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optical trap (13), such that external motions do not Optical Atomic Coherence at the decohere the superposition of the two states. Using optically cooled 87Sr atoms in a zero-differential– Stark shift one-dimensional (1D) optical lattice and 1-Second Time Scale a cavity-stabilized probe laser with a sub-hertz spectral width, we have achieved probe-time– Martin M. Boyd, Tanya Zelevinsky, Andrew D. Ludlow, Seth M. Foreman, limited resonance linewidths of 1.8 Hz at the Sebastian Blatt, Tetsuya Ido,* Jun Ye† optical carrier frequency of 4.3 × 1014 Hz. The ratio of these frequencies, corresponding to a Q ≈ Highest-resolution laser spectroscopy has generally been limited to single trapped ion systems 14 because of the rapid decoherence that plagues neutral atom ensembles. Precision spectroscopy of 2.4 × 10 , is the highest obtained for any co- ultracold neutral atoms confined in a trapping potential now shows superior optical coherence herent spectral feature. without any deleterious effects from motional degrees of freedom, revealing optical resonance This ultrahigh spectral resolution allows us linewidths at the hertz level with a good signal-to-noise ratio. The resonance quality factor of to perform experiments in the optical domain 2.4 × 1014 is the highest ever recovered in any form of coherent spectroscopy. The spectral resolution analogous to radio-frequency nuclear magnetic 1 3 resonance (NMR) studies. Under a small mag- permits direct observation of the breaking of nuclear spin degeneracy for the S0 and P0 optical clock states of 87Sr under a small magnetic bias field. This optical approach for excitation of nuclear spin netic bias field, we make direct observations of 1 3 the magnetic sublevels associated with the states allows an accurate measurement of the differential Landé g factor between S0 and P0.The optical atomic coherence demonstrated for collective excitation of a large number of atoms will have a nuclear spin. Furthermore, we have precisely determined the differential Landé g factor be- strong impact on quantum measurement and precision frequency metrology. 1 3 tween S0 and P0 that arises from hyperfine 3 3 1 mixing of P0 with P1 and P1. This optical he relative rates of coherent interaction atomic clocks (14) benefit directly from the measurement approach uses only a small mag- and decoherence in a quantum system are enhanced signal size and the high resonance netic bias field, whereas traditional NMR ex- of fundamental importance for both quan- quality factor Q. Tests of atomic theory can be periments performed on a single state (either T 1 3 tum information science (1) and precision performed with increased precision. The availa- S0 or P0) would need large magnetic fields to metrology (2). Enhancing their ratio, which is ble spectral resolution also enables a direct induce splitting in the radio frequency range. 3 3 equivalent to improving spectral resolving optical manipulation of nuclear spins that are Because the state mixing between P0, P1, on August 20, 2008 1 power, characterizes much of the recent progress decoupled from the electronic angular momen- and P1 arises from both hyperfine interactions in these fields. Trapped ions have so far provided tum. Nuclear spins can have an exceedingly long and external fields, the use of a small field the best platform for research in this direction, relaxation time, making them a valuable alter- permits an accurate, unperturbed measurement resulting in a number of seminal achievements native for quantum information processing and of mixing effects. Optical manipulation of (3–8). The principal advantage of the ion system storage. Two ground-state nuclear spins can, for nuclear spins shielded by two spin-paired lies in the clean separation between the internal example, be entangled through dipolar interac- valence electrons, performed with a superior atomic state and the external center-of-mass tions when photoassociation channels to high- spatial and atomic state selectivity, may pro- 3 motion, leading to long coherence times asso- lying electronic states (such as P1) are excited vide an attractive choice for quantum infor-

ciated with both internal and external degrees of (15). Combined with a quantum degenerate gas, mation science. www.sciencemag.org freedom. A large ensemble of neutral atoms the enhanced precision in measurement will Optical atomic clocks based on neutral atoms offers obvious benefits in the signal size and further strengthen the prospects of using optical benefit directly from a large signal-to-noise ratio scalability of a quantum system (9, 10). Multi- lattices to engineer condensed matter systems (S/N) and a superior line Q. Resolving nuclear atom collective effects can also dramatically (for example, allowing massively parallel quan- sublevels with optical spectroscopy permits enhance the coherent matter/field interaction tum measurements). improved measurements of systematic errors strength (11). However, systems based on Much of the recent interest in alkaline earth associated with the nuclear spin, such as linear neutral atoms normally suffer from decoher- atoms (and similar atoms and ions, such as Yb, Zeeman shifts, and tensor polarizability that

