《量子力学》课程教学资源（文献资料）波粒二象性_实物粒子波粒二象性的实验证实_过氟烷基化合物纳米球的干涉.pdf_大学文库

ARTICLE nature communications | 2:263 | DOI: 10.1038/ncomms1263 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. Received 5 Jan 2011 | Accepted 2 Mar 2011 | Published 5 Apr 2011 DOI: 10.1038/ncomms1263 The wave nature of matter is a key ingredient of quantum physics and yet it defies our classical intuition. First proposed by Louis de Broglie a century ago, it has since been confirmed with a variety of particles from electrons up to molecules. Here we demonstrate new high-contrast quantum experiments with large and massive tailor-made organic molecules in a near-field interferometer. Our experiments prove the quantum wave nature and delocalization of compounds composed of up to 430 atoms, with a maximal size of up to 60Å, masses up to m=6,910AMU and de Broglie wavelengths down to λdB=h/mv1pm. We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence. 1 University of Vienna, Vienna Center for Quantum Science and Technology, VCQ, Faculty of Physics, Boltzmanngasse 5, Vienna 1090, Austria. 2 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Street 38, Dresden D-01187, Germany. 3 Central Research and Development Department, E. I. DuPont de Nemours & Co. Inc., Experimental Station, PO Box 80328, Wilmington, Delaware 19880-0328, USA. 4 Department of Chemistry, University of Basel, St Johannsring 19, Basel CH-4056, Switzerland. 5 Karlsruhe Institute of Technology, Institute for Nanotechnology, PO Box 3640, Karlsruhe D-76021, Germany. Correspondence and requests for materials should be addressed to M.A. (email: markus.arndt@univie.ac.at). Quantum interference of large organic molecules Stefan Gerlich1 , Sandra Eibenberger1 , Mathias Tomandl1 , Stefan Nimmrichter1 , Klaus Hornberger2 , Paul J. Fagan3 , Jens Tüxen4, Marcel Mayor4,5 & Markus Arndt1

ARTICLE NATURE COMMUNICATIONS DOl:10.1038/ncomms1263 n many discussions on the foundations of physics,single-particle diffraction at a double slit!-or gratings-12 is regarded as a para- digmatic example for a highly non-classical feature of quantum mechanics,which has never been observed for objects of our mac- roscopic world.The quantum superposition principle has become of paramount importance also for the growing field of quantum information science'3.Correspondingly,research in many labora- tories around the world is focusing on our understanding of the role of decoherence for increasingly complex quantum systems and possible practical or truly fundamental limits to the observation of quantum dynamics 4s Here we report on a new leap in quantum interference with large organic molecules.In contrast to earlier successful experi- ments with internal molecular wave packets,our study focuses on the wave evolution in the centre of mass motion of the molecule as a whole,that is,pure de Broglie interference.We do this with compounds that have been customized to provide useful molecu- lar beams at moderate temperatures78.Figure 1 compares the size of two perfluoroalkylated nanospheres,PFNS8 and PFNS10,with a single Co fullerene and it relates a single tetraphenylporphyrin Figure 1|Gallery of molecules used in our interference study.(a)The molecule (TPP)to its complex derivatives TPPF84 and TPPF152. fullerene Cao(m=720 AMU,60 atoms)serves as a size reference and We demonstrate the wave nature of all these molecules in a three- for calibration purposes;(b)The perfluoroalkylated nanosphere PFNS8 grating near-field interferometer of the Kapitza-Dirac-Talbot- (Cao[CF2s]a,m=5.672 AMU,356 atoms)is a carbon cage with eight Lau type22,as shown in Figure 2. perfluoroalkyl chains.(c)PFNS10 (Cao[CFsm=6,910 AMU,430 atoms)has ten side chains and is the most massive particle in the set Results (d)A single tetraphenylporphyrin TPP(CHaoN,m=614 AMU,78 Experimental setup.The particles are evaporated in a thermal atoms)is the basis for the two derivatives(e)TPPF84(CHFNS source.Their velocity is selected using the gravitational free-fall m=2,814AMU,202 atoms)and (f)TPPF152 (CesHa4F s2O NS4. through a sequence of three slits.The interferometer itself consists m=5,310 AMU,430 atoms).In its unfolded configuration,the latter is the of three gratings G,G,and G:in a vacuum chamber at a pressure largest molecule in the set.Measured by the number of atoms,TPPF152 of p<10-mbar.The first grating is a SiN,membrane with 90-nm and PFNS10 are equally complex.All molecules are displayed to scale.The wide slits arranged with a periodicity ofd=266nm.Each slit of G scale bar corresponds to 10 A. imposes a constraint onto the transverse molecular position that, following Heisenberg's uncertainty relation,leads to a momentum Detector uncertainty.The