We theoretically study the transmission spectrum of the cavity field in a double-cavity optomechanical system with cross-Kerr(CK) effect. The system consists of two tunneling coupling optomechanical cavities with a me...We theoretically study the transmission spectrum of the cavity field in a double-cavity optomechanical system with cross-Kerr(CK) effect. The system consists of two tunneling coupling optomechanical cavities with a mechanical resonator as a coupling interface. By doping CK medium into the mechanical resonator, CK couplings between the cavity fields and the mechanical resonator are introduced. We investigate the effects of CK coupling strength on the transmission spectrum of the cavity field, including the transmission rate, nonreciprocity and four-wave mixing(FWM). We find that the transmission spectrum of the probe field can show two obvious transparent windows, which can be widened by increasing the CK coupling strength. For the transmission between the two cavity fields, the perfect nonreciprocity and reciprocity are present and modulated by CK coupling and phase difference between two effective optomechanical couplings. In addition, the effects of the optomechanical and CK couplings on FWM show that the single peak of FWM is split into three symmetrical peaks due to the introduction of the CK effect.展开更多
Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit ＇X＇ state. We formulate two binary equations for the relative...Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit ＇X＇ state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ＇X＇ state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.展开更多
We present a scheme of reversible waveform conversion between microwave and optical fields in the hybrid optoelectromechanical system. As an intermediate interface, nanomechanical resonator optomechanically couples bo...We present a scheme of reversible waveform conversion between microwave and optical fields in the hybrid optoelectromechanical system. As an intermediate interface, nanomechanical resonator optomechanically couples both optomechanical cavities in the optical and microwave frequency domains. We find the double-optomechanically induced transparency and achieve coherent signal waveform bi-directional transfer between microwave and optical fields based on quantum interference. In addition, we give an analytical expression of one-to-one correspondence between the microwave field and the optical output field, which intuitively shows the reversible waveform conversion relationship. In particular,by numerical simulations and approximate expression, we demonstrate the conversion effects of the three waveforms and discuss the bi-directional conversion efficiency and the bandwidth. such a hybrid opto-and electro-mechanical device has significant potential functions for electro-optic modulation and waveform conversion of quantum microwave-optical field in optical communications and further quantum networks.展开更多
The wave-particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theo- retically in a Mach-Zehnder interferometer. The famous duality relation D2 ＋ V2 〈 1 is always vali...The wave-particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theo- retically in a Mach-Zehnder interferometer. The famous duality relation D2 ＋ V2 〈 1 is always valid in this situation, where D is the distinguishability and V is the visibility. However, the sum of the particle information and the wave information, D2 V2, can be smaller than one for the input of a pure state if this initial pure state includes the internal degree of freedom of the particle, while the quantity D2~ V2 is always equal to one when the internal degree of freedom of the particle is excluded.展开更多
Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it,we could use the tool of instantaneous angular velocity for pure states to study the qu...Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it,we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit(QSL)of a mixed state.We derive a lower bound for the evolution time of a mixed state to a target state in a unitary system,which automatically reduces to the quantum speed limit induced by the Fubini–Study metric for pure states.The computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state,where we have to make a singular value decomposition(SVD)on the inner product between the two eigenvector matrices of the initial and target states.By combing these results,a lower bound for the evolution time of a general mixed state is presented.In order to compare the tightness among the lower bound proposed here and lower bounds reported in the references,two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically,respectively.All conclusions derived in this work are independent of the eigenvalues of the mixed state,which is in accord with the evolution properties of a quantum unitary system.展开更多
An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young＇s double-slit experiment, two density filters rotating at different freque...An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young＇s double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters.展开更多
In this Letter, a new fractional entangling transformation （FRET） is proposed, which is generated in the entangled state representation by a unitary operator exp{iθ（ab^＋ ＋ a^＋ b）} where a（b） is the Bosonic a...In this Letter, a new fractional entangling transformation （FRET） is proposed, which is generated in the entangled state representation by a unitary operator exp{iθ（ab^＋ ＋ a^＋ b）} where a（b） is the Bosonic annihilate operator. The operator is actually an entangled one in quantum optics and differs evidently from the separable operator, exp（iθ（a^＋a＋ b^＋ b）}, of complex fractional Fourier transformation. The additivity property is proved by employing the entangled state representation and quantum mechanical version of the FRET. As an application, the FrET of a two-mode number state is derived directly by using the quantum version of the FRET, which is related to Hermite polynomials.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61605225, 61772295, 12174247, and 11664018)the Natural Science Foundation of Shanghai (Grant No. 16ZR1448400)。
