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Chinese Physics B

State reconstruction of molecular spatial rotation

覃晓, 高军毅

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
We provide a unified theoretical framework for recently emerging experiments that retrieve fixed-in-space molecular information through time-domain rotational coherence spectroscopy. Unlike a previous approach by Makhija et al. (V. Makhija et al., arXiv:1611.06476), our method can be applied to the retrieval of both real-valued (e.g., ionization yield) and complex-valued (e.g., induced dipole moment) molecular response information. It is also a direct retrieval method without using iterations. We also demonstrate that experimental parameters, such as the fluence of the aligning laser pulse and the rotational temperature of the molecular ensemble, can be quite accurately determined using a statistical method.
Summary form only given. Determining the unknown state of a quantum system from measurements of observables, a question first posed by Pauli, is a nontrivial task, which does not always permit a solution. The few examples where this inverse problem was experimentally solved include light fields, molecular vibrations, the motion of trapped ions and free atomic waves. We describe a method to reconstruct the complete density matrix of a generally mixed spin state of trapped neutral atoms. Compared to spin- 1/2 systems, the reconstruction of the spin density matrix for a large angular momentum is a much more challenging task. In our system with cesium atoms in the hyperfine ground state, a reconstruction of the 9/spl times/9 density matrix requires 80 real numbers to be experimentally determined. This can be achieved by measuring the 2F+1=9 populations along 4F+1=17 carefully chosen orientations of a Stern-Gerlach apparatus. A numerical simulation of the reconstruction shows this method to be robust against expected experimental uncertainties. We report on an experiment in progress to implement this measurement protocol in a standard laser cooling and trapping arrangement of neutral cesium atoms.
We present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern–Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix in that it is insensitive to experimental fluctuations in j , and allows for a natural elimination of high-frequency noise in the Wigner function by taking into account the experimental uncertainties in the determination of j , its projection m and the quantization axis orientation. No data binning and no arbitrary smoothing parameters are necessary in this reconstruction. Using recently published data (Riedel et al 2010 Nature 464 1170), we reconstruct the Wigner function of a spin-squeezed state of a Bose–Einstein condensate of about 1250 atoms, demonstrating that measurements along quantization axes lying in a single plane are sufficient for performing this tomographic reconstruction. Our method does not guarantee positivity of the reconstructed density matrix in the presence of experimental noise, which is a general limitation of backprojection algorithms.