On the prospects of interferometry and deflectometry for characterizing large molecules

Transcription

1 Eur. Phys. J. Special Topics 159, 1 9 (2008) c EDP Sciences, Springer-Verlag 2008 DOI: /epjst/e THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS On the prospects of interferometry and deflectometry for characterizing large molecules M. Arndt a, M. Berninger, S. Deachapunya, S. Gerlich, L. Hackermüller, A.G. Major, M. Marksteiner, A. Stéfanov, and H. Ulbricht Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria Abstract. We investigate the prospects of near-field matter-wave interferometry for the sensitive determination of molecular properties, such as electric polarizabilities, electric and magnetic dipole moments or even life-times of some molecular states. We discuss how important principles of our present quantum experiments can be transferred to the classical regime, i.e. to a Moiré deflectometer in order to also measure characteristic properties of large clusters and biomolecules. 1 Introduction Matter-wave interferometry with clusters [13] and large molecules [6] is still a young research field and yet it already allows us to study both the foundation-oriented aspects of coherence and decoherence as well as new ideas concerning accurate measurements on molecules. In the present article we shall focus on the application of matter-wave interferometry and classical deflectometry for precision metrology, i.e. the determination of electric, magnetic and possibly structural properties of molecules, as well as for the sensitive sorting of mixed molecular beams according to electronic or structural properties. In the following we shall first use polarizability measurements to describe the current state-of-the-art and experimental ideas. We will then discuss the principles and merits of measurements in an either an interferometric set-up or a Moiré arrangement. The accurate measurement of the atomic polarizability α is among the frequently cited examples demonstrating the power of matter-wave interferometry [19]. The polarizability of molecules is of at least equal importance in various fields of physics and chemistry [10]. It is relevant for the understanding of long-distance molecular collisions [28] and it is indicative of the physical structure and shape of the molecules [2, 3]. Recently, the influence of α has also been emphasized in the context of quantum diffraction [5, 14] and interferometry [12]. Here, the attractive interaction between the molecule and the diffraction grating is very significant and it has even been argued that the strength of this interaction will set a rather strict boundary condition on the complexity of molecules in matter-wave interferometry [11]. Additionally, the polarizability of a molecule is used for the coherent manipulation of molecules using the matter wave analogue of the Kapitza-Dirac effect [20, 22, 36]. It is also important for slowing and trapping of molecules, both with optical or switched electric fields (see e.g. [8,9,21,32,39,41]). a markus.arndt@univie.ac.at Our work is supported by the Austrian FWF through SFBF1505, STARTY S. Deachapunya is supported through a Royal Thai Government scholarship. A. Major is sponsored by the FWF through a Lise Meitner fellowship.