文摘We theoretically study the transmission spectrum of the cavity field in a double-cavity optomechanical system with cross-Kerr(CK) effect. The system consists of two tunneling coupling optomechanical cavities with a mechanical resonator as a coupling interface. By doping CK medium into the mechanical resonator, CK couplings between the cavity fields and the mechanical resonator are introduced. We investigate the effects of CK coupling strength on the transmission spectrum of the cavity field, including the transmission rate, nonreciprocity and four-wave mixing(FWM). We find that the transmission spectrum of the probe field can show two obvious transparent windows, which can be widened by increasing the CK coupling strength. For the transmission between the two cavity fields, the perfect nonreciprocity and reciprocity are present and modulated by CK coupling and phase difference between two effective optomechanical couplings. In addition, the effects of the optomechanical and CK couplings on FWM show that the single peak of FWM is split into three symmetrical peaks due to the introduction of the CK effect.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10804042)supported by the Scientific Research Foundation of the Education Department of Jiangxi Province,China (Project No. GJJ09440)
文摘Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit ＇X＇ state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ＇X＇ state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61605225, 11774089, 12034007,11664018, and 61772295)the Natural Science Foundation of Shanghai,China (Grant No. 16ZR1448400)。
文摘We present a scheme of reversible waveform conversion between microwave and optical fields in the hybrid optoelectromechanical system. As an intermediate interface, nanomechanical resonator optomechanically couples both optomechanical cavities in the optical and microwave frequency domains. We find the double-optomechanically induced transparency and achieve coherent signal waveform bi-directional transfer between microwave and optical fields based on quantum interference. In addition, we give an analytical expression of one-to-one correspondence between the microwave field and the optical output field, which intuitively shows the reversible waveform conversion relationship. In particular,by numerical simulations and approximate expression, we demonstrate the conversion effects of the three waveforms and discuss the bi-directional conversion efficiency and the bandwidth. such a hybrid opto-and electro-mechanical device has significant potential functions for electro-optic modulation and waveform conversion of quantum microwave-optical field in optical communications and further quantum networks.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB921603)the National Natural Science Foundation of China(Grant Nos.11125418 and 11364022)
文摘The wave-particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theo- retically in a Mach-Zehnder interferometer. The famous duality relation D2 ＋ V2 〈 1 is always valid in this situation, where D is the distinguishability and V is the visibility. However, the sum of the particle information and the wave information, D2 V2, can be smaller than one for the input of a pure state if this initial pure state includes the internal degree of freedom of the particle, while the quantity D2~ V2 is always equal to one when the internal degree of freedom of the particle is excluded.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11664018,12174247,and U2031145)。
文摘Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it,we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit(QSL)of a mixed state.We derive a lower bound for the evolution time of a mixed state to a target state in a unitary system,which automatically reduces to the quantum speed limit induced by the Fubini–Study metric for pure states.The computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state,where we have to make a singular value decomposition(SVD)on the inner product between the two eigenvector matrices of the initial and target states.By combing these results,a lower bound for the evolution time of a general mixed state is presented.In order to compare the tightness among the lower bound proposed here and lower bounds reported in the references,two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically,respectively.All conclusions derived in this work are independent of the eigenvalues of the mixed state,which is in accord with the evolution properties of a quantum unitary system.
基金Supported by the National Science Foundation(INSPIRE CREATIV)under Grant No PHY-1241032the Robert A.Welch Foundation under Grant No A-1261the National Natural Science Foundation of China under Grant No 11664018
文摘An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young＇s double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters.
基金supported by the National Natural Science Foundation of China(Grant Nos.11264018 and11174118)the Natural Science Foundation of Jiangxi Province of China(Grant No.20132BAB212006)+1 种基金the Research Foundation of the Education Department of Jiangxi Province of China(No.GJJ14274)the Degree and Postgraduate Education Teaching Reform Project of Jiangxi Province(No.JXYJG-2013-027)
文摘In this Letter, a new fractional entangling transformation （FRET） is proposed, which is generated in the entangled state representation by a unitary operator exp{iθ（ab^＋ ＋ a^＋ b）} where a（b） is the Bosonic annihilate operator. The operator is actually an entangled one in quantum optics and differs evidently from the separable operator, exp（iθ（a^＋a＋ b^＋ b）}, of complex fractional Fourier transformation. The additivity property is proved by employing the entangled state representation and quantum mechanical version of the FRET. As an application, the FrET of a two-mode number state is derived directly by using the quantum version of the FRET, which is related to Hermite polynomials.
