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arXiv:1903.07584 · Physical Review A

Probing Stark-induced nonlinear phase variation with opto-optical modulation

Emma R. Simpson, Marie Labeye, Seth Camp, Neven Ibrakovic, Samuel Bengtsson, Anna Olofsson, Kenneth J. Schäfer, Mette B. Gaarde, J. Mauritsson

Published Aug 2, 2019• 8 citations
arXivHTMLPDF

Abstract

We extend the recently developed technique of opto-optical modulation (OOM) to probe state-resolved ac-Stark-induced phase variations of a coherently excited ensemble of helium atoms. In a joint experimental and theoretical study, we find that the spatial redirection of the resonant emission from the OOM process is different for the low-lying $1s2p$ state as compared with the higher-lying Rydberg states, and that this redirection can be controlled through the spatial characteristics of the infrared (IR) probe beam. In particular, we observe that the intensity dependence of the IR-induced Stark phase on the $1s2p$ emission is nonlinear, and that the phase accumulation changes sign for moderate intensities. Our results suggest that OOM, combined with precise experimental shaping of the probe beam, could allow future measurements of Stark-induced phase shifts of excited states.

DOI
10.1103/physreva.100.023403

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Dipole-dipole interactions between helium atoms in Rydberg-Stark states with principal quantum number n=53n=53n=53 and approximately linear Stark energy shifts, resulting from induced electric dipole moments of approximately 7900 D, have been investigated experimentally. The experiments were performed in pulsed supersonic metastable helium beams, with particle number densities of up to $\ensuremath{\sim}{10}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. In the presence of amplitude-modulated, radio-frequency electric fields, changes in the spectral intensity distributions associated with the transitions to these states that are attributed to dipole-dipole interactions within the ensembles of excited atoms have been observed. The experimental results are in excellent agreement with calculations of the Rydberg energy level structure carried out using Floquet methods, and excitations shared by up to four atoms. The use of these Rydberg-Stark states as sensors for nonresonant broadband radio-frequency electrical noise is also discussed.
Extreme ultraviolet (XUV) light is a valuable frequency range for ultrafast optics experiments. The short wavelength is a requirement for ultrashort pulses, which are widely used to characterize fast dynamics. Additionally, the high photon energy enables quantum control of high frequency transitions in atoms. These transitions are of interest for ultrafast quantum control as the bandwidth of the control pulses needs to be less than the transition frequency. Presently, however, no good modulators exist for these frequencies, which significantly reduces the possible ultrafast optics experiments or applications in the XUV regime. This thesis addresses this problem and focuses on the control of XUV light in time and space. To enable control of XUV light a method is described which modulates the phase of XUV light emitted from a gas of noble atoms. The atoms are resonantly excited with a coherent XUV pulse generated through high order harmonic generation. After the excitation pulse has passed through the gas, the atoms will emit light in the absence of an external field, known as free induction. The phase of the emitted light is changed by shifting the resonance frequencies through the AC Stark shift with a non-resonant infrared control pulse. This phase-control of the emitting atoms also translates into a control of the phase of the emitted XUV field.With the method described in the previous paragraph, the direction of XUV light emitted from noble gases was controlled, and the temporal dynamics of the emission was studied. The redirection of the XUV emission, through the use of a spatially offset IR pulse, was found to change both with intensity of the control pulse and by changing the spatial offset between the pulses. By varying the delay between the excitation and the control pulse the time of redirection was controlled, which enabled high signal to noise study of the temporal dynamics of the emission. Furthermore, with two control pulses the emission was redirected twice, resulting in an XUV pulse shape with controlled duration emitted with a certain angle. Hopefully the presented work will result in more research into the development of this technique, to fully realize the possibility to shape the amplitude and phase of XUV pulses. Such a development would open the door for ultrafast XUV quantum control.
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Recent developments in opto-optical modulation technique calls for improved temporal control of light modulation processes of coherent XUV light. This thesis project evaluates an experimental method aimed at achieving redirection and amplitude modulation of XUV-light, by using precise determination of decay times in states of noble gases that are deemed suitable for opto-optical control. It is possible to obtain a higher signal-to-noise ratio than previously possible when performing decay time measurements using a recently developed technique to obtain spatial phase control of the states that are being measured.
The four-wave mixing produced with two ultrashort phase-locked w-3w laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5w anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques.