We theoretically investigate the model of a quadratically coupled optomechanical system with a Newtonian gravitational potential in the weak-driving regime, where the optical cavity is driven by an external laser. The steady state of the whole system is treated in the framework of a few-photon subspace. We find that the conventional single-photon blockade, nonstandard types of single-photon blockade, two-photon blockade, and photon-induced tunneling can be induced by gravity when the quadratic optomechanical coupling strength remains constant. Moreover, we find that gravitational potential energy can compensate for the lack of quadratic optomechanical coupling for observation photon blockade. In particular, the photon stream with super-Poissonian distribution can be converted into a sub-Poissonian, antibunching photon stream by changing the driving detuning when the gravitational potential energy is included. These results show that the gravity has potential for realizing the manipulation of photon blockade in a quadratically coupled optomechanical system.

Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. this paper, we explore the application of information geometry in the realm of non-Hermitian quantum systems, focusing on the Fisher-Rao metric as a measure of parameter sensitivity. We approximate the Lindblad master equation for non-Hermitian Hamiltonians to analyze the temporal evolution of the quantum geometric metric. Utilizing the quantum spin Ising model with an imaginary magnetic field as an exemplar, we investigate energy spectrum and geometric metric evolution within PT-symmetry Hamiltonians. We demonstrate that detrimental effects of dissipation can be counteracted by introducing a control Hamiltonian, leading to improved accuracy in parameter estimation. Our work provides insights into the role of quantum control in mitigating dissipative impacts and enhancing the precision of quantum metrological tasks.

This paper studies the effect of single-photon light fields on quantum entanglement between two qubits and multiple identical qubits initially in a direct state. For two qubits, we first analyze the impact of the excited state's weight on single-photon-triggered entanglement, finding that excessive weight disrupts this process. We then explore how initial coherence affects entanglement, discovering that maximum initial coherence enables the single photon to achieve maximal entanglement. For multiple qubits, we similarly investigate the effects of the excited state's weight and initial coherence on entanglement control. In large qubit systems, we find that single photons cannot trigger entanglement when excited-state weights exceed ground-state weights or when all qubits are initially in the ground state. Interestingly, single photons can still trigger entanglement between any two qubits in systems with at least 2000 qubits, with the entanglement depending on initial state parameters rather than the number of qubits.

We study quantum phase sensing with an asymmetric two-mode entangled coherent state (ECS) in which the two local amplitudes have different values. We find the phenomenon of the asymmetry-enhanced phase sensing which the asymmetry can significantly increase the precise of the phase estimation. We further study the effect of decoherence induced by the photon loss on quantum phase sensing. It is shown that the asymmetric ECSs have stronger capability against decoherence over the symmetric ECSs. It is indicated that the asymmetric ECSs have obvious advantages over the symmetric ECSs in the quantum phase sensing. We also study the practical phase sensing scheme with the intensity-difference measurement, and show that the asymmetry in the asymmetric ECSs can enhance the phase sensitivity in the practical phase measurement scheme. Our work reveals the asymmetry in the asymmetric ECSs is a new quantum-sensing resource, and opens a new way to the ultra-sensitive quantum phase sensing in the presence of photon losses.

The ability to engineer entangled states that involve macroscopic objects is of particular importance for a wide variety of quantum-enabled technologies, ranging from quantum information processing to quantum sensing. Here we propose how to achieve coherent manipulation and enhancement of quantum entanglement in a hybrid optomechanical system, which consists of a Fabry-Pérot cavity with two movable mirrors, an optical parametric amplifier (OPA), and an injected squeezed vacuum reservoir. We show that the advantages of this system are twofold: (i) one can effectively regulate the light-mirror interactions by introducing a squeezed intracavity mode via the OPA; (ii) when properly matching the squeezing parameters between the squeezed cavity mode and the injected squeezed vacuum reservoir, the optical input noises can be suppressed completely. These peculiar features of this system allow us to generate and manipulate quantum entanglement in a coherent and controllable way. More importantly, we also find that such controllable entanglement, under some specific squeezing parameters, can be considerably enhanced in comparison with those of the conventional optomechanical system. Our work, providing a promising method to regulate and tailor the light-mirror interaction, are poised to serve as a useful tool for engineering various quantum effects which are based on cavity optomechanics.

