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Catch an electron: observing a process that takes a quintillionth of a second



In one second, many diverse and very fast processes take place around and within us. It takes only 300 milliseconds (0.3 s) to blink once, and 30 microseconds (0.00003 s) is enough for one lightning strike. Such fast processes are striking in their short duration, but there are also those whose speed is hard to imagine.

Certain chemical reactions are activated by the absorption of light. In the first moments after absorption, the distribution of electrons in the electron shell of the atom changes, which greatly affects the ongoing reaction and its outcome. These electronic transpositions occupy an incredibly short time span, often measured in attoseconds. And one attosecond is equal to one quintillionth of a second, i.e. 0.000000000000000001 seconds. Tracking such fast processes is extremely difficult, but realistically. Today we will get acquainted with a study in which scientists from the University of Freiburg (Germany) created a new technique that allows real-time observation of electron vibrations in the electron shell of noble gas atoms. What technologies formed the basis of the new method and what could be fixed? We will find answers in the report of scientists. Go.


One of the most important phenomena in the quantum world is coherence, when several vibrational or wave processes are coordinated in time. According to scientists, understanding coherence makes it possible to better understand the various processes in quantum systems, such as ultrafast decay or the formation of bonds.

In order to study real-time coherent dynamics, appropriate ultrafast techniques based on interferometric measurements representing the evolution of the vibrational phase of excited coherences are needed. From the point of view of electrons, this problem becomes an order of magnitude more complicated, since the periods of oscillations are scaled inversely with the excitation energy and, therefore, require extremely high synchronization stability in the range from attosecond to zeptosecond (10 −21c, i.e. 0.000000000000000000001 seconds). Nevertheless, it is impossible to exclude electronic processes, because in this case the information about the system as a whole will be incomplete.

One of the options for solving the above problem may be the extension of time-resolved coherent spectroscopy to extreme ultraviolet energies * (XUV).
Extreme ultraviolet * (XUV) - electromagnetic radiation in the part of the electromagnetic spectrum with wavelengths from 124 nm to 10 nm, when the photon energy is from 10 eV to 124 eV.
This will allow access to the states inside the electron shell of the atom and, therefore, to the observation of attosecond processes.

Despite the theoretical advantages of this technique, there are certain difficulties in its implementation. One of them is the lack of the required ultra-high phase stability and phase matching schemes to isolate weak coherence signals. Because of this, in practice, this XUV method for studying electronic coherence has not yet been implemented.

Another aspect of the XUV technique with great potential is the ability to control coherence. In the bichromatic research method, coherence control was achieved by manipulating the relative delay between two XUV pulses. There is also a method based on manipulating the phases of the XUV pulses.

Certain successes have been achieved in this area. So, the technology of pulse formation, available only in the infrared and ultraviolet ranges, has allowed the creation of advanced control circuits that can be used in nonlinear optics and in the management of chemical reactions. And in the XUV method, phase manipulation was partially demonstrated by changing the polarization of the excitation field.

However, direct manipulation of the phase and delay of the XUV pulse in the pulse sequence has not yet been implemented.

In the work we are considering today, scientists are implementing a phase modulation method for sequences of XUV pulses, which improves coherence management tools and coherent nonlinear spectroscopy.

To realize this, pairs of XUV pulses were prepared with full control over their delay and relative phase. A free electron laser (FEL) FERMI was used.


Image No. 1: experimental setup.

Phase synchronized ultraviolet pulses are created using a highly stable interferometer based on a monolithic structure and are used to incorporate into the main FEL process by generating high gain harmonics (HGHG). As a result, completely coherent pairs of XUV pulses are obtained at a specific harmonic of the interstitial wavelength. Exaggerated saying, there is a main laser pulse and a donor one, which is introduced into the main one to form a pair of XUV pulses. The harmonic generation in this case is the addition of the frequencies of the laser radiation, when several radiation is absorbed, and one is emitted with a frequency equal to the sum of the frequencies of the two absorbed.

Research results


As described in earlier studies, it is possible to manipulate the XUV phase through the properties of a donor impulse. In this study, as the authors themselves say, this method was improved by introducing high-precision, separate phase control and synchronization of pairs of XUV pulses, while avoiding the problem of phase formation at XUV wavelengths. To do this, we used two AOM (acousto-optical modulators) with phase synchronization, which control the relative phase ( ϕ 21 = ϕ 2 - ϕ 1 ) of the donor pulse. At the HGHG stage, the implanted phase goes over to a well-defined phase shift nϕϕ 21 for pulses XUV by n-th harmonic that allows you to flexibly manipulate the phase itself ( 2a ).


Image # 2: XUV phase manipulation.

The control of the XUV phase is demonstrated by the control of the phase of the XUV interference bands for photon energies up to 47.5 eV ( 2b and 2c ). The high stability shown in the interferograms indicates that insignificant fluctuations occur already at the HGHG stage, but not at the stage of generation of pulse pairs.

