Optics and interferometry with Na2 molecules

Quantum gas mixtures and dual-species atom interferometry in space

The capability to reach ultracold atomic temperatures in compact instruments has recently been extended into space1,2. Ultracold temperatures amplify quantum effects, whereas free fall allows further cooling and longer interactions time with gravity-the final force without a quantum description. On Earth, these devices have produced macroscopic quantum phenomena such as Bose-Einstein condensates (BECs), superfluidity, and strongly interacting quantum gases3. Terrestrial quantum sensors interfering the superposition of two ultracold atomic isotopes have tested the universality of free fall (UFF), a core tenet of Einstein's classical gravitational theory, at the 10-12 level4. In space, cooling the elements needed to explore the rich physics of strong interactions or perform quantum tests of the UFF has remained elusive. Here, using upgraded hardware of the multiuser Cold Atom Lab (CAL) instrument aboard the International Space Station (ISS), we report, to our knowledge, the first simultaneous production of a dual-species BEC in space (formed from 87Rb and 41K), observation of interspecies interactions, as well as the production of 39K ultracold gases. Operating a single laser at a 'magic wavelength' at which Rabi rates of simultaneously applied Bragg pulses are equal, we have further achieved the first spaceborne demonstration of simultaneous atom interferometry with two atomic species (87Rb and 41K). These results are an important step towards quantum tests of UFF in space and will allow scientists to investigate aspects of few-body physics, quantum chemistry and fundamental physics in new regimes without the perturbing asymmetry of gravity.

Vortex beams of atoms and molecules

[Figure: see text].

Effect of an echo sequence to a trapped single-atom interferometer with photon momentum kicks

We investigate a single-atom interferometer (SAI) in an optical dipole trap (ODT) with photon momentum kicks. An echo sequence is used for the SAI. We find experimentally that interference visibilities of a counter-propagating Raman type SAI decay much faster than the co-propagating case. To understand the underlying mechanism, a wave-packet propagating simulation is developed for the ODT-guided SAI. We show that in state dependent dipole potentials, the coupling between external dynamics and internal states makes the atom evolve in different paths during the interfering process. The acquired momentum from counter-propagating Raman pulses forces the external motional wave packets of two paths be completely separated and the interferometer visibility decays quickly compared to that of the co-propagating Raman pulses process. Meanwhile, the echo interference visibility experiences revival or instantaneous collapse which depends on the π pulse adding time at approximate integer multiples or half integer multiples of the trap period.

Antimatter Quantum Interferometry

The wave–particle duality hypothesis for massive particles has been confirmed by an overwhelming variety of indirect experimental evidence. In addition, direct interferometric tests have been made on particles like electrons, neutrons and even a few molecules, explicitly showing wave-like diffraction and interference phenomena. Of particular interest in this direction, single particle interference has also been demonstrated, but only for the electron case. No such kind of direct information was available for antiparticles or antimatter in general. After briefly discussing the subjects of antimatter research and interferometry, I present here the first evidence of single particle antimatter interference, made with positrons.

First demonstration of antimatter wave interferometry

Interference of matter waves is at the heart of quantum physics and has been observed for a wide range of particles from electrons to complex molecules. Here, we demonstrate matter wave interference of single positrons using a period-magnifying Talbot-Lau interferometer based on material diffraction gratings. The system produced high-contrast periodic fringes, which were detected by means of nuclear emulsions capable of determining the impact point of each individual positron with submicrometric resolution. The measured energy dependence of fringe contrast in the range of 8 to 16 keV proves the quantum-mechanical origin of the periodic pattern and excludes classical projective effects, providing the first observation to date of antimatter wave interference. Future applications of this interferometric technique include the measurement of the gravitational acceleration of neutral antimatter systems exploiting the inertial sensing capabilities of Talbot-Lau interference.

Experimental methods of molecular matter-wave optics

We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules.Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences.We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters.Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences.Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process.

