OTIMA - Interferometer
OTIMA - Interferometer
We demonstrate the new OTIMA (optical time-domain matter-wave) interferometer . In this apparatus the quantum wave nature of many different particles can be revealed and explored. The setup uses, for the first time, optical depletion gratings as diffraction elements. These light structures consist of 157 nm laser pulses which form periodic standing waves upon reflection at a mirror surface. Three of such gratings are used in the OTIMA to create a Talbot-Lau matter wave interferometer in the time-domain. Successful proof of principle experiments with anthracene clusters have recently demonstrated the functionality of the setup and are published in Nature Physics .
In the following we give a comprehensive review of the experiment dedicated also to a non-physicist readership.
Understanding certain physical phenomena does not necessarily require understanding physics. A child for instance learns how a ball behaves, how it bounces or collides, and that it doesn’t fit into a box much smaller than its own diameter. It also develops some intuition on how waves are created and propagate. It can observe how a water wave flows around an obstacle or passes through a gap. Unknowingly, every child gathers an intuitive insight into fundamental physics phenomena.
Atoms and molecules in many cases behave just like familiar billiard balls, they can be kicked, they bounce, collide and have mass. Also the water waves generated by a stone thrown into a pond find a microscopic equivalence in a number of physical wave phenomena. Despite such analogies some parts of the microscopic world cannot be modeled after the characteristics of everyday objects and rather have to be described by the more complete formalism of quantum mechanics: Atoms and molecules for instance can behave wave-like and yet maintain particle features. This characteristic is known as the wave-particle duality in quantum mechanics. Since we do not observe wave-particle dualities in our macroscopic environment we ask: is there a fundamental cut between classical physics and quantum mechanics or is quantum behavior of larger and larger objects simply progressively difficult to observe? Our goal is to find evidence for the wave-particle duality of increasingly massive and complex particles and we do this with a device that we call a matter-wave or molecule interferometer . Such an apparatus is comprised of a source which emits a stream of particles, elements which prepare and probe their wave-nature and finally a particle detector.
The particles leaving the source and hitting the detector are well described by classical physics. In between, however, the preparation and probing of the wave-nature can only be modeled with the rules of quantum mechanics.
When two waves are superposed their amplitudes cancel or add, depending on how the waves are shifted with respect to one another. This positioning of the wave troughs and crests is called the relative phase. If the phase varies over time or space, the sum of the wave amplitudes will vanish when the signal is averaged over time. In order to see the effect of the superposition - this effect is called interference - one thus has to ensure that the relative phase between the contributing waves is constant.
This is what we do in an interferometer: we prepare the phases of waves and bring them to superposition. The phase can be prepared by forcing the waves through a small slit which ensures that all emerging wavelets originate from the same region in space. This can be demonstrated with an optical interferometer: light passes through a slit which prepares the relative phases and subsequently illuminates a grating. From each slit of the grating a spherical wave emerges and these elementary wavelets overlap behind the grating - a phenomenon called diffraction. In certain positions in space the wave amplitudes add up, while in other regions of space they will cancel. Consequently some areas are dark and some are brighter: an interference pattern forms.
If we want to demonstrate the wave-nature of massive matter, we have to watch out for such interference. For matter waves the maxima and minima however do not consist of bright and dark spots but rather of areas where more and less particles are accumulated.
The quantum wavelength associated with a particle is the de Broglie wavelength 
and it is computed from the particle’s mass m, velocity v and the Planck’s constant h.
Wave diffraction has been demonstrated for atoms and molecules [4, 5, 6,]. However, the distance between the interference fringes are small and therefore require tightly collimated molecular beams, a small source and a long distance between the grating and the detector (far-field interference). This is unfavorable for dilute beams of large particles since the beam brightness decreases with the square of the flight distance.
An alternative is thus to exploit interference phenomena which occur close to the gratings (near-field interference). This is implemented in modern Talbot-Lau interferometers . The phase preparing slit is here replaced by an entire grating which acts as an array of thousands of slits . A second grating is then used to diffract the matter waves such that there is an interference pattern projected in a plane ahead of the gratings. When all gratings are parallel, have the same grating periods and are distanced from one another in a characteristic distance called the Talbot length  it is possible to create an interference pattern in which the fringe separation equals the grating period of the diffraction grating. If this is the case, a third grating identical to the first two can be used to cover all the dark (or bright) spots of the interference pattern. By shifting the third grating in the plane parallel to the other gratings one can thus detect the interference pattern as a modulation of the particle flux behind the interferometer.
