Ultrafast Physics and Frequency-Comb Laser Metrology

Fundamental tests using frequency-comb laser excitation

As explained here, a frequency comb laser produces high power pulses that are equivalent to many precisily known and simulataneously lasing modes. This gives unique opportunities for precision testing of e.g. quantum-electrodynamics (QED) and models for nuclear size by precision spectroscopy in simple atoms such as hydrogen, helium, or helium-ions. One needs to be pretty precise, because QED effects are usually very small (less than 1 in a million of the total excitation energy). In the picture below the relative energy scale is shown for excitation of these atoms from their respective ground states. Transitions like this (by one- or two photon excitation) can be used to compare the experimentally found transition frequency to the theoretical predictions. In hydrogen this has been extremely succesful on the 1S-2S transition, and the current accuracy is on the order of 14 decimal places (see the paper from the MPQ in Garching, Germany: M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)). However, the theoretical value for the 1S-2S transition in hydrogen depends on the size of the proton. This size is not known accurately enough anymore, and this hampers further progress.

 Hydrogen_helium

One way around this is to do spectroscopy in heavier atoms. Examples are shown above of helium and the helium-ion. Helium-ions are just like hydrogen, except for a heavier nucleaus (2 protons and 2 neutrons instead of 1 proton). Because QED effects scale with the number of protons in the nucleus to the fourth power and higher, these effects are at least 16 times larger. The accuracy of the nuclear size in helium is supposed to be a bit better than in hydrogen, so that a measurement in helium+ could perform a better test.
However, the wavelengths needed for excitation are very difficult to make. Already the experiment in hydrogen with a two-photon transition at 243 nm photon is very difficult, but that light is still possible to make with continuous precision lasers and nonlinear crystals. For 120 nm (Vacuum Ultraviolet: VUV), or even shorter wavelengths (Extreme Ultraviolet: XUV) can only be made in higher-order nonlinear processes that yield very low output and require high laser intensities.

This is where frequency comb lasers come in. Comb lasers can be both precise, and emit high power laser pulses (in the infrared) at the same time. If these pulses are enhanced further (by a resonator or by amplification), then it is possible to generate light at much shorter wavelengths via high-harmonics (HHG). If in this whole process the phases and delay between the pulses are not distorted, then the frequency comb is effectively converted to shorter wavelengths. This light (in the form of XUV pulses) can then be used to directly excite the atoms. One then changes the mode positions of the original comb laser, and as a result the modes in the XUV will scan as well. If you record an excitation signal (e.g. by ionizing excited atoms, and detecting the ions), you will see a repeating pattern from which the transitions frequency can be deduced. How the pattern looks depends on the amount of pulses you use for exciation. If excitation takes place with an infinite train of pulses (see the picture below, part a), then it looks like sharp resonances (apart from broadening effects): what you see is excitation with the modes of the comb laser.

 Direct_comb_spec_principle

 The earliest proposals and experiments with this kind of excitation were already published in 1978 (See e.g. Phys. Rev. Lett 40, 847 (1978)), but after the initial experiments not much progress was made anymore. This has all changed because of the invention of the frequency comb laser, so that it actually has become feasible to use it for precision experiments.

We employ amplification of the frequency comb pulses before upconversion to the XUV. This can only be done for a limited amount of pulses. The pattern you see depends on this amount of pulses via a Fourier relation. For only two pulses the comb laser spectrum will look like a sine wave, where the maxima of the sine coincide with the peaks of the original comb modes you will see for an infite pulse train. This situation is depicted in part b of the picture above. So even with only two pulses, you can do frequency comb spectroscopy. We have demonstrated this with an experiment in Krypton atoms at a wavelength of 212 nm. The comb laser was amplified in a Ti:Sapphire amplifier and frequency doubled twice to reach 212 nm. Then a two-photon transition was excited with these 212 nm pulses. Depending on whether a 'comb mode' was resonanti or not, more or less ions were produced by an ionisation pulse that was sent in after the upconverted comb pulses. The picture below shows the signals in krypton for three different cases. In part A, 1 to 3 pulses for the excitation are used. In each case the amount of excitation is monitored as a function of the position of the frequency comb laser modes (tuned over the resonance by changing the frep of the laser). With one pulse (blue curve) there is no comb structure. With two pulses (red curve) a comb structure appears in the form of a sine wave. For three pulses (green curve) the sine converts in a narrower reonances. For more pulses the peaks would get narrower and narrower. In part B we have changed the carrier-envelope phase slip of the pulses so that the modes shhift in frequency by one quarter of a repetition rate. Finally in part C we measure the signal for two different isotopes (84Kr and 86Kr).

 Kr_results

We were the first to demonstrate such a high resolution with amplified and upconverted frequency comb pulses, and published it in Science: "Deep-Ultraviolet Quantum Interference Metrology with Ultrashort Laser Pulses"
S. Witte, R. Zinkstok, W. Ubachs, W. Hogervorst, K.S.E. Eikema,
Science, vol. 307, 21 January 2005, page 400-403


Below is a photo of the Krypton experiment (on the right is the multi-pulse Ti:Sapphire amplifier, and on the left the vacuum setup with a krypton atomic beam):

 new_setup_spectroscopy2

 Using only two pulses for excitation reduces the resolution compared to many-pulse excitation. However, a sine can be fitted very accurately and one can choose to use frequency comb pulses further away from each other. The resolution then increases linearly with the pulse distance. We have demonstrated this with an experiment in Xenon at 125 nm. Below is a schematic of the vacuum setup and the harmonic conversion.

Xenon_setup 

As you can see in the picture below we can increase the resolution by either increasing the number of pulses, or the distance between the pulses. The latter will be persued further because it is easier to implement for even shorter wavelengths required to excite helium and helium+ ions. Also systematic effects such as phase shifts between the pulses can be measured far better with only two pulses. The resolution is then regained by simply taking the pulses further apart.

Xe_results_two_graphs

You can read about it in the following publication: R.Th. Zinkstok, S. Witte, W. Ubachs, W. Hogervorst, and K.S.E. Eikema, "Frequency comb laser spectroscopy in the vacuum-ultraviolet region", Phys. Rev. A 73, 06180(R) (2006).

Currently we are working on helium excitation at 51.5 nm, and the results are quite promising! The setup and laser techniques are completely different from the earlier experiments, and details will soon be posted on this page. One key ingedient of the experiments in Helium is the newly developed parametric amplifier which can amplifiy two subsequent pulses from a comb laser. After upconversion to XUV wavelengths we have a frequency comb in the XUV at 51.5 nm.
This is a photo of the present situation for the helium experiment:

 Helium_setup_photo2 

Here you can see the people that have been working on the setup, from left to right: Amandine Renault, Christoph Gohle, Dominik KandulaHelium_setup_photo 

 These experiments are sponsored by:

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Questions? Contact: K.S.E.Eikema@vu.nl