2 2 The European Physical Journal Special Topics All experiments that explicitly exploit α may also in principle be used to determine its accurate value. In the past, however, two main strategies were particularly useful for measurements on isolated neutral particles in molecular beams [10]. A classical beam deflection experiment normally operates with a coarsely collimated beam, typically several hundred micrometers wide, an interaction region with a constant electrical force field across the beam profile, and finally a position sensitive detection scheme to monitor the shift of the deflected molecules. Such arrangements are suitable for all sorts of clusters and molecules and they can operate on fast as well as slow beams. However, one always has to find a compromise between position resolution on the one hand and total useful molecular flux on the other hand. Both usually depend on the size of the collimator slits in opposite ways. High voltages are usually required for sufficiently high beam deflections ( 30 kv in [2]). Atom interferometry, on the other hand, has shown to be able to increase the accuracy in polarizability measurements by more than an order of magnitude, so far for alkali atoms [19, 35]. A tightly collimated beam is first split into two arms using matter wave diffraction. A homogeneous electric field in one of the arms then imprints a phase shift on the interference pattern, which can be detected with high resolution. The extremely high sensitivity is a consequence of the very narrow collimation required for operating the interferometer in a far-field regime, i.e. with genuinely separated atomic beams. This is also the reason why this technique cannot be applied directly to fast molecular beams: the collimation requirements are much too severe for the intensities that can be typically expected for beams of large molecules. In the present contribution, we discuss an experimental idea that combines the advantages of both methods. A near-field interferometer accepts uncollimated wide molecular beams, thus ensuring a high particle flux and signal. On the other hand, since it is composed of three gratings which may be as small as in far-field experiments a good spatial resolution is also guaranteed. 2 Measurements in a Talbot-Lau interferometer Our interferometer is of the Talbot-Lau type [11, 16] and is built of three identical gratings placed at equal distances (Fig. 1). The molecular beam may enter without any particular spatial coherence. The molecular elementary waves emerging from the small openings in the first grating then evolve such that their wavefunction is sufficiently spread out to cover a few neighbouring slits of the second grating coherently. Diffraction and interference then create a periodic molecular density signal at the position of the masking third grating. The total molecular flux behind the third grating is then measured as a function of its transverse position to retrieve the molecular interference pattern. This interferometer has proven to work very well and with high visibility with C 60 and C 70 [12] as well as with C 60 F 48 and the biomolecule tetraphenylporphyrin [25]. The advantage of this three-grating design lies mainly in the fact that the width of the beam (molecular flux) is decoupled from the deflection sensitivity (grating constant). An electrostatic deflector is then inserted close to the second grating and causes a lateral fringe shift: s x (α, v) αu 2 /mv 2 y. (1) The shift is proportional to the polarizability-to-mass ratio α/m and to the square of the applied electrode voltage U. Since we are aiming at deflecting the molecular beam along its long cross section (horizontally), the classical two-wire field, usually used in Stark deflection experiments [42], is not appropriate for our purposes. Instead, a electrode design is necessary that produces a constant force field over the entire, horizontally extended, beam diameter [7]. In order to illustrate the measurement principle we show the simulated shift of the interference fringes for four different deflection voltages (0, 6, 12 and 18 kv) in Fig. 2. Here we assume the molecular velocity distribution to be centered at v = 120 m/s with a width (1/e 1/2 )ofσ v = 6%. The shifts are computed with the published literature value for the polarizability of α =76.5 Å 3 [2]. The simulation shows that a good resolution should be achievable.

3 Emerging Quantum Technologies 3 Fig. 1. Design of both a Talbot-Lau interferometer (quantum) and Moiré deflectometer (classical). In either case the third grating scans the fringe pattern and a subsequent detector measures the integral particle flux. A voltage applied to the interaction region deflects the molecular fringe pattern and thus modulates the transmitted signal. Fig. 2. Interference pattern of C 60 without deflection voltage (solid line), at U = 6 kv (dashed), U = 12 kv (dotted) and at U = 18 kv (dash dotted). The voltage dependent shift allows to derive α/m. The decreasing fringe visibility at higher voltages is caused by the finite velocity spread: different v-component experience different shifts and tend to dephase the interferogram. 3 Future prospects of molecule metrology Our present apparatus was originally designed for investigations of coherence and decoherence phenomena, in the quest for a better understanding of the quantum-to-classical transition [6]. And it is natural to see that several improvements are still possible for precision measurements with different classes of molecules. First we focus on the requirements for polarizability studies before we extend the argument to other molecular properties.