Macroscopicity of mechanical quantum superposition states

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.

Nitric oxide beam intensity oscillations induced by the combined action of a static and a radio frequency electric field

This paper details an experimental and theoretical investigation in which a simplified version of the molecular beam electric resonance technique is employed that requires the use of a C-field only. In the experiment the forward intensity of a NO beam is measured as a function of the frequency of the oscillating electric field over the 900-1460 kHz range. Specifically, the interaction of the NO beam with a radio frequency (rf) field of 1.12 kV/m amplitude and -610 kV/m (2) of gradient at the horizontal plane during 72 micros produces a series of oscillations in the transmitted beam intensity. The theoretical analysis shows how the interaction between a beam of NO molecules and both a static and oscillating rf field produces interferences in the forward beam intensity and how the observed interferences are due to superposition of molecular internal states. Furthermore, the interference model reproduces satisfactorily the observed beam intensity oscillations. The present technique could be useful for the development of new schemes to achieve coherent control of molecular processes using radiowaves.

Interaction of polar molecules with resonant radio frequency electric fields: imaging of the NO molecular beam splitting

The interaction between a NO supersonic beam and a resonant radio frequency (RF) field is investigated using laser ionization coupled to imaging techniques. It is shown how the resonant interaction leads to a beam splitting of +/-0.2 degrees toward both positive and negative direction perpendicular to the beam propagation axis. This phenomenon is rationalized using a model based on molecular interferences produced by the action of the resonant RF electric field.

Speckle patterns with atomic and molecular de Broglie waves

We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity.

Coherent molecular optics using ultracold sodium dimers

Coherent molecular optics is performed using two-photon Bragg scattering. Molecules were produced by sweeping an atomic Bose-Einstein condensate through a Feshbach resonance. The spectral width of the molecular Bragg resonance corresponded to an instantaneous temperature of 20 nK, indicating that atomic coherence was transferred directly to the molecules. An autocorrelating interference technique was used to observe the quadratic spatial dependence of the phase of an expanding molecular cloud. Finally, atoms initially prepared in two momentum states were observed to cross pair with one another, forming molecules in a third momentum state. This process is analogous to sum-frequency generation in optics.

Bonding and (hyper)polarizability in the sodium dimer

We report a conventional ab initio and density functional theory study of the polarizability (alpha(alphabeta)/e(2)a(0) (2)E(h) (-1)) and hyperpolarizability (gamma(alphabetagammadelta)/e(4)a(0) (4)E(h) (-3)) of the sodium dimer. A large [18s14p9d2f1g] basis set is thought to yield near-Hartree-Fock values for both properties: alpha=272.28, Deltaalpha=127.22 and gamma=2157.6 x 10(3) at R(e)=3.078 87 A. Electron correlation has a remarkable effect on the Cartesian components of gamma(alphabetagammadelta). Our best value for the mean is gamma=1460.1 x 10(3). The (hyper)polarizability shows very strong bond-length dependence. The effect is drastically different for the longitudinal and transverse components of the hyperpolarizability. The following first derivatives were extracted from high-level coupled cluster calculations: (dalpha/dR)(e)=54.1, (dDeltaalpha/dR)(e)=88.1e(2)a(0)E(h) (-1), and (dgamma/dR)(e)=210 x 10(3)e(4)a(0) (3)E(h) (-3). We associate the (hyper)polarizability to bonding effects between the two sodium atoms by introducing the differential property per atom Q(diff)/2 identical with (Q[Na(2)(X (1)Sigma(g) (+))]/2-Q[Na((2)S)]). The differential (hyper)polarizability per atom is predicted to be strongly negative for the dimer at R(e), as [alpha(Na(2))/2-alpha(Na)]=-33.8 and [gamma(Na(2))/2-gamma(Na)]=-226.3 x 10(3). The properties calculated with the widely used B3LYP and B3PW91 density functional methods differ significantly. The B3PW91 results are in reasonable agreement with the conventional ab initio values. Last, we observe that low-level ab initio and density functional theory methods underestimate the dipole polarizability anisotropy. Experimental data on this important property are highly desirable.

