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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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Computational projects with the Landau–Zener problem in the quantum mechanics classroom
The Landau–Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational effort, but has a number of complex numerical and algorithmic issues that can be resolved through dedicated work. It can be used to teach computational concepts, such as accuracy, discretization, and extrapolation, and it reinforces quantum concepts of time-evolution via a time-ordered product and of extrapolation to infinite time via time-dependent perturbation theory. In addition, we discuss the concept of compression algorithms, which are employed in many advanced quantum computing strategies, and easy to illustrate with the Landau–Zener problem.
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- PAR ID:
- 10495182
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- American Journal of Physics
- Volume:
- 91
- Issue:
- 11
- ISSN:
- 0002-9505
- Page Range / eLocation ID:
- 885 to 892
- Subject(s) / Keyword(s):
- Equations of motion Hamiltonian mechanics Computational methods Interaction picture Perturbation theory Quantum mechanics Quantum tunneling
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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