Up to this point the text may have led to the conclusion that preparing matter waves with a fixed phase requires solely a slit or a grating. In reality, however, the situation is more complex because matter waves are very delicate and even weak perturbations by their environment can shift their phase. Such random phase shifts will destroy the wave interference.
In practice, many processes can introduce such detrimental phase shifts, for instance collisions with other molecules. For this reason, matter-wave interferometers are always placed in ultra-high vacuum chambers. Another dephasing may be caused by the attraction between the quantum particles and the diffraction grating . This imposes some limitations to the mass of the interfering particle since the strength of these interactions increases with the particle size. This can be circumvented by using optical gratings.
There are many analogies between interferometry of light and matter but there also exists an important experimental difference: while monochromatic light is easily provided by modern lasers, the de Broglie wavelength of a massive particle depends on its velocity. A monochromatic matter wave beam thus necessitates particles of the same velocity. Fortunately the monochromaticity requirement can be overcome with the right technology as illustrated by the following example.
|Figure 1: Demonstration of time evolution in a double slit matter-wave interferometer
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Figure 1 shows a sketch of a matter-wave interferometer. A cloud of particles with one mass is diffracted at a double slit. Within this cloud the slow particles are on the left side and the faster particles are on the right side. Upon diffraction at the double slit the particles are distributed among the bright areas of the interference pattern. When the fast fraction of particles has travelled the distance L an interference pattern is projected onto the screen. This is depicted in the simulation by the red pattern on the detector. Some time later the slower fraction of particles are detected and the green pattern is observed. Since the slow particles have travelled for a longer time over the distance L, their interference pattern is spread out further.
All velocity classes will contribute to the resulting pattern and the fringes will wash out, while they would be visible for a monochromatic beam. But by looking at the interference pattern before it hits the detector one can see that the pattern itself has a high contrast, independent of which velocity classes contribute to the clouds. It is simply the detection method of projecting the pattern onto a fixed screen that averages it out. The necessity of velocity filtering is thus not fundamental but imposed by the detection method. So which type of detection will facilitate the observation of interference in a beam of fast and slow particles?
The answer is: any technique that allows imaging an extended region of space for a short time. In the simulation one can imagine this as a camera that takes a snap shot when the clouds pass the interaction region.
A sketch of the current setup is depicted in figure 2. The pulsed source emits clouds of nanoparticles which travel through ultra-high vacuum and then reach the first grating. Here the phases of the matter waves are prepared so that interference can take place when the particles reach the region of the second grating. Subsequently the diffracted particles form an interference pattern which is imaged with the third grating. The number of particles exiting the interferometer and their masses are then measured with a mass spectrometer. This is a device that accelerates charged particles and clocks their time-of-flight over a certain reference distance.
The innovation of this setup lies in the fact that the gratings are composed of pulses of ionizing laser light. These pulses are reflected at normal incidence at a mirror so that the back and forth running waves are brought to a superposition. The result of this is the formation of a stationary wave in which bright and dark regions alternate with a period of half the laser wavelength. The OTIMA setup uses light with a wavelength of 157 nm which is in the vacuum ultraviolet end of the spectrum and invisible to the human eye. This short wavelength has two advantages: on the one hand the grating period is around 80 nm which is smaller than most machined material gratings. On the other hand 157 nm radiation is very powerful since the energy of light increases when its wavelength decreases. In the bright areas of the light structure there is in fact so much energy that particles can be deprived of an electron and consequently carry a net positive electric charge. This process is called photoionization and its occurrence turns the light structures into periodic spatial filters for uncharged particles. Optical gratings offer many advantages: they do not clog or break, they offer perfect periodicity and they can be switched on or off in few billionths of a second. The last feature is invaluable since it allows the gratings to form an interferometer in the time-domain. This means that all particles of the same mass contribute to the same interference pattern, irrespective of their velocity .