4 4 The European Physical Journal Special Topics 3.1 Elimination of phase-averaging effects So far we have discussed genuine quantum interference. It is very sensitive to α/m, but also sensitive to the molecular beam velocity. This is a much desired feature of the Talbot-Lau interferometer, as it permits to explicitly demonstrate the quantum wave-nature of the flying molecules [12]. On the other hand it causes various dephasing mechanisms which may reduce the fringe contrast and thus the measurement accuracy if different velocity classes are present in the beam. For instance, the Earth s gravity or rotation can give rise to dispersive dephasing effects [38]. However, we will ignore them in the following, since they can in principle be compensated for by a suitable mounting and alignment of the interferometer. The van der Waals (vdw) [14] or Casimir Polder (CP) [11,15] interaction between the molecules and the grating walls, V vdw,cp α, is also velocity dependent and thus a cause of dephasing. And this will even become more relevant for more complex molecules, as the interaction grows approximately linearly with mass at least within typical hydrocarbons [27]. But also the Stark deflection, and for that matter any external force field, causes a velocity dependent fringe shift s 1/v 2, as both the interaction time and the relative momentum change depend on v. The fringe visibility will therefore be reduced in the presence of a finite longitudinal velocity spread, and this dephasing will become more important for strong deflection fields or for high molecular polarizabilities. We see the onset of this effect already in Fig. 2, where the widest shift ( s =3.2 µm at 18 kv) in the highest external fields is accompanied by the lowest contrast. Any dephasing reduces the precision of our measurements and therefore has to be minimized. The vdw-effects may first of all be reduced by widening the grating openings. Increasing the grating period may appear as a counter-intuitive strategy, since much effort were necessary to get into the quantum diffraction regime in the first place. However, it is well established (see e.g. [37]) that a classical gradient force will shift quantum interference fringes by the same amount as classical Moiré (shadow) fringes. A Moiré setup is thus the most natural arrangement for very large molecules with short de Broglie wavelengths and high polarizabilities, such as those prepared in pulsed biomolecular beams [33]. Such a classical arrangement shares the key advantages with the quantum Talbot-Lau interferometer such as high transmission and still a high spatial resolution but it operates in the regime L L T = g 2 /λ db. In the classical case the grating constant g may be chosen large enough to minimize molecule-wall interactions. Then the fringe contrast is mainly determined by the open fraction f, i.e. by the ratio of the slit opening to the distance between two slits. And the contrast can reach 100 % for f 1/4 [37]. A particularly elegant way of avoiding grating-wall interactions is to avoid any walls at all. The combination of two material gratings and one optical standing light wave in a Kapitza- Dirac-Talbot-Lau interferometer as currently being investigated for fullerenes, and shown in Fig. 3, is expected to largely extend the range of metrology experiments. And also this quantum device has an unexplored classical analogue: a Moiré deflectometer built from two absorptive masks and one optical phase grating. It is interesting to note that such a device (in either classical or quantum mode) is already rather sensitive to the molecular polarizability even in the absence of an external deflecting field: the local electric field inside the laser beam can be rather strong, typically E = V/cm, and the field gradient can be very large inside the standing light field, where the full field amplitude falls to zero over a distance of a few hundred nanometers. The dependence of Talbot-Lau or Moiré fringes on the laser intensity will also allow us to extract a value for α with an expected accuracy of better than 10%. Almost all of the aforementioned dephasing effects will be significantly reduced by narrowing the velocity spread of the molecular beam. And various methods are conceivable for that: Our present v-selection scheme is based on the use of three height delimiters one each at the start, center and end of the molecular beam to select a free-flight parabola in the Earth s gravitational field [4]. This typically achieves a v-selection of v/v 10%. A rotating helical turbine as used in neutron physics for instance can achieve much better selection ratios with a higher relative transmission than the gravitational scheme. The turbine is compatible with both pulsed and continuous beam and detection methods. Such a

