We report a distinct two-photon blockade (termed as weak TPB) discovered in the strong-coupling regime of a parity-broken generalized quantum Rabi model, in addition to the other two-photon blockade (termed as strong TPB) in the ultrastrong coupling (USC) regime. In contrast to the strong TPB conventionally with opened cascade decay channel, the weak TPB phase emerges unconventionally with closed cascade decay channel. The closure of cascade channel originally allowed to open by parity breaking is unexpected and its opening in the strong-TPB regime is actually delayed. We extract a cubic law for the cascade transition rate that accounts for the suppression of cascade channel and the delayed opening in the two TPB regimes. Furthermore, we find that the population on the cascade state, which is crucial in the strong TPB, contrarily plays a minor role in the weak TPB. Instead, it is the upper state above the cascade that is relevant for the weak TPB. We demonstrate that the interplay of weak anharmonicity and resonant driving is the primary mechanism responsible for the upper-state population and the formation of weak TPB. Our analyses not only provide deeper insights into the nature of different TPBs, but also imply mechanism and manipulation diversities for the multi-photon blockade, which may open more avenues for developing quantum technologies on the manipulation level of individual quanta.

The experimental access to ultra-strong couplings in light-matter interactions has made the quantum phase transition (QPT) in the quantum Rabi model practically relevant, while the physics of the QPT has not yet been fully explored. The polaron picture is a method capable of analyzing in the entire coupling regime and extracting the essential physics behind the QPT. However, the asymmetric deformation of polarons is missing in the current polaron picture. In the present work we propose an improved variational method in asymmetric polaron picture (APP). Our APP not only increases the method accuracy but also reveals more underlying physics concerning the QPT. We find that in the ground state both the polarons and antipolarons are asymmetrically deformed to a large extent, which leads to a richer phase diagram. We also analyze the first excited state in which we unveil an asymmetry direction reversal for the polarons and an attraction/replusion transition differently from the ground state. Finally, we apply the APP in quantum Fisher information analysis and critical coupling extraction, the improvements indicate that the polaron asymmetry makes a considerable contribution to the quantum resource in quantum metrology and plays an unnegligible role in the QPT. Our results and mechanism clarifications expose more subtle energy competitions and abundant physics, and the method potentially might have broader applications in light-matter interactions.

Two-photon blockade (TPB) besides the conventional one-photon blockade can control the photon at the level of individual quanta in the input-output measurements of light-matter coupling systems. Apart from conventional TPB (C-TPB) with opened cascade decay channel, unconventional TPB (U-TPB) with closed cascade decay channel may open novel avenues for manipulation of TPB. However, currently found U-TPB in linear coupling is limited in a narrow coupling window and the blockade strength is weak, which would hinder its applications. In the present work we propose to enhance the U-TPB by the Stark nonlinear coupling. Indeed, the introduction of the Stark nonlinear coupling to the linear coupling enables tuning of both cascade energy level and the anharmonicity which play key roles in the formation of TPBs. By investigating photon correlation functions and extracting phase diagrams in dissipation, we demonstrate that our scheme not only dramatically broadens the window of U-TPB to cover the entire strong-coupling regime but also deepens the blockading degree of the U-TPB by two orders. The cascade decay rates, state populations and the anharmonicity, are examined to identify and track the U-TPB and C-TPB. In the overview of phase diagrams we also reveal a broad U-TPB in ultrastrong couplings, with a crossover to the C-TPB. Since the Stark nonlinear coupling is realizable and tailorable, our proposal may pave a practical way for manipulation of the TPB.

The quantum Rabi model (QRM) is a fundamental model for light-matter interactions; the finite-component quantum phase transition (QPT) in the QRM has established a paradigmatic application for critical quantum metrology (CQM). However, this paradigmatic application is restricted to a local regime of the QPT which has only a single critical point. In this work we propose a globalized CQM in the QRM by introducing an auxiliary nonlinear term which is realizable and can extend the critical point to a continuous critical regime. As a consequence, high measurement precision is globally available over the entire coupling regime from the original critical point of the QRM down to the weak-coupling limit, as demonstrated by the globally accessible diverging quantum Fisher information in the dynamics. We illustrate a measurement scheme using quadrature dynamics, with globally criticality-enhanced inverted variance as well as the scaling relation with respect to finite frequencies. In particular, we find that the globally high measurement precision still survives in the presence of decoherence. Our proposal paves the way to break the local limitation of the QPT of the QRM in CQM and enables a broader application, with implications for applicability in realistic situations.

We propose a scheme to implement Heisenberg-limited spin squeezing in a hybrid cavity optomechanical-spin system. In our system, $N$ two-level systems are coupled via Tavis-Cummings interactions to a mechanical resonator (MR) in a standard optomechanical setup. Within the dispersive coupling regime, adiabatic elimination of the optical mode induces a squeezing effect on the MR, which, in the squeezed representation, effectively transforms the collective spin operators into a Bogoliubov form. Under large detuning conditions, the phonon mode mediates interactions among the Bogoliubov collective spins, thereby enabling a two-axis twisting squeezing protocol through appropriate parameter tuning. Both theoretical analysis and numerical simulations show that in the presence of dephasing and phonon dissipation, the maximum squeezing degree asymptotically converges to a constant as $N$ increases, which implies the metrological precision asymptotically approaches the standard quantum limit without parameter optimization. Nevertheless, in parameter optimization we extract a scaling relation of the optimal squeezing which surpasses existing schemes in the literature. Moreover, the optimization also leads to a considerable reduction of the preparation time for the optimal squeezing. Our work may provide insights into dissipation effects in spin squeezing and offer a potential route for high-precision quantum metrology in many-body systems.

Squeezing as a quantum resource for quantum metrology is robust against decoherence and dissipation, while the conventional nonlinear two-photon quantum Rabi model (QRM) provides a squeezing resource immune to the divergence problem of preparation time of probe state (PTPS). However the critical point of the two-photon QRM is locally restricted to one single point, which hinders a wider application. In the present work we propose to combine the Stark coupling with the two-photon QRM to realize a tunable critical point so that the nonlinear critical quantum metrology can be globalized. As demonstrated by the diverging quantum Fisher information (QFI) the protocol enables us to acquire a high measurement precision in a wide range of coupling parameter rather than locally at a single critical point. Moreover, We find that the QFI not only manifests criticality but also exhibits universality. As a particular merit of our protocol, a strong squeezing can be globally retained as the leading quantum resource, while at the same time the PTPS remains in a finite order.

Applications of quantum systems with non-linear light-matter interaction have to deal with a peculiar instability in the ultra- and deep strong coupling regime, the so-called "spectral collapse." To solve this problem, the present work investigates a generalized quantum Rabi model (QRM) with two- and four-photon terms in view of applications for critical quantum metrology. In the introduced model, the spectral collapse occurring in the standard two-photon QRM is stabilized by the presence of the quartic potential. The collapse is then transformed into a quantum phase transition, which occurs in the low-frequency limit of the light mode, whose remnant at finite ratio between qubit and mode frequencies can be applied to critically enhanced quantum metrology. It is found that the four-photon term entails a much higher measurement precision compared to the standard two-photon QRM. The mechanism behind the higher precision can be traced to the different behavior of the ground state wave function as the system is tuned through the transition. As the standard two-photon QRM, despite the absence of the spectral collapse, the proposed model allows for a finite preparation time for the probe state (PTPS).

We investigate a generalized quantum Rabi model (QRM) with two- and four-photon terms with respect to applications for non-linear critical quantum metrology. In the introduced model, the spectral collapse occurring in the standard two-photon QRM is stabilized by the presence of the quartic potential. The collapse is then transformed into a quantum phase transition, which occurs in the low-frequency limit of the light mode, whose remnant at finite ratio between qubit and mode frequencies can be applied to critically enhanced quantum metrology. We find that the four-photon term entails a much higher measurement precision compared to the standard two-photon QRM. The mechanism behind the higher precision can be traced to the different behavior of the ground state wave function as the system is tuned through the transition. As the standard two-photon QRM, despite the absence of the spectral collapse, our model allows for a finite preparation time for the probe state (PTPS).