ence resulting from coupling between their Hg, In+, and Al+) arises from the study of the manifests itself as nuclear spin–dependent trap Downloaded from internal and external degrees of freedom (12). forbidden optical transitions, both for metro- polarization sensitivity. Tensor polarizability of 3 In this article, we report a record-level spectral logical applications and as a means for quantum the P0 state is one of the important potential resolution in the optical domain based on a control, with an important achievement being systematic uncertainties for fermion-based clocks doubly forbidden transition in neutral atomic highly effective narrow line laser cooling (16–18). and is one of the primary motivations for recent 1 3 strontium. The atoms are confined in an optical The spin-forbidden S0- P1 transition has been proposals involving electromagnetically induced trapping potential engineered for accurate extensively studied as a potential optical frequen- transparency resonances or dc magnetic field– separation between these degrees of freedom cy standard in Mg (19), Ca (20), and Sr (21, 22) induced state mixing in bosonic isotopes (27–29). (13). The large number of quantum absorbers and has recently been explored as a tool for high- The work reported here has permitted control of − provides a dramatic enhancement in signal size resolution molecular spectroscopy through pho- these systematic effects to ~5 × 10 16 (30). Given for the recovered hertz-linewidth optical reso- toassociation in ultracold Sr (15). The doubly the superior S/N from the large number of 1 3 nance profile. forbidden S0- P0 transition is weakly allowed quantum absorbers, we expect this system to be The demonstrated neutral-atom coherence as a result of hyperfine-induced state mixing, competitive among the best performing clocks in properties will affect a number of research fields, yielding a linewidth of ~1 mHz for 87Sr with a terms of stability. Accuracy is already approach- 9 with some initial results reported here. Optical nuclear spin of =2. This transition is a particularly ing the level of the best atomic fountain clocks attractive candidate for optical domain exper- (31, 32), and absolute frequency measurement is JILA, National Institute of Standards and Technology and iments, where long coherence times are desirable, limited by the Cs clock–calibrated maser signal University of Colorado, and Department of Physics, and is currently being aggressively pursued for the available to us by means of a fiber link (33). An University of Colorado, Boulder, CO 80309–0440, USA. realization of an optical atomic clock (23–26). all-optical clock comparison is necessary to re- *Present address: National Institute of Information and Communications Technology, Koganei, Tokyo, Japan. Furthermore, because of the lack of electronic veal its greater potential. †To whom correspondence should be addressed. E-mail: angular momentum, the level shifts of the two To fully exploit the ultranarrow hyperfine- [email protected] states can be matched with high accuracy in an induced transition for high-precision spectrosco-

1430 1 DECEMBER 2006 VOL 314 SCIENCE www.sciencemag.org REPORTS py, it is critical to minimize decoherence from spread among ~100 lattice sites. The vacuum- nearly equal amplitudes, corresponds to the trap both fundamental and technical origins. The limited lattice lifetime is >1 s. The atoms are oscillation frequency in the transverse plane. ~100-s coherence time available from the 87Sr confined in the Lamb-Dicke regime along the With atoms confined in the lattice, the lin- atoms is not yet experimentally practical as a axis of the optical lattice. The Lamb-Dicke early polarized (parallel to the lattice polarization) result of environmental perturbations to the probe parameter, or the square root of the ratio of 698-nm laser drives the p transitions (Fig. 1B) for laser phase at long time scales, but atomic co- recoil frequency to trap oscillation frequency, is probe times between 0.08 and 1 s, depending on herence in the optical domain at 1 s can already ~0.3. Both the axial and radial trap frequencies the desired spectral resolution limited by the 1 3 greatly improve the current optical clock and are much larger than the S0- P0 transition Fourier transform of the probe time. The effect of quantum measurements. To achieve long atomic linewidth, leading to the spectral feature com- the probe laser is detected in two ways. First, after 3 coherence times, we trap atoms in an optical posed of a sharp optical carrier and two sets of some atoms are excited to the long-lived P0 state 1 lattice with a zero net ac Stark shift between the resolved motional sidebands. One pair of side- by the probe laser, the remaining S0 population 1 1 two clock states, enabling a large number of bands is observed ±40 kHz away from the is measured by exciting the strong S0- P1 neutral atoms to be interrogated free of pertur- carrier, corresponding to the axial oscillation transition with a resonant pulse at 461 nm. The 1 1 bations. The tight atomic confinement enables frequency in the lattice. The red-detuned side- S0- P1 pulse scatters a large number of signal 1 long probing times and permits spectroscopy band is strongly suppressed, indicating that photons and heats the S0 atoms out of the lattice, 3 1 free of broadening by atomic motion and photon nearly all atoms are in the motional ground state leaving only the P0 atoms. Once the S0 atoms 3 recoil. along the lattice axis. The second pair of have been removed, the P0 population is 3 3 3 3 For the highest spectral resolution, it is nec- sidebands at ±125 Hz from the carrier, with determined by driving the P0- S1 and P2- S1 essary for the probe laser to have a narrow intrinsic linewidth and a stable center frequency. A cavity-stabilized 698-nm diode laser is used as 1 3 the optical local oscillator for S0- P0 spectros- copy (34). The linewidth of this oscillator has been characterized by comparison with a second laser operating at 1064 nm via an optical frequency comb linking the two distant colors.

