Elementary Open Quantum States

It is shown that the mixed states of a closed dynamics supports a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are defined as operators of the Liouville space in the irreducible representations of the symmetry of the open system. These are tensor operators in the case of rotational symmetry. The case of translation symmetry is discussed in more detail for harmonic systems.

Hyperpolarization and the physical boundary of Liouville space

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I=1/2, I=1, I=3/2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

Hyperpolarization and the Physical Boundary of Liouville Space

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region, and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I = 1 / 2, I = 1, I = 3 / 2, and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

Detecting electronic coherences by time-domain high-harmonic spectroscopy

Ultrafast spectroscopy is capable of monitoring electronic and vibrational states. For electronic states a few eV apart, an X-ray laser source is required. We propose an alternative method based on the time-domain high-order harmonic spectroscopy where a coherent superposition of the electronic states is first prepared by the strong optical laser pulse. The coherent dynamics can then be probed by the higher-order harmonics generated by the delayed probe pulse. The high nonlinearity typically modeled by the three-step mechanism introduced by Lewenstein and Corkum can serve as a recipe for generation of the coherent excitation with broad bandwidth. The main advantage of the method is that only optical (non–X-ray) lasers are needed. A semiperturbative model based on the Liouville space superoperator approach is developed for the bookkeeping of the different orders of the nonlinear response for the high-order harmonic generation using multiple pulses. Coherence between bound electronic states is monitored in the harmonic spectra from both first- and second-order responses.