Protostellar Feedback Halts the Growth of the First Stars in the Universe Takashi Hosokawa, et al. Science 334, 1250 (2011); DOI: 10.1126/science.1207433 This copy is for your personal, non-commercial use only. If you wish to distribute this article to others, you can order high-quality copies for your colleagues, clients, or customers by clicking here. Permission to republish or repurpose articles or portions of articles can be obtained by following the guidelines here. The following resources related to this article are available online at Downloaded from www.sciencemag.org on December 1, 2011 www.sciencemag.org (this infomation is current as of December 1, 2011 ): Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://www.sciencemag.org/content/334/6060/1250.full.html Supporting Online Material can be found at: http://www.sciencemag.org/content/suppl/2011/11/09/science.1207433.DC1.html This article cites 60 articles, 5 of which can be accessed free: http://www.sciencemag.org/content/334/6060/1250.full.html#ref-list-1 This article has been cited by 1 articles hosted by HighWire Press; see: http://www.sciencemag.org/content/334/6060/1250.full.html#related-urls This article appears in the following subject collections: Astronomy http://www.sciencemag.org/cgi/collection/astronomyScience (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by theAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyright2011 by the American Association for the Advancement of Science; all rights reserved. The title Science is aregistered trademark of AAAS.
REPORTS tostar was calculated directly from the mass in- flux through the sink-cell boundary, whereas the Protostellar Feedback Halts the Growth luminosity from the protostar, which controls the radiative feedback, was calculated consistent- ly from the protostellar model by using the de- of the First Stars in the Universe rived accretion rate. At its birth, a very small protostar of ∼0.01 Takashi Hosokawa,1,2* Kazuyuki Omukai,2 Naoki Yoshida,3 Harold W. Yorke1 M⊙ was surrounded by a molecular gas envelope of ∼1 M⊙, which was quickly accreted onto the The first stars fundamentally transformed the early universe by emitting the first light and by protostar. Atomic gas further out initially had producing the first heavy elements. These effects were predetermined by the mass distribution of too much angular momentum to be accreted di- the first stars, which is thought to have been fixed by a complex interplay of gas accretion and rectly, and a circumstellar disk formed. The in- protostellar radiation. We performed radiation-hydrodynamics simulations that followed the growth falling atomic gas first hit the disk plane roughly of a primordial protostar through to the early stages as a star with thermonuclear burning. The vertically at supersonic velocities. A shock front circumstellar accretion disk was evaporated by ultraviolet radiation from the star when its mass was formed; behind the shock, the gas cooled and 43 times that of the Sun. Such massive primordial stars, in contrast to the often-postulated settled onto the disk, and its hydrogen was con- extremely massive stars, may help explain the fact that there are no signatures of the pair-instability verted to the molecular form via rapid gas-phase Downloaded from www.sciencemag.org on December 1, 2011 supernovae in abundance patterns of metal-poor stars in our galaxy. heoretical studies and detailed computer the ionized region in its vicinity grows, and even- T simulations show that the cradles of the first stars were dense concentrations of primordial gas, with masses of ~1000 that of the tually the circumstellar disk is directly exposed to the stellar ionizing radiation. The gas on the disk surface is photoionized and heated and evap- Sun. Such gas clouds formed through radiative orates away from the star-disk system. A semi- cooling, with hydrogen molecules at the center analytical model of this process predicts that this of a dark matter halo of 106 solar mass (M⊙), photoevaporation quenches the accretion flow when the age of the universe was a few hundred of the disk material and puts an end to the stellar million years (1). growth (8). However, the interplay between the According to our current understanding of accretion flow and the stellar radiation is high- star formation, a gas cloud’s dense core grav- ly dynamical and complex. itationally contracts in a nonhomologous run- To identify the exact mechanism that halts away fashion, in which the densest parts become the growth of a first star and to determine its final denser faster than does the rest of the cloud (2–5). mass, we applied a method used for studying In a primordial gas cloud, one or a few embryo the present-day massive star formation (9, 10) protostars are formed near the center (2, 6). The to the case of the formation of the first stars in