Wave nature of biomolecules and fluorofullerenes

We demonstrate quantum interference for tetraphenylporphyrin, the first biomolecule exhibiting wave nature, and for the fluorofullerene C60F48 using a near-field Talbot-Lau interferometer. For the porphyrins, which are distinguished by their low symmetry and their abundant occurrence in organic systems, we find the theoretically expected maximal interference contrast and its expected dependence on the de Broglie wavelength. For C60F48, the observed fringe visibility is below the expected value, but the high contrast still provides good evidence for the quantum character of the observed fringe pattern. The fluorofullerenes therefore set the new mark in complexity and mass (1632 amu) for de Broglie wave experiments, exceeding the previous mass record by a factor of 2.

Glory oscillations in the index of refraction for matter waves

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and N2 over a wide range of sodium velocities. We observe glory oscillations--a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.

Matter-wave interferometer for large molecules

We demonstrate a near-field Talbot-Lau interferometer for C70 fullerene molecules. Such interferometers are particularly suitable for larger masses. Using three free-standing gold gratings of 1 microm period and a transversally incoherent but velocity-selected molecular beam, we achieve an interference fringe visibility of 40% with high count rate. Both the high visibility and its velocity dependence are in good agreement with a quantum simulation that takes into account the van der Waals interaction of the molecules with the gratings and are in striking contrast to a classical moiré model.

Coherent nonlinear spectroscopy: from femtosecond dynamics to control

This review focuses on the study of the dynamics of isolated molecules and their control using coherent nonlinear spectroscopic methods. Emphasis is placed on topics such as bound-to-free excitation and the study of concerted elimination reactions, free-to-bound excitation and the study of bimolecular reactions, and bound-to-bound excitation and the study of intramolecular rovibrational dynamics and coherence relaxation. For each case the detailed time-resolved information reveals possible strategies to control the outcome. Experimental results are shown for each of the reactions discussed. The methods discussed include pump-probe and four-wave mixing processes such as transient grating and photon echo spectroscopy. Off-resonance transient-grating experiments are shown to be ideal for the study of ground state dynamics, molecular structure, and the molecular response to strong field excitation.

Direct observation of a breit-wigner phase of a wave function

The Breit-Wigner phase of a wave function was obtained by measuring the interference between two independent ionization paths of a molecule. The state of interest was present in only one of the paths, thereby producing a phase shift in the observed signal. An analytical theory was used to determine the phase of the wave function from the observable.

Observation of ionization in a crystal interferometer

We present a new interferometric setup where interference of a fast probe electron affects the ionization cross section of an atom. Interference is detected in the intensity of the inelastically scattered electrons at the Bragg scattering angle in transmission. The crystal serves both as a target for core ionization and as a beam-splitting and phase-shifting device.

Pulsed standing-wave mirror for neutral atoms and molecules

Reflection of neutral atoms and molecules by a pulsed standing wave with a duration on the order of nanoseconds is studied. It is shown that, with a suitable choice of the laser parameter values, each period of the standing-wave pattern functions as an independent mirror, thus providing a novel way to manipulate large samples of neutral gas-phase particles even with a single laser pulse. At moderate field intensities, the pulsed standing-wave mirror would be directly applicable, e.g., for the manipulation of buffer-gas cooled molecules.

How to study the elusive efimov state of the 4He3 molecule through a new atom-optical state-selection technique

Excited states and excitation energies of weakly bound systems, e.g., atomic few-body systems and clusters, are difficult to study experimentally. For this purpose we propose a new and very general atom-optical method which is based on inelastic diffraction from transmission gratings. The technique is applicable to the recently found helium trimer molecule 4He3, allowing for the first time an investigation of the possible existence of an excited trimer state and determination of its excitation energy. This would be of fundamental importance for the famous Efimov effect.