latter turns into a growing delocalization and transverse coherence of the matter wave with increasing distance from G.The second grating,G,is a standing laser light wave with a wavelength of A=532 nm.The interaction between the electric laser light field and the molecular optical polarizability creates asinusoidal G potential,which phase-modulates the incident matter waves.The distance between the first two gratings is chosen such that quantum interference leads to the formation of a periodic molecular density pattern 105 mm behind G2.This molecular nanostructure is sampled by scanning a second SiN,grating(G3,identical to G,)across the Lens molecular beam while counting the number of the transmitted particles in a quadrupole mass spectrometer(QMS). In extension to earlier experiments,we have added various tech- nological refinements:the oven was adapted to liquid samples,a liquid-nitrogen-cooled chamber became essential to maintain the Oven source pressure low,a new mass analyser allowed us to increase the detected molecular flux by a factor of four and many optimi- zation cycles in the interferometer alignment were needed to meet Figure 2 Layout of the Kapitza-Dirac-Talbot-Lau (KDTL)interference all requirements for high-contrast experiments with very massive experiment.The effusive source emits molecules that are velocity-selected particles. by the three delimiters S,,S,and S.The KDTL interferometer is composed of two SiN,gratings G,and G,as well as the standing light wave G.The Observed interferograms.We recorded quantum interferograms optical dipole force grating imprints a phase modulation (x)P/(vw) for all molecules of Figure 1,as shown in Figure 3.In all cases the onto the matter wave.Hereis the optical polarizability,Pthe laser measured fringe visibility V,that is,the amplitude of the sinusoidal power,v the molecular velocity and w,the laser beam waist perpendicular modulation normalized to the mean of the signal,exceeds the maxi- to the molecular beam.The molecules are detected using electron impact mally expected classical moire fringe contrast by a significant multi- ionization and quadrupole mass spectrometry. ple of the experimental uncertainty.This is best shown for TPPF84 and PFNS8,which reached the highest observed interference con- for TPPF152 (see Figure 3),in which our classical model predicts trast in our high-mass experiments so far,with individual scans V=1%.This supports our claim of true quantum interference for up to V=33%for TPPF84 (m=2,814AMU)and Vh=49%for all these complex molecules. PFNS8 at a mass of m=5,672 AMU.In addition,we have observed The most massive molecules are also the slowest and therefore a maximum contrast of V=174%for PFNS10 and V=16+2%the most sensitive ones to external perturbations.In our particle NATURE COMMUNICATIONS 2:263 DOl:10.1038/ncomms1263 www.nature.com/naturecommunications 2011 Macmillan Publishers Limited.All rights reserved

ARTICLE nature communications | DOI: 10.1038/ncomms1263 nature communications | 2:263 | DOI: 10.1038/ncomms1263 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. I n many discussions on the foundations of physics, single-particle diffraction at a double slit1–4 or grating5–12 is regarded as a paradigmatic example for a highly non-classical feature of quantum mechanics, which has never been observed for objects of our macroscopic world. The quantum superposition principle has become of paramount importance also for the growing field of quantum information science13 . Correspondingly, research in many laboratories around the world is focusing on our understanding of the role of decoherence for increasingly complex quantum systems and possible practical or truly fundamental limits to the observation of quantum dynamics14,15. Here we report on a new leap in quantum interference with large organic molecules. In contrast to earlier successful experiments with internal molecular wave packets,16 our study focuses on the wave evolution in the centre of mass motion of the molecule as a whole, that is, pure de Broglie interference. We do this with compounds that have been customized to provide useful molecular beams at moderate temperatures17,18. Figure 1 compares the size of two perfluoroalkylated nanospheres, PFNS8 and PFNS10, with a single C60 fullerene19 and it relates a single tetraphenylporphyrin molecule (TPP) to its complex derivatives TPPF84 and TPPF152. We demonstrate the wave nature of all these molecules in a threegrating near-field interferometer20,21 of the Kapitza-Dirac-TalbotLau type22,23, as shown in Figure 2. Results Experimental setup. The particles are evaporated in a thermal source. Their velocity is