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arXiv:2312.14718 · Physical Review Research

Tripartite quantum Rabi model with trapped Rydberg ions

Thomas Hamlyn, Chi Zhang, Igor Lesanovsky, Weibin Li

Published May 31, 2024• 2 citations
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Abstract

We investigate a tripartite quantum Rabi model (TQRM) wherein a bosonic mode concurrently couples to two spin- 1/2 particles through a spin-spin interaction, resulting in a spin-spin-boson coupling—a departure from conventional quantum Rabi models featuring bipartite spin-boson couplings. The symmetries of the TQRM depend on the detuning parameter, representing the energy difference between the spin states. At zero detuning a parity symmetry renders the TQRM reducible to a quantum Rabi model. A subradiant-to-superradiant transition in the ground state is predicted as the tripartite coupling strength increases. For nonzero detuning the total spin emerges as the sole conserved quantity in the TQRM. It is found that superradiance prevails in the ground state as long as the tripartite coupling remains nonzero. We derive the Braak G function of the TQRM analytically, with which the eigenspectra are obtained. The TQRM can be realized in a viable trapped Rydberg ion quantum simulator, where the required tripartite couplings and single-body interactions in the TQRM are naturally present. Our study opens opportunities to explore and create correlations and entanglement in the spin and motional degrees of freedoms with the TQRM. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023223

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We investigate a tripartite quantum Rabi model (TQRM) wherein a bosonic mode concurrently couples to two spin- 1/2 particles through a spin-spin interaction, resulting in a spin-spin-boson coupling—a departure from conventional quantum Rabi models featuring bipartite spin-boson couplings. The symmetries of the TQRM depend on the detuning parameter, representing the energy difference between the spin states. At zero detuning a parity symmetry renders the TQRM reducible to a quantum Rabi model. A subradiant-to-superradiant transition in the ground state is predicted as the tripartite coupling strength increases. For nonzero detuning the total spin emerges as the sole conserved quantity in the TQRM. It is found that superradiance prevails in the ground state as long as the tripartite coupling remains nonzero. We derive the Braak G function of the TQRM analytically, with which the eigenspectra are obtained. The TQRM can be realized in a viable trapped Rydberg ion quantum simulator, where the required tripartite couplings and single-body interactions in the TQRM are naturally present. Our study opens opportunities to explore and create correlations and entanglement in the spin and motional degrees of freedoms with the TQRM. Published by the American Physical Society 2024
Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, the Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here, we report an experimental realization of the Rabi-Hubbard model using up to 16 trapped ions and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceeds 2^{57}, whose dynamics is intractable for classical supercomputers.
The tripartite quantum Rabi model couples two qubits to a bosonic mode through a collective spin-oscillator interaction, providing a simple setting for studying two-qubit entanglement. In the zero-detuning limit, the triplet part of the spectrum splits into branches with zero and maximal entanglement, while the antisymmetric singlet ladder remains exactly decoupled. Within the triplet sector, finite detuning turns the crossings between these branches into avoided crossings and redistributes this entanglement. We identify an eigenbranch whose entanglement grows from nearly zero to a nearly maximal value through such avoided-crossing mixing. The weak-coupling level ordering yields a simple analytic criterion for whether this eigenbranch has a separable weak-coupling endpoint. A three-state effective model explains how the Bell-state component becomes dominant as the coupling increases. We further use a finite-time linear ramp of the collective coupling to benchmark the final coupling and ramp time required for high Bell-state fidelity. These results show how collective spin-oscillator coupling reorganizes spectral entanglement and connects static branch structure to finite-time Bell-state preparation.
We propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and deep strong coupling regimes of such a paradigmatic light-matter interaction. Furthermore, associated with these extreme dipolar regimes, we study the controlled generation and detection of their entangled ground states by means of adiabatic methods. Ion traps have arguably performed the first quantum simulation of the Jaynes-Cummings model, a restricted regime of the quantum Rabi model where the rotating-wave approximation holds. We show that one can go beyond and experimentally investigate the quantum simulation of coupling regimes of the quantum Rabi model that are difficult to achieve with natural dipolar interactions.
The occurrence of a second-order superradiant quantum phase transition is brought to light in a quantum system consisting of two interacting qubits coupled to the same quantized field mode. We introduce an appropriate thermodynamic limit for the integrable two-qubit quantum Rabi model with spin-spin interaction. Namely, this limit is determined by the infinite ratios of the spin-spin and the spin-mode couplings to the mode frequency, regardless of the spin-to-mode frequency ratios. Published by the American Physical Society 2024
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
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.