A heterodyne optical beat signal between the two on August 20, 2008 lasers, measured by the frequency comb, reveals a laser linewidth of <0.3 Hz (resolution- bandwidth–limited) at 1064 nm for a 3-s integration time. This result demonstrates the 87 ability of the frequency comb to transfer optical Fig. 1. (A) Partial Sr energy-level diagram. Solid arrows show relevant electric dipole transitions with wavelengths in nanometers. Dashed arrows show the hyperfine interaction–induced state mixing phase coherence (~1 rad/s) across hundreds of 3 3 3 1 between P0 and P1 and between P0 and P1, which provides the nonzero electric dipole moment for terahertz. Our frequency comb is also refer- 3 the doubly forbidden 698-nm transition. (B) The mixing alters the Landé g factor of the P0 state such enced to a hydrogen maser calibrated by the 1 1 3 that it is ~50% larger than that of S0, resulting in a linear Zeeman shift for the S0- P0 transition in National Institute of Standards and Technology www.sciencemag.org the presence of a small magnetic field. The large nuclear spin of 87Sr (I = 9= ) results in 10 sublevels for (NIST) F1 Cs fountain clock (31), which allows 2 the 1S and 3P states, providing 28 possible transitions from the ground state. us to accurately measure the probe laser fre- 0 0 quency to 3 × 10−13 at 1 s. Additionally, the 698-nm laser has been compared with an inde- Fig. 2. Spectroscopy of the 1 3 87 pendent laser system operating at the same S0- P0 transition in Sr. A wavelength, revealing a resolution-bandwidth– pair of Helmholtz coils pro- limited laser linewidth of 0.2 Hz, which in- vides a variable field along creases to ~2 Hz for a 30-s integration time. the lattice (and probe) po- Downloaded from After removing the linear drift, the stability of larization axis, allowing a this local oscillator is ~1 × 10−15 from 1 to 1000 s, measurement of the field- which is limited by the thermal noise of the dependent transition line- cavity mirrors. Thus, the probe laser provides the width as shown in (A)where optical coherence needed to perform experiments an 80-ms interrogation pulse at the 1-s time scale. is used, limiting the width 87Sr atoms are captured from an atomic beam to ~10 Hz. Error bars in (A) and cooled to 1 mK by means of a magneto- indicate measurement un- optical trap (MOT) acting on the strong 1S -1P certainty in linewidth. (B) 0 1 A representative spectrum transition (Fig. 1A). This step is followed by a when the ambient field is well second-stage MOT with the use of the narrow 1 3 controlled. Here, a longer S0- P1 intercombination line that cools the m probetimeisused(~480ms atomsto~1.5 K. During narrow line cooling, or a 1.8-Hz Fourier limit) a nearly vertical 1D lattice is overlapped with but the linewidth is limited the atom cloud for simultaneous cooling and to 4.5 Hz by residual mag- trapping. The lattice is generated by a ~300-mW netic fields and possibly standing wave with a 60-mm beam waist at the residual Stark shifts. (C) A field of 0.77 G is applied along the polarization axis, and the individual 1 wavelength of 813.428(1) nm, where the S0 Fourier-limited (10 Hz) p transitions are easily resolved. Data are shown in red, and a fit of 10 evenly 3 and P0 ac Stark shifts from the trapping field are spaced transitions is shown in blue. The calculated transition probabilities based on Clebsch-Gordan (C-G) equal (35). The cooling and loading stages take coefficients are included in the inset. In (B) and (C), the population is scaled by the total number of atoms ~0.7 s and result in a sample of 104 atoms, available for spectroscopy (~104).

