## A generalized quantum Rabi model as a linear key to nonlinear and multiphoton interactions

Here, I will describe the theoretical framework which allows us to find an approximate equivalence among a family of quantum Rabi models, which holds even in the presence of decoherence processes [3], and provide relevant examples of the equivalence. In particular, our work implies that quantum simulation of multiphoton and nonlinearly-interacting system can be performed also in systems lacking actual multiphoton and nonlinear spin-boson coupling. As these multiphoton and nonlinear models are typically hard to control or even to implement, our work opens new avenues for the simulation and exploration of a large class of fundamentally different quantum models, allowing as well for the inspection of distinct dissipative processes.

[1] D. Braak et al. J. Phys. A: Math. Theor. 49, 300301 (2016); E. Solano Physics 4, 68 (2011)

[2] J. Casanova et al. npj Quantum Information 4, 47 (2018)

[3] R. Puebla et al. arxiv:1810.08465

## FOUCAULT PENDULUM, GIRATOR-COUPLED RESONANT CIRCUITS AND NEUTRAL KAONS: A GEOMETRICAL VIEWPOINT

## Non-Equilibrium Quantum Dynamics and Conservation Laws: A Trapped-Ion Experiment Proposal.

I will offer a review of these advances and discuss the limitations of QFRs when trying to obtain information about a quantum system with conserved charges. After this, I will present a new set of generalized fluctuation relations that are suitable for such a system, and illustrate its impact in a proposed trapped-ion experiment [5].

I will also provide an overview of ongoing research at interrogating complex quantum systems with quantum probes [6], and talk about new avenues opened up by certain recent advances that have been made concerning the trapping and cooling of diatomic molecules [7].

[1] See S. Vinjanampathy, J. Anders, Contemp. Phys. 57, 545 (2016) for a recent review.

[2] T. H. Johnson et al., Phys. Rev. A 93, 053619 (2016)

[3] R. Dorner et al., Phys. Rev. Lett. 110, 230601 (2013); also L. Mazzola et al., ibid. 110, 230602 (2013), and T. B. Batalhão et al., ibid. 113, 140601 (2014).

[4] S. An et al., Nature Phys. 11, 193 (2015); also J. Roßnagel et al., Science 352, 325 (2016).

[5] J. Mur-Petit, A. Relaño, R. A. Molina, D. Jaksch, Nature Comms. (2018); in the press, preprint available at arXiv:1711.00871.

[6] A. Usui, B. Buča, J. Mur-Petit. Quantum probe spectroscopy for cold atomic systems [arXiv:1804.09237].

[7] J. A. Blackmore et al., Ultracold Molecules: A Platform for Quantum Simulation [arXiv:1804.02372].

## Quantum simulation of molecular vibronic spectrum and quantum Rabi model with trapped ion system

The first is the quantum simulation of molecular vibronic spectrum lead by Yangchao Shen [1]. This simulation is a modification of the boson sampling algorithm, which is suitable for showing the power of a quantum computer. Thought the boson sampling algorithm is difficult to perform any useful tasks, by modifying the boson sampling protocol we are able to compute the molecular vibronic spectrum [2]. The trapped ion demonstration employs phonons that can deterministically prepared and detected, which would allow us the sampling of vibronic spectrum beyond photonic systems.

The second is the quantum simulation of quantum Rabi model demonstrated by Dingshun Lv [3]. Currently, the realizations of quantum simulation have been mostly limited to spin models. The quantum Rabi model is the most fundamental model that describes the interaction between spin and field. In particular, when the interaction strength is comparable or larger than the field frequency, various exotic phenomena and ground state entanglement can be occurred, which is observed in our trapped ion quantum simulator.

The current experimental demonstrations are limited to small systems, but we expect that as the system grows, it will provide solutions that exceed the existing limitations without the requirement of full quantum error corrections.

[1] Yangchao Shen, et al., Quantum simulation of molecular spectroscopy in trapped-ion device, Chemical Science DOI: 10.1039/C7SC04602B (2018).

[2] J. Huh, et al., Boson sampling for molecular vibronic spectra, Nature Photon. 9, 615 (2015).

[3] Dingshun Lv, et al., Quantum simulation of the quantum Rabi model in a trapped ion, arXiv:1711.00582 (2017).