At the HGHG stage, the temporal differences between the donor pulse and the electron flux (approximately 42 fs) lead to phase oscillations of the generated XUV pulses due to the residual energy LFM signal (linear frequency modulation) of the electron beam.

The first “experimental” was helium. The scientists decided to demonstrate the process of tracking the time evolution of attosecond electron coherences with phase-modulated sequences of XUV pulses.


Image 3: XUV electronic coherence in helium.

The model under consideration at 3a is a 1s 2 → 1s4p transition in helium. The first XUV pulse creates a coherent superposition of the ground and excited states (electronic wave packet or electronic WP), denoted by | ψ ( τ )⟩.

Second XUV pulse lagging behind the first one by the set time ( τ), projects this WP onto the stationary state of the electron population, which is measured by the ionization of the 1s4p state by a NIR pulse ( near-infrared , i.e., near infrared), giving the signal:

S ∝ ⟨ψ (τ) | 1s4p⟩ = A (τ) eiϕ (τ) , where A (τ) denotes the amplitude and ϕ (τ) is the phase evolution of WP.

In accordance with the transition energy 1s 2 → 1s4p equal to E = 23.74 eV, the signal oscillates with a period h / E = 174 ac (ac - attosecond), which requires extremely high pumping-probe stability ( δτ <20 ac) to obtain data.

To solve this problem, a phase-cyclic scheme was used. By combining the phase modulation of both XUV pulses with phase-synchronous detection, you can reduce the oscillation period of the signal by more than 50 times and remove most of the phase "jitter" from the signal.

Graph 3b shows the time interferogram recorded during helium excitation. It shows the pure periodic oscillations of the induced attosecond electron WP, which is in good agreement with the theoretical model ( 3c ). Despite the relatively low applied FEL energy (≤30 nJ) and low atomic density in the sample, accurate data were obtained. This indicates the presence of an excellent signal-to-noise ratio and high sensitivity of the technique even under difficult conditions of XUV wavelengths.

In addition, the signal quality allows direct Fourier analysis to obtain spectral information ( 3d ). Careful preparation of the electron flux in conjunction with a significant reduction in time to capture data made it possible to track WP oscillations up to 700 fs (fs - femtosecond).

Helium research has become a model for an unperturbed quantum system that demonstrates long-lived electron coherence and slight dephasing. After helium, the researchers began to consider argon, and more precisely, the 3s 2 3p 6 → 3s 1 3p 6 6p 1 transition in argon.


Image 4: real-time dephasing of Fano resonance in argon.

6p-valence orbital pairs are connected to the * Ar + continuum via configuration interaction ( 4a ), leading to autoionization *, which in turn leads to significant dephasing.
Continuum * is a continuous medium where processes are studied under various external conditions.
Autoionization * - spontaneous ionization of an atom, molecule or molecular particle in an excited state.
The graphs on 4b show the recorded transients in the time domain from which the complex WP signal S ( τ ) = A (τ) eiϕ (τ) was obtained . In this case, the signal attenuation reflects the tunneling of WP into the continuum. The Fourier transform S ( ω ) of such a signal is strongly related to the susceptibility of the sample x ( ω ) ∝ iS ( ω ) /. Therefore, it is possible to simultaneously obtain the absorption and dispersion curves of the resonance ( 4c ).

For a more detailed acquaintance with the nuances of the study, I recommend that you look into the report of scientists andadditional materials to it.

Epilogue


Summing up, we can say that the scientists quite successfully managed to realize their plan - to create a new method of ultra-precise coherent spectroscopy based on phase-cyclic oscillations. Thus, they were able to track and record the evolution of electronic WP, which takes place on an attosecond time scale.

A specially prepared sequence of two ultrashort laser pulses in the ultraviolet range on a FERMI free electron laser helped to implement the technique. The pulses had certain phase relationships relative to each other and were separated by a precisely defined time interval. The first pulse started the process in the electron shell (pumping process). The second impulse studied the state of the shell a little later in time (sensing process). By changing the time interval and phase ratio, the researchers could draw conclusions about the time development in the electron shell.

During a practical experiment with argon as a sample, an extremely fast and barely noticeable process was tracked. In argon, the pump pulse caused a special configuration of two electrons inside the atomic shell. This configuration decayed in such a way that one electron left the atom in a very short time, which eventually became an ion. It was this process of electron detachment that scientists managed to fix. And if we take into account that this process takes about 120 attoseconds, then such an experiment can be called extremely successful.

In the future, scientists plan to improve their methodology and apply it to study other fast processes. According to the authors, their work will provide additional information regarding processes that were previously described only on the basis of theoretical models.

Thank you for your attention, remain curious and have a good working week, guys. :)

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