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arXiv:1704.07303 · Journal of Modern Optics

Magnetic field fluctuations analysis for the ion trap implementation of the quantum Rabi model in the deep strong coupling regime

Ricardo Puebla, Jorge Casanova, Martin Bodo Plenio

Published Dec 1, 2017• 4 citations
arXivHTMLPDF

Abstract

The dynamics of the quantum Rabi model (QRM) in the deep strong coupling regime is theoretically analyzed in a trapped-ion set-up. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here, we discuss how to attain a faithful implementation of the QRM in the deep strong coupling regime which is robust against magnetic field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In addition, we study the role that amplitude fluctuations play to correctly attain the QRM using the proposed method. In this manner, the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.

DOI
10.1080/09500340.2017.1404651

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The dynamics of the quantum Rabi model (QRM) in the deep strong coupling regime is theoretically analyzed in a trapped-ion set-up. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here, we discuss how to attain a faithful implementation of the QRM in the deep strong coupling regime which is robust against magnetic field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In addition, we study the role that amplitude fluctuations play to correctly attain the QRM using the proposed method. In this manner, the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.
The dynamics of the quantum Rabi model in the deep strong coupling regime is investigated in a trapped-ion setup. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here we discuss how to attain a faithful implementation of the quantum Rabi model in the deep strong coupling regime which is robust against magnetic-field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In this manner the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.
We propose a robust realization of the two-photon quantum Rabi model in a trapped-ion setting based on a continuous dynamical decoupling scheme. In this manner the magnetic dephasing noise, which is identified as the main obstacle to achieve long-time coherent dynamics in ion-trap simulators, can be safely eliminated. More specifically, we investigate the ultrastrong coupling regime of the two-photon quantum Rabi model whose realization in trapped ions involves second-order sideband processes. Hence, the resulting dynamics becomes unavoidably slow and more exposed to magnetic noise requiring an appropriate scheme for its elimination. Furthermore, we discuss how dynamical decoupling methods take a dual role in our protocol, namely they remove the main source of decoherence from the dynamics while they actively define the parameter regime of the simulated model.
The interaction of a two-level system (TLS) with a single bosonic mode (BM) is one of the most fundamental processes in quantum optics. Microscopically, it is described by the quantum Rabi model (QRM). Here we propose a versatile implementation of this model based on single trapped cold atoms. Assuming realistic experimental conditions, we show that our approach is not restricted to the Jaynes-Cummings regime but also allows exploring the regimes of ultrastrong coupling, deep strong coupling, and dispersive deep strong coupling. In contrast to most other QRM platforms, all important system parameters, i.e., the emitter-field detuning and the coupling strength of the emitter to the mode, can be dynamically tuned over a wide range. The quantum state of the BM and the TLS can be prepared and read-out using standard cold-atom techniques, enabling the study of the QRM and its dynamics with unprecedented control. Our scheme implements the TLS using atomic Zeeman states, while the atom's vibrational states in the trap represent the BM. The coupling is mediated by a suitable fictitious magnetic field pattern. Finally, we show that our scheme also enables the implementation of important generalizations, namely, the driven QRM, the QRM with quadratic coupling, or the Dicke model.
We show that the technique known as concatenated continuous dynamical decoupling (CCD) can be applied to a trapped-ion setup for a robust implementation of the quantum Rabi model in a variety of parameter regimes. These include the case where the Dirac equation emerges, and the limit in which a quantum phase transition takes place. We discuss the applicability of the CCD scheme in terms of the fidelity between different initial states evolving under an ideal quantum Rabi model and their corresponding trapped-ion realization, and demonstrate the effectiveness of noise suppression of our method.
We study the quantum Rabi model (QRM) in the deep strong coupling (DSC) regime. To capture the full dynamics of the QRM in the DSC regime, we implemented single-qubit rotations combined with integrated digital steps and qubit-bosonic blocks. This approach leads to a paradigm known as digital analog quantum simulations (DAQSs). In this work, we review the encoding of QRM in the DSC regime through emerging paradigms of digital and analog techniques. Using DAQSs encoding, an efficient simulation can be performed on state-of-the-art circuit quantum electrodynamics platforms. Finally, we provide detailed information on the dynamics of the QRM in varity of parameter regions. We demonstrate the effectiveness of the DAQS paradigms in achieving prolonged coherent measurements during time evolution, even in the case of perturbative DSC regime dynamics. This proposal lays the groundwork for simulating complex many-body dynamics that involve bosonic modes.
The coupling of a two-level system with an electromagnetic field, whose fully quantized version is the quantum Rabi model, is among the central topics of quantum physics. When the coupling strength becomes large enough that the field mode frequency is reached, the deep strong coupling regime is approached, and excitations can be created from the vacuum. Here we demonstrate a periodic variant of the quantum Rabi model in which the two-level system is encoded in the Bloch band structure of cold rubidium atoms in optical potentials. With this method we achieve a Rabi coupling strength of 6.5 times the field mode frequency, which is far in the deep strong coupling regime, and observe a subcycle timescale raise in bosonic field mode excitations. In a measurement recorded in the basis of the coupling term of the quantum Rabi Hamiltonian, a freezing of dynamics is revealed for small frequency splittings of the two-level system, as expected when the coupling term dominates over all other energy scales, and a revival for larger splittings. Our work demonstrates a route to realize quantum-engineering applications in yet unexplored parameter regimes.