5 Integrating detector Emerging Quantum Technologies 5 L L Deflector g d X Y Source grating Optical grating Detection Mask Fig. 3. In order to avoid the strongly dispersive effect of the molecule-wall interaction one may replace the central grating by an immaterial, optical phase grating. Diffraction is then based on the periodic phase shift related to the electric force between matter and light. Because of its conceptual similarity to a proposal by Kapitza and Dirac [29] we designate this scheme as the Kapitza-Dirac-Talbot-Lau interferometer. rotor has also recently been developed in our group with particular care taken to minimize vibrations and to ensure compatibility with high vacuum requirements. Supersonic jets are also known to generate relative velocity spreads in the range of a few percent, at least for atoms. However, such beams are usually fast and therefore only weakly deflected. Moreover, the cooling effect of the adiabatic expansion can not be generally adapted to massive molecular systems, since the number of collisions and therefore the cooling power in the adiabatic expansion is limited. However, the combination of pulsed source and detection methods [17, 34] is very promising for our purpose since the short detection laser pulse will only act on a short time-slice out of the entire molecular beam and it will thus select v/v 0.1% [33]. This is certainly good enough to eliminate most of the dephasing effects mentioned before. 3.2 Towards larger shifts or shorter devices In order to increase the sensitivity we might increase the inter-grating distance L or the force field. Filling the deflectometer with electrodes from front to end offers the possibility to either increase the resolution. Alternatively, it would allow us to shorten the entire setup. In the aforementioned example this means that we might reduce the grating separation from currently 38.5 cm to 12 cm and still have the same fringe shift under otherwise equal conditions. We note that in our present interferometer configuration we can already measure differences in α/m of the order of a few percent [43]. For highly polished electrodes the breakdown voltage in high vacuum is known to be greater than 10 7 V/m [8,31]. In our setup this corresponds to a voltage U>40 kv, i.e. about two times larger than used for the present simulation. The accuracy of the polarizability measurements increases with growing deflection, since the scale of the position resolution is set by the grating period, which will remain constant. 4 Other molecular properties and new molecular species 4.1 Fullerenes In our present setup the sensitivity to differences in polarizability-to-mass ratio is already high enough to partially separate or enrich mixed beams of C 60 and C 70 [43]. Increasing this

6 6 The European Physical Journal Special Topics sensitivity to (α/m) = 1% would finally allow us to separate endohedral fullerenes from empty cages in free-flight before the endohedrals are deposited in a nanostructured Talbot-Lau pattern. This may be of particular relevance for recent proposals around quantum information processing with N@C 60 or P@C 60 [26]. Magnetic properties of Fullerenes can also be investigated in a Talbot-Lau setup. While C 60 exhibits no electronic spin in its singlet ground state S 0, it is well-known that an excitation to the singlet state S 1 will be followed by a transition to the triplet state T 1 with 99% efficiency and with a mean decay time of about 1 ns [18]. Published life times of the excited state vary by three orders of magnitude [18], as they depend on the molecular spin environment as well as the molecular temperature. Deflectometry promises at least to shed light of excited on molecules in free flight: since ground-state molecules have no spin, they experience only a negligible deflection even in strong external magnetic field gradients. However, once pumped to the triplet state which could be done with a time resolution of a few nanoseconds the molecular spin corresponds to that of two electrons. The molecules will therefore experience a significant Stern-Gerlach displacement in an external field gradient, as long as they remain in the excited state. Since the magnetic moments will not be aligned initially, the beam will be broadened and the fringe contrast in the interferometer will decrease. The value for the life time may then be retrieved from the degree of decoherence. In this sense decoherence will not only be an interesting subject for fundamental quantum studies but actually also a tool for accurate measurements. It can be assumed that the life time depends on the internal temperature. As we have shown in our earlier work [24], the high stability of fullerenes allows us to control this internal parameter with external laser beams. 4.2 Biomolecules Biomolecules are intriguing objects for matter-wave interferometry since they exhibit a rich internal structure and thus many handles for different couplings to the environment. This is interesting for fundamental reasons with respect to decoherence but also for practical applications, since interferometry allows us to measure those molecular properties that easily couple to the environment. In contrast to fullerenes, most biomolecules possess large polarizabilities, large electric dipole moments, and different conformational states will show strongly varying values in both quantities. It can also be expected that some structural information may become available through the determination of scattering cross sections between biomolecular beams and controlled noble gas environments inside an interferometer [28] or Stark deflectometer. The successful realization of such experiments is largely dependent on methods for volatilizing thermolabile molecules. Modern mass spectroscopy of peptides is usually based on electrospray ionization [44] or matrix assisted laser desorption ionization [30, 40]. However, interferometry and deflectometry will preferentially operate on neutral beams and the combination of pulsed laser desorption with cooling in an adiabatically expanding seed gas is identified as presently the method best suited for this aim [33]. In recent experiments we were, for instance, able to generate neutral beams of the polypeptide Gramicidin. In Fig. 4 we show both its complex structure and the mass spectrum obtained in a time-of-flight mass spectrometer after pulsed laser ionization, 30 cm downstream of the pulsed laser desorption. The figure shows that a good signal-to-noise ratio can be achieved and we also see that the mass resolution will be sufficient for the convenient selection of a narrow distribution in de Broglie wavelengths, with m/m 1%. It is still a matter of ongoing research up to which mass this method will be useful. Both the desorption and the detection of neutral protein jets are an interesting open challenge for various groups worldwide. 5 Overall experimental boundary conditions It is evident that all high-precision experiments will have to fulfill a set of boundary conditions: Earlier experiments have shown that the residual gas pressure in the interference chamber should be well below 10 7 mbar for C 60 in order to avoid collisional decoherence [28]. And

