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arXiv:1710.08862 · New Journal of Physics

Quantum criticality and state engineering in the simulated anisotropic quantum Rabi model

Yimin Wang, Wen-Long You, Maoxin Liu, Yu-Li Dong, Hong-Gang Luo, G Romero, J Q You

Published May 17, 2018• 46 citations
arXivHTMLPDF

Abstract

Promising applications of the anisotropic quantum Rabi model (AQRM) in broad parameter ranges are explored, which is realized with superconducting flux qubits simultaneously driven by two-tone time-dependent magnetic fields. Regarding the quantum phase transitions (QPTs), with assistance of fidelity susceptibility, we extract the scaling functions and the critical exponents, with which the universal scaling of the cumulant ratio is captured by rescaling the parameters related to the anisotropy. Moreover, a fixed point of the cumulant ratio is predicted at the critical point of the AQRM with finite anisotropy. In respect of quantum information tasks, the generation of the macroscopic Schrödinger cat states and quantum controlled phase gates are investigated in the degenerate case of the AQRM, whose performance is also investigated by numerical calculation with practical parameters. Therefore, our results pave the way to explore distinct features of the AQRM in circuit QED systems for QPTs, quantum simulations and quantum information processing.

DOI
10.1088/1367-2630/aac5b5

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Promising applications of the anisotropic quantum Rabi model (AQRM) in broad parameter ranges are explored, which is realized with superconducting flux qubits simultaneously driven by two-tone time-dependent magnetic fields. Regarding the quantum phase transitions (QPTs), with assistance of fidelity susceptibility, we extract the scaling functions and the critical exponents, with which the universal scaling of the cumulant ratio is captured by rescaling the parameters related to the anisotropy. Moreover, a fixed point of the cumulant ratio is predicted at the critical point of the AQRM with finite anisotropy. In respect of quantum information tasks, the generation of the macroscopic Schrödinger cat states and quantum controlled phase gates are investigated in the degenerate case of the AQRM, whose performance is also investigated by numerical calculation with practical parameters. Therefore, our results pave the way to explore distinct features of the AQRM in circuit QED systems for QPTs, quantum simulations and quantum information processing.
By manipulating the flux qubits with bichromatic time-dependent magnetic fluxes in standard circuit QED systems, we propose an experimentally-accessible method to approach the physics of the anisotropic quantum Rabi model (AQRM) in broad parameter ranges, where the rotating and counter-rotating interactions are governed by two different coupling constants. Assisted by theoretical derivations and numerical calculations, we show that our scheme not only allows for individual control of the parameters in the simulated AQRM but also reproduces the dynamics of the ultrastrong and deep strong coupling regimes. Therefore, our scheme advances the investigation of extremely strong interactions of the AQRM, which are usually experimentally unattainable. Furthermore, associated with the special case of the degenerate AQRM, we demonstrate that our setup may also find applications for protected quantum memory and quantum computation since it can be used to generate the Schr\{o}dinger cat states and the quantum controlled phase gates when scaling up.
We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.
We investigate the quantum phase transition (QPT) and quench dynamics in the anisotropic Rabi model when the ratio of the qubit transition frequency to the oscillator frequency approaches infinity. Based on the Schrieffer-Wolff transformation, we find an anti-Hermitian operator that maps the original Hamiltonian into a one-dimensional oscillator Hamiltonian within the spin-down subspace. We analytically derive the eigenenergy and eigenstate of the normal and superradiant phases and demonstrate that the system undergoes a second-order quantum phase transition at a critical border. The critical border is a straight line in a two-dimensional parameter space which essentially extends the dimensionality of QPT in the Rabi model. By combining the Kibble-Zurek mechanism and the adiabatic dynamics method, we find that the residual energy vanishes as the quench time tends to zero, which is a sharp contrast to the universal scaling where the residual energy diverges in the same limit.
Anisotropic quantum Rabi model is a generalization of quantum Rabi model, which allows its rotating and counter-rotating terms to have two different coupling constants. It provides us with a fundamental model to understand various physical features concerning quantum optics, solid-state physics, and mesoscopic physics. In this paper, we propose an experimental feasible scheme to implement anisotropic quantum Rabi model in a circuit quantum electrodynamics system via periodic frequency modulation. An effective Hamiltonian describing the tunable anisotropic quantum Rabi model can be derived from a qubit-resonator coupling system modulated by two periodic driving fields. All effective parameters of the simulated system can be adjusted by tuning the initial phases, the frequencies and the amplitudes of the driving fields. We show that the periodic driving is able to drive a coupled system in dispersive regime to ultrastrong coupling regime, and even deep-strong coupling regime. The derived effective Hamiltonian allows us to obtain pure rotating term and counter-rotating term. Numerical simulation shows that such effective Hamiltonian is valid in ultrastrong coupling regime, and stronger coupling regime. Moreover, our scheme can be generalized to the multi-qubit case. We also give some applications of the simulated system to the Schrödinger cat states and quantum gate generalization. The presented proposal will pave a way to further study the stronger anisotropic Rabi model whose coupling strength is far away from ultrastrong coupling and deep-strong coupling regimes in quantum optics.
We investigate the critical phenomena of the asymmetric quantum Rabi model (AQRM), where parity symmetry is broken by an external bias. Through both analytical and numerical calculations, we identify second-order and first-order phase transitions, with the latter absent in the standard quantum Rabi model. We derive an analytical two-variable scaling function that describes the finite-frequency scaling behavior of the AQRM, and numerical results confirm this framework. The introduction of bias leads to additional critical exponents, including a bias-related critical exponent ν_{h} and susceptibility exponent γ. Moreover, we demonstrate that critical scaling persists even below the conventional critical coupling, indicating the emergence of field-induced quantum criticality. These findings establish a robust theoretical framework for understanding universal quantum criticality in light-matter systems.
We present the quantum anisotropic Rabi model as a potential resource for a noise biased qubit. The system-environment coupling can be biased by tuning the relative strengths of the rotating-wave and counter-rotating-wave interactions, characterized by the anisotropy parameter ηηη. This anisotropy selectively suppresses dominant decoherence pathways, thereby enabling the construction of a protected logical qubit in the ultrastrong and deep-strong coupling regimes. The logical states (formed by the ground and first excited states of the anisotropic Rabi model) possess coherence times that are enhanced compared to the isotropic case. Moreover, we construct a set of universal gate operations within the logical-state subspace and demonstrate that the gate operations associated with different values of ηηη exhibit robustness against external noise. These findings are expected to inspire applications and research directions for the anisotropic Rabi model with promising potential impacts.