Dropleton – The New Semiconductor Quasiparticle

From Left to Right: (top row) Andrew E. Almand-Hunter, Hebin Li, Steven T. Cundiff, (bottom row) Martin Mootz, Mackillo Kira, Stephan.W. Koch

Authors: Andrew E. Almand-Hunter^1,2, Hebin Li¹, Steven T. Cundiff^1,2, Martin Mootz³, Mackillo Kira³, Stephan.W. Koch³

Affiliation: 
¹JILA, University of Colorado & National Institute of Standards and Technology, Boulder, CO, USA
²Department of Physics, University of Colorado, Boulder, CO, USA
³Department of Physics, Philipps-University Marburg, Germany.

The description of many-particle systems becomes significantly simplified if stable configurations of subsets of the particles can be identified, particularly when the particles are interacting with one another. Examples of stable configurations range from solar systems and galaxies on an astronomical scale [1] to atoms and nuclei on a microscopic scale [2]. In solid-state systems [3], the stable configurations are referred to as “quasiparticles” that have several particle-like features, even though their physical properties are influenced by the interactions. The dropleton is the latest addition to the “periodic table” of quasiparticles in solids, as reported in our recent publication [4].

Extended crystalline solids typically contain more than 10²⁰ interacting electrons per cm³, which makes the quantum many-body problem unsolvable based on overwhelming dimensionality. Therefore, finding quasiparticles is not only extremely useful but also instrumental in order to describe and understand the physics of solids. The “crystal electron’’ – or “Bloch electron’’ – is the simplest quasiparticle of solids. One can attribute a varying mass to an electron inside a crystal, in the same way as a swimmer’s bodyweight seems to change in water. As a quantum feature, crystal electron's effective mass not only depends on the electron-crystal interaction but also on its velocity [3]. When a single electron is removed from an ensemble of many electrons, the missing electron is also a quasiparticle called the “hole’’. The hole simply has the properties of the missing electron, such as a positive elementary charge and a negative effective mass. Conceptually, a hole resembles a bubble, i.e. particle vacancy, in water; its motion is clearly much simpler to track than that of remaining particles.

The quantum mechanically allowed electron-energy regions in solids are commonly known as energy bands and they can be separated by forbidden regions, the band gaps [3]. Without any doping and at low temperatures, a semiconductor is an insulator where all energetically low-lying bands are fully occupied by electrons and all energetically higher bands are completely free. The absorption of light transfers semiconductor electrons from the energetically highest fully occupied band – the valence band – into the originally unoccupied conduction band. Due to their opposite charge, the optically excited conduction-band electron and the simultaneously generated valence-band hole experience an attractive Coulomb interaction which may bind them to a new quasiparticle known as an exciton [5,6]. An exciton is similar in many ways to a hydrogen atom; however, it has a relatively short lifetime since the electron can return from the conduction into the valence band. In this electron-hole recombination process, the excess energy can be emitted as light or it can be transferred to the host crystal as heat.

Under suitable conditions, two excitons can bind into a molecule referred to as biexciton[7,8] which has strong analogies to the hydrogen molecule. Generally, it is an interesting open question if and in which form electron-hole pairs can form even larger clusters with quasiparticle character and how these clusters can be identified spectroscopically. One may distinguish the presence of distinct quasiparticles by the different color resonance they absorb or emit light [9-15], in the same way as atoms and molecules have distinct resonances in the absorption spectrum as fingerprints that provide a positive identification of the “culprit”.

However, identification of semiconductor quasiparticles from light absorption is not as simple as it seems. In general, an ordinary laser pulse only induces electron-hole-pair excitations whereas the more complex quasiparticles are created by the quantum mechanical many-particle interactions, yielding several possible outcomes [16] that blur the quasiparticle resonances. Since the state and the characteristic features of the excited state are very complex and depend sensitively on the detailed excitation conditions, it is generally very difficult to identify the quasiparticle signatures in spectra as long as “only” classical spectroscopy is used.

Figure 1: Classical vs. quantum-optical spectroscopy. In classical spectroscopy (left), the photons (wave symbols) are uncorrelated and they create unbound pairs of electrons (spheres) and holes (open circles). In quantum spectroscopy (right), the photons are correlated (yellow ellipse) such that they directly excite a correlated electron-hole cluster (yellow circle).

To overcome this problem, we developed the concept of quantum-optical spectroscopy [16,17] based on fundamental quantum properties of light. In general, quantized light can be described in terms of photons, i.e. the energy quanta of light. Whereas classical laser light basically contains isolated photons, i.e. no specific photon clusters, such clusters are characteristic for quantum light sources. Most important for our quasiparticle search, the cluster characteristics of the exciting light is directly transferred to the optically generated electron-hole excitations. Consequently, suitable quantum-light sources can e.g. generate predominantly excitons, or biexcitons, or even larger clusters [16,17]. In other words, one can directly excite new quasiparticles with a quantum-light source whose photon clusters match the cluster characteristics of the desired quasiparticle state. Figure 1 illustrates this main difference of classical and quantum-optical laser spectroscopy.

Even though freely adjustable quantum-light sources do not yet exist, we have demonstrated [18] that a large set of classical pump-probe spectra can be robustly projected into the desired quantum-optical spectra. To collect the data, we used short pulses to generate electrons and holes faster than they can decay. In our quasiparticle-search experiments [4], we actually apply pulses of light, produced by a laser, that are only 100 femtoseconds (1fs=10^-15s) in duration. To study the types of quasiparticles that can occur in a semiconductor, beyond just electrons, holes and excitons, we use a strong pulse, known as the “pump” pulse to excite a desired number of electrons and holes. We then monitor how a weak subsequent pulse, known as the “probe” pulse, is absorbed. To observe different types of quasiparticles, we perform these measurements very carefully as we slowly increase the intensity of the pump pulse. Then each pump-pulse intensity labels a probe-absorption spectrum within the massive set of raw data that is the input to the projected quantum-optical spectrum.

When we did this experiment, we noticed already in the raw data that the light began to be absorbed at a new color as the intensity of the pump pulse increased. This new color was distinct from the color corresponding to the creation of an exciton, or of unbound pairs of electrons and holes. We initially ascribed this observation to the formation of a biexciton. However, increasing the intensity of the pump caused this new absorption feature to change color, but very surprisingly, it did so in the wrong direction, namely opposite to the shift of the absorption due to the exciton. This gave us the hint that the new quasiparticles could be dormant underneath the blurred and shifted “biexciton” resonance.

Figure 2: Revealing new energy resonances of Dropletons. Dropleton's binding energy is determined from the light absorption that is sensitive to three-photon correlations. The spectra are plotted as a function of pump pulse's photon number. The red color denotes regions with high absorption.

To reveal which quasiparticle explains this curious behavior, we projected the raw data to an absorption spectrum that is sensitive to three-photon clusters; the quantum-optical absorption spectra are shown Fig. 2 as function of pump power. The energy is expressed in terms of binding energy with respect to exciton resonance. For low photon numbers, we observed only a biexciton resonance that had a fixed binding energy around 2.2meV, as intuitively expected. By increasing the number of photons in the pump pulse, we surprisingly observed that the semiconductor starts to absorb light at completely new colors identified by the steps. We also performed measurements that could reject molecular electron-hole states as an explanation for energy quantization, and demonstrated that the new quasiparticle evolves coherently living up to 25 picoseconds (1ps=10^-12s) [4].