|Figure 3: Experimental protocol of the OTIMA experiment
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Other than in a material grating setup, the grating action occurs when the particles are illuminated by the laser pulse rather than when they reach the position of a grating. Since each laser pulse is extended over a volume of 30 mm3 very many particles can be subjected to the pulses and the action of the grating may be triggered with high timing precision. In other words: interference occurs now on a characteristic time scale rather than a length scale. Other than in far field diffraction (figure 1) where the interference pattern persists over time-distance to the grating, the high-contrast OTIMA interference pattern can only be observed at specific times after the second grating. This first full recurrences period is called the Talbot time. It is determined by the particle mass m and the grating period d:
When the delays between the first and second grating and between the second and third grating are equal to the Talbot time, the interference pattern will have the same periodicity as the third grating. Due to this Talbot effect the third grating pulse may be used to either cover the maxima or the minima of the interference pattern. When the opaque (transparent) regions of the grating overlap with the particle maxima (minima) in the interference pattern the number of particles exiting the interferometer can be minimized (maximized).
The mass dependence of this effect is crucial for the experiment: when particles of different masses fly through the interferometer, only those particles will show a modulated transmission for which the time is set properly. The other particles will not influence or disturb the interference and simply pass through the gratings like classical particles would.
The OTIMA makes use of this mass dependence and is designed for a particle source from which a broad distribution of particle masses are emitted. Molecular or metal clusters are thus very well suited for the investigation in the setup.
Here we present results of the first OTIMA prototype with clusters of anthracene molecules . Anthracene is an organic molecule that consists of three aromatic rings. The source used to produce a beam of anthracene clusters is an Even-Lavie (EL) source . In this device the molecular powder is heated until it evaporates. The vapor is then picked up by a short high pressure pulse of a gas, e.g. argon or neon and carried to the interferometer. During this flight the molecules condensate to small drops consisting of up to 15 anthracene molecules. The lower panels of figure 4 each show two spectra of such clusters: the black graph was recorded when the interferometer timing was tuned "on resonance", i.e. when the pulse delays were equal and corresponded to the Talbot time for one of the cluster masses. The red spectra were recorded with the grating delays detuned and they serve as a reference. In this case the pulse delays were not equal and no interference was observable. This is shown in figure 3 which explains the protocol of OTIMA interference. Deviations between the black and red spectra occur only for masses which interfere. The left side of the figure shows results from an interference run where the clusters were a little bit slower than on the right side. While this does, thanks to the time-domain, not alter the quality of the results, it does shift the Talbot time so that in the two measurements different masses are forced to interfere. For this reason the difference between the black and red spectra are largest for the 10-anthracene-clusters on the left side and the 8-anthracene-cluster on the right side. A measure for the signal difference, the so called normalized contrast is represented by the green bars in the upper panels of figure 4. Since Talbot Lau interference does not only occur when the pulse delays are equal to the Talbot time but also when the delays equal integer fractions of the Talbot time. These higher order effects are manifest in the fact that the black and red spectra deviate also for the 5-fold cluster (on the left side) and the 4-fold cluster (on the right side). While the green bars show the experimental data, the purple bars represent simulation results which reproduce the green bars reasonably well. The small discrepancies between theory and experiment are attributed to the lack of knowledge on molecular cluster properties which enter the simulations. Also the deviations in the black and red spectra cannot be explained by classical physics which predicts the gray bars as a measurement outcome.
Figure 4: Measurement results of a typical OTIMA experiment with anthracene clusters
While these experiments are unambiguous evidence for the quantum interference of anthracene clusters, it is also desirable to image the interference pattern in space. This can be done by measuring the amount of interfering clusters exiting the interferometer while shifting the third grating over the interference pattern. Since the third grating has the same periodicity as the interference pattern, a continuous shift of the third grating will periodically alter the particle flux behind the interferometer. This behavior is shown for several clusters in figure 5. Each colored line represents the transmission of a cluster mass as a function of the grating shift. The figure clearly shows that the sinusoidal modulation of the flux appears only for the interfering clusters. For the other clusters the shift of the third grating has no effect.
Concluding, we are able to find unambiguous evidence for the quantum wave nature of anthracene clusters in the recorded mass spectra as well as in the variation of signal as a function of the grating positions. The good agreement of the results with the theoretical prediction shows that the experiment is well understood. This renders the setup a promising tool for many future quantum experiments with heavy and complex particles .