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transitions (Fig. 1A), resulting in atomic decay to ultrahigh spectral resolution has allowed a recent probed the spectra of a single resolved sublevel 3 5 the ground state via P1 for a second measure- measurement of systematic effects for the optical (mF = =2 in this case) using p polarization with 1 1 −16 ment with the use of the S0- P1 pulse. The sec- clock transition at the 9 × 10 level (30). the time window extended to 480 ms. Figure 3, ond measurement provides superior S/N because The high-resolution spectroscopy enables A and B, shows some sample spectra of the 1 5 3 5 only atoms initially excited by the 698-nm probe direct measurement of the differential Landé g isolated S0 (mF = =2)– P0 (mF = =2) transition 3 1 laser contribute to the fluorescence signal, and factor (Dg) between P0 and S0.Toobservethis with a Fourier-limited linewidth of 1.8 Hz, the zero background is not affected by shot-to- state mixing effect, we applied a small magnetic representing a line Q of~2.4×1014.ThisQ is shot atom number fluctuations. Combining both field (<1 G) along the direction of the lattice reproduced reliably, as evidenced by the histo- approaches permits signal normalization against polarization, and the probe laser polarization was gram of linewidths measured in the course of atom number fluctuations. again fixed along this quantization axis to drive p 1 hour (Fig. 3C). Typical linewidths are ~1 to 3 Hz, 3 1 Although the P0 and S0 states are magnet- transitions. Figure 2C shows a direct observation with the statistical scatter owing to residual probe ically insensitive to first order, the hyperfine- of the hyperfine-induced state mixing in the form laser noise at the 10-s time scale. induced state mixing, which allows the otherwise of 10 resolved transition components, with their To further explore the limit of coherent atom- 3 forbidden transition, modifies the P0 nuclear g relative amplitudes influenced by the Clebsch- light interactions, we have also performed two- factor by ~50%. This effect results in a linear Gordan coefficients. The narrow linewidth of pulse optical Ramsey experiments on an isolated 1 3 Zeeman shift in the S0- P0 transition of about the forbidden transition allows this nuclear- p transition. When a system is lifetime-limited, the –100 Hz/G per magnetic sublevel mF (36, 37), magnetic-resonance–like g-factor experiment Ramsey technique can achieve higher spectral where we use the convention that the g factor and to be performed optically at small magnetic resolution at the expense of S/N, leading to use- nuclear magnetic moment carry the same sign fields. The magnitude of Dg can be measured ful information on the decoherence process. and1G=10−4 T. This effect is shown sche- by mapping out the line splitting versus magnetic By performing the experiment in the lattice, the matically in Fig. 1B, where the 10 nuclear spin field. Alternatively, 18 s+ and s– transitions (Fig. Ramsey interrogation pulse can be prolonged, 1 3 sublevels are resolved for the S0 and P0 states in 1B) can be used to extract both the magnitude resulting in a markedly reduced Rabi pedestal 1 the presence of a magnetic field. The linear and sign [relative to the known S0 g factor (38)] width as compared to free-space spectroscopy. Zeeman shift is an important issue for high- of Dg, without accurate calibration of the field. The reduced number of fringes greatly simplifies resolution spectroscopy, because the magnetic Using the latter approach, we find Dg = –108.8(4) identification of the central fringe for applications sensitivity can cause undesirable broadening of Hz/G per mF. The measured Dg permits de- such as frequency metrology. The fringe period 3 the transition, as well as line center shifts due to termination of the P0 lifetime of 140(40) s, in (in Hz) is determined by the sum of the pulse on August 20, 2008 unbalanced population distribution among the agreement with recent ab initio calculations interrogation time tR and the free-evolution time sublevels. To achieve the narrowest resonance, (39, 40). The uncertainty is largely dominated by between pulses TR and is given by 1=ðtR þ TRÞ. the ambient magnetic field must be compensated inconsistencies among hyperfine mixing models Figure 3D shows a sample Ramsey spectrum, with three orthogonal sets of Helmholtz coils. An (36, 37). where tR =20msandTR = 25 ms, yielding a example of this zeroing process is shown in Fig. The linewidth of each spectral feature in fringe pattern with a period of 20.8(3) Hz and 2A, where the transition linewidths are measured Fig. 2C is Fourier-limited by the 80-ms probe fringe FWHM 10.4(2) Hz. For the same tran- under various field strengths. After zeroing the time to ~10 Hz. With the nuclear spin degen- sition with tR raised to 80 ms and TR to 200 ms field, narrow resonances as in Fig. 2B are eracy removed by a small magnetic field, in- (Fig. 3D, inset), the width of the Rabi pedestal is