After discovering these new energy resonances, we proceeded to identify the exact form of the new quasiparticle that matches the measured “fingerprints”. Since the quasiparticle has a stronger binding than biexciton it must contain more electron-hole pairs than biexciton, i.e. two. However, there is no quantum theory that can exactly solve the corresponding many-body problem. Therefore, we had to develop a new approach[19] to identify the new quasiparticles. More specifically, we expressed the system energy exactly in terms of pairwise electron-hole correlation function, instead of electron and hole densities that is the basis of the density functional theory [20]. Since the correlations uniquely define complicated quasiparticles, we could precisely determine the energies of different possible electron-hole configurations.

Figure 3: Illustration of a dropleton. In a dropleton, the probability distribution of the electrons and holes forms a ring-like pattern; a representative pair-correlation function is shown as a function of the electron-hole separation. The shell defines the size of the dropleton; roughly one electron-hole pair resides within each ring.

After a thorough search, all experimental observations were explained [4] only by a configuration where electrons and holes are not bound into excitons, but they rather are loosely organized, much like particles in a liquid. However, the liquid was confined inside a small bubble, which directly explained the quantization as a confinement effect. Due to liquid characteristics, quantization, and small size, we called the new quasiparticle a dropleton. The jumps in the dropleton energy levels were shown [4] to correspond to adding a new electron-hole pair to the dropleton. In total, we could detect dropletons with four, five, six, and seven electron-hole pairs and conclude that the quantum droplet size was in the range of 200nm (1nm=10^-9m) in diameter.

The discovery of dropleton is the first tangible demonstration that the quantum-optical spectroscopy excites and controls quasiparticles with unprecedented accuracy. To make full use of this encouraging advancement, it will be an important future goal to develop ultrafast and strong light sources whose quantum fluctuations can be freely adjusted. Since the dropletons are brand new addition to the quasiparticle family, it is not predictable how and when they can be seen in practical use. However, all quasiparticles also influence the operation of optoelectronic devices such as laser diodes which are already used in DVD readers/writers and in optical communications. Thus, the improved control of quasiparticles will certainly enhance our ability to design these types of devices. In addition, dropletons couple strongly with quantum light, which should be extremely useful when designing lasers and devices capable of encoding and processing quantum information. This level of control of light-matter interaction will provide intriguing possibilities to test foundations of quantum mechanics as well as introduce new ways to utilize them to build devices with an incredible performance.

References:
[1] Jack J. Lissauer, "Chaotic motion in the solar system", Reviews of Modern Physics, 71, 835 (1999). Abstract.
[2] Yu. Ts. Oganessian, A. V. Yeremin, A. G. Popeko, S. L. Bogomolov, G. V. Buklanov, M. L. Chelnokov, V. I. Chepigin, B. N. Gikal, V. A. Gorshkov, G. G. Gulbekian, M. G. Itkis, A. P. Kabachenko, A. Yu. Lavrentev, O. N. Malyshev, J. Rohac, R. N. Sagaidak, S. Hofmann, S. Saro, G. Giardina, K. Morita "Synthesis of nuclei of the superheavy element 114 in reactions induced by ⁴⁸Ca". Nature, 400, 242 (1999). Abstract.
[3] Charles Kittel, "Introduction to solid state physics" (Wiley & Sons, 8th Ed., 2005). 
[4] A.E. Almand-Hunter, H. Li, S.T. Cundiff, M. Mootz, M. Kira, S.W. Koch, "Quantum droplets of electrons and holes". Nature, 506, 471 (2014). Abstract.
[5] J. Frenkel, "On the transformation of light into heat in solids. I". Physical Review, 37, 17 (1931). Abstract.
[6] Gregory H. Wannier, "The structure of electronic excitation levels in insulating crystals". Physical Review, 52, 191 (1937). Abstract.
[7] Murray A. Lampert, "Mobile and immobile effective-mass complexes in nonmetallic solids". Physical Review Letters, 1, 450 (1958). Abstract.
[8] J.R. Haynes, "Experimental observation of the excitonic molecule". Physical Review Letters, 17, 860 (1966). Abstract.
[9] A.G. Steele, W.G. McMullan, and M.L.W. Thewalt, "Discovery of polyexcitons". Physical Review Letters, 59, 2899 (1987). Abstract.
[10] Daniel B. Turner, Keith A. Nelson, "Coherent measurements of high-order electronic correlations in quantum wells". Nature, 466, 1089 (2010). Abstract.
[11] Carson D. Jeffries, "Electron–hole condensation in semiconductors". Science 189, 955 (1975). Abstract.
[12] Takeshi Suzuki, Ryo Shimano, "Time-resolved formation of excitons and electron–hole droplets in Si studied using terahertz spectroscopy". Physical Review Letters, 103, 057401 (2009). Abstract.
[13] R.A. Kaindl, M.A. Carnahan, D. Hagele, R. Lovenich, D.S. Chemla, "Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas". Nature, 423, 734 (2003). Abstract.
[14] R. P. Smith, J. K. Wahlstrand, A. C. Funk, R. P. Mirin, S. T. Cundiff, J. T. Steiner, M. Schafer, M. Kira, S. W. Koch, "Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells". Physical Review Letters, 104, 247401 (2010). Abstract.
[15] R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, A. Leitenstorfer, "How many-particle interactions develop after ultrafast excitation of an electron–hole plasma". Nature, 414, 286 (2001). Abstract.
[16] Mackillo Kira, Stephan W. Koch, "Semiconductor quantum optics" (Cambridge University Press, 2011).
[17] M. Kira and S.W. Koch, "Quantum-optical spectroscopy in semiconductors". Physical Review A, 73, 013813 (2006). Abstract.
[18] M. Kira, S.W. Koch, R.P. Smith, A.E. Hunter, S. T. Cundiff, "Quantum spectroscopy with Schrödinger-cat states". Nature Physics, 7, 799 (2011). Abstract.
[19] M. Mootz, M. Kira and S.W. Koch, "Pair-excitation energetics of highly correlated many-body states", New J. Phys. 15, 093040 (2013). Full Article.
[20] David Sholl and Janice A. Steckel, "Density Functional Theory: A Practical Introduction" (Wiley, 2009).

Entangled Photons are Used to Enhance the Sensitivity of Microscope.

(From left to right) Ryo Okamoto, Shigeki Takeuchi, Takafumi Ono

Authors: Takafumi Ono, Ryo Okamoto, Shigeki Takeuchi

Affiliation:
Research Institute for Electronic Science, Hokkaido University, Japan,
The Institute of Scientific and Industrial Research, Osaka University, Japan.

We demonstrated a microscope whose sensitivity is enhanced by using quantum entanglement -- over the limit set by the conventional (classical) light illumination. This is the first experimental demonstration of the application of entangled photons for microscopy.

Quantum entanglement is a unique feature of quantum particles, like photons, electrons, and so on. Quantum entanglement was first introduced by Schrödinger, and later a famous debate on it occurred between Einstein and Bohr; Einstein called it `spooky action at a distance’. Now, quantum entanglement is attracting attention as the resources for quantum information technologies like quantum cryptography and quantum computation. We demonstrated that quantum entanglement is useful not only for such information technologies, but also in other broader fields, like microscopy.