selected using the gravitational free-fall through a sequence of three slits. The interferometer itself consists of three gratings G1, G2 and G3 in a vacuum chamber at a pressure of p<10−8mbar. The first grating is a SiNx membrane with 90-nm wide slits arranged with a periodicity of d=266nm. Each slit of G1 imposes a constraint onto the transverse molecular position that, following Heisenberg’s uncertainty relation, leads to a momentum uncertainty. The latter turns into a growing delocalization and transverse coherence of the matter wave with increasing distance from G1. The second grating, G2, is a standing laser light wave with a wavelength of λ=532nm. The interaction between the electric laser light field and the molecular optical polarizability creates a sinusoidal potential, which phase-modulates the incident matter waves. The distance between the first two gratings is chosen such that quantum interference leads to the formation of a periodic molecular density pattern 105mm behind G2. This molecular nanostructure is sampled by scanning a second SiNx grating (G3, identical to G1) across the molecular beam while counting the number of the transmitted particles in a quadrupole mass spectrometer (QMS). In extension to earlier experiments, we have added various technological refinements: the oven was adapted to liquid samples, a liquid-nitrogen-cooled chamber became essential to maintain the source pressure low, a new mass analyser allowed us to increase the detected molecular flux by a factor of four and many optimization cycles in the interferometer alignment were needed to meet all requirements for high-contrast experiments with very massive particles. Observed interferograms. We recorded quantum interferograms for all molecules of Figure 1, as shown in Figure 3. In all cases the measured fringe visibility V, that is, the amplitude of the sinusoidal modulation normalized to the mean of the signal, exceeds the maximally expected classical moiré fringe contrast by a significant multiple of the experimental uncertainty. This is best shown for TPPF84 and PFNS8, which reached the highest observed interference contrast in our high-mass experiments so far, with individual scans up to Vobs=33% for TPPF84 (m=2,814AMU) and Vobs=49% for PFNS8 at a mass of m=5,672AMU. In addition, we have observed a maximum contrast of Vobs=17±4% for PFNS10 and Vobs=16±2% for TPPF152 (see Figure 3), in which our classical model predicts Vclass=1%. This supports our claim of true quantum interference for all these complex molecules. The most massive molecules are also the slowest and therefore the most sensitive ones to external perturbations. In our particle Figure 1 | Gallery of molecules used in our interference study. (a) The fullerene C60 (m=720AMU, 60 atoms) serves as a size reference and for calibration purposes; (b) The perfluoroalkylated nanosphere PFNS8 (C60[C12F25]8, m=5,672AMU, 356 atoms) is a carbon cage with eight perfluoroalkyl chains. (c) PFNS10 (C60[C12F25]10, m=6,910AMU, 430 atoms) has ten side chains and is the most massive particle in the set. (d) A single tetraphenylporphyrin TPP (C44H30N4, m=614AMU, 78 atoms) is the basis for the two derivatives (e) TPPF84 (C84H26F84N4S4, m=2,814AMU, 202 atoms) and (f) TPPF152 (C168H94F152O8N4S4, m=5,310AMU, 430 atoms). In its unfolded configuration, the latter is the largest molecule in the set. Measured by the number of atoms, TPPF152 and PFNS10 are equally complex. All molecules are displayed to scale. The scale bar corresponds to 10Å. y X Detector G1 G2 G3 S3 S2 S1 Oven Lens Laser Z Figure 2 | Layout of the Kapitza-Dirac-Talbot-Lau (KDTL) interference experiment. The effusive source emits molecules that are velocity-selected by the three delimiters S1 , S2 and S3. The KDTL interferometer is composed of two SiNx gratings G1 and G3, as well as the standing light wave G2. The optical dipole force grating imprints a phase modulation ϕ(x)∝αopt·P/(v·wy) onto the matter wave. Here αopt is the optical polarizability, P the laser power, v the molecular velocity and wy the laser beam waist perpendicular to the molecular beam. The molecules are detected using electron impact ionization and quadrupole mass spectrometry

