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Quantum state tomography of molecular rotation

Mouritzen, A S, Klaus Mølmer

Published Dec 22, 2005• 21 citations
OpenAlex

Abstract

We show how the rotational quantum state of a linear or symmetric top rotor can be reconstructed from finite time observations of the polar angular distribution under certain conditions. The presented tomographic method can reconstruct the complete rotational quantum state in many non-adiabatic alignment experiments. Our analysis applies for measurement data available with existing measurement techniques.

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We show how the rotational quantum state of a linear or symmetric top rotor can be reconstructed from finite time observations of the polar angular distribution under certain conditions. The presented tomographic method can reconstruct the complete rotational quantum state in many non-adiabatic alignment experiments. Our analysis applies for measurement data available with existing measurement techniques.
We establish a reconstruction approach for the rotational quantum state of linear molecules possessing a magnetic manifold.Our approximate method contains an iteration with generalized matrix inverses,processing the tomographic integral of the time-dependent molecular-axis distribution in a polar angle.As shown in a simulated example for an alignment state,the density matrix is determined in a high fidelity.An analytic tomographic formula is also derived for the symmetric top rotation.The state coherent in the quantum space of both the angular momentum and its magnetic projection can be approximately retrieved from the observable time-resolved solid-angle distribution of the molecular axis.
We establish a reconstruction approach for the rotational quantum state of linear molecules possessing a magnetic manifold. Our approximate method contains an iteration with generalized matrix inverses, processing the tomographic integral of the time-dependent molecular-axis distribution in a polar angle. As shown in a simulated example for an alignment state, the density matrix is determined in a high fidelity. An analytic tomographic formula is also derived for the symmetric top rotation. The state coherent in the quantum space of both the angular momentum and its magnetic projection can be approximately retrieved from the observable time-resolved solid-angle distribution of the molecular axis.
With the ability to directly obtain the Wigner function and density matrix of photon states, quantum tomography (QT) has had a significant impact on quantum optics, quantum computing and quantum information. By an appropriate sequence of measurements on the evolution of each degreeof freedom (DOF), the full quantum state of the observed photonic system can be determined. The first proposal to extend the application of QT to reconstruction of complete quantum states of matter wavepackets had generated enormous interest in ultrafast diffraction imaging and pump-probe spectroscopy of molecules. This interest was elevated with the advent of ultrafast electron and X-ray diffraction techniques using electron accelerators and X-ray free electron lasers to add temporal resolution to the observed nuclear and electron distributions. However, the great interest in this area has been tempered by the illustration of an impossibility theorem, known as the dimension problem. Not being able to associate unitary evolution to every DOF of molecular motion, quantum tomography could not be used beyond 1D and categorically excludes most vibrational and all rotational motion of molecules. Here we present a theoretical advance to overcome the notorious dimension problem. Solving this challenging problem is important to push imaging molecular dynamics to the quantum limit. The new theory has solved this problem, which makes quantum tomography a truly useful methodology in ultrafast physics and enables the making of quantum version of a molecular movie. With the new theory, quantum tomography can be finally advanced to a sufficient level to become a general method for reconstructing quantum states of matter, without being limited in one dimension. Our new concept is demonstrated using a simulated dataset of ultrafast diffraction experiment of laser-aligned nitrogen molecules.
When the dynamics of a quantum system of interest is known, an informationally complete set of observables is not needed for state reconstruction via tomographic techniques: letting the system evolve before performing the measurement allows one to effectively extend the available ways to probe the system. This idea leads to dynamical quantum tomography, whose feasibility we characterize for general quantum dynamics using Krylov-based methods. Specializing in Markovian ones, we also provide deterministic tests and randomized ones to effectively assess parametric dynamics. The limits of the methods are explored by comparing unitary and open dynamics when a single observable is available, and the set of observables whose expectation can be reconstructed from the available ones characterized. The framework is illustrated with applications to a spin chain (with or without dissipation) and an electron-nuclear system.
Emission tomography provides a method for the characterization of quantum states of those degrees of freedom of material quantum systems that are coupled to electronic states of the system. In such systems, the time-dependent fluorescence spectrum contains complete information about the non-electronic degree of freedom. Phase-space or, in certain cases, density matrix representations of the state can be reconstructed from the spectrum using standard methods of computer-assisted tomography or linear algebra. The principles and implementation of this procedure are described in detail and applied to the specific example of the reconstruction of the quantum state of the vibrational mode of a diatomic molecule excited into a non-stationary wavepacket state.