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The Isaacson picture provides a general method for describing the effects of gravitational waves, established on two sets of basic equations. The first set of equations describes the propagation of gravitational waves within a given background, while the second set elucidates the interaction between the effective energy-momentum tensor of gravitational waves and the background metric. These two sets of equations are typically derived by expanding the field equations to second-order perturbations. In addition to the method of perturbing field equations, there is an alternative method: obtaining the two sets of basic equations by expanding the action to the second-order of perturbations. In this paper, we elaborate on this method, establishing its foundations more rigorously. Especially, the second-order perturbation action, with the Minkowski metric as the background, contains all necessary information to construct the Isaacson picture far from the source. We outline the derivation of the two sets of basic equations to describe the gravitational wave effects in the Isaacson picture, based on the second-order perturbation action. This will enable us to analyze the following effects: polarizations of gravitational waves, the wave speed for each polarization mode, the effective energy-momentum tensor of gravitational waves, and the nonlinear memory effect of gravitational waves. We illustrate this method by applying it to the most general second-order vector-tensor theory including parity-breaking terms. We further analyze the polarization modes of gravitational waves in this theory. We highlight that this method facilitates model-independent research on various gravitational wave effects in general modified gravity theories. These effects are anticipated to be identified by the upcoming generation of gravitational wave detectors, aimed at testing potential modifications to gravity theory., Comment: 85 pages, 1 figure

Quantum noise and thermal noise are the two primary sources of noise that limit the sensitivity of weak magnetic field sensing. Although quantum noise has been widely addressed, effectively reducing thermal noise remains challenging in detecting weak magnetic fields. We employ an anisotropic elliptical YIG sphere as a magnetic field probe to establish a parametric amplification interaction of magnons and induce magnon squeezing effects. These effects can effectively suppress thermal noise in the magnon mode and amplify weak magnetic field signals from external sources. Specifically, complete suppression of thermal noise can be achieved by placing the YIG sphere in a squeezed vacuum reservoir. Our scheme has the potential to inspire advancements in thermal noise suppression for quantum sensing.

In the realm weak force sensing, an important issue is to suppress fundamental noise (quantum noise and thermal noise), as they limit the accuracy of force measurement. In this paper, we investigate a weak force sensing scheme that combines a degenerate optical parametric amplifier (OPA) and an auxiliary mechanical oscillator into a cavity optomechanical system to reduce quantum noise. We demonstrate that the noise reduction of two coupled oscillators depends on their norm mode splitting. and provide a classic analogy and quantum perspective for further clarification. Besides, the noise reduction mechanism of OPA is to reduce the fluctuation of photon number and enhance the squeezing of the cavity field. We propose a specific design aimed at enhancing the joint effect of both, beyond what can be achieved using OPA alone or two series coupled oscillators. This scheme provides a new perspective for deeper understanding of cavity field squeezing and auxiliary oscillator in force sensing., Comment: 9 pages,10 figures

We study the polarization modes of gravitational waves in general Einstein-vector theory with an arbitrary constant background vector field under a Minkowski background. We compare these polarization modes with those of other vector-tensor theories and constrain the parameter spaces based on the gravitational-wave event GW170817 with its electromagnetic counterpart GRB170817A and observations of pulsar timing arrays. The presence of the background vector field leads to the anisotropy of space and a rich variety of gravitational waves contents. Our results reveal that the polarization modes of gravitational waves depend on the parameter spaces. There are at least two and at most five independent polarization modes in one parameter space. In different parameter spaces, some mixture modes are allowed, including tensor-vector, tensor-scalar, tensor-vector-scalar, vector-scalar, and scalar-scalar mixture modes, as well as five independent modes (excluding $P_l$): $P_+$, $P_{\times}$, $P_x$, $P_y$, and $P_b$. In all regions of the parameter spaces, there are always two tensor modes, which can be either independent of or mixed with other modes. The independent $P_b$ mode consistently exhibits the same speed as light. If the speed of tensorial gravitational waves strictly equals that of light, only the $P_+$, $P_{\times}$, and $P_b$ modes are permitted. Furthermore, through comparisons of some vector-tensor theories and based on the observations of gravitational waves, the $P_b$ mode is expected to be allowed.

The crucial limitation of improving the sensitivity of the detection of weak magnetic fields is the unavoidable measurement noise. In this paper, we propose a scheme to achieve precise sensing robust against additional noise by employing a dual-frequency bias field modulation within a cavity magnon system. We find that the anti-rotating wave term can amplify the signal of the detected magnetic field, but this amplification effect must coexist with the rotating wave term. In particular, by the bias field modulation, we find the robustness against cavity field thermal noise is substantially enhanced, quantum noise and cavity field thermal noise is greatly reduced, and the external magnetic field signal is amplified, thereby improving the weak magnetic field sensing system's sensitivity. Compared with the previous scheme, our scheme requires neither an ultra- or deep-strong coupling mechanism nor the suppression of the additional noise by increasing the electromagnetic cooperativity. Our scheme could provide a valuable candidate for weak magnetic field sensing.