Figure 1: A schematic image of the entanglement-enhanced microscope.

Some years ago, we reported the experiment of four photon interference with high visibility -- enough to beat the standard quantum limit for the phase sensitivity [2].　In that experiment, we used so called `NOON’ state, a path-entangled state where N-photon state is either in one of the two paths (and 0 photons in the opposite path). We demonstrated the quantum interference fringe using a four-photon NOON state with a high-visibility (91%) that was enough to beat the standard quantum limit of the phase sensitivity.

Perhaps the next natural step is to demonstrate entanglement-enhanced metrology. Among the applications of optical phase measurement, the differential interference contrast microscope (DIM) is widely used for the evaluation of opaque materials or biological tissues. The depth resolution of such measurements is determined by the signal-to-noise ratio (SNR) of the measurement, and the SNR is in principle limited by the standard quantum limit. In the advanced measurements using DIM, the intensity of the probe light is tightly limited for a non-invasive measurement, and the limit of the SNR has become a critical issue.

In our recent work [1], we proposed and demonstrated an entanglement-enhanced microscope, which is a confocal-type DIM where an entangled photon pair source is used for illumination. An image of a glass plate sample, where a Q shape is carved in relief on the surface with a ultra-thin step of ~17 nm, is obtained with better visibility than with a classical light source. The signal-to-noise ratio is 1.35±0.12 times better than that limited by the standard quantum limit. The success of this research will enable more highly sensitive measurements of living cells and other objects, and it has the potential for application in a wide range of fields, including biology and medicine.

Figure 2: (a) Atomic force microscope (AFM) image of a glass plate sample (BK7) on whose surface a Q shape is carved in relief with an ultra-thin step using optical lithography. (b) The section of the AFM image of the sample, which is the area outlined in red in a. The height of the step is estimated to be 17.3nm from this data. (c) The image of the sample using an entanglement-enhanced microscope where two-photon entangled state is used to illuminate the sample. (d) The image of the sample using single photons (a classical light source).

We believe this experimental demonstration is an important step towards entanglement- enhanced microscopy with ultimate sensitivity, using a higher NOON state or other quantum states of light. There are some other related works harnessing such nonclasical light for metrology[3-5].

References:
[1] Takafumi Ono, Ryo Okamoto, Shigeki Takeuchi, “An entanglement-enhanced microscope”. Nature Communications, 4, 2426 (2013). Abstract.
[2] Tomohisa Nagata, Ryo Okamoto, Jeremy L. O'Brien, Keiji Sasaki, Shigeki Takeuchi, “Beating the standard quantum limit with four-entangled photons”. Science, 316, 726–729 (2007). Abstract.
[3] Andrea Crespi, Mirko Lobino, Jonathan C. F. Matthews, Alberto Politi, Chris R. Neal, Roberta Ramponi, Roberto Osellame, Jeremy L. O’Brien, “Measuring protein concentration with entangled photons”. Applied Physics Letters, 100, 233704 (2012). Abstract.
[4] Florian Wolfgramm, Chiara Vitelli, Federica A. Beduini, Nicolas Godbout, Morgan W. Mitchell, “Entanglement- enhanced probing of a delicate material system”. Nature Photonics, 7, 28–32 (2013). Abstract.
[5] Michael A. Taylor, Jiri Janousek, Vincent Daria, Joachim Knittel, Boris Hage, Hans-A. Bachor, Warwick P. Bowen, “Biological measurement beyond the quantum limit”. Nature Photonics, 7, 229–233 (2013). Abstract.

Polarization-controlled Photon Emission from Site-controlled InGaN Quantum Dots

Left to Right: (top row) Chih-Wei Hsu, Anders Lundskog, K. Fredrik Karlsson, Supaluck Amloy. (bottom row) Daniel Nilsson, Urban Forsberg, Per Olof Holtz, Erik Janzén.

Authors: Chih-Wei Hsu¹, Anders Lundskog¹, K. Fredrik Karlsson¹, Supaluck Amloy^1,2, Daniel Nilsson¹, Urban Forsberg¹, Per Olof Holtz¹, Erik Janzén¹

Affiliation:
¹Department of Physics Chemistry and Biology (IFM), Linköping University, Sweden.
²Department of Physics, Faculty of Science, Thaksin University, Phattalung, Thailand.

A common requirement to realize several optoelectronic applications, e.g. liquid-crystal displays, three-dimensional visualization, (bio)-dermatology [1] and optical quantum computers [2], is the need of linearly-polarized light for their operation. For existing applications today, the generation of linearly-polarized light is obtained by passing unpolarized light through a combination of polarization selective filters and waveguides, with an inevitable efficiency loss as the result. These losses could be drastically reduced by employment of sources, which directly generate photons with desired polarization directions.

Quantum dots (QDs) have validated their important role in current optoelectronic devices and they are also seen as promising as light sources for generation of “single-photons-on-demand”. Conventional QDs grown via the Stranski-Krastanov (SK) growth mode are typically randomly distributed over planar substrates and possess different degrees of anisotropies. The anisotropy in the strain field and/or the geometrical shape of each individual QD determines the polarization performance of the QD emission. Accordingly, a cumbersome post-selection of QDs with desired polarization properties among the randomly-distributed QDs is required for device integration [3]. Consequently, an approach to obtain QDs with controlled site and polarization direction is highly desired.

Figure 1. Magnified SEM images of GaN EHPs with various α. The values of α are defined as the angles between the long axis of EHPs and the underlying GaN template.

Here, we demonstrate an approach to directly generate a linearly-polarized QD emission by introducing site-controlled InGaN QDs on top of GaN-based elongated hexagonal pyramids (GaN EHPs). The polarization directions of the QD emission are demonstrated to be aligned with the orientations of the EHPs (Figure 1). The reliability and consistency for this architecture are tested by a statistical analysis of InGaN QDs grown on GaN EHP arrays with different in-plane orientations of the elongations. Details of the process and optical characterizations can be found in our resent publication [4].

Figure 2. a) µPL spectra of EHPs with the polarization analyzer set to θ_max (θ_min), by which the maximum (minimum) intensity of sharp emission peaks are detected. b) Distribution histograms of measured polarization directions from the GaN EHPs for various α.

Figure 2a shows representative polarization-dependent micro-photoluminescence (µPL) spectra from a EHP measured at 4^o K. A broad emission band peaking at 386 nm and several emission peaks in the range between 410 and 420 nm are observed. These sharp emission lines are originating from the multiple QDs formed on top of the GaN EHP. Despite the formation of multiple QDs on a GaN EHP, the emission peaks from all QDs tend to be linearly-polarized in the same direction as revealed in Figure 3a and all peaks have their maximum and minimum intensities in the same direction, θ. The correlation between the outcome of the polarization-resolved measurements and the orientations of GaN EHPs (as defined by α) reveals that the polarization direction is parallel to the elongation (α≅φ in Figure 2b). A polarization guiding (α≅φ) is unambiguously revealed for GaN EHPs with α = 0^o, 60^o and 120^o. For the remaining group of GaN EHPs with α = 30^o, 90^o and 150^o, preferential polarization directions are seemly revealed, but α≅φ is less strictly obeyed. The polarization guiding effect and the high degree of polarization are further elucidated in the following.