Squeezing as a quantum resource for quantum metrology is robust against decoherence and dissipation, while the conventional nonlinear two-photon quantum Rabi model (QRM) provides a squeezing resource immune to the divergence problem of the preparation time of the probe state (PTPS). However, the critical point of the two-photon QRM is locally restricted to one single point, which hinders a wider application. In the present work we propose to combine the Stark coupling with the two-photon QRM to realize a tunable critical point so that the nonlinear critical quantum metrology can be globalized. As demonstrated by the diverging quantum Fisher information (QFI) the protocol enables us to acquire a high measurement precision in a wide range of coupling parameters rather than locally at a single critical point. Moreover, we find that the QFI not only manifests criticality but also exhibits universality. As a particular merit of our protocol, a strong squeezing can be globally retained as the leading quantum resource, while at the same time the PTPS remains in a finite order.

We explore the exotic quantum states emerging in the ground state (GS) of a strongly-correlated spin-1 Bose-Einstein condensate confined in two-dimensional concentric annular traps with a spin-orbit coupling (SOC). In the antiferromagnetic case, the GS density manifests various patterns of distributions, including facial-makeup states, petal states, topological fissure states, multiple-half-ring states and property-distinguished vertical and horizonal stripe states. We notice a peculiar phenomenon of density-phase separation in the sense that the variations of density and phase tend to be independent. In ferromagnetic case, the GS exhibits a semi-circular or half-disk status of density embedded with vortices and anti-vortices. The spin distribution can self-arrange into an array of half-skyrmions and we also find a half-antiskyrmion fence separating vortex-antivortex pairs. Our study indicates that one can manipulate the emergence of exotic quantum states via the interplay of the SOC, interaction and potential geometry and the abundant state variations might also provide potential resources for quantum metrology.

Spin-orbit coupling (SOC) has broad relevances and its interplay with other interactions and potential geometry may induce novel quantum states. This work explores exotic quantum states emerging in the ground state (GS) of a strongly-correlated spin-1 Bose-Einstein condensate confined in 2D concentric annular traps with SOC. In the antiferromagnetic case, the GS density manifests various patterns of distributions, including facial-makeup states, petal states, topological fissure states, multiple-half-ring states and property-distinguished vertical and horizontal stripe states. A peculiar phenomenon of density-phase separation is noticed in the sense that the variations of density and phase tend to be independent. In ferromagnetic case, the GS exhibits a semi-circular or half-disk status of density embedded with vortices and antivortices. The spin distribution can self-arrange into an array of half-skyrmions and a half-antiskyrmion fence separating vortex-antivortex pairs is also found. This study indicates that one can manipulate the emergence of exotic quantum states and the locations of the topological defects via the interplay of the SOC, interactions and potential geometry and the abundant state variations might also provide potential resources for quantum metrology.

Dipole-dipole interaction (DDI) possesses characteristics different from the conventional isotropic s-wave interaction in Bose-Einstein condensates (BECs), the interplay of DDI with spin-orbit coupling (SOC) and rotation may induce novel quantum properties. We systematically analyze the effects of the DDI, Weyl-like SOC, rotation and trap anharmonicity in the ground state of two-componen BECs. The interplay of these factors leads to a kaleidoscope of quantum states of quantum defects and quantum droplets in lattice, wheel and ring forms of distributions, with transitions of topology of density and a critical behavior in varying the parameters. We also show a bunch of exotic spin topological structures, including centric vortex surrounded by layers of spin flows, compound topological structure of edge defect, and various coexistence states of skyrmions with different topological charge. In particular, we find quarter skyrmions and other possible fractional skyrmions. Rashba-type SOC and Weyl-like SOC are compared as well. Our study implies that one can manipulate both the density topology and the spin topological structure via these tunable parameters in BECs. The abundant variations of the topological structures and particularly the revealed critical behavior may provide various quantum resources for potential applications in quantum metrology.

