Isotope Selective Ionization by Optimal Control Using Shaped Femtosecond Laser Pulses Albrecht Lindinger, * Cosmin Lupulescu, Mateusz Plewicki, Franziska Vetter, Andrea Merli, Stefan M.Weber, and Ludger Wo ¨ste Institut fu ¨r Experimentalphysik, Freie Universita ¨t Berlin, Arnimallee 14, D-14195 Berlin, Germany (Received 9 January 2004; published 15 July 2004) We report on selective optimization of different isotopes in an ionization process by means of spectrally broad shaped fs-laser pulses. This is demonstrated for 39;39 K 2 and 39;41 K 2 by applying evolution strategies in a feedback loop, whereby a surprisingly high enhancement of one isotope versus the other and vice versa is achieved (total factor 140). Information about the dynamics on the involved vibrational states is extracted from the optimal pulse shapes, which provides a new spec- troscopical approach of yielding distinct frequency pattern on fs-time scales. The method should, in principle, be feasible for all molecules. DOI: 10.1103/PhysRevLett.93.033001 PACS numbers: 33.80.Rv, 28.60.+s, 82.53.–k Selection of particular isotopes is a topic of great interest in several fields of science and technology like medicine, paleontology, history, etc., and a variety of technical applications have emerged so far (MRI, nuclear enrichment, etc.). Previous isotope separation methods like gaseous diffusion and centrifugation take advantage of small mass differences [1], whereas laser isotope sepa- ration utilizes minor isotope shifts of spectral lines [2,3]. Yet, cw lasers allow only to separate the fraction present in a single quantum state. In a more recent treatment femtosecond laser pulses were employed to obtain isotope selective molecular dynamics [4,5] and to perform iso- tope separation by generating spatially localized vibra- tional wave packets due to differences in the free evolution of the different isotopes [6]. We report on an approach to apply feedback control for optimizing isotope ratios by means of shaped fs-laser pulses. Various optimal control experiments have been performed so far [7–16] since in 1992 Judson and Rabitz [17] proposed closed loop adaptive feedback ex- periments. By using an iterative process the method en- ables one to find an optimal pulse form which forces the system into the target state, whereby pulse shapers [18] were combined with optimization algorithms. However, according to our knowledge no feedback control mea- surements have been performed up to now to optimize the ratio of different isotopes. So far, only a theoretical study on Br 2 is present [19]. Information about the photoinduced process itself can be gained by analyzing the acquired optimal pulse form. In order to aid the interpretation, simple model systems are primarily investigated, where the number of possible pathways is limited. K 2 dimers were chosen here since they can be ionized in a resonant three-photon process (REMPI, see Fig. 1) at relatively low pulse energies within the available wavelengths range (810–833 nm). They are prepared in an adiabatic coexpansion of potassium vapor and argon carrier gas through a nozzle of 80 m diame- ter into the vacuum. The stagnation conditions of the molecular beam are chosen to produce K 2 with no larger clusters present. Thereto, the oven temperature is set to about 400  C and the argon pressure to 2.5 bars. The laser beam is focused onto the cluster beam and produces the photoions which are extracted into a quadrupole mass spectrometer and detected by a secondary electron multi- plier. A Ti:sapphire oscillator (Tsunami; Spectra Physics) provides pulses of low energy. Thus, the experiments are carried out in the weak field regime. Pulses of 120 fs duration (FWHM), a spectral width of   8 nm, and an energy of 10 nJ per pulse are generated with a repeti- tion rate of 80 MHz, which is sufficiently high to irradiate every molecule. The pulse shaper consists of a liquid 3.5 4.0 4.5 5.0 5.5 6.0 6.5 11.2 11.4 11.6 11.8 12.0 12.2 v' = 15 v' = 11 Energy / 10 3 cm -1 r / Å u + Σ A 1 Energy / 10 3 cm -1 3 4 5 6 7 0 5 10 15 20 25 30 35 40 r / Å Energy / 10 3 cm -1 K + 2 X 2 + g Σ (2) 1 g Π b 3 u Π A 1 + u Σ X 1 Σ + g 3.5 4.0 4.5 5.0 5.5 6.0 6.5 23.8 24.0 24.2 24.4 r / Å v' = 10 v' = 5 (2) 1 g Π (a) (b) (c) Laser K 2 FIG. 1. (a) Ionization path of K 2 proposed in Refs. [23,24]. On the right are the potential energy curves and vibrational levels of the 2 1  g (b) and A 1   u state (c). The solid lines indicate the vibrational levels of the 39;39 K 2 isotope and the dotted lines the levels of the 39;41 K 2 isotope. The states v 0 A  12, 13 of the lighter isotope are disturbed by spin-orbit cou- pling with the b 3  u state and therefore shifted by 1:2 cm 1 and 2:1 cm 1 , respectively [5,25]. (c) also shows the spec- trum of the unshaped laser light at 833 nm central wavelength. PHYSICAL REVIEW LETTERS week ending 16 JULY 2004 VOLUME 93, NUMBER 3 033001-1 0031-9007= 04=93(3)=033001(4)$22.50  2004 The American Physical Society 033001-1