routinely obtained. The displayed transition line- dividual transition components allow exploration reduced to ~10 Hz, and the recorded fringe www.sciencemag.org width of 4.5 Hz [full width at half maximum of the ultimate limit of our spectral resolution linewidth is 1.7(1) Hz. (FWHM)] represents a resonance Q of ~1014. by eliminating any broadening mechanisms This linewidth is recovered without substan- The good S/N for the narrow line resonance due to residual magnetic fields or light shifts, tial degradation of the fringe signal size, sug- achieved without any averaging or normalization the likely limitation for data such as in Fig. 2B. gesting that the spectral resolution is limited by arises from the contribution of 104 atoms. The To reduce the Fourier limit for the linewidth, we phase decoherence between light and atoms and not by effects such as trap lifetime. A limit of 1 to 2 Hz is consistent with our measurements of

Fig. 3. Spectroscopy of the probe laser noise integrated over the time Downloaded from 1 the isolated S0 (mF = scales used for spectroscopy. Other potential 5= 3 5= 2)– P0 (mF = 2) tran- limitations to the spectral width include Doppler sition. Resolving indi- broadening resulting from the relative motion vidual sublevels allows between the lattice and probe beams and spectroscopy without mag- broadening as a result of tunneling in the lattice. netic or Stark broaden- Future measurements will be improved by ing. Spectra in (A)and locking the probe laser to one of the resolved (B) are taken under iden- nuclear spin transitions to further suppress tical experimental condi- residual laser fluctuations. Although the S/N tions by means of a pulse associated with a sublevel resonance is reduced time of 480 ms, and when compared to a measurement involving all linewidths of 1.5(2) and 3 2.1(2) Hz are achieved. degenerate sublevels, >10 atoms still contribute (C)Ahistogramofthe to the signal, which allows measurement to linewidths of 28 traces proceed without averaging. Clearly, reaching the obtained within ~1 hour. atom shot-noise limit and performing quantum The average linewidth is state preparations will further enhance the S/N. 14 near the 1.8-Hz Fourier The line Q of ~2.4 × 10 achieved here limit (dashed red line). provides practical improvements in the fields of (D) Ramsey fringes with precision spectroscopy and quantum measure- a 20.8(3)-Hz period and 10.4(2)-Hz fringe width, with data shown as open circles. Inset shows a Ramsey ment. The neutral atom–based spectroscopic pattern with a 1.7(1)-Hz fringe FWHM. system now parallels the best ion systems in