The mechanical strain can control the frequency of two-level atoms in amorphous material. In this work, we would like to employ two coupled two-level atoms to manipulate the magnitude and direction of heat transport by controlling mechanical strain to realize the function of a thermal switch and valve. It is found that a high-performance heat diode can be realized in the wide Piezo voltage range at different temperatures. We also discuss the dependence of the rectification factor on temperatures and couplings of heat reservoirs. We find that the higher temperature differences correspond to the larger rectification effect. The asymmetry system-reservoir coupling strength can enhance the magnitude of heat transfer, and the impact of asymmetric and symmetric coupling strength on the performance of the heat diode is complementary. It may provide an efficient way to modulate and control heat transport's magnitude and flow preference. This work may give insight into designing and tuning quantum heat machines., Comment: 10 pages, 9 figures;Accepted for publication in Physical Review E

A quantum thermal device based on three nearest-neighbor coupled spin-1/2 systems controlled by the magnetic field is proposed. We systematically study the steady-state thermal behaviors of the system. When the two terminals of our system are in contact with two thermal reservoirs, respectively, the system behaves as a perfect thermal modulator that can manipulate heat current from zero to specific values by adjusting magnetic field direction over different parameter ranges, since the longitudinal magnetic field can completely block the heat transport. Significantly, the modulator can also be achieved when a third thermal reservoir perturbs the middle spin. We also find that the transverse field can induce the system to separate into two subspaces in which neither steady-state heat current vanishes, thus providing an extra level of control over the heat current through the manipulation of the initial state. In addition, the performance of this device as a transistor can be enhanced by controlling the magnetic field, achieving versatile amplification behaviors, in particular substantial amplification factors., Comment: 18 pages, 9 figures

In this paper, we establish a unified parameterized framework for analyzing the polarization modes of gravitational waves in the general metric theory (gravity is only described by the metric) and the general scalar-tensor theory (gravity is described by the metric and an additional scalar field). Specifically, we study the polarization modes of gravitational waves in the most general metric theory and general scalar-tensor theory that satisfy the following conditions: (1) Spacetime is four-dimensional; (2) The theory satisfies the principle of least action; (3) The theory is generally covariant; (4) The action describing a free particle is $\int ds$. We find that the polarization modes of gravitational waves in the theory satisfying the above conditions depends on the selection of parameters in the framework, and the theory allows for up to all six polarization modes. Once we have established our framework, the analysis of the polarization modes of gravitational waves in specific theories will depend on determining the corresponding parameters within our framework. In our analysis, we also find that the polarization modes of gravitational waves in the general metric theory and the general scalar-tensor theory that satisfy the conditions also have some interesting universal properties., Comment: v3: 38 pages, 1 figure, 2 tables, typos corrected

Quantum superconducting circuit with flexible coupler has been a powerful platform for designing quantum thermal machines. In this letter, we employ the tunable coupling of two superconducting resonators to realize a heat valve by modulating magnetic flux using a superconducting quantum interference device (SQUID). It is shown that a heat valve can be realized in a wide parameter range. We find a consistent relation between the heat current and quantum entanglement, which indicates the dominant role of entanglement on the heat valve. It provides an insightful understanding of quantum features in quantum heat machines., Comment: 9 figures, 4 figures

A quantum thermal diode is designed based on three pairwise coupled qubits, two connected to a common reservoir and the other to an independent reservoir. It is found that the internal couplings between qubits can enhance heat currents. If the two identical qubits uniformly couple with the common reservoir, the crossing dissipation will occur, leading to the initial-state-dependent steady state, which can be decomposed into the mixture of two particular steady states: the heat-conducting state generating maximum heat current and the heat-resisting state not transporting heat. However, the rectification factor does not depend on the initial state. In particular, we find that neither quantum entanglement nor quantum discord is present in the steady state, but the pure classical correlation shows a remarkably consistent behavior as the heat rectification factor, which reveals the vital role of classical correlation in the system.