A proposal is made on how to manipulate photon blockades (PBs) and photon-induced tunneling (PIT) in an optomechanical cavity with a Bose-Einstein Condensate. It is shown that the single-photon blockade (1PB) can emerge with appropriate scattering strength between atoms. Further, by tuning interatomic scattering strength, the switch between 1PB and PIT at the fixed optical detuning can be realized in interatomic repulsion or attraction conditions. The enhancement of 1PB can also be achieved. The scattering control of PBs can be understood from the perspective of the anharmonicity of the energy levels modulated by the interatomic collision. Such a system can be equivalent to a conventional optomechanical system plus an interatomic scattering term. It is found that although there are no PBs in the conventional optomechanical system, in the BEC optomechanical system (BECOMS), PBs can occur at the fixed optical detuning. Moreover, the BECOMS can exhibit stronger 1PB under the same optomechanical coupling intensity. Due to the advantages of intrinsic strong optomechanical nonlinearity and the negligible thermal noise of the mechanical environment, BECOMS is promising for experimental realization of PBs. The results open new possibilities for manipulating few-photon states in quantum regime in cavity optomechanics with a Bose-Einstein Condensate. This paper studies the photon blockades in an optomechanical cavity with a Bose-Einstein Condensate. By tuning interatomic scattering strength, the switch between single-photon blockade and photon-induced tunneling and the enhancement of single-photon blockade can be realized in interatomic repulsion or attraction conditions. Moreover, the system can exhibit the stronger 1PB under the same optomechanical coupling than conventional optomechanical system. image

Quantum metrology is recognized for its capability to offer high-precision estimation by utilizing quantum resources, such as quantum entanglement. Here, we propose a generalized Tavis-Cummings model by introducing the $XY$ spin interaction to explore the impact of the many-body effect on estimation precision, quantified by the quantum Fisher information (QFI). By deriving the effective description of our model, we establish a closed relationship between the QFI and the spin fluctuation induced by the $XY$ spin interaction. Based on this exact relation, we emphasize the indispensable role of the spin anisotropy in achieving the Heisenberg-scaling precision for estimating a weak magnetic field. Furthermore, we observe that the estimation precision can be enhanced by increasing the strength of the spin anisotropy. We also reveal a clear scaling transition of the QFI in the Tavis-Cummings model with the reduced Ising interaction. Our results contribute to the enrichment of metrology theory by considering many-body effects, and they also present an alternative approach to improving the estimation precision by harnessing the power provided by many-body quantum phases.

We theoretically studied the quantum dynamics of a cavity–Bose–Einstein condensate (BEC) system in a gravitational field, which is composed of a Fabry–Pérot cavity and a BEC. We also show how to deterministically generate the transient macroscopic quantum superposition states (MQSSs) of the cavity by the use of optomechanical coupling between the cavity field and the BEC. The quantum dynamics of the cavity–BEC system specifically include phase space trajectory dynamics, system excitation number dynamics, quantum entanglement dynamics, and quantum coherence dynamics. We found that the system performs increasingly complex trajectories for larger values of the Newtonian gravity parameter. Moreover, the number of phonon excitations of the system can be increased by coupling the cavity–BEC system to Newtonian gravity, which is analogous to an external direct current drive. The scattering of atoms inside the BEC affects the periodicity of the quantum dynamics of the system. We demonstrate a curious complementarity relation between the quantum entanglement and quantum coherence of cavity–BEC systems and found that the complementarity property can be sustained to some extent, despite being in the presence of the cavity decay. This phenomenon also goes some way to show that quantum entanglement and quantum coherence can be referred to together as quantum resources.

In this paper, we investigate how the evolution of the states of two qubits initially in a direct product state can be controlled by the optical field in a Tavis-Cummings (TC) model. For the two qubits initially in the direct product state, we find that their matrix elements at any moment can be modulated by the coefficients of the optical field initial states in the number state space. We propose a method for preparing an X-type state of two qubits. Subsequently, for descriptive convenience, we divide the Bell states of the two qubits into two kinds in the paper. When both qubits are initially in the ground state, we find that the two qubits can be controlled to produce the first type of Bell state by the superposition state optical field that is initially in the next-nearest-neighbor number state and that the production of any of the first type of Bell states can be controlled by controlling the phase between the two next-nearest-neighbor number states. When one of the two qubits is in the ground state, and the other is in the excited state, we can control the two qubits to produce the second type of Bell state by the single-photon number state optical field. Finally, we study the generation of Werner states by controlling two qubits initially, both in the ground state, using an optical field.