a initial mass of these embryo protostars is only proper cosmological context. We followed the ≅0.01 M⊙; the bulk of the dense core material radiation hydrodynamic evolution in the vicin- remains in the surrounding envelope and is sub- ity of an accreting protostar, incorporating ther- sequently drawn toward the protostar (or proto- mal and chemical processes in the primordial gas stars) through gravity. With the typical angular in a direct manner. We also followed the evolu- momentum of dense cores, the centrifugal barrier tion of the central protostar self-consistently by allows only a small amount of infalling gas to solving the detailed structure of the stellar inte- accrete directly onto the star. Instead, a circum- rior with zero metallicity as well as the accretion stellar disk is formed, and the gas is accreted flow near the stellar surface [supporting online onto the central star through the disk (7). The material (SOM) text] (11, 12). We configured the final mass of these first stars is fixed when the initial conditions by using the results of a three- mass accretion terminates. However, when and dimensional (3D) cosmological simulation, which how this termination occurs are largely unknown. followed the entire history from primeval density Because the luminosity increases rapidly with fluctuations to the birth of a small seed protostar protostellar mass, radiative feedback is expected at the cosmological redshift 14 (6). Specifical- to regulate the mass accretion and ultimately shut ly, when the maximum particle number density off the accretion flow, setting the final mass of reached 106 cm−3 in the cosmological simulation, the first stars. A primordial star more massive than we considered a gravitationally bound sphere of Fig. 1. (A to D) Evolution of the stellar radius, a few tens times the mass of the Sun radiates a radius 0.3 pc around the density peak, which en- bolometric luminosity, evolutionary time scales, and copious amount of hydrogen-ionizing photons closed a total gas mass of ≅300 M⊙. We reduced ionizing (hν ≥ 13.6 eV) and dissociating (11 eV ≤ (>13.6 eV). As an accreting star grows in mass, the 3D data to an axisymmetric structure by av- hν ≤ 13.6 eV) photon number luminosity. In (B), eraging over azimuthal angles. the total luminosity Ltot (black) is the sum of the 1 Jet Propulsion Laboratory, California Institute of Technology, The system was evolved until the central stellar luminosity L* (red) and accretion luminosity Pasadena, CA 91109, USA. 2Department of Physics, Kyoto Uni- particle number density reached 1012 cm−3. We versity, Kyoto 606-8502, Japan. 3Institute for the Physics and Lacc (blue). The KH time scale tKH (red) and accre- Mathematics of the Universe, Todai Institutes for Advanced then introduced a sink cell of size ≅10 astro- tion time scale tacc (blue) are depicted in (C). The Study, University of Tokyo, Kashiwa, Chiba 277-8568, Japan. nomical units (AU) and followed the subsequent yellow and blue backgrounds denote the adiabatic *To whom correspondence should be addressed. E-mail: evolution of the central protostar with a stellar accretion phase and KH contraction phase in the email@example.com evolution code. The accretion rate onto the pro- protostellar evolution.1250 2 DECEMBER 2011 VOL 334 SCIENCE www.sciencemag.org
REPORTSthree-body reactions. The molecular disk ex- In the early accretion phase, the stellar radi- (UV) flux rapidly rose (Fig. 1D). Thus, ionizationtended out to ≅400 AU from the protostar, when us remained almost constant at ≅50 solar radius and heating by UV photons became importantthe stellar mass was 10 M⊙. Accretion onto the (R⊙) (Fig. 1A). The stellar luminosity was sub- already in the KH contraction stage.protostar proceeded through this molecular disk stantially lower than the accretion luminosity When the stellar mass was 20 M⊙, an ionizedas angular momentum was transported outward. (Fig. 1B), and the KH time scale was much longer region rapidly expanded in a bipolar shape per-The accretion rate onto the protostar was ≅1.6 × than the accretion time (Fig. 1C). Consequent- pendicular to the disk, where gas was cleared10−3 M⊙ year−1 at that moment. ly, entropy carried by the accreted gas accumu- away (Fig. 2A). At this moment, the disk ex- The evolution of the central protostar is de- lated at the stellar surface nearly without loss. tended out to ≅600 AU. The disk was self-shieldedtermined by competition between mass growth During this quasi-adiabatic stage (M* < 7 M⊙), against the stellar H2-dissociating (11.2 eV ≤ hν ≤by accretion and radiative energy loss from the the luminosity L* increased with stellar mass. 13.6 eV) as well as the ionizing radiation. Thestellar interior. The time scale for the former When the star grew to 8 M⊙, the KH time scale ionized atomic hydrogen (H II) region continued ˙is the accretion time scale