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Controllable anisotropic quantum Rabi model beyond the ultrastrong coupling regime with circuit QED systems

Yimin Wang, Wen‐Long You, Maoxin Liu, Yuli Dong, Hong‐Gang Luo, Guillermo Romero, J. Q. You

Published Oct 24, 2017• 1 citation
OpenAlex

Abstract

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.

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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.
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 propose a circuit QED architecture that realizes the full anisotropic Rabi model (ARM) with in-situ tunability of its interaction symmetry. The circuit comprises a superconducting qubit coupled to a resonator through two simultaneous channels: a direct inductive path and a flux-tunable capacitive path mediated by a transmon coupler. By controlling the external magnetic flux, the destructive and constructive interferences between these paths continuously tune the ratio of the Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) couplings, sweeping the system across the entire ARM parameter space---from pure JC, through the standard Rabi regime, to pure AJC---without requiring rotating-wave approximations or external parametric drives. Furthermore, we identify a coherence sweet spot where the dispersive shift and photon shot-noise dephasing are suppressed. In the pure AJC regime, we demonstrate that the vacuum Rabi splitting vanishes and the Purcell decay rate is strongly mitigated while preserving high qubit readout contrast.
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.
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.
In the ultrastrong-coupling regime, the quantum Rabi model can exhibit quantum phase transition (QPT) when the ratio of the qubit transition frequency to the frequency of the cavity field approaches infinity. However, it is challenging to control the QPT in few-body systems because of the limited coupling strength and the A2{A}^{2}A2 term. Here, we propose a practical scheme to manipulate the QPT of quantum Rabi model in the strong-coupling regime. By applying a periodic frequency modulation to the two-level system in a quantum Rabi model in the strong-coupling regime, an anisotropic quantum Rabi model with ultrastrong and tunable coupling strengths for rotating and counterrotating terms is obtained. The ground state and excitation energy of this model, in terms of the modulation parameters, are studied. We find that the QPT of the quantum Rabi model can be observed in the strong-coupling regime and externally controlled by the modulation.
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.