Distilling quantum coherence is important for optimizing the performance of quantum technologies, however, it cannot always be accomplished with certainty. Then, the probabilistic distillation of quantum coherence has been developed and successfully implemented in experiments. We introduce a proposal to realize the one-shot coherence distillation in the superconducting circuit system. The target maximally coherent state can be extracted from a single copy of the prepared state by using appropriate incoherent operations and a finite error tolerance is allowed. It is easy to implement our scheme in the experiment that only a superconducting qubit is required to be the auxiliary system. To demonstrate the feasibility of our scheme, we numerically simulate the distillation process under the influence of dephasing (according to the typical experimental parameters). We find that the distillation rate of the coherence resource can be well achieved with the current experimental technique.

geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this paper, we explore the Fisher-Rao metric with the non-Hermitian systems. By approximating the Lindblad master equation in the non-Hermitian Hamiltonian, we calculate the time evolution of the quantum geometric metric. Finally, we give an example of the quantum spin Ising model of the imaginary magnetic field, explore the energy spectrum of PT-symmetric Hamiltonian and the evolution of geometric metric, and discuss that the dissipative effect of the imaginary magnetic field can be eliminated under the condition of adding the control Hamiltonian, so as to improve the accuracy of parameter estimation.

We investigate the quantum phase transition (QPT) in the XXZ central spin model, which can be described as a spin-1/2 particle coupled to N bath spins. In general, the QPT is supposed to occur only in the thermodynamical limit. In contrast, we present that the central spin model exhibits a normal-to-superradiant phase transition in the limit where the ratio of the transition frequency of the central spin to that of the bath spins and the number of the bath spins tend to infinity. We give the low-energy effective Hamiltonian analytically in the normal phase and the superradiant phase, and we find that the longitudinal interaction can significantly influence the excitation number and the coherence of the ground state. These two quantities are remarkably enhanced for the negative longitudinal interaction while suppressed for the positive longitudinal interaction. We also use the quantum Fisher information (QFI) to characterize the QPT and illustrate a measurement scheme that can be applied in practice. This work builds a novel connection between the qubit-spin systems and the qubit-field systems, which provides a possibility for the realization of criticality-enhanced quantum sensing in central spin systems.

We theoretically study the model of a hybrid cavity–Bose–Einstein condensates (BEC) system that consists of a two-level impurity atom coupled to a cavity–BEC system with radiation pressure coupling, where the system is weakly driven by a monochromatic laser field. The steady-states behavior of the entire system is researched in the framework of the impurity–cavity coupling dispersive limit. We find that the multiple types of photon steady-state antibunching effects can be obtained when only the dissipation of the cavity is included. Moreover, the strength and frequency range of conventional steady-state antibunching effects of the cavity can be significantly modified by the impurity atom and intrinsic non-linearity of BEC. This result shows that our study can provide a method to tune the antibunching effects of the cavity field. In addition, the non-standard photon blockade or superbunching effect with the suppression of two-photon correlation and enhancement of three-photon correlation can be realized. The frequency range of the superbunching effect also can be changed by the impurity atom and intrinsic non-linearity of BEC. Therefore, our study shows many quantum statistical characteristics in a hybrid cavity–BEC quantum system and its manipulation.

Lee‐Yang zeros lie on the complex plane of the control parameters for many‐body systems with finite size, such as the transverse magnetic field and the inverse temperature. Here, an anisotropic spin system with nearest‐neighbor interactions for finite‐size parity space is considered. The Lee‐Yang zeros are obtained in anisotropic XY$XY$ model for the complex plane of the transverse magnetic field and in the isotropic XY$XY$ model for the complex fugacity plane of the quantum coherence. A characteristic function to represent the probe spin coherence for the isotropic XY$XY$ model, and study on Lee‐Yang zeros, quantum coherence, and quantum Fisher information at the complex fugacity plane is presented. The relationship between quantum Fisher information and quantum coherence in decoherence channels is demonstrated and it is illustrated that information cannot be acquired at high temperatures. Meanwhile, the ground‐state energy on the complex plane for the anisotropic XY$XY$ model is studied and the free energy cumulants with the partition function of the anisotropic XY$XY$ model for parity space is calculated.

In this paper, we present a method for measuring arbitrary-order correlation functions of the light field using a two-level atomic system. Theoretically, light field information should be mapped onto the atomic system after the light interacts with the atom. Therefore, we can measure the atomic system and thus obtain information about the light field. We study two typical models, the p-photon Jaynes–Cummings model, and the p-photon Tavis–Cummings model. In both models, we find that the pth-order correlation function of an unknown light field can be obtained by measuring the instantaneous change of energy of the two-level atoms with the aid of a known reference light field. Moreover, we find that the interactions other than the dipole interactions between light and atoms have no effect on the measurement results.