tacc ≡ M*/M , where finally fell below the accretion time scale (Fig. to grow and finally broke out of the accreting ˙M* is the mass of the protostar and M is the 1C). After this, the protostar began its so-called envelope. At M* ≅ 25 M⊙, the size of the bipolarmass accretion rate, whereas that for the latter KH contraction, in which it gradually contracted H II region exceeded 0.1 pc (Fig. 2B). Becauseis the Kelvin-Helmholtz (KH) time scale tKH ≡ as it radiated its energy away (Fig. 1A). The stel- of the high pressure of the heated ionized gas,G M*2/R*L*, where L* is the luminosity from lar luminosity was the main component of the the opening angle of the ionized region alsothe stellar interior, R* is the radius of the pro- total luminosity after this evolutionary stage (Fig. increased as the star grew (Fig. 2C). Shockstostar, and G is the gravitational constant. The 1B). The stellar luminosity L* increased, and propagated into the envelope preceding the ex- Downloaded from www.sciencemag.org on December 1, 2011total luminosity of the protostar Ltot is the sum stellar radius R* decreased, as the stellar mass pansion of the ionized region. The shocked gasof the stellar luminosity L* and accretion lumi- increased. As a result, the stellar effective tem- was accelerated outward at a velocity of several ˙nosity Lacc ≡ GM*M/R* (13). perature Teff º (L*/R*2)1/4 and the ultraviolet kilometers per second. The shock even reached regions shielded against direct stellar UV irra- diation. The outflowing gas stopped the infall of material from the envelope onto the disk (fig. S7). Without the replenishment of disk mate- rial from the envelope, the accretion rate onto the protostar decreased (Fig. 3). In addition, the absence of accreting material onto the cir- cumstellar disk means that the disk was ex- posed to the intense ionizing radiation from the star. The resulting photoevaporation of disk gas also reduced the accretion rate onto the protostar. The photoevaporated gas escaped to- ward the polar direction within the ionized re- gion. The typical velocity of the flow was several tens of kilometers per second, comparable with the sound speed of the ionized gas, which was high enough for the evaporating flow to escape from the gravitational potential well of the dark matter halo. When central nuclear hydrogen burning first commenced at a stellar mass of 35 M⊙, it was via the proton-proton (pp)–chain normally associ- ated with low-mass stars. The primordial mate- rial does not have the nuclear catalysts necessary for carbon–nitrogen–oxygen (CNO)–cycle hy- drogen burning. Because the pp-chain alone can- not produce nuclear energy at the rate necessary to cover the radiative energy loss from the stel- lar surface, the star continues to contract until central temperatures and densities attain values that enable the 3-a process of helium burning (11). The product of helium burning is carbon, and once the relative mass abundance of carbon reaches ∼10−12, CNO-cycle hydrogen burning takes over as the principal source of nuclear en- ergy production, albeit at much higher central densities and temperatures than those of stars with solar abundances. These first-generation ZAMS (zero-age main sequence) stars are thusFig. 2. UV radiative feedback from the primordial protostar. The spatial distributions of gas temper- more compact and hotter than are their present-ature (left), number density (right), and velocity (right, arrows) are presented in each panel for the central day counterparts of equal mass (14). The subse-regions of the computational domain. The four panels show snapshots at times when the stellar mass quent evolution of the accreting star followedis M* = 20 M⊙ (A), 25 M⊙ (B), 35 M⊙ (C), and 42 M⊙ (D). The elapsed time since the birth of the along the ZAMS mass-radius relationship (Fig.primordial protostar is labeled in each panel. 1A). By the time the star attained 40 M⊙, the www.sciencemag.org SCIENCE VOL 334 2 DECEMBER 2011 1251
REPORTS Fig. 3. Evolution of the 0.01 stantially. Thus, our radiation-hydrodynamic cal- accretion rate onto the pri- culations predict final masses systematically lower Acc. Rate: M ( M / yr ) mordial protostar. The blue than those of the semianalytic models. line indicates the evolu- Although the results described above provide tion, which includes the a complete picture of how a primordial protostar effect of UV radiative feed- 0.001 No feedback regulates and terminates its growth, there are a back from the protostar. (a) few key quantities that determine the strength of The red line indicates a nu- (b) the feedback effect, as suggested by the semi- merical experiment with (c) analytic model (8). With smaller initial rotation no UV feedback. The open of the natal dense core, the density in the en- and solid circles denote 1e-4 (d) velope near the polar directions would be