be limited by inelastic collisions, possibly enhanced
by the formation of long-lived molecular complexes
(31), or by trapping light-induced collisions.
Collisions between ultracold molecules, both
elastic and inelastic, are currently a topic of strong
interest (32), and future insights may lead to a
substantial increase in the lifetimes of dense molecular gases.
Our observation of second-scale coherence times
in trapped 23Na40K molecules provides strong support for the use of molecules as a versatile quantum
resource for quantum information (10). Confined
in optical lattices under quantum-gas microscopes
(33, 34), in optical microtraps (35), or in ion traps
(36), it will be possible to individually address,
control, and detect internal states of single molecules. Coherent manipulation of molecular rotational states with microwave radiation allows full
control of long-range dipolar interactions, which
should enable gate operations between pairs of
molecules (11). This work also suggests routes for
precision metrology with ultracold molecules. Transitions between nuclear spin states of different
vibrational states may exhibit similarly long coherence times, enabling hertz-level molecular spectroscopy in the optical domain and bringing optical
molecular clocks into experimental reach (37–39).
REFERENCES AND NOTES
1. S. Haroche, J. M. Raimond, Exploring the Quantum (Oxford
Univ. Press, 2006).
2. L. D. Carr, D. DeMille, R. V. Krems, J. Ye, New J. Phys. 11,
3. R. Krems, B. Friedrich, W. C. Stwalley, Eds., Cold Molecules:
Theory, Experiment, Applications (CRC Press, 2009).
4. T. Zelevinsky, S. Kotochigova, J. Ye, Phys. Rev. Lett. 100,
5. D. DeMille et al., Phys. Rev. Lett. 100, 043202 (2008).
6. J. Baron et al., Science 343, 269–272 (2014).
7. A. Micheli, G. K. Brennen, P. Zoller, Nat. Phys. 2, 341–347 (2006).
8. N. R. Cooper, G. V. Shlyapnikov, Phys. Rev. Lett. 103, 155302
9. H. P. Büchler et al., Phys. Rev. Lett. 98, 060404 (2007).
10. D. DeMille, Phys. Rev. Lett. 88, 067901 (2002).
11. S. F. Yelin, K. Kirby, R. Cote, Phys. Rev. A 74, 050301 (2006).
12. A. André et al., Nat. Phys. 2, 636–642 (2006).
13. J. G. Danzl et al., Science 321, 1062–1066 (2008).
14. K. K. Ni et al., Science 322, 231–235 (2008).
15. T. Takekoshi et al., Phys. Rev. Lett. 113, 205301 (2014).
16. P. K. Molony et al., Phys. Rev. Lett. 113, 255301 (2014).
17. J. W. Park, S. A. Will, M. W. Zwierlein, Phys. Rev. Lett. 114,
18. M. Guo et al., Phys. Rev. Lett. 116, 205303 (2016).
19. S. Ospelkaus et al., Phys. Rev. Lett. 104, 030402 (2010).
20. S. A. Will, J. W. Park, Z. Z. Yan, H. Loh, M. W. Zwierlein,
Phys. Rev. Lett. 116, 225306 (2016).
21. P. D. Gregory, J. Aldegunde, J. M. Hutson, S. L. Cornish,
Phys. Rev. A 94, 041403 (2016).
22. B. Neyenhuis et al., Phys. Rev. Lett. 109, 230403 (2012).
23. B. Yan et al., Nature 501, 521–525 (2013).
24. S. Gupta et al., Science 300, 1723–1726 (2003).
25. M. W. Zwierlein, Z. Hadzibabic, S. Gupta, W. Ketterle,
Phys. Rev. Lett. 91, 250404 (2003).
26. A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, P. O. Schmidt,
Rev. Mod. Phys. 87, 637–701 (2015).
27. See supplementary materials.
28. J. W. Park, S. A. Will, M. W. Zwierlein, New J. Phys. 17, 075016
29. K. R. A. Hazzard, A. V. Gorshkov, A. M. Rey, Phys. Rev. A 84,
30. A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith,
Z. Hadzibabic, Phys. Rev. Lett. 110, 200406 (2013).
31. M. Mayle, G. Quéméner, B. P. Ruzic, J. L. Bohn, Phys. Rev. A 87,
32. G. Quéméner, P. S. Julienne, Chem. Rev. 112, 4949–5011
33. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, M. Greiner, Nature
462, 74–77 (2009).
