Controlling Quantum Particles By Looking At Them

[Left to Right] M.S. Blok, C. Bonato, R. Hanson.

Authors: M.S. Blok¹, C. Bonato¹, M.L. Markham², D.J. Twitchen², V.V. Dobrovitski³, R. Hanson¹ 

Affiliation:
¹Kavli Institute of Nanoscience Delft, Delft University of Technology, The Netherlands.
²Element Six Ltd, Ascot, Berkshire, UK.
³Ames Laboratory and Iowa State University, Ames, Iowa, USA.

Quantum measurements differ from their classical counterparts in the sense that they not only extract information from a system but also alter its state. The disturbance of a measurement, known as the measurement back-action, is probabilistic but can be used as a control tool when it is combined with real-time feedback. Here we show that we can manipulate a nuclear spin using only the back-action of sequential quantum measurements in combination with a feedback loop [1].

To gain control over the measurement back-action we exploited the fundamental trade-off between information gain and disturbance that is characteristic for quantum measurements [2-4]. Where a ‘conventional’ projective measurement gives maximal information, it also induces maximal disturbance since it collapses the system to an eigenstate, thus limiting the amount of accessible states. By using an intermediate particle as a probe to measure the system, one can create a tuneable amount of correlation between the system and the probe by letting them interact for a certain time (Fig 1a). A subsequent measurement of the probe will give no information about the system if the two were not correlated at all, meaning that the measurement back-action will be zero. When the two-system and the probe are maximally correlated, a projective measurement is performed. Thus by choosing a certain interaction time, one can tune the measurement strength and therefore control the amount of back-action associated with a measurement.

Figure 1: a) Representation of a quantum measurement where a system (spin, pointing up or down) is coupled to a probe, in this case a quantum clock where the pointer either rotates clockwise or anticlockwise depending on the state of the system. b) Nitrogen-Vacancy center in diamond and the two spins associated with it.

We demonstrated these variable strength measurements using an NV-center in diamond. This is a defect in the diamond lattice consisting of a Nitrogen atom and a vacancy at an adjacent lattice position (Fig 1b). As a system we used the spin of the nitrogen atom, while the probe is implemented by the electron spin associated with the NV-center. At low temperatures (4K) the electron spin can be readout in a single shot using spin-selective optical transitions [5] and manipulated using MW pulses. The interaction is governed by the hyperfine coupling and it can effectively be turned on by bringing the electron in a superposition. In figure 2 a we show that we can tune the amount of information by plotting the probe (electron) readout for varying interaction time in a Ramsey-type experiment. In Figure 2 b we show the state of the system after a variable strength measurement, post-selected on 1 of the two possible probe outcomes. In this case the system receives a kick from the measurement that increases with increased measurement strength, just as expected.

Figure 2: Variable strength quantum measurements. a) Result of the ancilla (electron spin) readout after a variable strength interaction. B) State of the system (nitrogen spin) after a variable strength measurement and postselected on the ancilla measurement outcome.

Although the amount of backaction can be accurately controlled, the direction of the collapse for a given instance is still probabilistic. To manipulate a quantum system with only measurements it is therefore crucial to have some form of feedback. We implemented a proof-of-principle feedback protocol which prepares the nuclear spin in a desired state with two sequential partial measurements where the strength of the second measurement depends on the outcome of the first (Fig 3). For the implementation it was crucial to develop a probe measurement that does not induce any extra noise, apart from the measurement backaction. The bloch spheres in fig 3 show the measured state of the system at each step of the protocol, illustrating the steering of a nuclear spin by merely looking at it.

Figure 3: Real-Time feedback protocol. We perform two sequential measurements where the strength of the second measurement depends on the outcome of the first measurement. At each step of the protocol we perform quantum state tomography of the nitrogen spin state to reconstruct the state. The reduction of the bloch vector is attributed to some residual dephasing of the system during ancilla readout.

