Matter-wave metrology field of a standing light wave to imprint a position- (G)grating can be arranged to redirect and recom- dependent phase onto the matter-wave field.Pho bine those wavelets to obtain quantum interference todepletion gratings mask portions of the wave- The intensity profiles of the two recombined beams function-for instance,by transferring particles behind G:are complementary and depend on the that pass through the grating's antinodes to unde- phase shift between the two arms of the inter- tectable states.Light masks may ionize atoms,dis- ferometer.Additional interference pathways arise sociate molecular clusters,or change a particle's in- through higher diffraction orders.They can be spa- ternal state to make the particle undetectable if it tially separated with a slit. passes through an antinode of the light field.The Well-collimated atomic beams have been split effect closely resembles that of nanomechanical into arms separated by as much as 27 um,sufficient gratings. to expose two wavelets to different electric fields or A collimated particle source,a single grating, to regions of different gas pressure.That approach and a detecting screen can be interpreted as a full produced the most precise measurement of an interferometer.If the source is sufficiently small or atomic ground state polarizability to date and a so- distant to the grating,a coherent wave field may phisticated analysis of atom-atom scattering cross evolve that covers transverse distances larger than sections.3 the grating period d.The wavelets emerging from neighboring slits will then interfere on a screen in Interfering incoherent beams the far field,even without the help of additional Mach-Zehnder interferometry can be generalized beamsplitters and beam-steering elements.Modern to many atoms in the periodic table and to some precision experiments,however,typically include molecules.It requires,however,an intense and three or four optical elements to achieve larger beam transversely coherent beam,which can be routinely separation,longer coherence times,and higher sen- achieved for many atoms but remains an open chal- sitivity to external perturbations lenge for molecules and nanoparticles.Atomic In 1991 a group led by David Pritchard com- beams are typically formed by evaporation or sub- bined three equidistant,nanofabricated gratings, limation,sometimes at temperatures exceeding configured as shown in figure 1b,to realize a Mach- 1000 K.Massive molecules tend to be less volatile Zehnder interferometer for sodium atoms.3The first and would require still higher temperatures.Many grating (G)splits the wavefront into wavelets of molecules,atomic and molecular clusters,and various diffraction orders.A second(G2)and third nanoparticles,however,need to be studied at cool a Collimator le,p+hk gP) b a lBP+hk1-k2》 Collimator BP P〉 Figure 2.Splitting matter waves.(a)A nanomechanical diffraction mask splits an atomic or molecular beam by dividing the matter wavefront into beams of varying diffraction order.(Beams of diffraction order 0 and+1 are shown here.)(b)A beam can be similarly split using a standing light wave,which may remove parts of the matter wave via ionization or fragmentation or may modulate the wavefront's phase via dipole interaction. (c)Amplitude beamsplitters use laser pulses to create a coherent superposition between an atom's ground statelg)and a resonantly coupled excited state le).Upon excitation,the momentum p of the atom is enhanced by the momentum hk of the photon.The atom therefore ends up in an entangled state,where neither the internal nor the center-of-mass state is known but where the two are strictly correlated.(d)When the superposition is created between two hyperfine ground states Ig,)and Ig,)via a two-photon Raman transition,the apparatus is known as a Raman beamsplitter.Wider arm separations can be achieved with higher-order Raman transitions.(Panels c and d adapted from ref.16.) 32May2014 Physics Today www.physicstoday.org32 May 2014 Physics Today www.physicstoday.org Matter-wave metrology field of a standing light wave to imprint a position- dependent phase onto the matter- wave field. Pho￾todepletion gratings mask portions of the wave￾function—for instance, by transferring particles that pass through the grating’s antinodes to unde￾tectable states. Light masks may ionize atoms, dis￾sociate molecular clusters, or change a particle’s in￾ternal state to make the particle undetectable if it passes through an antinode of the light field. The effect closely resembles that of nanomechanical gratings. A collimated particle source, a single grating, and a detecting screen can be interpreted as a full interferometer. If the source is sufficiently small or distant to the grating, a coherent wave field may evolve that covers transverse distances larger than the grating period d. The wavelets emerging from neighboring slits will then interfere on a screen in the far field, even without the help of additional beamsplitters and beam- steering elements. Modern precision experiments, however, typically include three or four optical elements to achieve larger beam separation, longer coherence times, and higher sen￾sitivity to external perturbations. In 1991 a group led by David Pritchard com￾bined three equidistant, nanofabricated gratings, configured as shown in figure 1b, to realize a Mach– Zehnder interferometer for sodium atoms.3 The first grating (G1) splits the wavefront into wavelets of various diffraction orders. A second (G2) and third (G3) grating can be arranged to redirect and recom￾bine those wavelets to obtain quantum interference. The intensity profiles of the two recombined beams behind G3 are complementary and depend on the phase shift between the two arms of the inter - ferometer. Additional interference pathways arise through higher diffraction orders. They can be spa￾tially separated with a slit. Well- collimated atomic beams have been split into arms separated by as much as 27 μm, sufficient to expose two wavelets to different electric fields or to regions of different gas pressure. That approach produced the most precise measurement of an atomic ground state polarizability to date and a so￾phisticated analysis of atom–atom scattering cross sections.3 Interfering incoherent beams Mach–Zehnder interferometry can be generalized to many atoms in the periodic table and to some molecules. It requires, however, an intense and transversely coherent beam, which can be routinely achieved for many atoms but remains an open chal￾lenge for molecules and nanoparticles. Atomic beams are typically formed by evaporation or sub￾limation, sometimes at temperatures exceeding 1000 K. Massive molecules tend to be less volatile and would require still higher temperatures. Many molecules, atomic and molecular clusters, and nanoparticles, however, need to be studied at cool Figure 2. Splitting matter waves. (a) A nanomechanical diffraction mask splits an atomic or molecular beam by dividing the matter wavefront into beams of varying diffraction order. (Beams of diffraction order 0 and ±1 are shown here.) (b) A beam can be similarly split using a standing light wave, which may remove parts of the matter wave via ionization or fragmentation or may modulate the wavefront’s phase via dipole interaction. (c) Amplitude beamsplitters use laser pulses to create a coherent superposition between an atom’s ground state ∣g〉 and a resonantly coupled excited state ∣e〉. Upon excitation, the momentum p of the atom is enhanced by the momentum ħk of the photon. The atom therefore ends up in an entangled state, where neither the internal nor the center- of- mass state is known but where the two are strictly correlated. (d) When the superposition is created between two hyperfine ground states ∣g1〉 and ∣g2〉 via a two- photon Raman transition, the apparatus is known as a Raman beamsplitter. Wider arm separations can be achieved with higher-order Raman transitions. (Panels c and d adapted from ref. 16.) This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 202.120.2.30 On: Thu, 01 May 2014 23:26:12