In this paper, we analyze the quantum criticality of the Rabi-Stark model at finite ratios of the qubit and cavity frequencies in terms of the energy gap, the order parameter, as well as the fidelity, if the Stark coupling strength is the same as the cavity frequency. The critical exponents are derived analytically. The energy gap and the length critical exponents are different from those in the quantum Rabi model and the Dicke model. The finite size scaling analysis for the order parameter and the fidelity susceptibility is also performed. The universal scaling behaviors are demonstrated and several finite size exponents can be then extracted. Furthermore, universal critical behavior can be also established in terms of the bosonic Hilbert space truncation number, and the corresponding critical scaling exponents are found. Interestingly, the critical correlation length exponents in terms of the photonic truncation number as well as the equivalently effective length scales are different in the Rabi-Stark model and the quantum Rabi model, suggesting they belong to different universality classes. The second-order quantum phase transition is convincingly corroborated in the Rabi-Stark model at finite frequency ratios, by contrast, it only emerges at the infinite frequency ratio in the original quantum Rabi model without the Stark coupling.
The analytically exact solutions to the two-photon Rabi-Stark model are given by using the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived. The zeros of the transcendental functions reproduce completely the regular spectra. The first-order quantum phase transitions are also detected by the pole structure of the derived transcendental functions, similar to the one-photon Rabi-Stark model, different from the two-photon Rabi model where the energy levels for the ground-state and the first excited state do not cross. The spectra collapse char…
The superradiant phase transition (SPT) controlled by the interacting strength between the two-level atom and the photons has been a hot topic in the Rabi model and the Rabi-dimer model. The latter describes two Rabi cavities coupled with an inter-cavity hopping parameter. Moreover, the SPT in the Rabi-dimer model is found to be the same universal class that in the Rabi model by investigating the correlation-length critical exponent. In this paper, we are concerned about whether the inter-cavity hopping parameter between two Rabi cavities (i.e., the Rabi-dimer model) will induce the SPT and to…
We study the dynamic sensitivity of the quantum Rabi model, which exhibits quantum criticality in the finite-component-system case. This dynamic sensitivity can be detected by introducing an auxiliary two-level atom far-off-resonantly coupled to the cavity field of the quantum Rabi model. We find that when the quantum Rabi model goes through the critical point, the auxiliary atom experiences a sudden decoherence, which can be characterised by a sharp decay of the Loschmidt echo. Our scheme will provide a reliable way to observe quantum phase transition in ultrastrongly coupled quantum systems.
The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling are present on an equal footing, are studied within the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived in a compact way, much simpler than previous ones obtained in the Bargmann representation. The zeros of transcendental functions reproduce completely the regular spectra. In terms of the explicit pole structure of these functions, two kinds of exceptional eigenvalues are obtained and distinguished in a transparent manner. Very interestin…
Affine spin-pencil factorization of generalized driven anisotropic Rabi--Stark Hamiltonians in an inhomogeneous orthosymplectic superalgebra
Universidad Politécnica Metropolitana de Hidalgo（伊达尔戈大都会理工大学）；SECIHTI-Instituto Nacional de Astrofísica, Óptica y Electrónica（国家天体物理学、光学和电子学研究所）；Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional（国立理工学院高级研究中心）
Various quantum phase transitions in the anisotropic Rabi-Stark model with both the nonlinear Stark coupling and the linear dipole coupling between a two-level system and a single-mode cavity are studied in this work. The first-order quantum phase transitions are detected by the level crossing of the ground-state and the first-excited state with the help of the pole structure of the transcendental functions derived by the Bogoliubov operators approach. As the nonlinear Stark coupling is the same as the cavity frequency, this model can be solved by mapping to an effective quantum oscillator. Al…