References:
[1] M.S. Blok, C. Bonato, M.L. Markham, D.J. Twitchen, V.V. Dobrovitski, R. Hanson, "Manipulating a qubit through the backaction of sequential partial measurements and real-time feedback". Nature Physics 10, 189–193 (2014). Abstract.
[2] Christine Guerlin, Julien Bernu, Samuel Deléglise, Clément Sayrin, Sébastien Gleyzes, Stefan Kuhr, Michel Brune, Jean-Michel Raimond, Serge Haroche, "Progressive field-state collapse and quantum non-demolition photon counting". Nature, 448, 889–893 (2007). Abstract.
[3] M. Hatridge, S. Shankar, M. Mirrahimi, F. Schackert, K. Geerlings, T. Brecht, K. M. Sliwa, B. Abdo, L. Frunzio, S. M. Girvin, R. J. Schoelkopf, M. H. Devoret, "Quantum back-action of an individual variable-strength measurement". Science 339, 178–181 (2013). Abstract.
[4] K. W. Murch, S. J. Weber, C. Macklin, I. Siddiqi, "Observing single quantum trajectories of a superconducting quantum bit". Nature, 502, 211–214 (2013). Abstract.
[5] Lucio Robledo, Lilian Childress, Hannes Bernien, Bas Hensen, Paul F. A. Alkemade, Ronald Hanson, "High-fidelity projective read-out of a solid-state spin quantum register". Nature, 477, 574–578 (2011). Abstract.

A Cosmic Web Filament Revealed in Lyman α Emission around a Luminous High-redshift Quasar

[Left to Right] Sebastiano Cantalupo, Fabrizio Arrigoni-Battaia, J. Xavier Prochaska, Joseph F. Hennawi, Piero Madau.

Authors: Sebastiano Cantalupo^1,2, Fabrizio Arrigoni-Battaia², J. Xavier Prochaska^1,2, Joseph F. Hennawi², Piero Madau¹

Affiliation:
¹Department of Astronomy and Astrophysics & UCO/Lick Observatory, University of California, Santa Cruz, USA
²Max-Planck-Institut für Astronomie, Heidelberg, Germany

Galaxies are believed to be embedded in a “cosmic web”, the three-dimensional cellular foam arrangement of matter in the Universe predicted by the standard cold dark matter cosmological paradigm [1]. Most of the baryons do not reside in galaxies, but are spread along this web in highly ionized gaseous medium [2] that is too rarefied to form stars. While intergalactic gas may have been observed as absorption features in the spectra of background sources [3], direct constraints on the three-dimensional properties and morphology of the cosmic web are still missing. Limited by the rarity of bright background sources, absorption studies are only able to provide one-dimensional skewers of the cosmic web that are typically separated by several tens of Mpc. Direct detection of intergalactic gas in emission would instead provide a full three-dimensional image significantly improving our understanding of cosmological structure formation and the cycle of baryons in and out of galaxies.

Despite the predicted low surface brightness, there have been attempts to detect the cosmic web in Lyman α emission, e.g., by means of low-resolution spectroscopy [4] to search blindly for fluorescence generated by optically thick gas illuminated by the cosmic UV background [5]. Achieving a very deep flux limit of 8x10^-20erg s^-1 cm^-2 arcsec^-2, these observations failed to reveal the cosmic web. Positive fluctuations in the ionizing background may be used to increase the expected fluorescent signal [6]. In a pilot survey obtained in 2010 using a custom-built, narrow-band (NB) filter on the VLT-FORS we demonstrated indeed that bright quasars can, like a flashlight, “illuminate” the densest knots in the surrounding cosmic web and boost fluorescent Lyman α emission to detectable levels [7]. In this survey we found several compact ”dark galaxies” and extended nebulae (up to 65 physical kpc) around star forming galaxies, but none of them extending on intergalactic scales. Following the same experiment, we have initiated in 2012 a NB imaging campaign on Keck/LRISb centered on z~2 bright quasars and we have reported in a recent Nature letter [8] the first result of this new imaging survey.

Figure 1 : Processed and combined images of the field surrounding the quasar UM287. Each image is 2 arcmin on a side and the quasar is located at the center. In the narrow-band (NB3985) image (panel 'a'), which is tuned to the Lyman α line of the systemic redshift for UM287, one identifies very extended (≈ 55 arcsec across) emission – that we named "Slug Nebula". The deep V-band image (panel 'b') does not show any extended emission associated with UM287. This requires the Slug Nebula to be line-emission, and we identify it as Lyman α at the redshift of the quasar.