Figure 3. a) Statistical histogram showing the overall measured degree of polarization from GaN EHPs. b) The computed degree of polarization plotted as a function of the split-off energy. The QD shape is assumed to be lens-shaped with an in-plane asymmetry of b/a= 0.8. The single particle electron (hole) eigenstates are obtained from an effective mass Schrödinger equation (with a 6 band k•p Hamiltonian), discretized by finite differences. The Hamiltonians include strain and internal electric fields originating from spontaneous and piezoelectric polarizations. The polarized optical transitions are computed by the dipole matrix elements.

The polarization direction of the ground-state-related emission from the QDs reflects the axis of the in-plane anisotropy of the confining potential, concerning both strain and/or QD shape [5]. The same polarization direction monitored for the different QDs indicates that all grown QDs possess unidirectional in-plane anisotropy. The polarization control observed in our work can be explained in three ways: (1) the GaN EHPs transfer an anisotropic biaxial strain field to the QDs resulting in the formation of elongated QDs. The direction of the strain field in the EHPs should be strongly correlated with α. (2) Given that the top parts of the GaN EHPs are fully strain relaxed, as concluded for the GaN SHPs [6], the asymmetry induced by a ridge will result in an anisotropic relaxation of the in-plane strain of the QDs on the ridge. The degree of relaxation is higher along the smallest dimension of the top area, i.e. along the direction perpendicular to the ridge elongation, resulting in a ground state emission of the QD being polarized in parallel with the ridge. (3) The edges of the ridges form a Schwoebel–Ehrlich barrier, which prevents adatoms of diffusing out from the (0001) facet [7,8]. Since the adatoms have larger probability to interact with an edge barrier parallel rather than orthogonal to the ridge elongation, the adatoms will preferentially diffuse parallel to the ridge. As the strain and the shape of the QDs are not independent factors and accurate structural information of the QDs is currently unavailable, the predominant factors determining the polarization is to be verified.

The polarization degree of the III-Ns is more sensitive to the in-plane asymmetry compared to other semiconductor counterparts due to the significant band mixing and the identical on-axis effective masses of the A and B bands in the III-N [5]. A statistical investigation of the value of P performed on 145 GaN EHPs reveals that 93% of the investigated GaN EHPs possess P > 0.7 with an average value of P = 0.84 (Figure 3a). The polarization of the emissions is related to the QD asymmetry determined by the anisotropy of the internal strain and electric fields, as well as by the structural shape of the QD itself [5]. Numerical computations predict a high degree of polarization for small or moderate in-plane shape anisotropies of GaN and InGaN QDs [9]. This is related to the intrinsic valence band structure of the III-Ns. In particular, the split-off energy has been identified as the key material parameter determining the degree of polarization for a given asymmetry. Figure 3b shows the computed degree of polarization plotted against a variation of the split-off energy. Given a fixed asymmetry of the QDs, it is concluded that the material with the smallest split-off energy exhibits the highest degree of polarization. The high degree of polarization observed for InGaN QDs can be rationalized by the small split-off energies of InN and GaN, resulting in an extreme sensitivity to the asymmetry. Such a characteristic implies its inherent advantage for the generation of photons possessing a specific polarization.

In summary, we have demonstrated an effective method to achieve site-controlled QDs emitting linearly-polarized emission with controlled polarization directions by growing InGaN QDs on top of elongated GaN pyramids in a MOCVD (metal organic chemical vapor deposition) system. The polarization directions of the QD emission can be guided by the orientations of the underlying elongated GaN pyramids. Such an effect can be realized as the elongated GaN pyramids provide additional in-plane confinement for the InGaN QDs implanting unidirectional in-plane anisotropy into the QDs, which subsequently emit photons linearly-polarized along the elongated direction of the GaN EHPs.

References:
[1] Zeng Nan, Jiang Xiaoyu, Gao Qiang, He Yonghong, Ma Hui, "Linear polarization difference imaging and its potential applications". Applied Optics, 48, 6734-6739 (2009). Abstract.
[2] E. Knill, R. Laflamme, G.J. Milburn, "A scheme for efficient quantum computation with linear optics". Nature, 409, 46-52 (2001). Abstract.
[3] Robert J. Young, D.J.P. Ellis, R.M. Stevenson, Anthony J. Bennett, "Quantum-dot sources for single photons and entangled photon pairs". Proceedings of the IEEE, 95, 1805–1814 (2007). Abstract.
[4] Anders Lundskog, Chih-Wei Hsu, K Fredrik Karlsson, Supaluck Amloy, Daniel Nilsson, Urban Forsberg, Per Olof Holtz, Erik Janzén, "Direct generation of linearly-polarized photon emission with designated orientations from site-controlled InGaN quantum dots". Light: Science & Applications 3, e139 (2014). Full Article.
[5] R. Bardoux, T. Guillet, B. Gil, P. Lefebvre, T. Bretagnon, T. Taliercio, S. Rousset, F. Semond, "Polarized emission from GaN/AlN quantum dots: single-dot spectroscopy and symmetry-based theory". Physical Review B, 77, 235315 (2008). Abstract.
[6] Q.K.K. Liu, A. Hoffmann, H. Siegle, A. Kaschner, C. Thomsen, J. Christen, F. Bertram, "Stress analysis of selective epitaxial growth of GaN". Applied Physics Letters, 74, 3122-3124 (1999). Abstract.
[7] O. Pierre-Louis, M.R. D’Orsogna, T.L. Einstein, "Edge diffusion during growth: The kink Schwoebel-Erhlich effect and resulting instabilities". Physical Review Letters, 82, 3661-3664 (1999). Abstract.
[8] S.J. Liu, E.G. Wang, C.H. Woo, Hanchen Huang, "Three-dimensional Schwoebel–Ehrlich barrier". Journal of Computer-Aided Materials Design, 7, 195–201 (2001). Abstract.
[9] S. Amloy, K.F. Karlsson, T.G. Andersson, P.O. Holtz, "On the polarized emission from exciton complexes in GaN quantum dots". Applied Physics Letters, 100, 021901 (2012). Abstract.

Quantum Up-Conversion of Squeezed Vacuum States

From Left to Right: Christina E. Vollmer, Christoph Baune, and Aiko Samblowski

Authors: Christina E. Vollmer, Christoph Baune, Aiko Samblowski, Tobias Eberle, Vitus Händchen, Jaromír Fiurášek, Roman Schnabel

Affiliation: Institut für Gravitationsphysik der Leibniz Universität Hannover, Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Hannover, Germany

Squeezed vacuum states of light belong to the special class of ‘nonclassical states’ that can not be fully described by either a classical or a semi-classical model. Overlapped with a (bright) coherent laser beam, they are able to reduce (to ‘squeeze’) the photon counting statistics, i.e. the light’s shot noise, thereby enhancing the sensitivity of optical measurement devices. There are applications in spectroscopy [1] and imaging [2] and in particular in interferometric length measurements in gravitational wave detectors [3-6], once the kick-off for research in squeezed states. With squeezed vacuum states it is also possible to teleport quantum states [7], to generate so-called Schrödinger kitten states [8], and to improve quantum cryptography [9].