A quantum two level system coupled to a harmonic oscillator represents a ubiquitous physical system. New experiments in circuit QED and nano-electromechanical systems (NEMS) achieve unprecedented coupling strength at large detuning between qubit and oscillator, thus requiring a theoretical treatment beyond the Jaynes Cummings model. Here we present a new method for describing the qubit dynamics in this regime, based on an oscillator correlation function expansion of a non-Markovian master equation in the polaron frame. Our technique yields a new numerical method as well as a succinct approxima…
We demonstrate the emergence of selective $k$-photon interactions in the strong and ultrastrong coupling regimes of the quantum Rabi model with a Stark coupling term. In particular, we show that the interplay between the rotating and counter-rotating terms produces multi-photon interactions whose resonance frequencies depend, due to the Stark term, on the state of the bosonic mode. We develop an analytical framework to explain these $k$-photon interactions by using time-dependent perturbation theory. Finally, we propose a method to achieve the quantum simulation of the quantum Rabi model with …
Quantum systems that undergo quantum phase transitions exhibit divergent susceptibility and can be exploited as probes to estimate physical parameters. We generalize the dynamic framework for criticality-enhanced quantum sensing by the quantum Rabi model (QRM) to its anisotropic counterpart and derive the correspondingly analytical expressions for the quantum Fisher information (QFI). We find that the contributions of the rotating-wave and counterrotating-wave interaction terms are symmetric at the limit of the infinite ratio of qubit frequency to field frequency, with the QFI reaching a maxim…
A quantum memory protocol of controlled ac Stark echoes (CASE) based on a double rephasing photon echo scheme via controlled Rabi flopping is proposed. A double rephasing scheme of photon echoes inherently satisfies the no-population inversion requirement for quantum memories, but the resultant absorptive echo has been a fundamental problem. In the present studies, firstly, the first echo in the double rephasing scheme is dynamically controlled not to affect the second echo by using unbalanced ac Stark shifts. Secondly, a control Rabi pulse coherently manipulates the second echo to be emissive…
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 assistant of fidelity susceptibility, we extract the scaling functions and the critical exponents, with which the universal scaling of the cumulant ratio is captured with rescaling of the parameters due to the anisotropy. Moreover, a fixed point of the cumulant ratio is predicted at the critical point of the AQRM. In res…
In this work we report the modification of the normal Auger line shape under the action of an intense x-ray radiation. Under strong Rabi-type coupling of the core, the Auger line profile develops into a doublet structure with an energy separation mainly determined by the relative strength of the Rabi coupling. In addition, we find that the charge resolved ion yields can be controlled by judicious choice of the x-ray frequency.
We explore the quantum criticality of a two-site model combining quantum Rabi models with hopping interaction. Through a combination of analytical and numerical approaches, we find that the model allows the appearance of a superradiant quantum phase transition (QPT) even in the presence of strong $\mathbf{A}^2$ terms, preventing single-site superradiance. In the two-site model the effect of $\mathbf{A}^2$ terms can be surmounted by the photon delocalization from hopping, and a reversed superradiant QPT occurs as a consequence of the competition between $\mathbf{A}^2$ terms and the hopping inte…
The atoms trapped in microcavities and interacting through the exchange of virtual photons can be modeled as an anisotropic Heisenberg spin-1/2 lattice. We study the dynamics of the geometric phase of this system under the linear quenching process of laser field detuning which shows the XX criticality of the geometric phase in presence of single Rabi frequency oscillation. We also study the quantum criticality for different quenching rate in the presence of single or two Rabi frequencies oscillation in the system.