On November 12 and 13, 2012, we imaged the field of the quasar UM 287 with a custom NB filter tuned to Lyman α at z = 2.279 inserted into the Keck/LRISb camera on the 10m Keck-I telescope. We acquired 10 hours of integration in a series of dithered, 1200s exposures in clear conditions. In parallel (enabled by a dichroic), we obtained broad-band V images with the LRISr camera. Figure 1 presents the processed and combined images, centered on UM287. The V -band image is very deep and hundreds of compact sources are present in the field. We expect the majority of these are background galaxies, unrelated to the system. In the NB3985 image, however, one identifies a very extended source originating near the quasar with a projected size of about 1 arcmin (500kpc physical or 1.6 Mpc co-moving). We will refer to this extended emission as the ”Slug Nebula” in the reminder of this article. Within the nebula, very few sources are identified in the broad-band images nor is any extended emission observed. This requires the narrow-band light to be line-emission, and we identify it as Lyman α at the redshift of UM287.

Figure 2 : Lyman α image of the Slug Nebula. We subtracted from the NB image the continuum contribution estimated from the broad-band images. The location of the quasar UM287 is labeled with the letter “a”. The color map and the contours indicates, respectively, the Lyman α surface brightness and the signal-to-noise ratio (S/N) per arcsec² aperture. The extended emission spans a projected angular size of ≈ 55 arcsec (about 460 physical kpc), measured from the 2σ (~10⁻¹⁸ erg s^-1 cm^-2 arcsec^-2) contours. Object “b” is an optically faint (g~23AB) quasar at the same redshift of UM287. The Nebula appears broadly filamentary and asymmetric, extending mostly on the eastern side of quasar “a” up to a projected distance of about 35 arcsec (~285 physical kpc) measured from the 2σ isophotal.

Figure 2 presents the NB3985 image, continuum subtracted using standard techniques [8]. One identifies several compact sources including UM287 (labeled “a” in the figure) with excess Lyman α emission. The second brightest compact emitter (indicated by the letter “b”) is an optically faint (g~22 AB) quasar at the same redshift of UM287. The image is dominated, however, by the filamentary and asymmetric Slug Nebula. Although Lyman α nebulae extending up to about 250 kpc have been previously detected [9-13], the Slug Nebula represents so far a unique system as we show in Figure 3: with a size of about 55” or 460 physical kpc, it extends well beyond the virial radius of any plausible dark matter halo associated with UM287. Indeed, in order to be fully contained within the virial radius of a dark matter halo centered on UM287, the quasar host halo should have a total halo mass of 10^13.5 M_sun. This is ten times larger than the typical value associated with radio-quiet quasars (10^12.5 M_sun, see [8] for discussion) and it would make the host halo of UM287 one of the largest know at z > 2. However, this possibility is clearly excluded by the absence of an excess of Lyman α emitting galaxies around UM287 compared to other radio-quiet quasars. Our analysis of the galaxy distribution around UM287 suggests instead that this quasar is residing in a typical or under-dense environment for radio-quiet quasars and that its total halo mass therefore does not exceed 10^12.5 M_sun. Differently from any previous detection, the Slug Nebula is therefore the first possible image of intergalactic gas at z > 2 extending beyond any individual, associated dark matter halo. The rarity of these systems may be explained by the combination of anisotropic emission from the quasars (typically only about 40% of the solid angle around a bright, high-redshift quasar is unobstructed [14]), the anisotropic distribution of dense filaments and light travel effects that, for quasar ages younger than a few Myr, further limit the possible ”illuminated” volume.

Figure 3 : Luminosity-size relations for previously detected, bright Lyman α nebulae and the Slug Nebula around the quasar UM287. The plot includes nebulae surrounding AGN and Lyman α blobs (LAB). The dashed line indicates the virial diameter of a dark matter halo with total mass M ~ 10^12.5 M_sun, the typical host of radio-quiet quasars including UM287, as confirmed by the analysis of the galaxy overdensity in our field. The Slug Nebula, differently from any previous detection, extends on Intergalactic Medium scales that are well beyond any possible associated dark matter halo. Note that, even if we restrict the size measurement of the UM287 Nebula to the 4 × 10⁻¹⁸ erg s^-1 cm^-2 arcsec^-2 isophotal to be comparable with the majority of the previous surveys, the measured apparent size of the Slug Nebula will be reduced only by about 20%.