higher. the characteristic epochs feedback Hydrogen recombination occurs rapidly in the of the protostellar evolu- dense gas, which prevents the breakout of the tion, beginning of the KH contraction, and the pro- 0 10 20 30 40 50 60 ionized region. Gas accretion can last for a longer tostar’s arrival to the ZAMS. time in this case and would form more massive Stellar Mass: M ( M ) Fig. 2, A to D, shows the stars (SOM text). Nevertheless, even considering snapshots at the moments marked here with asterisks. variations among dark halos bearing the first stars, a substantial fraction of the first stars should Downloaded from www.sciencemag.org on December 1, 2011 be less massive than 100 M⊙ and end their lives as ordinary core-collapse supernovae. Gas ac- entire region above and below the disk (Fig. 2D) than the first stars because of a different gas ther- cretion might not be completely halted in a few was ionized. Mass accretion was terminated when mal evolution, with additional radiative cooling exceptional cases, thus leading to the formation the stellar mass was 43 M⊙ (Fig. 3). via H2 and HD molecules (21, 22). However, this of a small number of extremely massive stars The entire evolution described above took mode of star formation is suppressed even with that are >100 M⊙ in the early universe (26). Black about 0.1 million years from the birth of the em- weak H2 photodissociating background radia- holes left after such very massive stars’ deaths bryo protostar to the termination of the accretion. tion (22). If so suppressed, the formation process might have grown up to be the supermassive The star is expected to live another few million of the later-generation primordial stars would black holes lying in galaxies. years before exhausting all available nuclear fuel be similar to that of the very first stars, and most Recent 3D cosmological simulations showed and exploding as a core-collapse supernova (15). primordial stars could have experienced the evo- that a primordial gas cloud breaks up into several Our calculations show that the first stars reg- lution presented in this article regardless of their embryo protostars in an early phase (27, 28). ulated their growth by their own radiation. They generations. One might argue that today’s ob- Each of these protostars would continue to grow were not extremely massive, but rather similar in served metal-deficient stars formed after an epi- through mass accretion, but it remained uncertain mass to the O-type stars in our Galaxy. This re- sode of star formation with nonzero metallicity. how and when the growth is halted. Our radiation- solves a long-standing enigma regarding the el- For the star formation process to differ substan- hydrodynamics calculations explicitly show that emental abundance patterns of the Galactic oldest tially from that of the very first stars, one would the parent gas cloud is evaporated by intense metal-poor stars, which contain nucleosynthetic require metallicities in excess of [Fe/H] > −5 radiation from the central star when its mass is signatures from the earliest generation of stars. (23, 24). Caffau and co-workers (25) report on ob- several tens of solar masses. The circumstellar If a substantial number of first stars had masses servations of a metal-deficient star with [Fe/H] ≅ disks in our simulations are marginally stable in excess of 100 M⊙, they would end their lives −5, but without the corresponding enhancement against gravitational fragmentation (fig. S5). We through pair-instability supernovae (16, 17), ex- of carbon, nitrogen, and oxygen found in metal- expect that these disks—in a 3D simulation— pelling heavy elements that would imprint a deficient stars. The abundance pattern of this star would evolve analogously to our numerical sim- characteristic nucleosynthetic signature to the agrees with expectations from core-collapse su- ulations with assumed axial symmetry and have a elemental abundances in metal-poor stars. How- pernovae, implying that it formed from gas en- similar time-averaged structure. It is conceivable ever, no such signatures have been detected in hanced by material ejected from primordial stars that a few protostars are ejected dynamically the metal-poor stars in the Galactic halo (18, 19). with masses less than 100 M⊙. from the parent cloud, to remain as low-mass For example, the abundances of elements with We have performed radiation-hydrodynamic stars. Observationally, however, there have been odd atomic numbers are generally reduced in simulations only for a single star-forming region no low-mass zero-metallicity stars discovered in remnants of primordial supernovae. The odd- embedded in a cosmological simulation. Our se- the Galaxy. This fact suggests the limited for- even contrast pattern expected in pair-instability lected dark halo was typical in mass, spin, and mation efficiency of such