The major goal of quantum metrology (QM) is to exploit the quantum resources to raise the measurement precision (MP) as high as possible. When the quantum resources such as squeezing has been widely explored, light-mater interaction systems set up a highly controllable platform applicable for QM in novel pursuit of high MP. However, critical QM by the conventional linear interaction is confronted with the restriction of low-frequency-limit condition and the detrimental problem of diverging preparation time of the probe state (PTPS). This work shows that mixed interactions by linear and nonlinear light-matter couplings in the presence of bias field can provide various quantum resources, including squeezing, degeneracy lifting, displacement and quantum phase transition. These resources manifest high sensitivity for QM as demonstrated by analytically obtained critical components or exponential behavior of quantum Fisher information. We find that these sensitivity resources can be combined to upgrade the upper bound of MP by many orders over the widely-applied squeezing resource. As further advantages, such an upgraded metrology protocol not only breaks the frequency-limit restrictions but also avoids the detrimental problem of diverging PTPS which were both encountered in linear interaction. Our work paves a way to exploit and combine all the resources in momentum, position and spin spaces to maximize the MP and expand the applicable conditions simultaneously.

Squeezing and transition criticality are two main sensitivity resources for quantum metrology (QM), combination of them may yield an upgraded metrology protocol for higher upper bound of measurement precision (MP). We show that such a combination is feasible in light-matter interactions by a realizable asymmetric non-linear quantum Rabi model (QRM). Indeed, the non-linear coupling possesses a squeezing resource for diverging MP while the non-monotonous degeneracy lifting by the asymmetries induces an additional tunable transition which further enhances the MP by several orders, as demonstrated by the quantum Fisher information. Moreover, the protocol is immune from the problem of diverging preparation time of probe state that may hinder the conventional linear QRM in application of QM. This work establishes a paradigmatic case of combining different sensitivity resources to manipulate QM and maximize MP.

Besides exploring novel transition patterns, acquiring a full understanding of the transition nature is an ultimate pursuit in studies of phase transitions. The fundamental models of light-matter interactions manifest single-qubit topological phase transitions, which is calling for an analytical demonstration apart from numerical studies. We present a rigorous study for topological transitions in Jaynes-Cummings Model generally with Stark non-linear Coupling. In terms of the properties of Hermite polynomials, we show that the topological structure of the eigen wave function has an exact correspondence to the spin winding by nodes, which yields a full spin winding without anti-winding nodes. The spurious fractional contribution to the winding number of the winding angle at infinity is found to be actually integer. Thus, the phase transitions in the model have a nature of topological phase transitions and the excitation number is endowed as a topological quantum number. The principal transition establishes a paradigmatic case that a transition is both symmetry-breaking Landau class of transition and symmetry-protected topological class of transition simultaneously, while conventionally these two classes of transitions are incompatible due to the contrary symmetry requirements. We also give an understanding for the origin of unconventional topological transitions in the presence of counter-rotating terms. Our results may provide a deeper insight for the few-body phase transitions in light-matter interactions.

Light-matter interactions provide an ideal testground for interplay of critical phenomena, topological transitions, quantum metrology and non-Hermitian physics. We consider two fundamental non-Hermitian Jaynes-Cummings models which possess real energy spectra in parity-time (PT) symmetry and anti-PT symmetry. We show that the quantum Fisher information is critical around the transitions at the exceptional points and exhibits a super universality with respect to different parameters, all energy levels, both models, symmetric phases and symmetry-broken phases. The transitions are found to be both symmetry-breaking Landau-class transitions (LCTs) and symmetry-protected topological-class of transitions (TCTs), thus realizing a simultaneous occurrence of critical LCTs and TCTs which are conventionally incompatible due to contrary symmetry requirements.

The Jaynes-Cummings Model (JCM) is a fundamental model and building block for light-matter interactions, quantum information and quantum computation. We analytically analyze the topological feature manifested by the JCM in the presence of non-Hermiticity which may be effectively induced by dissipation and decay rates. Indeed, the eigenstates of the JCM are topologically characterized by spin windings in two-dimensional plane. The non-Hermiticity tilts the spin winding plane and induces out-of-plane component, while the topological feature is maintained. In particular, besides the invariant spin texture nodes, we find a non-Hermiticity-induced reversal transition of the tilting angle and spin winding direction with a fractional phase gain at gap closing, a partially level-independent reversal transition without gap closing, and a completely level-independent super invariant point with untilted angle and also without gap closing. Our result demonstrates that the topological feature is robust against non-Hermiticity, which would be favorable in practical applications. On the other hand, one may conversely make use of the disadvantageous dissipation and decay rates to reverse the spin winding direction, which might add a control way for topological manipulation of quantum systems in light-matter interactions.