34. J. F. Sherson et al., Nature 467, 68–72 (2010).
35. A. M. Kaufman, B. J. Lester, C. A. Regal, Phys. Rev. X 2, 041014
36. H. Loh et al., Science 342, 1220–1222 (2013).
37. S. Schiller, D. Bakalov, V. I. Korobov, Phys. Rev. Lett. 113,
38. J.-P. Karr, J. Mol. Spectrosc. 300, 37–43 (2014).
39. C. Cheng et al., Phys. Rev. Lett. 117, 253201 (2016).
We thank R. Field and collaborators, K.-K. Ni, and T. Nicholson for
fruitful discussions. This work was supported by the NSF, the
Air Force Office of Scientific Research (AFOSR) Presidential
Early Career Award for Scientists and Engineers, the U.S. Army
Research Office (ARO), an ARO Multidisciplinary University
Research Inititative (MURI) on “High-Resolution Quantum Control
of Chemical Reactions,” an AFOSR MURI on “Exotic Phases of
Matter,” and the David and Lucile Packard Foundation. Z.Z. Y.
acknowledges additional support from the NSF Graduate Research
Fellowship Program. The data supporting this manuscript are
available from the corresponding author on request.
Materials and Methods
Figs. S1 and S2
1 December 2016; accepted 23 June 2017
Spectral narrowing of x-ray pulses
for precision spectroscopy with
K. P. Heeg,1 A. Kaldun,1 C. Strohm,2 P. Reiser,1 C. Ott,1 R. Subramanian,1 D. Lentrodt,1
J. Haber,2 H.-C. Wille,2 S. Goerttler,1 R. Rüffer,3 C. H. Keitel,1 R. Röhlsberger,2
T. Pfeifer,1 J. Evers1*
Spectroscopy of nuclear resonances offers a wide range of applications due to the
remarkable energy resolution afforded by their narrow linewidths. However, progress
toward higher resolution is inhibited at modern x-ray sources because they deliver only a
tiny fraction of the photons on resonance, with the remainder contributing to an off-resonant background. We devised an experimental setup that uses the fast mechanical
motion of a resonant target to manipulate the spectrum of a given x-ray pulse and to
redistribute off-resonant spectral intensity onto the resonance. As a consequence, the
resonant pulse brilliance is increased while the off-resonant background is reduced.
Because our method is compatible with existing and upcoming pulsed x-ray sources,
we anticipate that this approach will find applications that require ultranarrow
As a result of the Mössbauer effect (1), nuclei may absorb and emit photons without appreciable recoil, giving rise to extremely narrow resonance widths. This narrow line- width provides the basis for most applications of Mössbauer spectroscopy, which is a
well-established tool to measure magnetic, structural, and dynamic properties of matter (2). It
also provides a natural platform for various fundamental tests (1, 3–5). Further applications include the study of solid-state phenomena (6),
battery development (7), and x-ray quantum optics
(8–13). Most experiments use measurements on
the 57Fe Mössbauer nuclear resonance, for which
the energy resolution DE/E, defined as the ratio of
transition linewidth and energy, is 3 × 10−13. The
achievable energy resolution could even increase
by orders of magnitude with other Mössbauer
isotopes, such as 45Sc (DE/E 10−19), 107Ag and
109Ag (DE/E 10−22), or 103Rh (DE/E 10−24) (1).
Even though the brilliance of pulsed x-ray sources
is much higher than that of radioactive sources,
it needs to be boosted further for metrology
with these ultranarrow resonances. Furthermore,
higher signal rates translate into better energy,
temporal, or spatial resolution (1), such that more
efficient excitation of narrow resonances could
also advance their applications in general. On
the other hand, broader transitions are suitable
candidates for realizing nonlinear effects in the
x-ray regime (12, 14–16).
Unfortunately, state-of-the-art pulsed x-ray
sources provide radiation with bandwidths orders
of magnitude larger than the nuclear resonances.
Monochromators remove off-resonant background
photons but cannot enhance the resonant component. Attempts to create spectrally narrow
x-rays via g-ray lasers have proven unsuccessful
so far (17, 18).
We propose a different approach that neither
increases the total x-ray intensity nor directly
creates narrow-band x-ray light. Instead, we manipulate the spectra of given broadband x-ray
1Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany.
2Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg,
Germany. 3ESRF–European Synchrotron, CS40220, 38043
Grenoble Cedex 9, France.
*Corresponding author. Email: email@example.com