7 Emerging Quantum Technologies 7 Fig. 4. Neutral polypeptide beams, here of Gramicidin D (left), can be generated using pulsed laser desorption, and detected in a pulsed multi-photon ionization process. A simple time-of-flight mass spectrometer selects m 1%. The detection process intrinsically also selects v/v < 1% [33]. Such complex objects are interesting candidates for interferometry and metrology. we will have to achieve p< mbar for large polypeptides or proteins [23]. Such low pressures are also favourable for all high-voltage applications. An accurate determination of the distance between the gratings is required and possible to the level of 10 4 by standard means. The high-voltage supply in a Stark deflection experiment needs to reach a high accuracy and stability. Values of better than 0.01%. are commercially available. In the proposed magnetic deflection or life time experiments, the laboratory noise is well below the 10 4 level of the externally applied fields (approximately 1 Tesla), and the short-term stability of permanent magnets is much better than that. In a rigid mount, the distance between the electrodes or magnets can be stabilized to better than 20 nm, i.e. to the level of 10 5 of their absolute distance. Measuring this distance with the same accuracy is rather difficult, however. Straightforward measurements would rather lead to an accuracy of 10 µm, i.e. a relative error of at least This is also approximately the level of accuracy that might be reached by calibrating the entire setup with well-characterized objects, such as alkali atoms. Their static polarizabilities are α = (24.11 ± 0.06) Å 3 for Sodium [19], α = (24.33 ± 0.16) Å 3 for Lithium [35] and α = (59.42 ± 0.08) Å 3 for Cesium [1]. As mentioned in the context of dephasing, the velocity is a critical parameter, since it enters quadratically in Eq. (1). However, in particular in pulsed molecular beam experiments with start and stop pulses as short as 5 ns, the selectivity is mainly given by the spatial width of the laser beams and can reach values as small as 0.1%. Also, the v-dependence would be softened significantly inside a KDTL-interferometer. Altogether we can therefore expect to reach a resolution of 10 3 in the long run for several molecular parameters. A higher precision would only be meaningful if we had state selected molecules, since averaging over various internal molecular states may cause a much larger systematic effect than the uncertainties in the measurement. Cooling of both internal and external degrees of freedom will therefore be an important task for future research. 6 Conclusions We have shown that a three-grating setup, both in its quantum and classical version, combines the advantages of high spatial resolution with a high molecule transmission. Our present experiments may serve for the measurement of the polarizability of fullerenes, with an error of a few percent. Various improvements on the experimental set-up will allow us to improve the accuracy to below one percent. Our design is expected to find applications for the characterization

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