Haitan Xu

Recovering the rotational density matrix of a molecular ensemble from time-resolved angular distributions is central to understanding ultrafast rotational dynamics, yet the inverse problem is severely underdetermined. We analyze the forward operator that maps the density matrix of laser-aligned symmetric-top molecules to the angular distribution retrieved in pump-probe experiments and demonstrate through singular value decomposition that 74%-88% of the real density matrix unknowns lie in the null space for maximum angular momentum quantum numbers Jmax = 2-5. This rank deficiency is intrinsic to the measurement geometry and imposes a linear lower bound on reconstruction error: the minimum-norm least-squares (pseudoinverse) solution sets all null-space components to zero, establishing the best achievable error for any linear, unbiased estimator. Nonlinear constraints-positive semidefiniteness, trace conservation, and block symmetries-partially recover null-space information, but the residual error grows with Jmax, reaching 15%-44% for Jmax = 5. We present a two-stage pipeline in which a convolutional neural network trained on simulated data provides a warm start for the fast iterative shrinkage-thresholding algorithm. For both CF3I and CH3Cl across Jmax = 2-6, this approach reduces the Frobenius reconstruction error by 80%-99% relative to optimization from thermal equilibrium, maintaining stable errors of 0.5%-1.1% as Jmax increases. The pipeline is robust to data noise down to a 20 dB signal-to-noise ratio and operates ten times faster than the baseline and outperforms the maximum-entropy approach by a factor of 15-39×. The classical iterative quantum tomography algorithm becomes numerically unstable for Jmax ≥ 4, whereas the proposed method converges reliably at all tested truncation levels.

Circular-dichroic magnetic X-ray scattering at XFELs images molecular spin dynamics: 278 fs spin–orbit beating in NO, attosecond singlet–triplet oscillation in core-excited TiCl ₄ , and Berry-phase spin separation in CH ₂ OH.

Crystalline undulator radiation (CUR) is emitted by charged particles channeling through a periodically bent crystal. We show that entangled high-energy photons of the order of 100 MeV can be generated from CUR and obtain the quantum entanglement properties of the double-photon emission of CUR with a nonperturbative quantum field theory. We demonstrate that the crystalline undulator (CU) can induce a 3D free-electron lattice with premicrobunched electrons, and the resulting free-electron lattice can enhance the entangled high-energy photon emission for certain angles by phase matching. We also examine the effects of demodulation and dechanneling during the electron beam channeling process, and show the dependence of the dechanneling and demodulation lengths on the undulator parameters.

The Jahn-Teller (JT) effect, as a spontaneous symmetry-breaking mechanism arising from the coupling between electronic and nuclear degrees of freedom, is a widespread phenomenon in molecular and condensed matter systems. Here, we investigate the influence of the JT effect on the photodissociation dynamics of CF3I molecules. Based on ab initio calculation, we obtain the three-dimensional potential energy surfaces for 3 Q 0+ and 1 Q 1 states and establish a diabatic Hamiltonian model to study the wavepacket dynamics in the CF3I photodissociation process. Using the wave function of the final state after dissociation, we calculate the rotational density matrix of the CF3 fragment and analyze its rotational excitation under the JT effect, as well as its partial coherence property and selection rules. Our work paves the way to the experimental observation and quantification of the JT effect in molecular dissociation dynamics beyond the classical ball-and-stick model.

We propose a terahertz quantum illumination (QI) scheme utilizing emissions from free-electron lasers (FELs) based on joint photon number measurement and quantum state discrimination using maximum a posteriori estimation. We analyze the performance of our QI scheme and quantify it with error probabilities. We numerically demonstrate the quantum advantage of our QI scheme over classical illumination. Our work paves the way to using FELs as entangled photon sources for quantum illumination in the terahertz regime.

Ghost imaging can be implemented with illumination light with pronounced quantum characters. In this work, we address the inverse problem of ghost imaging, i.e., the tomography of the quantum states of illumination light based on ghost imaging. We showcase the characterization of multimode Gaussian state light represented by its covariance matrix. With the information of spatial modes, we reconstruct the quantum states of light using the variation of SNR of the ghost images formed by the input light under a given set of optical operations. We demonstrate that ghost imaging can also be used to characterize the non-Gaussian light by its deviation from Gaussian states, which can serve as a criterion for the non-Gaussianity of the input light. The spatial resolving power of the proposed method can be advantageous for quantum information applications involving structured light, such as multiplexing with spatial modes.

We investigate entangled x-ray photon pair emissions in a free-electron laser (FEL) and establish a quantum electrodynamical theory for coherently amplified entangled photon pair emission from microbunched electron pulses in the undulator. We provide a scheme to generate highly entangled x-ray photon pairs and numerically demonstrate the properties of entangled emission, which is of great importance in x-ray quantum optics. Our work shows a unique advantage of FELs in entangled x-ray photon pair generation.

We studied the transport properties of a driven-dissipative photonic network, where multiple photonic cavities are coupled through a nonreciprocal bus with unidirectional transmission. For short-range coupling between the cavities, the occurrence of nonreciprocal amplification can be linked to a topological phase transition of the underlying dynamic Hamiltonian. However, for long-range coupling, we show that the correspondence between the nonreciprocal amplification transition and the topological phase transition breaks down as the transition conditions deviate significantly from each other. We found the exact transition condition for nonreciprocal amplification, supported by analytical calculation and numerical simulation. We also investigated the stability, the crossover from short- to long-range coupling, and the bandwidth of the nonreciprocal amplification. Our work has potential applications in signal transmission and amplification, and also paves the way to study other topological and non-Hermitian systems with long-range coupling and nontrivial boundary effects.