NATURE COMMUNICATIONS DOl:10.1038/ncomms1263 ARTICLE a a 00 2000 400 200 00 100 400 200 4006008001.000 xs Position (nm) 012.3456 on (nm d 1.400 Figure 4 |Quantum interference visibility as a function of the diffracting 1200 laser power.The best distinction between quantum and classical behaviour .000 is made by tracing the interference fringe visibility as a function of the laser 800 power,which determines the phase imprinted by the second grating.Each 00 of the two experimental runs per molecule is represented by full circles 400 and the error bar provides the 68%confidence bound of the sinusoidal fit 200 to the interference fringe.The thick solid line is the quantum fit in which 600 800 1.000 200 400800800 1.000 the shaded region covers a variation of the mean molecular velocity by Xs Position (nm) 气3 Position(nm) Av=+2ms-1.(a)The TPPF84 data are well reproduced by the quantum model (see text)and completely missed by the classical curve (thin line Figure 3 Quantum interferograms of tailor-made large organic on the left).(b)The same holds for PFNS8.The following parameters molecules.Quantum interference well beyond the classical expectations were used for the models:TPpF84:v=95ms-1±16%，a=200A3x4πeo has been observed for all molecules in the set.In all panels,the black (ft),ce=10-nm-2,w,=34±3μn and w,=500±50μm.PFNS8: circles represent the experimental result,the blue line is a sinusoidal v=75ms1±10%，a=190A3×4re。(ft),Got=10-m-2,w,=27±3μmand fit to the data and the shaded area indicates the detector dark rate. w,=620±50m. (a)The beam of perfluoroalkylated nanospheres,PFNS8,is characterized by a mean velocity of v=63mswith a full width AvwM=13ms. The observed contrast of Vobs=49+6%is in good agreement with the with the full quantum calculation and in clear discrepancy with the expected quantum contrast of Vm=51%and is clearly discernible from classical prediction.The abscissa scaling of the V(P)curve is a good the classically expected visibility of V1%.The stated uncertainty is indicator for that.The quantum prediction mimics the classical the standard deviation of the fit to the data.(b)For PFNS10,the signal curve qualitatively,but it is stretched in the laser power by a factor of about six (see Methods). was too weak to allow a precise velocity measurement and quantum calculation.The oven position for these particles,however,limits the The laser power can be calibrated with an accuracy of1% but the abscissa also scales in proportion to the optical molecular molecular velocity to v<80ms-and therefore allows us to define an upper bound to the classical visibility.(c)For TPPF84,we measure v=95ms- polarizability and inversely with the vertical laser waist.The theo- with AvEwHM=34ms-1.This results in V=33+3%with V=30%and retical curves of Figure 4 are plotted assumingp=200A3x4 V<1%.(d)The signal for TPPF152 is equally low compared with that for TPPF84 and =190 A3x4nE for PFNS8.These numbers have of PFNS10.For this compound we find Vabs=16+2%,Vua=45%and to be compared with the static polarizabilities computed using Vss=1%. Gaussian09 (ref.24).These are=155A3x4rteo for TPPF84 and =200A3x4r for PFNS8.A variation in the polarizability changes the horizontal scale of the plot as does a different laser set,these are PFNS10 and TPPF152,which,in addition,exhibited waist.Both are bound by a relative uncertainty of less than 30%. the smallest count rates and therefore the highest statistical fluc- A classical explanation is therefore safely excluded as an explanation tuations.To record the interferograms,we had to open the vertical for the experiments. beam delimiter S,and accept various imperfections:an increased The quantitative agreement of the experimental and expected velocity spread,a higher sensitivity to grating misalignments and contrast is surprisingly good,given the high complexity of the also an averaging over intensity variations in the Gaussian-shaped particles.Various factors contribute to the remaining small discrep- diffraction laser beam G2.In addition,we had to enhance the QMS ancies.The interference visibility is highly sensitive to apparatus transmission efficiency at the expense of transmitting a broader vibrations,variations in the grating period on the level of 0.5A and mass range.The recorded signals associated with PFNS10 and a misalignment below 100urad in the grating roll angle. TPPF152 covered a mass window of AmwHM=500 AMU around their nominal masses.Although all samples were well characterized Discussion before the evaporation process,we can therefore not exclude some PFNS10 and TPPF152 contain 430 atoms covalently bound in contamination with adducts or fragments in this high mass range. one single particle.This is ~350%more than that in all previous But even if there were a relative mass spread of 10%,this would only experiments and it compares well with the number of atoms in influence the wavelength distribution A the same way as does small Bose-Einstein condensates26(BEC),which,of course,oper- the velocity spread.Owing to the inherent design of the Kapitza- ate in a vastly different parameter regime:The molecular de Broglie Dirac-Talbot-Lau interferometer2,these