In this paper, we investigate the effect of the Dicke quantum phase transition on the speed of evolution of the system dynamics. At the phase transition point, the symmetry associated with the system parity operator begins to break down. By comparing the magnitudes of the two types of quantum speed limit times, we find that the quantum speed limit time of the system is described by one of the quantum speed limit times, whether in the normal or superradiant phase. We find that, in the normal phase, the strength of the coupling between the optical field and the atoms has little effect on the dynamical evolution speed of the system. However, in the superradiant phase, a stronger atom–photon coupling strength can accelerate the system dynamics’ evolution. Finally, we investigate the effect of the entanglement of the initial state of the system on the speed of evolution of the system dynamics. We find that in the normal phase, the entanglement of the initial state of the system has almost no effect on the system dynamics’ evolution speed. However, in the superradiant phase, larger entanglement of the system can accelerate the evolution of the system dynamics. Furthermore, we verify the above conclusions by the actual evolution of the system.

In quantum systems, the measurement of operators and the measurement of the quantum states of the system are very challenging tasks. In this Letter, we propose a method to obtain the average value of one operator in a certain state by measuring the instantaneous change of the average value of another operator with the assistance of a known reference state. We refer to this measurement method as the instantaneous indirect measurement method. By studying the application of this method to some typical models, we find that this measurement can be applied to the measurement of an arbitrary state of a quantum system. Furthermore, for the system to be measured, we find that such measurement neither significantly affects the wave function of the system nor causes wave function collapse of the system. Also, our study shows that when two independent systems are coupled, the information mapping between them is done instantaneously. Finally, we discuss applying this measurement method to the measurement of quantum Fisher information, which quantizes the limited accuracy of estimating a parameter from a quantum state.

In this paper, we investigate the dynamical synchronization of atomic populations in two Bosonic Josephson junctions(BJJs). The two BJJs are placed in two optical cavities, respectively. When there is no coupling between the two optical cavities, the dynamical evolution of the two BJJs is independent, and they can be in macroscopic quantum self-trapping regime or Josephson oscillation regime by controlling the strength of the interatomic interactions, respectively. However, when there is a coupling between the two optical cavities, we can adjust an external driving field to a specific value so that the two BJJs are dynamically synchronized even though the parameters of the two subsystems are different. We also found that it is possible to control the transition of the BJJ from the Josephson oscillation regime to the macroscopic quantum self-trapping regime by controlling the strength of the external driving field.

We consider the probability distribution when the monotonic function F (X ) of the independent variable X takes the maximum or minimum expected value under the two constraints of a certain probability and a certain expected value of the independent variable X. We proposed an equal probability and equal expected value splitting method. With this method, we proved four inequalities, and two of them can be reduced to Jensen's inequalities. Subsequently, we found that after dividing the nonmonotone function H (X ) into multiple monotone intervals the problem of solving the maximum and minimum expected values of H (X ) can be transformed into the problem of solving the extreme value of a multiple-variable function. Finally, we apply the proved theory to solve two problems in quantum metrology. When studying the quantum parameter estimation in a Mach-Zehnder interferometer, for an equal total input photon number, we found an optimal path-symmetric entangled state that makes the quantum Fisher information of the outcome state take the maximum value, and we proved that the NOON state is the path-symmetric entangled state that makes the quantum Fisher information of the outcome state take the minimum value. Finally, when studying the quantum parameter estimation in the Landau-Zener-Jaynes-Cummings model, we found the optimal initial state of the cavity field that makes the final state of the system obtain the maximum quantum Fisher information.

Macroscopic quantum superposition is an important embodiment of the core of the quantum theory. The engineering of macroscopic quantum superposition states is the key to quantum communication and quantum computation. Thus, we present a theoretical proposal to engineer macroscopic quantum superposition (MQS) states of a Bose-Einstein condensate (BEC) via impurity atoms. We firstly propose a deterministic generation scheme of transient multi-component MQS states of the BEC via impurity catalysing. It is found that the structure of the generated transient multi-component MQS states can be manipulated by the impurity number parity. Then, we illustrate the influence of impurity number parity on MQS states through three aspects: generation of approximately orthogonal continuous-variable cat states, manipulation of non-classicality in phase space, and switching of non-classical degree of BEC states. The influence of the BEC decoherence on the generation of MQS states is discussed by the fidelity between actually generated states and target states. Finally, the results show that the high-fidelity multi-component MQS states of the BEC can be fast generated by increasing the coherent interaction strength between impurities and the BEC in an open system.