A universal matter-wave interferometer with optical ionization gratings in the time domain

Journal name:
Nature Physics
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Published online

Matter-wave interferometry with atoms1 and molecules2 has attracted a rapidly growing level of interest over the past two decades, both in demonstrations of fundamental quantum phenomena and in quantum-enhanced precision measurements. Such experiments exploit the non-classical superposition of two or more position and momentum states that are coherently split and rejoined to interfere3, 4, 5, 6, 7, 8, 9, 10, 11. Here, we present the experimental realization of a universal near-field interferometer built from three short-pulse single-photon ionization gratings12, 13. We observe quantum interference of fast molecular clusters, with a composite de Broglie wavelength as small as 275fm. Optical ionization gratings are largely independent of the specific internal level structure and are therefore universally applicable to different kinds of nanoparticle, ranging from atoms to clusters, molecules and nanospheres. The interferometer is sensitive to fringe shifts as small as a few nanometres and yet robust against velocity-dependent phase shifts, because the gratings exist only for nanoseconds and form an interferometer in the time domain.

At a glance


  1. Layout of the OTIMA interferometer.
    Figure 1: Layout of the OTIMA interferometer.

    a, Set-up for nanoparticle interferometry with three short-pulse optical ionization gratings. From left to right: the Even–Lavie valve (V) produces a 30μs pulse of neutral Ac clusters that are cooled in an adiabatic co-expansion with a noble gas jet. The cluster beam is delimited by two slits that are variable in height (H) and width (W). The laser pulses at t1=0,t2=T and t3=2T are back-reflected by a single 2-inch mirror to form three standing light waves. These are responsible for preparing the initial spatial coherence, for matter-wave diffraction and for spatially filtering the emerging cluster interferogram. The detection laser (L) ionizes the transmitted neutral clusters for TOF-MS. A photodiode (P) is used to monitor the laser timing with nanosecond accuracy. MCP, micro-channel plate. b, The interferogram is formed by multiple paths from the first to the third grating that correspond to an effective momentum transfer of nplanckk in each grating, with nZ. Accurate timing ensures that the interfering paths branch and close at the same points on the grating axis x, irrespective of the cluster’s initial velocities v1 (red)>v2 (green). The stars indicate the localization of the matter waves.

  2. Cluster interference visualized by means of the mass spectrum, for two pulse separation times.
    Figure 2: Cluster interference visualized by means of the mass spectrum, for two pulse separation times.

    a, Lower panel: mass spectra recorded for a resonant (black line) and off-resonant (ΔT=200ns, red line) pulse separation of T=25.9μs (clusters seeded in an argon jet). Each cluster signal splits into isotopic sub-peaks. The x-ticks correspond to a mass separation of 4AMU. The two spectra differ for masses that fulfil TmT. Upper panel: histogram of the cluster interference contrast, as measured by the signal difference ΔSN integrated over the main isotopes of a given cluster. The predictions of the quantum/classical model13 are shown in violet/grey. The light violet/grey regions indicate the variation of the fringe contrast with a ±30% variation of the cluster polarizability α157. For further details, see Methods and Supplementary Information Se. b, The same as in a but with neon seeding and T=18.9μs. The error bars represent 1s.d. of statistical error (see Supplementary Information Sh).

  3. Interferometric resonance and timing precision.
    Figure 3: Interferometric resonance and timing precision.

    Cluster self-imaging in a pulsed near-field interferometer is a resonant process with a short acceptance window for the matter waves to rephase. a, Pulse sequence. b, Difference ΔSN between the resonant and off-resonant signals detected at a mass of Ac7 as a function of ΔT. In our set-up and for a pulse separation time T of 18.9μs, interference occurs during a time window of 48ns (full-width at half-maximum). The error bars represent 1.s.d. of statistical error (see Supplementary Information Sh).

  4. [Delta]SN as a function of the mirror displacement for different clusters.
    Figure 4: ΔSN as a function of the mirror displacement for different clusters.

    The second grating laser beam was tilted by 5.1±0.3mrad in the direction of the molecular beam to stretch the effective grating period by about 0.013 per mille. This suffices to induce a fringe shift of half a grating period for molecules travelling around 1.5mm distance from the mirror surface. The mirror height is varied to effectively shift the second grating with regard to the other two, which allows us to scan the cluster interference pattern. We extract the periodicity for ΔSN as a function of the mirror distance by fitting a damped sine curve to the experimental data. This periodicity corresponds to the expected effective period13 of the interferogram of about 78.8nm. The error bars represent 1s.d. of statistical error (see Supplementary Information Sh).


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  1. Faculty of Physics, University of Vienna, VCQ, Boltzmanngasse 5, A-1090 Vienna, Austria

    • Philipp Haslinger,
    • Nadine Dörre,
    • Philipp Geyer,
    • Jonas Rodewald,
    • Stefan Nimmrichter &
    • Markus Arndt


P.H., N.D., P.G. and J.R. built the interferometer and performed the measurements. P.H. contributed the initial experimental layout and the time-domain perspective of the experiment. P.G. developed the customized software and data acquisition system in feedback with the team. Data analysis was done by N.D., J.R. and P.H. S.N. contributed the theoretical description. M.A. initiated and supervised the experiment. P.H., N.D., J.R., S.N. and M.A. wrote the paper with input by all co-authors.

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