 82, 2313 (2010). Abstract.
[9] Michael Fleischhauer, Atac Imamoglu, Jonathan P. Marangos, "Electromagnetically induced transparency: Optics in coherent media". Review of Modern Physics, 77, 633 (2005). Abstract.
[10] Y. O. Dudin and A. Kuzmich, "Strongly Interacting Rydberg Excitations of a Cold Atomic Gas". Science 336, 887 (2012). Abstract.
[11] Ofer Firstenberg, Thibault Peyronel, Qi-Yu Liang, Alexey V. Gorshkov, Mikhail D. Lukin, Vladan Vuletić, "Attractive photons in a quantum nonlinear medium". Nature, 502, 71 (2013). Abstract.
[12] L. Li, Y. O. Dudin, and A. Kuzmich, "Entanglement between light and an optical atomic excitation". Nature, 498, 466 (2013). Abstract.
[13] Simon Baur, Daniel Tiarks, Gerhard Rempe, Stephan Dürr, "Single-Photon Switch Based on Rydberg Blockade". Physical Review Letters, 112, 073901 (2014). Abstract.
[14] Wenlan Chen, Kristin M. Beck, Robert Bücker, Michael Gullans, Mikhail D. Lukin, Haruka Tanji-Suzuki, Vladan Vuletić, "All-Optical Switch and Transistor Gated by One Stored Photon". Science 341, 768 (2013). Abstract.
[15] H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, S. Hofferberth, "Single-Photon Transistor Mediated by Interstate Rydberg Interactions". Physical Review Letters, 113, 053601 (2014). Abstract.
[16] Daniel Tiarks, Simon Baur, Katharina Schneider, Stephan Dürr, Gerhard Rempe, "Single-Photon Transistor Using a Förster Resonance". Physical Review Letters, 113, 053602 (2014). Abstract.
[17] 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 (2012). Abstract.
[18] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, A. Browaeys, "Direct Measurement of the van der Waals Interaction between Two Rydberg Atoms". Physical Review Letters, 110, 263201 (2013). Abstract.
[19] Weibin Li, Daniel Viscor, Sebastian Hofferberth, Igor Lesanovsky, "Electromagnetically Induced Transparency in an Entangled Medium". Physical Review Letters, 112, 243601 (2014). Abstract.
[20] Alexey V. Gorshkov, Johannes Otterbach, Michael Fleischhauer, Thomas Pohl, Mikhail D. Lukin, "Photon-Photon Interactions via Rydberg Blockade". Physical Review Letters, 107, 133602 (2011). Abstract.