experimental settings are wavelength is about six orders of magnitude smaller than that still compatible with sizeable quantum interference,even under of ultracold atoms and the internal molecular temperature exceeds such adverse conditions. typical BEC values (T<1uK)by about nine orders of magnitude. Although matter wave interference of BECs relies on the de Broglie Comparison of theory and experiment.The experimental values wavelength of the individual atoms,our massive molecules always have to be compared with the theoretical predictions based on a clas- appear as single entities sical and a quantum model.The measured interference visibility is One can find various definitions in the literature for what a true plotted as a function of the diffracting laser power P in Figure 4 for Schrodinger cat2 should be and a number of intriguing experiments TPPF84(4a)and PFNS8(4b).Our data are in very good agreement have reported the generation of photonic?s or atomic cat-states290. NATURE COMMUNICATIONS 2:263 DOl:10.1038/ncomms1263 www.nature.com/naturecommunications 2011 Macmillan Publishers Limited.All rights reserved

ARTICLE nature communications | DOI: 10.1038/ncomms1263 nature communications | 2:263 | DOI: 10.1038/ncomms1263 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. set, these are PFNS10 and TPPF152, which, in addition, exhibited the smallest count rates and therefore the highest statistical fluctuations. To record the interferograms, we had to open the vertical beam delimiter S2 and accept various imperfections: an increased velocity spread, a higher sensitivity to grating misalignments and also an averaging over intensity variations in the Gaussian-shaped diffraction laser beam G2. In addition, we had to enhance the QMS transmission efficiency at the expense of transmitting a broader mass range. The recorded signals associated with PFNS10 and TPPF152 covered a mass window of ∆mFWHM =500AMU around their nominal masses. Although all samples were well characterized before the evaporation process, we can therefore not exclude some contamination with adducts or fragments in this high mass range. But even if there were a relative mass spread of 10%, this would only influence the wavelength distribution ∆λdB/λdB the same way as does the velocity spread. Owing to the inherent design of the KapitzaDirac-Talbot-Lau interferometer22 , these experimental settings are still compatible with sizeable quantum interference, even under such adverse conditions. Comparison of theory and experiment. The experimental values have to be compared with the theoretical predictions based on a classical and a quantum model23 . The measured interference visibility is plotted as a function of the diffracting laser power P in Figure 4 for TPPF84 (4a) and PFNS8 (4b). Our data are in very good agreement with the full quantum calculation and in clear discrepancy with the classical prediction. The abscissa scaling of the V(P) curve is a good indicator for that. The quantum prediction mimics the classical curve qualitatively, but it is stretched in the laser power by a factor of about six (see Methods). The laser power can be calibrated with an accuracy of ±1% but the abscissa also scales in proportion to the optical molecular polarizability and inversely with the vertical laser waist. The theoretical curves of Figure 4 are plotted assuming αopt=200Å3 ×4πε0 for TPPF84 and αopt=190Å3 ×4πε0 for PFNS8. These numbers have to be compared with the static polarizabilities computed using Gaussian09 (ref. 24). These are αstat=155Å3 ×4πε0 for TPPF84 and αstat=200Å3 ×4πε0 for PFNS8. A variation in the polarizability changes the horizontal scale of the plot as does a different laser waist. Both are bound by a relative uncertainty of less than 30%. A classical explanation is therefore safely excluded as an explanation for the experiments. The quantitative agreement of the experimental and expected contrast is surprisingly good, given the high complexity of the particles. Various factors contribute to the remaining small discrepancies. The interference visibility is highly sensitive to apparatus vibrations, variations in the grating period on the level of 0.5Å and a misalignment below 100µrad in the grating roll angle. Discussion PFNS10 and TPPF152 contain 430 atoms covalently bound in one single particle. This is ~350% more than that in all previous experiments25 and it compares well with the number of atoms in small Bose–Einstein condensates26 (BEC), which, of course, operate in a vastly different parameter regime: The molecular de Broglie wavelength λdB is about six orders of magnitude smaller than that of ultracold atoms and the internal molecular temperature exceeds typical BEC values (T<1µK) by about nine orders of magnitude. Although matter wave interference of BECs relies on the de Broglie wavelength of the individual atoms, our massive molecules always appear as single entities. One can find various definitions in the literature for what a true Schrödinger cat27 should be and a number of intriguing experiments have reported the generation of photonic28 or atomic cat-states29,30. Counts/2s 0 200 400 600 800 1,000 1,200 1,400 Counts/8s 0 200 400 600 800 1,000 0 100 200 300 400 0 100 200 300 400 500 Counts/2s x3 Position (nm) 0 200 400 600 800 1,000 x3 Position (nm) 0 200 400 600 800 1,000 x3 Position (nm) 0 200 400 600 800 1,000 x3 Position (nm) 0 500 1,000 1,500 2,000 Counts/8s Figure 3 | Quantum interferograms of tailor-made large organic molecules. Quantum interference well beyond the classical expectations has been observed for all molecules in the set. In all panels, the black circles represent the experimental result, the blue line is a sinusoidal fit to the data and the shaded area indicates the detector dark rate. (a) The beam of perfluoroalkylated nanospheres, PFNS8, is characterized by a mean velocity of v=63ms−1 with a full width ∆vFWHM =13ms−1 . The observed contrast of Vobs=49±6% is in good agreement with the expected quantum contrast of Vquant=51% and is clearly discernible from the classically expected visibility of Vclass<1%. The stated uncertainty is the standard deviation of the fit to the data. (b) For PFNS10, the signal was too weak to allow a precise velocity measurement and quantum calculation. The oven position for these particles, however, limits the molecular velocity to v<80ms−1 and therefore allows us to define an upper bound to the classical visibility. (c) For TPPF84, we measure v=95ms−1 with ∆vFWHM =34ms−1 . This results in Vobs=33±3% with Vquant=30% and Vclass<1%. (d) The signal for TPPF152 is equally low compared with that of PFNS10. For this compound we find Vobs=16±2%, Vquant=45% and Vclass=1%. 0 1 2 3 4 5 6 7 8 9 0 10 20 30 40 50 60 Visibility (%) Power (W) 0 1 2 3 4 5 0 10 20 30 40 50 60 Visibility (%) Power (W) Figure 4 | Quantum interference visibility as a function of the diffracting laser power. The best distinction between quantum and classical behaviour is made by tracing the interference fringe visibility as a function of the laser power, which determines the phase imprinted by the second grating. Each of the two experimental runs per molecule is represented by full circles and the error bar provides the 68% confidence bound of the sinusoidal fit to the interference fringe. The thick solid line is the quantum fit in which the shaded region covers a variation of the mean molecular velocity by ∆v= ±2ms−1 . (a) The TPPF84 data are well reproduced by the quantum model (see text) and completely missed by the classical curve (thin line on the left). (b) The same holds for PFNS8. The following parameters were used for the models: TPPF84: v=95ms−1 ±16%, α=200Å3 ×4πε0 (fit), σopt=10−21m−2 , wx=34±3µm and wy=500±50µm. PFNS8: v=75ms−1 ±10%, α=190Å3 ×4πε0 (fit), σopt=10−21m−2 , wx=27±3µm and wy=620±50µm

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In conclusion,our experiments reveal the quantum wave nature 19.Kroto,H.W.,Heath,J.R.,O'Brian,S.C..Curl,R.F.&Smalley,R.E.C60 of tailor-made organic molecules in an unprecedented mass and size Buckminsterfullerene.Nature 318,162-163(1985). 20.Clauser,J.F.in Experimental Metaphysics (eds Cohen,R.S..Home,M. domain.They open a new window for quantum experiments with Stachel,J.)1-11 (Kluwer Academic,1997). nanoparticles in a complexity class comparable to that of small pro- 21.Brezger,B..Arndt,M.&Zeilinger,A.Concepts for near-field interferometers teins,and they demonstrate that it is feasible to create and maintain with large molecules./Opt.B 5,S82-S89 (2003). high quantum coherence with initially thermal systems consisting 22.Gerlich,S.et al.A Kapitza-Dirac-Talbot-Lau interferometer for highly of more than 1,000 internal degrees of freedom. polarizable molecules.Nature Physics 3,711-715 (2007). 23.Hornberger,K.et al.Theory and experimental verification of Kapitza-Dirac- Talbot-Lau interferometry.New J.Phys.11,043032(2009). Methods 24.Frisch,M.J.et al.Gaussian 09,Revision A.1.