In order to constrain the physical properties of this, so far, unique system, we use a set of Lyman α radiative transfer calculations [15] combined with hydrodynamical simulation of cosmological structure formation around a quasar halo host similar to UM287. We consider two possible, extreme scenarios for the Lyman α emission mechanism of the intergalactic gas associated with the Slug Nebula: a) the gas is mostly ionized and the Lyman α emission is mainly produced by hydrogen recombinations. b) the gas is mostly neutral and the emission is mainly due to scattering of the Lyman α and continuum photons produced by the quasar Broad Line Region (BLR). In both cases, we performed a full three dimensional Lyman α radiative transfer calculation including gas temperature and velocity field effects on Lyman α scattering within the Nebula. The models are used to obtain the scaling relations between the observable Lyman α surface brightness from the intergalactic gas surrounding the quasar and the hydrogen column densities. Through these relations, we converted the observed SB into an estimated gas column density for the two extreme scenarios. Note that the estimated column densities for case ”a” are degenerate with the ionized gas clumping factor (C =2

>/², where n is the electron density) below the simulation resolution scale, ranging from ~10 proper kpc for diffuse intergalactic gas to ~100 pc for the densest regions within galaxies.

The results, using the observed BLR Lyman α luminosity and C = 1, are presented in Fig.4. The observed Lyman α emission from the intergalactic gas associated with the Slug Nebula requires very large column density of ”cold” (T < 5 x 10⁴ K) gas to be matched by current simulations. The implied total, cold gas mass ”illuminated” by the quasar is M_gas ~10^11.4±0.6 M_sun for the ”mostly neutral” case (”b”) and M_gas ~10^12±0.5M_sun for the ”mostly ionized” case (”a”) and C = 1. Note that the total estimated mass for the case ”a” scales as C^1/2. For comparison, a typical simulated filament in our cosmological simulation of structure formation with size and morphology similar to the Slug Nebula around a similar halo has a total gas mass of about 10^11.3 M_sun, but only about 15% of this gas is ”cold” (T < 5x10⁴ K), i.e. 10^10.5 M_sun and therefore able to emit substantial Lyman α emission. These estimates are consistent with other recent, grid-based hydrodynamical simulations of structure formation [16].

Figure 4 : Inferred hydrogen column densities associated with the Slug Nebula. We have converted the observed Lyman α Surface Brightness into gas column densities using a set of scaling relations obtained with detailed radiative transfer simulations. We have explored two extreme cases: a) the gas is mostly ionized by the quasar radiation (panel “a”), b) the gas is mostly neutral (panel “b”). Two circular regions with a diameter of 7 arcsec (~ 8 times the seeing radius) have been masked at the location of the quasars (black circles). The inferred hydrogen column density in panel “a” scales as C^−1/2, where C is the gas clumping factor below a spatial length of up to about 10 physical kpc at moderate overdensities (less than about 40 times the mean density of the Universe at z~2). The implied column densities and gas masses, in both cases, are at least a factor of ten larger than what is typically observed within cosmological simulations around massive haloes, suggesting, e.g., that a large number of small clumps within the diffuse Intergalactic medium may be missing within current numerical models.

How one can explain the large differences between the estimated, cold gas mass of the Slug Nebula and the available amount of cold gas predicted by numerical simulations on similar scales? The Slug Nebula seems to point in the direction of a second, fainter quasar companion of UM287. However, because of the large distance from UM287 -- at least 200 proper kpc and up to 4 proper Mpc considering the 1σ redshift error, and the morphology of the Nebula we can exclude that the UM287 Nebula is the result of tidal interaction due to a merging event between the two quasar hosts. Indeed, such a large separation would imply that any possible encounter between the two quasars is likely a high velocity interaction or an encounter with large impact parameter. We note that it is not impossible but extremely difficult to produce a long and massive tidal tail during a ”fast” encounter but the amount of gas stripped by the quasar host galaxies in the best scenario would likely be a very small fraction (< 10%) of its total ISM and certainly cannot account for the total amount of gas detected in the Nebula. Irrespective of the details of the possible interaction between the two quasar host galaxies, any resulting, long tidal tail would be very thin with sizes of the order of few kpc or less while the observed Nebula has a thickness of at least 100 physical kpc in its widest point.