1432 1 DECEMBER 2006 VOL 314 SCIENCE www.sciencemag.org REPORTS terms of fractional resolution but greatly sur- 11. A. T. Black, H. W. Chan, V. Vuletic, Phys. Rev. Lett. 91, associated with the lattice and the probe beams, passes the latter in signal size. For optical fre- 203001 (2003). magnetic shift, density shift, and blackbody shift. For 12. J. Ye, D. W. Vernooy, H. J. Kimble, Phys. Rev. Lett. 83, further details, see M. M. Boyd et al.; preprint available quency standards, the high resolution presented 4987 (1999). at http://arxiv.org/PS_cache/physics/pdf/0611/0611067.pdf. here has improved studies of systematic errors for 13. H. Katori, M. Takamoto, V. G. Pal'chikov, V. D. Ovsiannikov, 31. T. P. Heavner, S. R. Jefferts, E. A. Donley, J. H. Shirley, the evaluation of clock accuracy. With these Phys. Rev. Lett. 91, 173005 (2003). T. E. Parker, Metrologia 42, 411 (2005). narrow resonances, clock instability below 10−16 14. See, for example, Science 306, no. 5700 (2004). 32. S. Bize et al., J. Phys. B Atom. Mol. Opt. Phys. 38, S449 (2005). 15. T. Zelevinsky et al., Phys. Rev. Lett. 96, 203201 (2006). 33. J. Ye et al., J. Opt. Soc. Am. B 20, 1459 (2003). at 100 s is anticipated in the near future. For 16. T. Mukaiyama, H. Katori, T. Ido, Y. Li, M. Kuwata-Gonokami, 34. A. D. Ludlow et al.; preprint available at http://arvix.org/ quantum physics and engineering, this system Phys. Rev. Lett. 90, 113002 (2003). ftp/physics/papers/0610/0610274.pdf. opens the door to using neutral atoms for ex- 17. T. H. Loftus, T. Ido, A. D. Ludlow, M. M. Boyd, J. Ye, 35. A. Brusch, R. Le Targat, X. Baillard, M. Fouche, periments in which long coherence times are Phys. Rev. Lett. 93, 073003 (2004). P. Lemonde, Phys. Rev. Lett. 96, 103003 (2006). necessary, motional and internal atomic quantum 18. T. H. Loftus, T. Ido, M. M. Boyd, A. D. Ludlow, J. Ye, 36. H. J. Kluge, H. Sauter, Z. Phys. 270, 295 (1974). Phys. Rev. A 70, 063413 (2004). 37. A. Lurio, M. Mandel, R. Novick, Phys. Rev. 126, 1758 states must be controlled independently, and 19. F. Ruschewitz et al., Phys. Rev. Lett. 80, 3173 (1998). (1962). many parallel processors are desired. 20. U. Sterr et al., C. R. Phys. 5, 845 (2004). 38. L. Olschewski, Z. Phys. A 249, 205 (1972). 21. T. Ido et al., Phys. Rev. Lett. 94, 153001 (2005). 39. S. G. Porsev, A. Derevianko, Phys. Rev. A 69, 042506 References and Notes 22. G. Ferrari et al., Phys. Rev. Lett. 91, 243002 (2003). (2004). 1. D. Leibfried, R. Blatt, C. Monroe, D. Wineland, Rev. Mod. 23. I. Courtillot et al., Phys. Rev. A 68, 030501 (2003). 40. R. Santra, K. V. Christ, C. H. Greene, Phys. Rev. A 69, Phys. 75, 281 (2003). 24. M. Takamoto, F. L. Hong, R. Higashi, H. Katori, Nature 042510 (2004). 2. R. J. Rafac et al., Phys. Rev. Lett. 85, 2462 (2000). 435, 321 (2005). 41. We thank T. Parker and S. Diddams for providing the NIST 3. P. O. Schmidt et al., Science 309, 749 (2005). 25. A. D. Ludlow et al., Phys. Rev. Lett. 96, 033003 (2006). hydrogen maser signal; J. C. Bergquist, I. H. Deutsch, 4. H. Häffner et al., Phys. Rev. Lett. 90, 143602 (2003). 26. R. Le Targat, Phys. Rev. Lett. 97, 130801 (2006). C.H.Greene,J.L.Hall,andP.Julienneforhelpful 5. H. Häffner et al., Nature 438, 643 (2005). 27. R. Santra, E. Arimondo, T. Ido, C. H. Greene, J. Ye, discussions; and X. Huang for technical assistance. The work 6. H. S. Margolis et al., Science 306, 1355 (2004). Phys. Rev. Lett. 94, 173002 (2005). at JILA is supported by the Office of Naval Research, NIST, 7. T. Schneider, E. Peik, C. Tamm, Phys. Rev. Lett. 94, 28. T. Hong, C. Cramer, W. Nagourney, E. N. Fortson, and NSF. A.D.L. is supported by NSF–Interdisciplinary 230801 (2005). Phys. Rev. Lett. 94, 050801 (2005). Graduate Education, Research and Training and the 8. P. Dubé et al., Phys. Rev. Lett. 95, 033001 29. Z. W. Barber et al., Phys. Rev. Lett. 96, 083002 (2006). University of Colorado Optical Science and Engineering (2005). 30. The magnetic field–induced frequency uncertainty is Program. T.Z. is a National Research Council postdoctoral 9. D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, determined from the product of the measured residual fellow. T.I. acknowledges support from the Japan Science P. S. Jessen, Phys. Rev. Lett. 85, 3365 (2000). magnetic field by means of the clock transition linewidth and Technology Agency. 10. I. Bloch, M. Greiner, in Advances in Atomic Molecular and experimentally determined frequency shifts versus

