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Spatio-temporal pulse shaping

We have proposed a spatio-temporal control method, that utilizes not only temporal phase manipulations, but also controls the pulse shape evolution along the propagation axis. We established our method as a spectroscopic technique, where information that is difficult or impractical to measure using purely temporal methods can be extracted. This approach allows a simple, intuitive visualization of multi-dimensional control space, which is easily visualized by mapping the data on a two-dimensional landscape.

The spatio-temporal scheme was employed to investigate and control non-resonant and resonant two photon absorption processes in Cesium and Rubidium in the weak and strong field coupling regimes. Those include: Generation of dark nonlinear focus and Simultaneous visualization of the 1-photon response and the 2-photon response in three level systems, In the weak coupling regime, and the observation of single shot stimulated Raman adiabatic passage (STIRAP) process in Rubidium, and the characterization of dynamical Stark shift in a non-resonant 2-photon absorption medium in the strong field coupling regime.

The powerful approach known as geometrical control theory, which have been harnessed in recent years to study quantum systems, provides a general framework for determining controllability. In this approach, controllability is assessed using a criterion based on the Lie algebra structure of the control Hamiltonians. This criterion, has been used to determine the controllability of few-level systems, where its main advantage is its complete generality. However, as is, it fails to give insight into what is missing when full controllability is not present. The aim of our theoretical research on uncontrollable quantum systems was to answer the question - can we control sub-systems in a system which was shows to be uncontrollable? Our analysis clearly separates two mutually exclusive sources of uncontrollability. One, intuitive and well-known, is the lack of coupling between states which leads to ’dark-spaces’. The dynamics then conserves the mean value of some Hermitian operators. The other, less well-known source of uncontrollability, results from a generalized entanglement symmetry. In our research, we give a general procedure that reveals the building-blocks of this symmetry and we give explicit examples of uncontrollable few-levels systems that have not previously been identified.

Relevant Publication:

  1. 1.H. Suchowski, D. Oron, Y. Silberberg, “Generation of a dark nonlinear focus by spatiotemporal coherent control”, Opt. Comm. 264, 482-487 (2006).  PDF

  2. 2.H. Suchowski, A. Natan, B. D. Bruner, Y. Silberberg, "Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps", J. Phys. B: At. Mol. Opt. Phys. 41, 074008 (2008). PDF

  3. 3.T. Polack, H. Suchowski, D. J. Tannor, "Uncontrollable quantum systems: A classification scheme based on Lie subalgebras", Phys. Rev. A, 79, 053403 (2009). PDF

  4. 4.B. D. Bruner, H. Suchowski, N. V. Vitanov, Y. Silberberg, "Spatio-temporal coherent control of three level systems", Phys. Rev. A, 81, 063410 (2010). PDF