Similarly, it would be very difficult to explain the properties of the Nebula assuming a galactic gas outflow origin produced by possible quasar feedback events. Indeed, although radio-quiet quasar outflows are highly unconstrained from current observations and poorly understood theoretically, the large size of the Nebula, extending well beyond the virial radius of the quasar host halo, would require a high velocity outflow that is incompatible with the “cold” temperature of the gas required by the Lyman α emission. A recent spectroscopic follow-up (Cantalupo et al., in preparation) provides additional evidences that the Nebula is kinematically quiet and therefore that it cannot be generated by “quasar feedback”. The size, morphology and kinematical properties of the gas are instead broadly consistent with our expectations from a filament of the “cosmic web”.

How one can then reconcile the intergalactic nature of the Slug Nebula with the large mass discrepancy with intergalactic gas simulations? One possibility is to assume that the simulations are not resolving a large population of small, cold gas clumps within the low-density Intergalactic medium that are illuminated and ionized by the intense radiation of the quasar. In this case, an extremely high clumping factor, namely C ~1000, on scales below few kpc would be required in order to explain the large luminosity of the Slug Nebula with the cold gas mass within the intergalactic filaments predicted by the simulations. On the other hand, if some physical process that is not fully captured by current grid-based simulations increases the fraction of cold gas around the quasar, e.g. a proper treatment of metal mixing, a smaller clumping factor may be required. In the extreme – and rather unrealistic - case that all the hot gas is turned into a cold phase, the required clumping factor would be C ~20. Even if the gas is not ionized by the quasar (case ”b” above), the simulations are able to reproduce the observed mass only if a substantial amount of hot gas is converted into a cold phase. Incidentally, this is exactly the same result found comparing the properties of Lyman α absorption systems around a large statistical sample of quasars with simulations [17].

The discovery of the Slug Nebula represents both a unique laboratory and a challenge for our knowledge of cosmological structure formation on Intergalactic scales around massive haloes. On one hand, it provides a fundamental confirmation that specifically designed, deep narrow-band surveys centered on bright quasars are able to provide - for the first time - an image of cosmic gas on intergalactic scales. The rarity of such detection however, may imply that several conditions regarding, e.g. the geometry of the quasar "illumination" are met arguing for the necessity of a very large sample of quasars. On the other hand, our observation indicates that current models of cosmological structure formation (at least numerical methods based on Adaptive Mesh Refinement algorithms) are far from providing an accurate picture of the gas properties - not only within galaxies - but also for diffuse Intergalactic gas within several hundreds of physical kpc from massive haloes at z ~2. In particular, the size and luminosity of the Slug Nebula suggest that a large population of cold, sub-kpc scale clumps may be present within the diffuse Intergalactic medium in proximity of quasars. Proper modeling of this gas phase will require a new generation of numerical models that are able - simultaneously - to spatially resolve these small intergalactic clumps within large simulation boxes, treat the multiphase nature of this gas and its interaction with galaxies and quasars.