In this paper, we study polarization modes of gravitational waves in generalized Proca theory in the homogeneous and isotropic Minkowski background. The results show that the polarizations of gravitational waves depend on the parameter space of this gravity theory and can be divided into quite rich cases by parameters. In some parameter space, it only allows two tensor modes, i.e., the $+$ and $\times$ modes. In some parameter space, besides tensor modes, it also allows one scalar mode, or two vector (vector-$x$ and vector-$y$) modes, or both one scalar mode and two vector modes. The scalar mode is a mixture mode of a breathing mode and a longitudinal mode, or just a pure breathing mode. Interestingly, it is found that the amplitude of the vector modes is related to the speed of the tensor modes. This allows us to give the upper bound of the amplitude of the vector modes by detecting the speed of the tensor modes. Specifically, if the speed of tensor modes is strictly equal to the speed of light, then the amplitude of vector modes is zero., Comment: v2: 28 pages, 1 figure, 2 tables, improved version

The most important difference between ultrastrong and non-ultrastrong coupling regimes is that the ground state contains excitations. We consider a qubit-plasmon-phonon ultrastrong coupling (USC) system with a three-level atom coupled to the photon and phonon via its upper two energy levels and show that spontaneous emission of the atom from its intermediate to its ground state produces photon and phonon pairs. It is shown that the current system can produce a strong photon/phonon stream and the atom-phonon coupling plays the active role, which ensures the experimental detection. The emission spectrum and various high-order correlation functions confirm the generation of the pairs of photons and phonons. Our study has important implications for future research on virtual photon and phonon pairs creation in the ground state of the USC regime., Comment: 15 pages, 7 figures

Precisely controlling heat transfer in a quantum mechanical system is particularly significant for designing quantum thermodynamical devices. With the technology of experiment advances, circuit quantum electrodynamics (circuit QED) has become a promising system due to controllable light matter interactions as well as flexible coupling strengths. In this paper, we design a thermal diode in terms of the two-photon Rabi model of the circuit QED system. We find that the thermal diode can not only be realized in the resonant coupling but also achieve better performance, especially for the detuned qubit-photon ultrastrong coupling. We also study the photonic detection rates and their nonreciprocity, which indicates similar behaviors with the nonreciprocal heat transport. This provides the potential to understand thermal diode behavior from the quantum optical perspective and could shed new insight into the relevant research on thermodynamical devices., Comment: 12 pages, 12 figures. To appear in Physical Review E

In this paper, we investigate the possible parameter space of Palatini-Horndeski theory with gravitational waves in a spatially flat Universe. We find that if the theory satisfies the following condition: in any spatially flat cosmological background, the tensor gravitational wave speed is the speed of light $c$, then only $S = \int d^4x \sqrt{-g} \big[K(\phi,X)-G_{3}(\phi,X){\tilde{\Box}}\phi+G_{4}(\phi)\tilde{R}\big]$ is left as the possible action in Palatini-Horndeski theory., Comment: 23 pages, no figure

The direct detection of gravitational waves opens the possibility to test general relativity and its alternatives in the strong field regime. Here we focus on the test of the existence of extra dimensions. The classification of gravitational waves in metric gravity theories according to their polarizations in higher-dimensional space-time and the possible observation of these polarizations in 3-dimensional subspace are discussed in this work. And we show that the difference in the response of gravitational waves in detectors with and without extra dimensions can serve as evidence for the existence of extra dimensions., Comment: 19 pages, 4 figures

This paper systematically studied heat transfer through two transversely coupled qubits in contact with two types of heat reservoirs. One is the independent heat reservoir which essentially interacts with only a single qubit, the other is the common heat reservoir which is allowed to simultaneously interact with two qubits. Compared to independent heat reservoirs, common reservoirs always suppress heat current in most cases. However, the common environment could enhance heat current, if the dissipation rate corresponding to the higher eigenfrequency is significantly higher than that corresponding to the lower eigenfrequency. In particular, in the case of resonant coupling of two qubits and the proper dissipations, the steady state can be decomposed into a stationary dark state which doesn't evolve and contributes zero heat current, and a residual steady state which corresponds to the maximal heat current. This dark state enables us to control steady-state heat current with an external control field and design a thermal modulator. In addition, we find that inverse heat currents could be present in the dissipative subchannels between the system and reservoirs, which interprets the suppression roles of common heat reservoirs. We also calculate the concurrence of assistance (COA) of the system and find that heat current and COA have the same trend with temperature, which further indicates that entanglement can be regarded as a resource to regulate heat transport., Comment: 30 pages,8 figures

Quantum thermal transistor is a microscopic thermodynamical device that can modulate and amplify heat current through two terminals by the weak heat current at the third terminal. Here we study the common environmental effects on a quantum thermal transistor made up of three strong-coupling qubits. It is shown that the functions of the thermal transistor can be maintained and the amplification rate can be modestly enhanced by the skillfully designed common environments. In particular,the presence of a dark state in the case of the completely correlated transitions can provide an additional external channel to control the heat currents without any disturbance of the amplification rate. These results show that common environment effect can offer new insight on improving the performance of quantum thermal devices., Comment: 14 pages, 9 figures