Past 2Physics articles by this group:
September 25, 2011: "A Gravitational Wave Observatory Operating Beyond the Quantum Shot-Noise Limit" by Hartmut Grote, Roman Schnabel, Henning Vahlbruch.
April 03, 2008: "Squeezed Light – the first real application starts now" by Roman Schnabel and Henning Vahlbruch

Fig.1: Schematic of the experiment. A squeezed vacuum state at 1550 nm is overlapped with a bright pump field at 810 nm inside a periodically poled KTP crystal inside an optical resonator for sum-frequency generation. The output is a squeezed vacuum state at 532 nm.

In our recent work [10] we demonstrated for the first time the frequency up-conversion of squeezed vacuum states of light in an external setup, i.e. ‘on the fly’. Our scheme can be applied to quantum networks that first use a squeezing wavelength of 1550 nm for transmission through optical fibres and then use a shorter wavelength to meet the requirements of a quantum memory for storing the squeezed state. In our experiment we converted a 4dB squeezed state at 1550nm to a 1.5dB squeezed state at 532nm. The degradation was due to optical loss and in full agreement with our model.

With our experiment we also demonstrated a scheme that provides access to short squeezing wavelengths. Today, squeezed states are most efficiently produced at near-infrared wavelengths. Due to the lack of appropriate nonlinear media it is difficult to produce them with conventional techniques at visible or even ultra-violet wavelengths. In future work we plan to reduce the optical loss of our setup to be able to demonstrate strong squeezing at visible wavelengths.

Fig. 2: Photograph of parts of the experiment. In total, the experiment required five frequency conversion steps. First, a 1064 nm continuous-wave laser beam was frequency doubled. The produced 532 nm beam was used to generate two beams at 1550 nm and 810 nm via optical parametric oscillation. The 1550 nm light was frequency doubled and the generated 775 nm light used to pump a parametric down converter to produce squeezed vacuum states at 1550nm. The final step was the up-conversion as shown in Fig. 1.

References:
[1] E. Polzik, J. Carri, H. Kimble, “Spectroscopy with squeezed light”. Physical Review Letters, 68, 3020 (1992). Abstract.
[2] G. Brida, M. Genovese, I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging”. Nature Photonics 4, 227 (2010). Abstract.
[3] Carlton M. Caves, “Quantum-mechanical noise in an interferometer”. Physical Review D,  23, 1693 (1981). Abstract.
[4] Roman Schnabel, Nergis Mavalvala, David E. McClelland, Ping K. Lam, “Quantum metrology for gravitational wave astronomy”. Nature Communications, 1:121 (2010). Abstract.
[5] The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit”. Nature Physics, 7, 962 (2011). Abstract. 2Physics Article.
[6] The LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light”. Nature Photonics, 7, 613 (2013). Abstract.
[7] A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998). Abstract.
[8] Alexei Ourjoumtsev, Rosa Tualle-Brouri, Julien Laurat, Philippe Grangier, “Generating Optical Schrödinger Kittens for Quantum Information Processing,” Science 312, 83 (2006). Abstract.
[9] Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J. Cerf, Timothy C. Ralph, Jeffrey H. Shapiro, Seth Lloyd, “Gaussian quantum information,” Review of Modern Physics, 84, 621 (2012). Abstract.
[10] C. E. Vollmer, C. Baune, A. Samblowski, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel, “Quantum Up-Conversion of Squeezed Vacuum States from 1550 to 532 nm”, Physical Review Letters, 112, 073602 (2014). Abstract.

Demon-like Algorithmic Quantum Cooling

Man-Hong Yung

Author: Man-Hong Yung

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

Efficient cooling methods are indispensable for studying fundamental physical phenomena at low temperatures, leading to important discoveries such as superconductivity, Bose-Einstein condensation and the quantum Hall effect in the laboratory. As numerical tools, cooling algorithms are crucial for studying ground-state problems in computational physics, and for solving complex optimization problems in computer science. Recent advances in quantum information science open new venues for scientific discovery in physics and chemistry. However, simulating low-temperature properties of many-body systems remains one of the major challenges for both theory and experiment. In a recent work published in Nature Photonics [1], we developed a novel cooling method, called demon-like algorithmic quantum cooling (DLAC), that provides a solution to the problem of cooling quantum systems in a way similar to that of Maxwell’s demon. The method of DLAC share some features of heat-bath algorithmic cooling [2,3,4] and an approach of cooling that we call the dissipative open-system approach [5,6].

Heat-bath algorithmic cooling [2,3,4] is one way of cooling classical spin systems, which would be useful for initializing qubits in the ‘0’ state. The idea of heat-bath algorithmic cooling is to first re-distribute the entropy within a group of spins. Then, the spin (or the group of spins) containing relatively high entropy is put into contact with a heat reservoir to pump away the excess entropy. This procedure causes the overall entropy of the system to decrease.

The dissipative open-system approach [5,6] aims to drive a quantum state to the ground state of a certain kind of Hamiltonians, called frustrated Hamiltonians. This approach is based on the application of appropriate quantum jump operators to the subspace of the quantum state that would give an energy penalty.

Our DLAC approach is similar to the heat-bath algorithmic cooling, in the sense that the entropy of the system is re-distributed, but in a superposition of states, instead of different spins. DLAC is also similar to the dissipative open-system approach, in the sense that the superposition is collapsed once through a projective measurement of the ancilla qubit. The resulting operation is equivalent to applying a jump operator that causes the entropy to increase or decrease, depending on the measurement outcome. A more detailed analysis is shown in Fig. 1.

Fig 1. (View higher resolution by clicking on the figure) Basic principle of the cooling method. (a) Logic diagram of the feedback cooling system. The cooling module produces two outcomes, correlated with heating and cooling. The measurement result can be mapped into the position x of a 1D random walker; when the walker goes beyond its starting position x = 0 to the negative position x = −1, the particle is either rejected or recycled. (b) The quantum circuit diagram of the cooling module. It includes a controlled evolution for time t and an energy bias parameter γ. (c) The relative change in the population of the output state post-conditioned with a “cooling” measurement result depends on the eigenenergy. The lower the energy, the higher the gain.

The DLAC approach can be implemented in many systems such as trapped ions, quantum dots, and superconducting qubits. We chose to implement it in a quantum-optical system operated by the optics group Key Laboratory of Quantum Information of the University of Science and Technology of China (USTC). The optics group is lead by Prof. Chuan-Feng Li and the experimental setup (see Fig. 2) is mainly designed and performed by Prof. Jin-Shi Xu. The quantum system to be cooled is the polarization of a single photon.

Fig 2. (View higher resolution by clicking on the figure) Experimental setup. (a) The input photon state is prepared by a polarization beam splitter (PBS), a half-wave plate (HWP) and a quarter-wave plate (QWP). The cooling module is a polarization-dependent Sagnac interferometer. Split by the PBS, the horizontal and vertical components of a polarized photon propagate in opposite paths within the interferometer. Two HWPs operate on the corresponding polarization components. The quartz plate compensator (PC) is used to compensate for the relative phase in the interferometer. These elements simulate the system Hamiltonian. Both paths are then recombined on the same PBS. The photons at output ports 0 and 1 represent the cases of cooling and heating, respectively. The photon proceeds to the next cooling module depending on the value of the position x of the random walker. The final quantum state is reconstructed using quantum state tomography, with the measurement bases defined by a QWP, HWP and PBS. The photon is detected by a single photon detector (SPD) equipped with a 3 nm interference filter (IF). (b) Sketch of the random walker evolution.