References:
[1] J. Richard Bond, Lev Kofman, Dmitry Pogosyan, "How filaments of galaxies are woven into the cosmic web". Nature, 380, 603–606 (1996). Abstract. arXiv:astro-ph/9512141.
[2] Renyue Cen, Jordi Miralda-Escude, Jeremiah P. Ostriker, Michael Rauch, "Gravitational collapse of small-scale structure as the origin of the Lyman-alpha forest". Astrophysical Journal Letters, 437, L9–L12 (1994). arXiv:astro-ph/9409017.
[3] Michael Rauch, "The Lyman Alpha Forest in the Spectra of QSOs". Annual Reviews of Astronomy and Astrophysics, 36, 267–316 (1998). Abstract. arXiv:astro-ph/9806286.
[4] Michael Rauch, Martin Haehnelt, Andrew Bunker, George Becker, Francine Marleau, James Graham, Stefano Cristiani, Matt Jarvis, Cedric Lacey, Simon Morris, Celine Peroux, Huub Röttgering, Tom Theuns, "A Population of Faint Extended Line Emitters and the Host Galaxies of Optically Thick QSO Absorption Systems". Astrophysical Journal, 681, 856–880 (2008). Full Text.
[5] Andrew Gould, David H. Weinberg, "Imaging the Forest of Lyman Limit Systems". Astrophysical Journal, 468, 462 (1996). arXiv:astro-ph/9512138.
[6] Sebastiano Cantalupo, Cristiano Porciani, Simon J. Lilly, Francesco Miniati, "Fluorescent Lyα Emission from the High-Redshift Intergalactic Medium". Astrophysical Journal, 628, 61–75 (2005). Full Text.
[7] Sebastiano Cantalupo, Simon J. Lilly, Martin G. Haehnelt, "Detection of dark galaxies and circum-galactic filaments fluorescently illuminated by a quasar at z = 2.4". Monthly Notices of the Royal Astronomical Society, 425, 1992–2014 (2012). Abstract. arXiv:1204.5753 [astro-ph.CO].
[8] Sebastiano Cantalupo, Fabrizio Arrigoni-Battaia, J. Xavier Prochaska, Joseph F. Hennawi, Piero Madau, "A Cosmic Web Filament revelead in Lyman-α emission around a luminous high-z quasar". Nature, 506, 63 (2014). Abstract.
[9] T.M. Heckman, G.K. Miley, M.D. Lehnert, W. van Breugel, "Spatially resolved optical images of high-redshift quasi-stellar objects". Astrophysical Journal, 370, 78–101 (1991).
[10] Patrick J. McCarthy, "High redshift radio galaxies". Annual Reviews of Astronomy and Astrophysics, 31, 639–688 (1993). Abstract.
[11] Charles C. Steidel, Kurt L. Adelberger, Alice E. Shapley, Max Pettini, Mark Dickinson, Mauro Giavalisco, "Lyα Imaging of a Proto-Cluster Region at =3.09". Astrophysical Journal, 532, 170–182 (2000). Full Article.
[12] Michiel Reuland, Wil van Breugel, Huub Röttgering, Wim de Vries, S. A. Stanford, Arjun Dey, Mark Lacy, Joss Bland-Hawthorn, Michael Dopita, George Miley, "Giant Lyα Nebulae Associated with High-Redshift Radio Galaxies". Astrophysical Journal, 592, 755–766 (2003). Full Text.
[13] Y. Matsuda, T. Yamada, T. Hayashino, R. Yamauchi, Y. Nakamura, N. Morimoto, M. Ouchi, Y. Ono, K. Kousai, E. Nakamura, M. Horie, T. Fujii, M. Umemura, M. Mori, "The Subaru Ly-alpha blob survey: a sample of 100-kpc Ly-alpha blobs at z= 3". Monthly Notices of the Royal Astronomical Society, 410, L13–L17 (2011). arXiv:1010.2877 [astro-ph.CO].
[14] M. Polletta, D. Weedman, S. Hönig, C. J. Lonsdale, H. E. Smith, J. Houck, "Obscuration in Extremely Luminous Quasars". Astrophysical Journal, 675, 960–984 (2008). Full Text.
[15] Sebastiano Cantalupo, Cristiano Porciani, "RADAMESH: cosmological radiative transfer for Adaptive Mesh Refinement simulations". Monthly Notices of the Royal Astronomical Society, 411, 1678–1694 (2011). Full Article.
[16] Michele Fumagalli, Joseph F. Hennawi, J. Xavier Prochaska, Daniel Kasen, Avishai Dekel, Daniel Ceverino, Joel Primack, "Confronting Simulations of Optically Thick Gas in Massive Halos with Observations at z=2-3". arXiv:1308.1669 [astro-ph.CO].
[17] J. Xavier Prochaska, Joseph F. Hennawi, Khee-Gan Lee, Sebastiano Cantalupo, Jo Bovy, S. G. Djorgovski, Sara L. Ellison, Marie Wingyee Lau, Crystal L. Martin, Adam Myers, Kate H. R. Rubin, Robert A. Simcoe, "Quasars Probing Quasars VI. Excess HI Absorption within One Proper Mpc of z~2 Quasars". Astrophysical Journal, 776, 136 (2013). Abstract.

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.