Seminars from 2018

The interaction between a spin-1/2 particle and a bosonic mode is one of the most fundamental models in quantum mechanics and in the description of light-matter systems. In particular, when the interaction between the subsystems comprises a linear exchange of quantum excitations, that is, when the spin state changes by absorbing or emitting only one bosonic excitation, the model is known as quantum Rabi model. This celebrated model is of paramount importance not only for a comprehensive description of light-matter interaction, but also because it describes different physical systems such as trapped ions or circuit QED, and it has thus become a milestone in the development of quantum-based technologies and quantum information processing [1]. There are yet other possible interaction mechanisms between a spin-1/2 particle and a bosonic mode beyond the linear case. For example, it may be possible that the spin state changes at the expense of emitting or absorbing n>1 bosonic excitations. Such a multiphoton interaction dramatically modifies the system’s properties with respect to its linear counterpart, and thus the features of a light-matter interacting system. Although there is no unitary transformation between linear and multiphoton quantum Rabi models, it has been shown that their dynamics are equivalent to a very good approximation in a wide range of parameters [2], also including models featuring spin-boson coupling that changes with the Fock occupation number [3].
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

A careful visit to the systems mentioned in the title allows one to find an equivalence among their dynamics. From this finding, a geometrical interpretation of the complex phase of he Cabibbo-Kobayashi-Maskawa matrix naturally appears.

Non-equilibrium dynamics of quantum many-body systems pose some of the most challenging open problems in Physics, such as how do quantum systems relax towards equilibrium or how could it be possible to extract work from them [1]. The emergent field of quantum thermodynamics applies principles and ideas from statistical mechanics and provides general results about these open questions. Among these results, the quantum fluctuation relations (QFRs) are especially powerful, as they lead to the formulation of new measurement protocols for thermometry in ultra-cold setups [2] and on work statistics in out-of-equilibrium processes [3], as recently demonstrated in pioneering experiments with trapped ions [4].

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].

In the quite near future, a quantum computer capable of handling 50-100 qubits would be expected to be developed. Such quantum computer is large enough to be impossible to be simulated by existing classical computers, but it may not be sufficient to perform the full quantum error correction and to execute Shor algorithms. Therefore, it is an important question at this stage to find something meaningful tasks with such levels of quantum computers. In this seminar, I’d like to show that an analogue quantum simulation can be a promising solution to perform beyond classical computation by discussing two examples of experimental demonstrations that we’ve recently conducted in our simple 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).