Applications In Quantum Control Research Articles

The von Neumann representation as a joint time–frequency parameterization for polarization-shaped femtosecond laser pulses

We generalize the joint time–frequency von Neumann representation of femtosecond laser pulses for usage with time-dependent polarization states. The electric field is expanded in terms of Gaussian-shaped transform-limited subpulses located on a discrete time–frequency lattice, each with a specific polarization state. This formalism provides an intuitive picture for the time- and frequency-dependent polarization state. It can also serve as a basis for polarization pulse shaping. As an illustration, we define pulses for which polarization parameters (ellipticity and orientation) are given directly in time–frequency phase space. This approach has applications in quantum control and other areas for which time- and frequency-dependent light polarization is relevant.

Experimental quantum control landscapes: Inherent monotonicity and artificial structure

Unconstrained searches over quantum control landscapes are theoretically predicted to generally exhibit trap-free monotonic behavior. This paper makes an explicit experimental demonstration of this intrinsic monotonicity for two controlled quantum systems: frequency unfiltered and filtered second-harmonic generation (SHG). For unfiltered SHG, the landscape is randomly sampled and interpolation of the data is found to be devoid of landscape traps up to the level of data noise. In the case of narrow-band-filtered SHG, trajectories are taken on the landscape to reveal a lack of traps. Although the filtered SHG landscape is trap free, it exhibits a rich local structure. A perturbation analysis around the top of these landscapes provides a basis to understand their topology. Despite the inherent trap-free nature of the landscapes, practical constraints placed on the controls can lead to the appearance of artificial structure arising from the resultant forced sampling of the landscape. This circumstance and the likely lack of knowledge about the detailed local landscape structure in most quantum control applications suggests that the a priori identification of globally successful (un)constrained curvilinear control variables may be a challenging task.

Relative C -numerical ranges for applications in quantum control and quantum information

Motivated by applications in quantum information and quantum control, a new type of C-numerical range, the relative C-numerical range denoted as WK (C, A), is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical C-numerical range by any of its compact and connected subgroups K ⊂ U(N). The geometric properties of the relative C-numerical range are analyzed in detail. Counterexamples prove that its geometry is more intricate than in the classical case: e.g., W K (C, A) is neither star-shaped nor simply connected. Yet, a well-known result on the rotational symmetry of the classical C-numerical range extends to WK (C, A), as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup , i.e., the n-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for WK (C, A) being a circular disc centered at the origin of the complex plane. Finally, the previous results are illustrated in detail for SU(2) ⊗ SU(2).

Actively shaped supercontinuum from a photonic crystal fiber for nonlinear coherent microspectroscopy

The combination of broadband pulses from a photonic crystal fiber (PCF) pumped by a standard 100 fs oscillator and pulse shaping is successfully employed for coherently controlled nonlinear spectroscopy. The pulse shaper manages not only to compress the PCF supercontinuum in a closed-loop optimization scheme but also to manipulate the phase at the same time for quantum control applications. This approach is demonstrated by single-beam coherent anti-Stokes Raman microspectroscopy and should be, due to its simplicity, well suited for general applications in nonlinear microscopy.