and Optical Physics (Academic Press, San Diego, CA, given magnetic fields along three orthogonal directions. 10 August 2006; accepted 18 October 2006 on August 20, 2008 2005), vol. 52, pp. 1–47. The total systematic uncertainty includes Stark shifts 10.1126/science.1133732

(1), especially if combined with physical pro- cesses such as dewetting and contact-line Macroscopic Hierarchical Surface pinning. Here we report the spontaneous forma- tion of periodic patterns of exceptionally long Patterning of Porphyrin Trimers via (up to 1 mm) columnar stacks of porphyrin dye

molecules at a solid/liquid interface, with highly www.sciencemag.org Self-Assembly and Dewetting defined spatial and parallel ordering. These self- assembled patterns were then used to align Richard van Hameren,1 Peter Sch¨on,1 Arend M. van Buul,1 Johan Hoogboom,2 liquid crystals (LCs) in domains measuring sev- Sergiy V. Lazarenko,1 Jan W. Gerritsen,1 Hans Engelkamp,1 Peter C. M. Christianen,1 eral square millimeters. Hans A. Heus,1 Jan C. Maan,1 Theo Rasing,1 Sylvia Speller,1 Alan E. Rowan,1 Porphyrin dye molecules can self-organize Johannes A. A. W. Elemans,1* Roeland J. M. Nolte1 on a surface into small columnar stacks of sub- micrometer length (13, 14). These architectures

The use of bottom-up approaches to construct patterned surfaces for technological applications is are generated as a result of combined self- Downloaded from appealing, but to date is applicable to only relatively small areas (~10 square micrometers). We assembly and dewetting, which take place simul- constructed highly periodic patterns at macroscopic length scales, in the range of square taneously when a drop-casted solution of the millimeters, by combining self-assembly of disk-like porphyrin dyes with physical dewetting porphyrin molecules is evaporated on a surface. phenomena. The patterns consisted of equidistant 5-nanometer-wide lines spaced 0.5 to In order to enhance the columnar stacking and 1 micrometers apart, forming single porphyrin stacks containing millions of molecules, and were hence the length of the assemblies, we have formed spontaneously upon drop-casting a solution of the molecules onto a mica surface. On glass, synthesized compound 1 (Fig. 1) (15), which thicker lines are formed, which can be used to align liquid crystals in large domains of square consists of three porphyrin moieties that are millimeter size. linked via amide bonds to a central benzene core, a motif that is known to form extended he formation of complex submicrometer applications, such as detection arrays and optical hydrogen-bonded networks (16–19). Each por- patterns on surfaces that extend over elements, well-defined symmetrical patterns can phyrin was equipped with three aliphatic hydro- Tmacroscopic distances underlies the fab- be exploited, especially if the methods decrease carbon chains to increase the solubility of the rication of integrated circuits and microelectro- the number of processing steps needed or avoid stack in organic solvents. mechanical devices (1–3). However, for many surface-invasive steps that scratch, rub, or etch The high tendency of 1 to form aggregates the surface. Examples of complex pattern for- can be directly observed, in that at a concentra- 1Institute for Molecules and Materials, Radboud University mation by noninvasive techniques are still few, tion of 8 mg/ml, the chloroform solution formed Nijmegen, Toernooiveld 1, 6525 ED, Nijmegen, Nether- 2 usually require large polymeric molecules, and a gel. This strong aggregation is highly de- lands. Department of Chemistry, Massachusetts Institute – of Technology, 77 Massachusetts Avenue, Cambridge, MA are often of small spatial extent (4 12). Self- pendent on the presence of the alkyl chains, 02139, USA. assembly of molecules on a surface can be a because porphyrin trimers without these chains *To whom correspondence should be addressed. E-mail: simple, versatile, and less time-consuming ap- appeared not to gelate the solvent. In the proton [email protected] proach and may lead to defect-free structures nuclear magnetic resonance (NMR) spectrum of

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