low-mass primordial supernovae is much stronger than the observed formation epoch when compared with those in stars (19). Low-mass stars (<1 M⊙) and extreme- patterns in Galactic metal-poor stars (17). More- other studies (5). The evolution presented here is ly high mass stars (>100 M⊙), if any, are thus a over, pair-instability supernovae predict a small somewhat similar to that predicted by the semi- minor population among the first stars. abundance ratio [Zn/Fe], but observed values are analytic model, in which the expansion of the Our self-consistent calculations show that much larger (16). Detailed spectroscopic studies ionized region begins when the stellar mass is the characteristic mass of the first stars is several of extremely metal-deficient stars indicate that ≅25 M⊙ and the final mass is ≅57 M⊙ (8), the tens of solar masses. Although this is less than the metal-poor stars were born in an interstellar lowest final stellar mass predicted by the semi- that of the conventionally proclaimed extremely medium that had been metal-enriched by super- analytic treatment. If input parameters of the massive stars (>100 M⊙), it is still much larger novae of ordinary massive stars (20). semianalytic models are chosen to fit our initial than the characteristic mass of stars in our galaxy Second-generation stars, which formed from gas cloud, however, the final mass should be (<1 M⊙) (29). the primordial gas affected by radiative or me- higher, ≅90 M⊙ (SOM text). Our calculations fol- chanical feedback from the first stars, could have low the dynamical response of the infalling gas References and Notes dominated the metallicity of the young inter- onto the circumstellar disk. The expansion of 1. V. Bromm, N. Yoshida, L. Hernquist, C. F. McKee, Nature 459, 49 (2009). stellar medium, which then spawned the observed the ionized region around the protostar generates 2. K. Omukai, R. Nishi, Astrophys. J. 508, 141 (1998). Galactic halo stars. These second-generation stars a powerful outflow even behind the surrounding 3. T. Abel, G. L. Bryan, M. L. Norman, Science 295, 93 could have been more numerous but less massive disk. This effect reduces the accretion rate sub- (2002).1252 2 DECEMBER 2011 VOL 334 SCIENCE www.sciencemag.org
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McKee, J. C. Tan, Astrophys. J. 681, 771 (2008). L117 (2007). which is supported by NASA. Data analysis was (in part) 9. H. W. Yorke, A. Welz, Astron. Astrophys. 315, 555 (1996). 23. [Fe/H] ≡ log(Fe/H)star − log(Fe/H) sun, where (Fe/H) is carried out on the general-purpose PC farm at Center for10. H. W. Yorke, C. Sonnhalter, Astrophys. J. 569, 846 (2002). mass ratio of Fe to H. Computational Astrophysics (CfCA) of National Astronomical11. K. Omukai, F. Palla, Astrophys. J. 589, 677 (2003). 24. T. Hosokawa, K. Omukai, Astrophys. J. 703, 1810 (2009). Observatory of Japan.12. T. Hosokawa, K. Omukai, Astrophys. J. 691, 823 (2009). 25. E. Caffau et al., Nature 477, 67 (2011).13. This definition of accretion luminosity includes the 26. T. Ohkubo, K. Nomoto, H. Umeda, N. Yoshida, S. Tsuruta, Supporting Online Material mechanical luminosity of an accretion-driven wind, and Astrophys. J. 706, 1184 (2009). www.sciencemag.org/cgi/content/full/science.1207433/DC1 Materials and Methods the ratio tKH/tacc is equal to the ratio Lacc/L*. 27. M. J. Turk, T. Abel, B. O’Shea, Science 325, 60114. D. Ezer, A. G. W. Cameron, Astrophys. Space Sci. 14, 399 (2009). SOM Text Figs. S1 to S7 (1971). 28. P. C. Clark et al., Science 331, 1040 (2011). Tables S1 and S215. D. Schaerer, Astron. Astrophys. 382, 28 (2002). 29. G. Chabrier, Publ. Astron. Soc. Pac. 115, 763 (2003).16. H. Umeda, K. Nomoto, Astrophys. J. 565, 385 (2002). References (30–64)17. A. Heger, S. E. Woosley, Astrophys. J. 567, 532 (2002). Acknowledgments: We thank T. Nakamura, K. Nomoto, 25 April 2011; accepted 28 October 201118. J. Tumlinson, A. Venkatesan, J. M. Shull, Astrophys. J. S. Inutsuka, and N. Turner for stimulating discussions on this Published online 10 November 2011; 612, 602 (2004). topic. Comments by an anonymous referee helped improve the 10.1126/science.1207433 Downloaded from www.sciencemag.org on December 1, 2011 of two counter-oscillating sublattices within theEntangling Macroscopic Diamonds diamond structure. The optical phonons are mac- roscopic, persistent excitations distributed overat Room Temperature ∼1016 atoms within the crystals. The phonons have a very high carrier frequency of 40 THz owingK. C. Lee,1* M. R. Sprague,1* B. J. Sussman,2 J. Nunn,1 N. K. Langford,1 X.