In the experiment, we were able to achieve three steps of cooling (see Fig. 3) with two different strategies, namely evaporative and recycling. These two strategies determine what we do when we have a resulting state that has an entropy higher than the initial state. The evaporative strategy basically throws away those states and recycling strategy replace them with the original state.

Fig 3. (View higher resolution by clicking on the figure) a, Mean energies of the evaporative and recycling pseudo cooling strategies. b, The corresponding theory and experiment for the number n of copies obtained out of N initial copies at consecutive steps. The total probability of the recycling algorithm is set to 1, correcting for experimental losses. c, Mean energies for 3 pseudo cooling steps of the evaporative (non-recycling) strategy for different θ. Different maps correspond to theory and experiment for Hamiltonians Pauli Z and Pauli X, and different initial states (step 0). Error bars represent the statistical distribution of experimental measurements.

In conclusion, this optical experiment has adequately verified the feasibility of the our DLAC approach of cooling quantum systems. To extend the implementation of the cooling method to a larger quantum system, the key consideration is to choose a system where both projective measurement and feedback control can be efficiently incorporated. These technologies are currently not widely available, but they should become mature in the near future. For an extended discussion of this work in the context of Maxwell’s demon, see the associated News and View [7] by Seth Lloyd.

References:
[1] Jin-Shi Xu, Man-Hong Yung, Xiao-Ye Xu, Sergio Boixo, Zheng-Wei Zhou, Chuan-Feng Li, Alán Aspuru-Guzik, Guang-Can Guo, "Demon-like algorithmic quantum cooling and its realization with quantum optics". Nature Photonics, 8, 113-118 (2014). Abstract.
[2] P. Oscar Boykin, Tal Mor, Vwani Roychowdhury, Farrokh Vatan, Rutger Vrijen, "Algorithmic cooling and scalable NMR quantum computers". Proceedings of the National Academy of Scienses USA, 99, 3388-3393 (2002). Full Article.
[3] J. Baugh, O. Moussa, C.A. Ryan, A. Nayak, R. Laflamme, "Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance". Nature, 438, 470-473 (2005). Abstract.
[4] José M. Fernandez, Seth Lloyd, Tal Mor, Vwani Roychowdhury, "Algorithmic cooling of spins: a practicable method for increasing polarization". International Journal of Quantum Information, 2, 461–477 (2004). Abstract.
[5] B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, P. Zoller, "Preparation of entangled states by quantum Markov processes". Physical Review A, 78, 042307 (2008). Abstract.
[6] Frank Verstraete, Michael M. Wolf, J. Ignacio Cirac, "Quantum computation and quantum-state engineering driven by dissipation". Nature Physics, 5, 633-636 (2009). Abstract.
[7] Seth Lloyd, "Quantum optics: Cool computation, hot bits". Nature Photonics, 8, 90–91 (2014). Abstract.

Combining Infrared Spectroscopy and Scanning Tunneling Microscopy

Graduate students working on the project (from left to right): Xiaoping Hong, Giang D. Nguyen, Ivan V. Pechenezhskiy

Authors:
Ivan V. Pechenezhskiy^1,2, Xiaoping Hong¹, Giang D. Nguyen¹, Jeremy E. P. Dahl³, Robert M. K. Carlson³, Feng Wang¹, and Michael F. Crommie^1,2

Affiliation:
¹Department of Physics, University of California at Berkeley, California, USA
²Materials Sciences Division, Lawrence Berkeley National Laboratory, California, USA
³Stanford Institute for Materials and Energy Science, Stanford University, California, USA

Scanning tunneling microscopy (STM) [1] is an outstanding tool for probing electronic structures and surface morphologies at the nanoscale. In a scanning tunneling microscope, a metallic tip moves above the surface in a raster-like manner and measures variations in the quantum mechanical tunneling current that exists in a nanometer-sized vacuum gap between the tip and the surface. These days STM is routinely used to explore metallic, semiconducting, and superconducting substrates, novel two-dimensional materials, as well as atomic and molecular adsorbates on these surfaces.

While STM allows us to image surfaces with unparalleled atomic resolution, one significant drawback of STM is the lack of chemical contrast. For the purpose of chemical recognition, however, vibrational spectroscopy (specifically infrared spectroscopy) can be used because precise knowledge of molecular vibrational modes often leads to identification of the corresponding molecular structures. A significant breakthrough in probing molecular vibrations with STM was made in 1998 with the invention of STM-based inelastic electron-tunneling spectroscopy (STM-IETS) [2]. However, STM-IETS has some disadvantages, such as its relatively poor spectral resolution which is dependent on temperature and bias modulation [3]. Therefore, combining STM with infrared spectroscopy to probe molecular vibrations is still an extremely appealing idea, and a successful combination has so far eluded scientists.

There have been a number of attempts to combine light and STM for many different purposes [4]. However, in such studies, it is typically very difficult to separate useful information in measured signals from artifacts induced by the light heating up the tip. For example, one very common trick that is used to increase measurement sensitivity — light modulation in combination with phase-sensitive detection — does not work particularly well with STM since varying light intensity not only modulates the optical field at the junction but also modulates the tip-sample separation, and therefore the tunneling current. We realized that this problem can be bypassed if the laser light illumination is confined to a part of the surface away from the junction. The challenge, however, is to show that valuable information can still be obtained in this configuration. If so, all of the complex problems caused by the presence of light in the junction, such as tip thermal expansion, rectification and thermoelectric current generation [5], could be avoided.

How can one still do optical spectroscopy with an STM without direct illumination of the junction? The main idea behind our new spectroscopy technique is to use an STM tip as an extremely sensitive detector that measures surface expansion in the direction perpendicular to the surface. As the light frequency is tuned to a particular molecular vibrational resonance, the molecules absorb more light. The absorbed energy dissipates into the substrate and leads to substrate expansion. This expansion results in an increased tunneling current since the tip-sample separation decreases. In the actual setup, a feedback control system is used to keep the tunneling current constant by moving the tip away from the surface when the surface expands, and we measure the distance by which the tip retracts. Accordingly, when the substrate contracts, the tip moves closer to the surface to maintain the tunneling current. Recorded traces of the tip motion plotted versus laser light frequency immediately yield molecular absorption spectra. Attempts to make similar measurements have been made previously [6] but the recent progress, including demonstration of high spectral sensitivity in our measurements, only recently became possible thanks to our advances in designing and building a state-of-the-art tunable infrared laser with a stable power output (shown in Figure 1) [7].

Figure 1: IRSTM setup. An ultra-high vacuum chamber with a home-made STM is on the left and our home-made infrared laser based on an optic parametric oscillator is on the right.

