Optical frequency combs based on mode-locked lasers have revolutionised the field of metrology and precision spectroscopy by providing precisely calibrated optical frequencies and coherent pulse trains. Amplification of the pulsed output from these lasers is very desirable, as nonlinear processes can then be employed to cover a much wider range of transitions and wavelengths for ultra-high precision, direct frequency comb spectroscopy. Therefore full repetition rate laser amplifiers and enhancement resonators have been employed to produce up to microjoule-level pulse energies. Here we show that the full frequency comb accuracy and resolution can be obtained by using only two frequency comb pulses amplified to the millijoule pulse energy level, orders of magnitude more energetic than what has previously been possible. The novel properties of this approach, such as cancellation of optical light-shift effects, is demonstrated on weak two-photon transitions in atomic rubidium and caesium, thereby improving the frequency accuracy up to thirty times.Comment: 16 pages (including supporting material), 6 figures and 2 table

An experimental realization of high-precision direct frequency comb spectroscopy using counterpropagating femtosecond pulses on two-photon atomic transitions is presented. The Doppler broadened background signal, hampering precision spectroscopy with ultrashort pulses, is effectively eliminated with a simple pulse shaping method. As a result, all four 5S-7S two-photon transitions in a rubidium vapor are determined with both statistical and systematic uncertainties below 10(-11), which is an order of magnitude better than previous experiments on these transitions.

Quantum coherent control (1-3) is a powerful tool for steering the outcome of quantum processes towards a desired final state, by accurate manipulation of quantum interference between multiple pathways. Although coherent control techniques have found applications in many fields of science (4-9), the possibilities for spatial and high-resolution frequency control have remained limited. Here, we show that the use of counter-propagating broadband pulses enables the generation of fully controlled spatial excitation patterns. This spatial control approach also provides decoherence reduction, which allows the use of the high frequency resolution of an optical frequency comb (10,11). We exploit the counterpropagating geometry to perform spatially selective excitation of individual species in a multi-component gas mixture, as well as frequency determination of hyperfine constants of atomic rubidium with unprecedented accuracy. The combination of spectral and spatial coherent control adds a new dimension to coherent control with applications in e.g nonlinear spectroscopy, microscopy and high-precision frequency metrology.In traditional coherent control experiments pulse shaping techniques (12) are used to steer light-matter interaction by manipulating the relative phases between different quantum paths leading to the same final state. Numerous control schemes have been shown in the past to provide frequency control and selectivity with a resolution exceeding the bandwidth of the individual pulses by 2-3 orders of magnitude. The vast majority of these schemes rely on a twophoton interaction with a single broadband shaped pulse. Even though the laser systems used in these experiments produce trains of pulses, decoherence effects due to the atomic motion wash out the interference between different pulses, and therefore blur the underlying atomic structure. Spatially, the interaction with a single shaped pulse creates a signal that is practically identical along the whole beam path.Here we demonstrate how the control level of light-matter interaction is significantly enhanced by the interaction with multiple pulses. First, we show that the addition of a counterpropagating pulse changes the quantum interference and can even invert the properties of the excitation. In combination with pulse shaping techniques this geometry provides full spatial control and is able to produce complex excitation patterns over an extended region. Second, excitation from counter-propagating beams inherently reduces decoherence effects, allowing coherent accumulation of quantum interference over long pulse trains, even without the use of cooling techniques (13). Combined with the excellent phase stability of an optical frequency comb, this enables high-resolution excitation which is able to resolve the smallest features of the atomic structure. 2In order to gain insight in the properties of spatial control, we derive an analytical expression for the spatial excitation pattern. Consider the two-photon interaction of a simple two-level atom with a li...

Extreme UV (XUV) frequency comb generation in the wavelength range of 51 to 85 nm is reported based on high-order harmonic generation of two consecutive IR frequency comb pulses that were amplified in an optical parametric chirped pulse amplifier. The versatility of the system is demonstrated by recording direct XUV frequency comb excitation signals in He, Ne, and Ar with visibilities of up to 61%.

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