-M. Jin,1,3 to the extremely strong interactions between neigh-T. Champion,1 P. Michelberger,1 K. F. Reim,1 D. England,1 D. Jaksch,1,3 I. A. Walmsley1† boring atoms, giving rise to a mechanically stiff lattice. This large energy, compatible with the ul-Quantum entanglement in the motion of macroscopic solid bodies has implications both for trashort pulses in our experiment (bandwidthquantum technologies and foundational studies of the boundary between the quantum and ∼7 THz), also eliminates the need for cooling orclassical worlds. Entanglement is usually fragile in room-temperature solids, owing to strong optical pumping, because thermal excitations areinteractions both internally and with the noisy environment. We generated motional entanglement negligible at room temperature. The specific ex-between vibrational states of two spatially separated, millimeter-sized diamonds at room perimental protocol that we use is based on thetemperature. By measuring strong nonclassical correlations between Raman-scattered photons, well-known DLCZ scheme (12) and previouswe showed that the quantum state of the diamonds has positive concurrence with 98% probability. pioneering experiments in cold atomic ensem-Our results show that entanglement can persist in the classical context of moving macroscopic bles (13–16). We first create a phonon via spon-solids in ambient conditions. taneous Raman scattering from a strong optical pump pulse, an event that is simultaneously ac- ur intuition about the nature of the phys- approach is to design systems with well-defined companied by the emission of a Stokes photonO ical world is strongly conditioned by the experience that macroscopic solidsmove according to the rules of classical mechan- and long-lived normal modes that can be selec- tively excited, and then to cool them to remove thermal noise and isolate them from the environ- (red-shifted from the pump). After this interac- tion, the joint state of the diamond and the Stokes mode can be written asics. Quantum theory, however, asserts that super- ment. Substantial progress has been made toward Â Ã positions and entanglement are possible even for demonstrating strong quantum signatures in larger ys ≈ 1 þ es s† (ts )b† (ts ) vac ð1Þlarge objects. Therefore, exploration of the persist- systems—for example, in optomechanical (3–5),ence of quantum correlations in the traditionally molecular (6), and superconducting (7) systems. where |es|2 1 is the scattering probabilityclassical realm is important for both fundamental Mechanical oscillators can now be cooled to the and |vac〉 = |vacopt〉 ⊗ |vacvib〉 is the joint op-science and technology, because of the impli- thermal ground state (7–9). tical and vibrational vacuum state containingcations for physics beyond conventional quan- A different approach is required, however, no photons and no phonons; s and b are thetum mechanics (1) and for quantum information to reveal quantum features in the motion of “or- bosonic annihilation operators for the Stokesprocessing, which requires sustained coherence dinary” solids in the high-entropy environment and phonon modes, respectively, evaluated atacross many particles (2). present at ambient conditions. Without a spe- the time ts when the pump pulse exits the dia- The two main barriers for creating superpo- cially engineered system, measurements must be mond. Equation 1 describes an entangled statesitions and entanglement in the mechanical mo- made on time scales shorter than the character- of optical and material modes, which is alreadytion of macroscopic systems are strong internal istically fast coherence decay times of a real-world nonclassical. To entangle two diamonds, we simul-interactions, which complicate the dynamics, and system. This can be achieved with ultrashort op- taneously pump two separate crystals—producingstrong coupling with the environment, which tical pulses. Recent studies of quantum coherence the state |Ys〉 = |ysL〉|ysR〉, where L and R denoteleads to short decoherence times. The standard in biology have used ultrafast probes and inter- the left and right diamonds, respectively—and ference measurements to establish the persist- we combine their Stokes modes on a polarizing1 Clarendon Laboratory, University of Oxford, Parks Road, Oxford ence of quantum behavior in naturally occurring beamsplitter (Fig. 1). The Stokes modes are causedOX1 3PU, UK. 2National Research Council of Canada, Ottawa, bulk systems (10, 11). To probe entanglement, to interfere with relative phase ϕs by means of aOntario K1A 0R6, Canada. 3Centre for Quantum Technologies,National University of Singapore, Singapore. however, it is also necessary to access the cor- half-wave plate and polarizer. Detection of a*These authors contributed equally to this work. relations of the excited modes. Stokes photon at a detector Ds placed behind†To whom correspondence should be addressed. E-mail: We study excitations of the optical phonon the polarizer corresponds to application of firstname.lastname@example.org mode in diamond, a bulk vibration consisting measurement (17) E = 〈vacopt|s(t′s), where t′s is www.sciencemag.org SCIENCE VOL 334 2 DECEMBER 2011 1253