(Gaussian,Inc.,Wallingford CT. Chemical synthesis.The porphyrin derivatives were synthesized by the attach- 2009). ment of a highly fluorous thiol to meso-tetra(pentafluorophenyl)porphyrin in 25.Tuxen,J.,Gerlich,S.,Eibenberger,S.,Arndt,M.Mayor,M.Quantum a nucleophilic aromatic substitution reaction by applying a modified literature interference distinguishes between constitutional isomers.Chem.Comm.46, procedure.To assemble TPPF84,the commercially available 1H,1H.2H2H- 4145-4147(2010). perfluorododecane-1-thiol as nucleophilic fluorous part was introduced to the 26.Bradley.C.C.,Sackett,C.A.,Tollett,J.J.Hulet,R.G.Evidence of Bose- porphyrin unit.The branched thiol building block for TPPF152 was synthesized Einstein condensation in an atomic gas with attractive interactions.Phys.Rev in three reaction steps.A reaction sequence including mono-functionalization Lett.79,1170(1997). of tris(bromomethyl)benzene with a protected thiol,introduction of two 27.Schrodinger,E.Die gegenwartige Situation in der Quantenmechanik fluorous ponytails and a final deprotection of the thiol functionality yielded the Naturwissenschaften 23,844-849 (1935). desired fluorous thiol suitable for the envisaged substitution reaction.All 28.Brune,M.et al.Observing the progressive decoherence of the 'meter'in a target structures were purified by column chromatography and characterized quantum measurement.Phys.Rev:Lett.77,4887-4890(1996) by nuclear magnetic resonance spectroscopy and mass spectrometry 29.Leibfried,D.et al.Creation of a six-atom 'Schrodinger Cat'state.Nature 438, (Supplementory Methods). 639-642(2005). 30.Monz,T.et al.Coherence of large-scale entanglement.arXiv:1009.6126v Differences between the classical and quantum predictions.The func- [quant-ph](2010). tional dependence of the interference fringe visibility on the laser power 31.Hornberger,K.et al.Collisional decoherence observed in matter wave is qualitatively similar in both a classical and a full quantum treatment.As interferometry.Phys.Rev.Lett.90,160401(2003). observed from the treatment described in ref.23 the abscissa scaling dif- 32.Hackermuller,L.et al.Decoherence of matter waves by thermal emission of fers,however,by the factor E/sin()with=L/where L is the distance radiation.Nature 427,711-714 (2004). between two consecutive gratings and Lr=d/Aas is the Talbot length.For 33.Samaroo,D.,Vinodu,M.,Chen,X.Drain,C.M.Meso-tetra(pentafluorophenyl)- the case of Figure 4,we find /sin()=5.9.The experimental data are in porphyrin as an efficient platform for combinatorial synthesis and the selection clear agreement with the quantum model. of new photodynamic therapeutics using a cancer cell line.I.Comb.Chem.9, 998-1011(2007). Equipment.The diffracting laser beam is generated by a Coherent Verdi V18 laser at 532 nm.The QMS is an Extrel CMS with a rod diameter of 9.5 mm,operated at a radio frequency of 440kHz.The SiN,gratings in G,and G,were made by Dr Tim Acknowledgments Savas,nm2 LLC MIT Cambridge. We thank Lucia Hackermuller(now University of Nottingham)for important contributions to the setup of a first version of this experiment until the end of 2006, and Hendrik Ulbricht(now University of Southampton)for his collaboration until References 2008.We thank Anton Zeilinger for his role as an initiator of the 'foundations of 1.Zeilinger,A.,Gahler,R.,Shull,C.G.,Treimer,W.Mampe,W.Single-and quantum physics'research programme in Vienna.The interference experiments were double-slit diffraction of neutrons.Rev.Mod.Phys.60,1067-1073(1988). financed through the Austrian FWF Wittgenstein grant(Z149-N16),the doctoral NATURE COMMUNICATIONS|2:263 DOl:10.1038/ncomms1263 www.nature.com/naturecommunications 2011 Macmillan Publishers Limited.All rights reserved

ARTICLE nature communications | DOI: 10.1038/ncomms1263 nature communications | 2:263 | DOI: 10.1038/ncomms1263 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. In as far as the term designates the quantum superposition of two macroscopically distinct states of a highly complex object, the molecules in our new experimental series are among the fattest Schrödinger cats realized to date. Schrödinger reasoned whether it is possible to bring a cat into a superposition state of being ‘dead’ and ‘alive’. In our experiment, the superposition consists of having all 430 atoms simultaneously ‘in the left arm’ and ‘in the right arm’ of our interferometer, that is, two possibilities that are macroscopically distinct. The path separation is about two orders of magnitude larger than the size of the molecules. Schrödinger’s thought experiment originally also required the entanglement between a microscopic atom and the final state of the macroscopic cat. Such a mechanism is not needed to create the molecular superposition state in our experiment. Entanglement between a molecule and a microscopic probe particle does, however, occur in decoherence processes in which the quantum interaction with the environment reveals which-path information14,15 and destroys the interference pattern. Collisions with residual gas