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arXiv:1611.08404 · Nature Communications

Analog quantum simulation of the Rabi model in the ultra-strong coupling regime

Jochen Braumüller, Michael Marthaler, Andre Schneider, Alexander Stehli, Hannes Rotzinger, Martin P. Weides, Alexey Vladimirovich Ustinov

Published Sep 27, 2017• 170 citations
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Abstract

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.

DOI
10.1038/s41467-017-00894-w

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The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.
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.
We propose and experimentally demonstrate a scheme to simulate the interaction between a two-level system and a classical light field. Under the transversal driving of two microwave tones, the effective Hamiltonian in an appropriate rotating frame is identical to that of the general semi-classical Rabi model. We experimentally realize this Hamiltonian with a superconducting transmon qubit. By tuning the strength, phase, and frequency of the two microwave driving fields, we simulate the quantum dynamics from the weak to extremely strong driving regime. Under these conditions, we observe that, as a function of increased Rabi drive strength, the qubit evolution gradually deviates from the normal sinusoidal Rabi oscillation, in accordance with the predictions of the general semi-classical Rabi model far beyond the weak driving limit. Our scheme provides an effective approach to investigate the extremely strong interaction between a two-level system and a classical light field. Such strong interactions are usually inaccessible in experiments.
The quantum Rabi model describes the coupling of a two-state system to a bosonic field mode. Recent theoretical work has pointed out that a generalized periodic version of this model, which maps onto Hamiltonians applicable in superconducting qubit settings, can be quantum simulated with cold trapped atoms. Here, we experimentally demonstrate atomic dynamics predicted by the periodic quantum Rabi model far in the deep strong-coupling regime. The two-state system is represented by two Bloch bands of cold atoms in an optical lattice, and the bosonic mode by oscillations in a superimposed optical dipole trap potential. The observed dynamics beyond the usual quantum Rabi physics becomes relevant when the edge of the Brillouin zone is reached, and evidence for collapse and revival of the initial state is revealed at extreme coupling conditions. Published by the American Physical Society 2024
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We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.
We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.