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1. Quantum Phase Transition in Strongly-Correlated Cavity Polaritons

   https://doi.org/10.1109/ACP.2018.8596265  

   Xue, Jian; Seo, Kangjun; Tian, Lin; Xiang, Tao (October 2018, IEEE Conference Proceeding for Asia Communications and Photonics Conference 2018)

   We study the quantum critical behavior in a multiconnected Jaynes-Cummings lattice using the density-matrix renormalization group method, where cavity polaritons exhibit a Mott-insulator-to-superfluid phase transition. We calculate the phase boundaries and the quantum critical points. 

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2. State preparation in a Jaynes-Cummings lattice with quantum optimal control

   https://doi.org/10.1038/s41598-023-47002-1  

   Parajuli, Prabin; Govindarajan, Anuvetha; Tian, Lin (November 2023, Scientific Reports)

   Abstract High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation. 

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3. Nuclear gradient expressions for molecular cavity quantum electrodynamics simulations using mixed quantum-classical methods

   https://doi.org/10.1063/5.0109395  

   Zhou, Wanghuai; Hu, Deping; Mandal, Arkajit; Huo, Pengfei (September 2022, The Journal of Chemical Physics)

   We derive a rigorous nuclear gradient for a molecule-cavity hybrid system using the quantum electrodynamics Hamiltonian. We treat the electronic–photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclei as the classical subsystem. Using the adiabatic basis for the electronic DOF and the Fock basis for the photonic DOF and requiring the total energy conservation of this mixed quantum–classical (MQC) system, we derived the rigorous nuclear gradient for the molecule–cavity hybrid system, which is naturally connected to the approximate gradient under the Jaynes–Cummings approximation. The nuclear gradient expression can be readily used in any MQC simulations and will allow one to perform the non-adiabatic on-the-fly simulation of polariton quantum dynamics. The theoretical developments in this work could significantly benefit the polariton quantum dynamics community with a rigorous nuclear gradient of the molecule–cavity hybrid system and have a broad impact on the future non-adiabatic simulations of polariton quantum dynamics. 

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4. Robust preparation of many-body ground states in Jaynes–Cummings lattices

   https://doi.org/10.1038/s41534-021-00433-y  

   Cai, Kang; Parajuli, Prabin; Long, Guilu; Wong, Chee Wei; Tian, Lin (December 2021, npj Quantum Information)

   Abstract Strongly correlated polaritons in Jaynes–Cummings (JC) lattices can exhibit quantum phase transitions between the Mott-insulating and superfluid phases at integer fillings. The prerequisite to observe such phase transitions is to pump polariton excitations into a JC lattice and prepare them into appropriate ground states. Despite previous efforts, it is still challenging to generate many-body states with high accuracy. Here, we present an approach for the robust preparation of many-body ground states of polaritons in finite-sized JC lattices by optimized nonlinear ramping. We apply a Landau–Zener type of estimation to this finite-sized system and derive the optimal ramping index for selected ramping trajectories, which can greatly improve the fidelity of the prepared states. With numerical simulation, we show that by choosing an appropriate ramping trajectory, the fidelity in this approach can remain close to unity in almost the entire parameter space. This approach can shed light on high-fidelity state preparation in quantum simulators and advance the implementation of quantum simulation with practical devices. 

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5. Leveraging Hamiltonian simulation techniques to compile operations on bosonic devices

   https://doi.org/10.1088/1751-8121/adb5df  

   Kang, Christopher; Soley, Micheline B; Crane, Eleanor; Girvin, Steven M; Wiebe, Nathan (April 2025, Journal of Physics A: Mathematical and Theoretical)

   Abstract Circuit quantum electrodynamics enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e. qubit-oscillator) operations are realizable only through optimal control theory, which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter–Suzuki and Baker–Campbell–Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, namely $\left(a{)}^p\right(a^{†}{)}^q$for integer $p,q$. We show examples of this paradigm including obtaining universal control within a subspace of the entire Fock space of an oscillator, state preparation of a fixed photon number in the cavity, simulation of the Jaynes–Cummings Hamiltonian, and simulation of the Hong-Ou-Mandel effect. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid qubit-boson devices. 

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