In order to demonstrate the performance of the technique, referred to as infrared scanning tunneling microscopy (IRSTM) [8], we prepared samples of two different isomers of tetramantane by depositing these molecules on a Au(111) surface. These molecules, with chemical formula C₂₂H₂₈, belong to a class of molecules called diamondoids (as their structures closely-resemble that of diamond) [9]. When deposited on the gold surface, both isomers, [121]tetramantane and [123]tetramantane, form very similar single-layered close-packed assemblies as shown in Figure 2 (a, c). To obtain infrared spectra of these self-assembled structures, a beam of light from our tunable infrared laser was focused about 1 mm away from the tip-sample junction to a spot size of 1.2 mm in diameter. The spectra were recorded by tracing the motion of the tip while sweeping the laser frequency as described above. The measured IRSTM spectra for [121]tetramantane and [123]tetramantane are shown in Figure 2 (b, d). Several peaks corresponding to different modes of tetramantane CH-stretch vibrations are seen in the spectra and the spectra of the two isomers are clearly different. To compare with the STM-IETS technique, in Figure 2(b) the blue line shows an STM-IETS spectrum that has been previously obtained on a [121]tetramantane molecule [10]. In that work, STM-IETS resolution was not nearly enough to resolve any specific CH-stretch modes that exist in this frequency range. In contrast, Figure 2 demonstrates the remarkable chemical sensitivity of our new IRSTM technique.

Figure 2: (a) STM image of [121]tetramantane molecules on Au(111). (b) IRSTM spectrum (black line) of [121]tetramantane on Au(111). The blue line (with a single broad peak) shows an STM-IETS spectrum of [121]tetramantane on Au(111) from Ref. [10]. (c) STM image of [123]tetramantane molecules on Au(111). (d) IRSTM spectrum of [123]tetramantane on Au(111). Vibrational peaks for [123]tetramantane are seen to differ significantly from vibrational peaks for [121]tetramantane.

Vibrational spectra of molecules on surfaces can be used to study molecule-molecule and molecule-substrate interactions. Using IRSTM we have been able to observe the notable influence of molecule-molecule interactions between tetramantane molecules on their vibrational spectra. To investigate molecule-molecule and molecule-substrate interactions in detail, IRSTM measurements were also performed on monolayers formed by the simplest diamondoid molecule, which is called adamantane. These measurements were supported by first-principle calculations and new interesting insights have been reported in another recent study [11].

While IRSTM allows atomic-scale imaging and the probing of vibrational modes of molecules in the same setup, the phenomenal spatial resolution inherent to conventional STM measurements cannot (yet) be attributed to the IRSTM vibrational spectra. The measured signal in IRSTM comes from excitations of all molecules that are illuminated by the laser beam, i.e. from roughly a trillion molecules in our measurements. Though extension of IRSTM to the single-molecule limit will not be trivial, and will require some bright ideas, there is a lot of room for improvement in the current technique. In addition, the indirect measurement of absorbed heat in a scanning probe microscopy setup could be applied to a number of other important technological applications.

References:
[1] Gerd Binnig and Heinrich Rohrer, “Scanning tunneling microscopy — from birth to adolescence”, Reviews of Modern Physics, 59, 615 (1987). Abstract.
[2] B. C. Stipe, M. A. Rezaei, W. Ho, “Single-Molecule Vibrational Spectroscopy and Microscopy”, Science, 280, 1732 (1998). Abstract.
[3] L. J. Lauhon and W. Ho, “Effects of temperature and other experimental variables on single molecule vibrational spectroscopy with the scanning tunneling microscope”, Review of Scientific Instruments, 72, 216 (2001). Abstract.
[4] Stefan Grafström, “Photoassisted scanning tunneling microscopy”, Journal of Applied Physics, 91, 1717 (2002). Abstract.
[5] M. Völcker, W. Krieger, T. Suzuki, and H. Walther, “Laser‐assisted scanning tunneling microscopy”, Journal of Vacuum Science & Technology, B 9, 541 (1991). Abstract.
[6] D. A. Smith and R. W. Owens, “Laser-assisted scanning tunnelling microscope detection of a molecular adsorbate”, Applied Physics Letters, 76, 3825 (2000). Abstract.
[7] Xiaoping Hong, Xinglai Shen, Mali Gong, Feng Wang, “Broadly tunable mode-hop-free mid-infrared light source with MgO:PPLN continuous-wave optical parametric oscillator”, Optics Letters, 37, 4982 (2012). Abstract.
[8] Ivan V. Pechenezhskiy, Xiaoping Hong, Giang D. Nguyen, Jeremy E. P. Dahl, Robert M. K. Carlson, Feng Wang, Michael F. Crommie, “Infrared Spectroscopy of Molecular Submonolayers on Surfaces by Infrared Scanning Tunneling Microscopy: Tetramantane on Au(111)”, Physical Review Letters, 111, 126101 (2013). Abstract.
[9] J. E. Dahl, S. G. Liu, and R. M. K. Carlson, “Isolation and Structure of Higher Diamondoids, Nanometer-Sized Diamond Molecules”, Science, 299, 96 (2003). Abstract.
[10] Yayu Wang, Emmanouil Kioupakis, Xinghua Lu, Daniel Wegner, Ryan Yamachika, Jeremy E. Dahl, Robert M. K. Carlson, Steven G. Louie, Michael F. Crommie, “Spatially resolved electronic and vibronic properties of single diamondoid molecules”, Nature Materials, 7, 38 (2008). Abstract.
[11] Yuki Sakai, Giang D. Nguyen, Rodrigo B. Capaz, Sinisa Coh, Ivan V. Pechenezhskiy, Xiaoping Hong, Feng Wang, Michael F. Crommie, Susumu Saito, Steven G. Louie, Marvin L. Cohen, “Intermolecular interactions and substrate effects for an adamantane monolayer on the Au(111) surface”, arXiv:1309.5090. 

Hybrid Quantum Teleportation

[From Left to Right] Shuntaro Takeda, Maria Fuwa, and Akira Furusawa

Authors: Shuntaro Takeda, Maria Fuwa, and Akira Furusawa

Affiliation: Department of Applied Physics, School of Engineering, University of Tokyo, Japan

Link to Furusawa Laboratory >>

The principles of quantum mechanics allow us to realize ultra-high-capacity optical communication and ultra-high-speed quantum computation beyond the limits of current technology. One of the most fundamental steps towards this goal is to transfer quantum bits (qubits) carried by photons through “quantum teleportation” [1]. Quantum teleportation is the act of transferring qubits from a sender to a spatially distant receiver by utilizing shared entanglement and classical communications.

After its original proposal in 1993 [1], a research group in Austria succeeded in its realization in 1997 [2]. However, this scheme involved several deficiencies. One is its low transfer efficiency, estimated to be far below 1%. This is due to the probabilistic nature of entanglement generation and the joint measurement of two photons. This scheme also required post-selection of the successful events by measuring the output qubits after teleportation [3]. The transferred qubits are destroyed in this process, and thus cannot be used for further information processing. Various other related experiments have been reported thus far, but most withhold the same disadvantages. This problem has been a major limitation in the development of optical quantum information processing.

In our recent publication [4], we demonstrated “deterministic” quantum teleportation of photonic qubits for the first time. That is, photonic qubits are always teleported in each attempt, in contrary to the former probabilistic scheme. In addition, it does not require post-selection of the successful events. The success of the experiment lies in a hybrid technique of photonic qubits and continuous-variable quantum teleportation [5,6,7]; this required the combination of two conceptually different and previously incompatible approaches.

Figure 1: Concept of our hybrid technique for quantum teleportation. Single-photon-based qubits are combined with continuous-variable quantum teleportation to transfer optical waves.