molecules31 , the emission of heat radiation32 and the absorption of blackbody radiation are among the most important decoherence mechanisms for interferometry with massive particles. We estimate that they lead to a visibility reduction of less than 1% under the conditions of the present experimental arrangement, in spite of the high internal molecular temperatures and substantial dipole fluctuations. Specifically for PFNS8, a microscopically realistic account of the decoherence processes31,32 predicts a visibility reduction of 10% only if the temperature of either the molecule or the radiation field exceeds 1,500K, or if the residual nitrogen gas pressure exceeds 2×10−7mbar. In conclusion, our experiments reveal the quantum wave nature of tailor-made organic molecules in an unprecedented mass and size domain. They open a new window for quantum experiments with nanoparticles in a complexity class comparable to that of small proteins, and they demonstrate that it is feasible to create and maintain high quantum coherence with initially thermal systems consisting of more than 1,000 internal degrees of freedom. Methods Chemical synthesis. The porphyrin derivatives were synthesized by the attachment of a highly fluorous thiol to meso-tetra(pentafluorophenyl)porphyrin in a nucleophilic aromatic substitution reaction by applying a modified literature procedure33 . To assemble TPPF84, the commercially available 1H,1H,2H,2Hperfluorododecane-1-thiol as nucleophilic fluorous part was introduced to the porphyrin unit. The branched thiol building block for TPPF152 was synthesized in three reaction steps. A reaction sequence including mono-functionalization of tris(bromomethyl)benzene with a protected thiol, introduction of two fluorous ponytails and a final deprotection of the thiol functionality yielded the desired fluorous thiol suitable for the envisaged substitution reaction. All target structures were purified by column chromatography and characterized by nuclear magnetic resonance spectroscopy and mass spectrometry (Supplementory Methods). Differences between the classical and quantum predictions. The functional dependence of the interference fringe visibility on the laser power is qualitatively similar in both a classical and a full quantum treatment. As observed from the treatment described in ref. 23 the abscissa scaling differs, however, by the factor ξ/sin(ξ) with ξ = π·L/LT, where L is the distance between two consecutive gratings and LT = d2 /λdB is the Talbot length. For the case of Figure 4, we find ξ/sin(ξ)5.9. The experimental data are in clear agreement with the quantum model. Equipment. The diffracting laser beam is generated by a Coherent Verdi V18 laser at 532nm. The QMS is an Extrel CMS with a rod diameter of 9.5mm, operated at a radio frequency of 440 kHz. The SiNx gratings in G1 and G3 were made by Dr Tim Savas, nm2 LLC & MIT Cambridge. References 1. Zeilinger, A., Gähler, R., Shull, C. G., Treimer, W. & Mampe, W. Single- and double-slit diffraction of neutrons. Rev. Mod. Phys. 60, 1067–1073 (1988). 2. Carnal, O. & Mlynek, J. Young’s double-slit experiment with atoms: a simple atom interferometer. Phys. Rev. Lett. 66, 2689–2692 (1991). 3. Zimmermann, B. et al. 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Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 844–849 (1935). 28. Brune, M. et al. Observing the progressive decoherence of the ‘meter’ in a quantum measurement. Phys. Rev. Lett. 77, 4887–4890 (1996). 29. Leibfried, D. et al. Creation of a six-atom ‘Schrödinger Cat’ state. Nature 438, 639–642 (2005). 30. Monz, T. et al. Coherence of large-scale entanglement. arXiv:1009.6126v1 [quant-ph] (2010). 31. Hornberger, K. et al. Collisional decoherence observed in matter wave interferometry. Phys. Rev. Lett. 90, 160401 (2003). 32. Hackermüller, L. et al. Decoherence of matter waves by thermal emission of radiation. Nature 427, 711–714 (2004). 33. Samaroo, D., Vinodu, M., Chen, X. & Drain, C. M. Meso-tetra(pentafluorophenyl)- porphyrin as an efficient platform for combinatorial synthesis and the selection of new photodynamic therapeutics using a cancer cell line. J. Comb. Chem. 9, 998–1011 (2007). Acknowledgments We thank Lucia Hackermüller (now University of Nottingham) for important contributions to the setup of a first version of this experiment until the end of 2006, and Hendrik Ulbricht (now University of Southampton) for his collaboration until 2008. We thank Anton Zeilinger for his role as an initiator of the ‘foundations of quantum physics’ research programme in Vienna. The interference experiments were financed through the Austrian FWF Wittgenstein grant (Z149-N16), the doctoral