Quantum Criticality from Spectral Collapse in the Two-Photon Rabi Model
Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学院和高等研究院）；Zhejiang Key Laboratory of Micro-Nano Quantum Chips and Quantum Control, School of Physics, Zhejiang University（浙江大学物理学院微纳量子芯片与量子控制浙江省重点实验室）
We propose a theoretical scheme to achieve strong photon blockade via a single atom in cavity. By utilizing optical Stark shift, the dressed-state splitting between higher and lower branches is enhanced, which results in significant increasing for lower (higher) branch and decreasing for higher (lower) branch at the negative (positive) Stark shift, and dominates the time-evolution of photon number oscillations as well. Furthermore, the two-photon excitation is suppressed via quantum interference under optimal phase and Rabi frequency of an external microwave field. It is shown that the interpl…
When an atom strongly couples to a cavity, it can undergo coherent vacuum Rabi oscillations. Controlling these oscillatory dynamics quickly relative to the vacuum Rabi frequency enables remarkable capabilities such as Fock state generation and deterministic synthesis of quantum states of light, as demonstrated using microwave frequency devices. At optical frequencies, however, dynamical control of single-atom vacuum Rabi oscillations remains challenging. Here, we demonstrate coherent transfer of optical frequency excitation between a single quantum dot and a cavity by controlling vacuum Rabi o…
The hidden $\mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) has recently been revealed via a systematic construction of the underlying symmetry operator. Based on the AQRM result, we propose an ansatz for the general form of the symmetry operators for AQRM-related models. Applying this ansatz we obtain the symmetry operator for three models: the anisotropic AQRM, the asymmetric Rabi-Stark model (ARSM) and the anisotropic ARSM.
We show that quantum-interference-related phenomena, such as electromagnetically induced transparency, gain without inversion and enhanced refractive index may occur on electric-dipole forbidden transitions. Gain/dispersion characteristics of such transitions strongly depend upon the relative phase between the driving and probe fields. Unlike allowed transitions, gain/absorption behavior of forbidden transitions exhibit antisymmetric feature on the Rabi sidebands. Absorption/gain spectra possess extremely narrow sub-natural resonances.
Quantum criticality usually occurs in many-body systems. Recently it was shown that the quantum Rabi model, which describes a two-level atom coupled to a single model cavity field, presents quantum phase transitions from a normal phase to a superradiate phase when the ratio between the frequency of the two level atom and the frequency of the cavity field extends to infinity. In this work, we study quantum phase transitions in the quantum Rabi model from the fidelity susceptibility perspective. We found that the fidelity susceptibility and the generalized adiabatic susceptibility present univer…
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a non-linear coupling term exhibits much higher measurement precisions due to its first order like phase transition at \emph{finite} frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magne…
Quantum criticality, as a fascinating quantum phenomenon, may provide significant advantages for quantum sensing. Here we propose a dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPT). By giving the formalism of the quantum Fisher information (QFI) for quantum sensing based on critical quantum dynamics, we demonstrate its divergent feature when approaching the critical point. We illustrate the basic principle and the details of experimental implementation using quantum Rabi model. The framework is applicable to a variety of examples …
The interplay of interactions, symmetries and gauge fields usually leads to intriguing quantum many-body phases. To explore the nature of emerging phases, we study a quantum Rabi triangle system as an elementary building block for synthesizing an artificial magnetic field. We develop an analytical approach to study the rich phase diagram and the associated quantum criticality. Of particular interest is the emergence of a chiral-coherent phase, which breaks both the $\mathbb{Z}_2$ and the chiral symmetry. In this chiral phase, photons flow unidirectionally and the chirality can be tuned by the …
Non-Equilibrium Criticality-Enhanced Quantum Sensing with Superconducting Qubits
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；University of Electronic Science and Technology of China（电子科技大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）
A three level ladder system is analyzed and the coherence of initially electric-dipole forbidden transition is calculated. Due to the presence of two laser fields the initially dipole forbidden transition becomes dynamically permitted due to ac Stark effect. It is shown that such transitions exhibit quantum-interference-related phenomena, such as electromagnetically induced transparency, gain without inversion and enhanced refractive index. Gain and dispersion characteristics of such transitions strongly depend upon the relative phase between the driving and the probe fields. Unlike allowed tr…
Present protocols of criticality-enhanced sensing with open quantum sensors assume direct measurement of the sensor and omit the radiation quanta emitted to the environment, thereby potentially missing valuable information. Here we propose a protocol for criticality-enhanced sensing via continuous observation of the emitted radiation quanta. Under general assumptions, we establish a scaling theory for the global quantum Fisher information of the joint system and environment state at dissipative critical points. We derive universal scaling laws featuring transient and long-time behavior governe…