Continuous-variable quantum teleportation, first demonstrated in 1998 [7], has long been used to teleport the amplitude and phase signals of optical waves, rather than photonic qubits. The advantage of continuous-variable teleportation is its deterministic success due to the on-demand availability of entangled waves and the complete joint measurement of two waves. However, its application to photonic qubits had long been hindered by experimental incompatibilities: typical pulsed-laser-based qubits have a broad frequency bandwidth that is incompatible with the original continuous-wave-based continuous-variable teleporter, which works only on narrow frequency sidebands. We overcame this incompatibility by developing an innovative technology: a broadband continuous-variable teleporter [8] and a narrowband qubit compatible with that teleporter [9].

Figure 2: Configuration of the teleportation experiment. Laser sources and non-linear optical processes supply the qubit and the required entanglement. More than 500 mirrors and beam splitters constitute the teleportation circuit.

This hybrid technique enabled the realization of completely deterministic and unconditional quantum teleportation of photonic qubits. The transfer accuracy (fidelity) ranged from 79 to 82 percent in four different qubits. Another strength of our hybrid scheme lies in the fact that the qubits were teleported much more efficiently than the previous scheme, even with low degrees of entanglement. This is a decisive breakthrough in the field of optical teleportation 16 years after the first experimental realizations.

References:
[1] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels”, Physical Review Letters, 70, 1895 (1993). Abstract.
[2] Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter, Anton Zeilinger, “Experimental quantum teleportation”, Nature, 390, 575 (1997). Abstract.
[3] Samuel L. Braunstein and H. J. Kimble, “A posteriori teleportation”, Nature 394, 840 (1998). Abstract.
[4] Shuntaro Takeda, Takahiro Mizuta, Maria Fuwa, Peter van Loock, Akira Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique”, Nature 500, 315 (2013). Abstract.
[5] Lev Vaidman, “Teleportation of quantum states”, Physical Review A 49, 1473 (1994). Abstract.
[6] Samuel L. Braunstein and H. J. Kimble, "Teleportation of Continuous Quantum Variables", Physical Review Letters, 80, 869 (1998). Abstract.
[7] A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation”, Science 282, 706 (1998). Abstract.
[8] Noriyuki Lee, Hugo Benichi, Yuishi Takeno, Shuntaro Takeda, James Webb, Elanor Huntington, Akira Furusawa, “Teleportation of Non-Classical Wave-Packets of light”, Science 332, 330 (2011). Abstract.
[9] Shuntaro Takeda, Takahiro Mizuta, Maria Fuwa, Jun-ichi Yoshikawa, Hidehiro Yonezawa, Akira Furusawa, “Generation and eight-port homodyne characterization of time-bin qubits for continuous-variable quantum information processing”, Physical Review A 87, 043803 (2013). Abstract.

Studying Light Pulses By Counting Photons

Elizabeth A. Goldschmidt (left) 
and Alan Migdall (right) 
[Photo courtesy: JQI/NIST/University of Maryland]

The photodetectors in Alan Migdall’s lab often see no light at all, and that’s a good thing since he and his colleagues at the Joint Quantum Institute (JQI) perform physics experiments that require very little light, the better to study subtle quantum effects. The bursts of light they observe typically consist of only one or two photons--- the particle form of light---or (statistically speaking) even less than one photon. Their latest achievement is to develop a new way of counting photons to understand the sources and modes of light in modern physics experiments.

Migdall’s lab, located at the National Institute for Standards and Technology (NIST), is just outside Washington, DC in the US. The new light-measuring protocol is summarized in a recent issue of the journal Physical Review A [1]. The work reported there was performed in collaboration with NIST’s Italian counterpart, the Instituto Nazionale de Ricerca Metrologica (INRIM).

Light Modes

Generating light suitable for quantum mechanical applications such as quantum computing and quantum cryptography requires exquisite control over properties such as the frequency, polarization, timing, and direction of the light emitted. For instance, probing atoms with light involves matching the frequency of the light to the atoms’ natural resonance frequency often to within one part in a billion. Moreover, communicating with light means encoding information in the arrival time or frequency or spatial position of the light, so high-speed communication means using very closely- spaced arrival times for light pulses, and pinpoint knowledge of the light frequencies and positions of the arriving light in order to fit in as much information as possible.

When a light pulse contains a mixture of light photons with different frequencies (or polarizations, arrival times, emission angles, etc.) it is said to have multiple modes. In some cases, a single light source will naturally produce such multi-mode light, whereas in others multiple modes are a signature of the presence of additional, and generally unwanted, light sources in the system. Discriminating the different modes in a light field, especially a weak light field that has very few photons, can be extremely difficult as it requires very sensitive detection that can discriminate between modes that are very close together in frequency, space, time, etc.

For instance, to study a pair of entangled photons (created by shooting light into a special crystal where one photon is converted into a pair of secondary, related photons) detection efficiency is all important; and folded into that detection efficiency is a requirement that the arrival of each of the daughter photons be matched to the arrival of the other daughter photon. In addition to this temporal alignment, the spatial alignment of detectors, (each oriented at a specific angle respect to the beamline) must be exquisite. To correct for any type of less-than-perfect alignment, it is necessary to know how many different light modes are arriving at the detector.

Photon Number

The laws of quantum mechanics ensure that light always exhibits natural intensity fluctuations. Even from an ultra-stable laser, the number of photons arriving at a detector will vary randomly in time. By recording the number of photons in each pulse of light over a long time, however, the form of the fluctuations of a particular light field will become clear. In particular, we can learn the probability of generating 0, 1, 2, 3, etc. photons in each pulse.

The handy innovation in Migdall’s lab was to develop a method to use this set of probabilities to determine the modes in a very weak light field. This method is very useful because most light detectors that can see light at the level of a single photon cannot tell the exact frequency or position of the light, which makes determining the number of modes difficult for such fields.

The JQI-INRIM experiment used a detector “tree” that counts photon number. It did this by taking the incoming light pulse, using partial mirrors to divide the pulse into four, and then allowing these to enter four detectors set up to record individual photons. If the original pulse contained zero photons then none of the detectors will fire. If the pulse contained one photon, then one of the detectors will fire, and so on.

Elizabeth A. Goldschmidt, a JQI researcher and University of Maryland graduate student, is the first author on the research paper. “By looking at just the intensity fluctuations of a light field we have shown that we can learn about the underlying processes generating the light,” she said. “This is a novel use of higher-order photon-number statistics, which are becoming more and more accessible with modern photodetection.”

Goldschmidt believes that this method of counting photons and statistically analyzing the results as a way of understanding the modes present in light pulses will help in keeping tight control over light sources that emit single photons (where, for instance, you want to ensure that unwanted photons are not being produced). And those that emit pairs of entangled photons---where the quantum relation between the two photons is exactly right, such as in “heralding” experiments, where the detection of a photon in one detector serves as an announcement for the existence of a second, related, photon in a specially staged detector nearby.

Alan Migdall compares the photon counting approach to wine tasting. “Just as some experts can taste different flavors in a wine---a result of grapes coming from different parts of the Loire Valley---so we can tell apart various modes of light coming from a source.”

References:
[1] Elizabeth A. Goldschmidt, Fabrizio Piacentini, Ivano Ruo Berchera, Sergey V. Polyakov, Silke Peters, Stefan Kück, Giorgio Brida, Ivo P. Degiovanni, Alan Migdall, Marco Genovese, "Mode reconstruction of a light field by multi-photon statistics", Physical Review A, 88, (2013). Abstract.