By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordluate coupling terms, and derive the density matrix of the system. The results show that the ground st...By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordluate coupling terms, and derive the density matrix of the system. The results show that the ground state of the system is a rotated two single-mode squeezed state.展开更多
The characteristic time τD for decoherence process of a quantum nonlinear oscillator system under a nonzero temperature thermal bath is studied by expanding the linear entropy. By numerical analysis, it is shown that...The characteristic time τD for decoherence process of a quantum nonlinear oscillator system under a nonzero temperature thermal bath is studied by expanding the linear entropy. By numerical analysis, it is shown that at a non-zero temperature, the quantum coherence decays much faster than at zero temperature. Moreover, the non-zero temperature thermal bath will bring a crucial suppression to the quantum effects of the observables, which causes these quantum effects to become unable to persist up to the Ehrenfest time but is insufticient to destroy the quantum-classical transition.展开更多
The notes here presented are of the modifications introduced in the application of WKB method.Theproblems of two-and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulationof quant...The notes here presented are of the modifications introduced in the application of WKB method.Theproblems of two-and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulationof quantization rule respectively.It is found that the energy spectrum of the radial harmonic oscillator,which isreproduced exactly by the standard WKB method with the Langer modification,is also reproduced exactly without theLanger modification via the new quantization rule approach.An alternative way to obtain the non-integral Maslov indexfor three-dimensional harmonic oscillator is proposed.展开更多
We derive the analytical expression of microcavity-enhanced factor for third harmonic generation in terms of detunings, linewidths, and the Purcell factors of the relevant microcavity modes. It is suitable for microca...We derive the analytical expression of microcavity-enhanced factor for third harmonic generation in terms of detunings, linewidths, and the Purcell factors of the relevant microcavity modes. It is suitable for microcavities with any dimensions and arbitrary geometric shapes.展开更多
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt d...We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.展开更多
The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed ...The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.展开更多
In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product o...In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.展开更多
Deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the ease of both coordinates and momenta being no...Deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the ease of both coordinates and momenta being noneommutative. In order to simplify solutions of the relevant .-genvalue equation, we introduce a new kind of Seiberg Witten-like map to change the variables of the noncommutative phase space into ones of a commutative phase space, and demonstrate its role via an example of two-dimensional oscillator with both kinetic and elastic couplings in the noneommutative phase space.展开更多
Schrodinger＇s thought experiment to prepare a cat in a superposition of both alive and dead states reveals profound consequences of quantum mechanics and has attracted enormous interests. Here we propose a straight- ...Schrodinger＇s thought experiment to prepare a cat in a superposition of both alive and dead states reveals profound consequences of quantum mechanics and has attracted enormous interests. Here we propose a straight- forward method to create quantum superposition states of a living microorganism by putting a small cryopreserved bacterium on top of an electromechanical oscillator. Our proposal is based on recent developments that the center- of-mass oscillation of a 15-pro-diameter aluminum mem- brane has been cooled to its quantum ground state （Teufel et al. in Nature 475：359, 2011）, and entangled with a microwave field （Palomaki et al. in Science 342：710, 2013）. A microorganism with a mass much smaller than the mass of the electromechanical membrane will not signifi- cantly affect the quality factor of the membrane and can be cooled to the quantum ground state together with themembrane. Quantum superposition and teleportation of its center-of-mass motion state can be realized with the help of superconducting microwave circuits. More importantly, the internal states of a microorganism, such as the electron spin of a glycine radical, can be entangled with its center-of- mass motion and teleported to a remote microorganism. Our proposal can be realized with state-of-the-art tech- nologies. The proposed setup is a quantum-limited mag- netic resonance force microscope. Since internal states of an organism contain information, our proposal also pro- vides a scheme for teleporting information or memories between two remote organisms.展开更多
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinea...In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.展开更多
The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar p...The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.展开更多
文摘By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordluate coupling terms, and derive the density matrix of the system. The results show that the ground state of the system is a rotated two single-mode squeezed state.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 60472017 and 10347103, and the Natural Science Foundation of Liaoning Province of China under Grant No. 20031073
文摘The characteristic time τD for decoherence process of a quantum nonlinear oscillator system under a nonzero temperature thermal bath is studied by expanding the linear entropy. By numerical analysis, it is shown that at a non-zero temperature, the quantum coherence decays much faster than at zero temperature. Moreover, the non-zero temperature thermal bath will bring a crucial suppression to the quantum effects of the observables, which causes these quantum effects to become unable to persist up to the Ehrenfest time but is insufticient to destroy the quantum-classical transition.
基金National Natural Science Foundation of China under Grant No.10747130the Foundation of East China University of Science and Technology
文摘The notes here presented are of the modifications introduced in the application of WKB method.Theproblems of two-and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulationof quantization rule respectively.It is found that the energy spectrum of the radial harmonic oscillator,which isreproduced exactly by the standard WKB method with the Langer modification,is also reproduced exactly without theLanger modification via the new quantization rule approach.An alternative way to obtain the non-integral Maslov indexfor three-dimensional harmonic oscillator is proposed.
文摘We derive the analytical expression of microcavity-enhanced factor for third harmonic generation in terms of detunings, linewidths, and the Purcell factors of the relevant microcavity modes. It is suitable for microcavities with any dimensions and arbitrary geometric shapes.
文摘We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.
基金The project supported by the Research Fund for the Doctorial Program of Higher Education of China under Grant No.20010284036+2 种基金National Natural Science Foundation of China under Grant No.10125521the 973 State Basic Key Research and Development of China under Grant No.G20000077400
文摘The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102,10871135,11031005,11075014
文摘In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.
基金supported by National Natural Science Foundation of China under Grant No.10675106
文摘Deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the ease of both coordinates and momenta being noneommutative. In order to simplify solutions of the relevant .-genvalue equation, we introduce a new kind of Seiberg Witten-like map to change the variables of the noncommutative phase space into ones of a commutative phase space, and demonstrate its role via an example of two-dimensional oscillator with both kinetic and elastic couplings in the noneommutative phase space.
基金the support from Purdue University and helpful discussions with G.Csathy,F.Robicheaux, C.Greene,and V.ShalaevZQY is funded by the National Basic Research Program of China (2011CBA00300 and 2011CBA00302)the National Natural Science Foundation of China (11105136, 11474177 and 61435007)
文摘Schrodinger＇s thought experiment to prepare a cat in a superposition of both alive and dead states reveals profound consequences of quantum mechanics and has attracted enormous interests. Here we propose a straight- forward method to create quantum superposition states of a living microorganism by putting a small cryopreserved bacterium on top of an electromechanical oscillator. Our proposal is based on recent developments that the center- of-mass oscillation of a 15-pro-diameter aluminum mem- brane has been cooled to its quantum ground state （Teufel et al. in Nature 475：359, 2011）, and entangled with a microwave field （Palomaki et al. in Science 342：710, 2013）. A microorganism with a mass much smaller than the mass of the electromechanical membrane will not signifi- cantly affect the quality factor of the membrane and can be cooled to the quantum ground state together with themembrane. Quantum superposition and teleportation of its center-of-mass motion state can be realized with the help of superconducting microwave circuits. More importantly, the internal states of a microorganism, such as the electron spin of a glycine radical, can be entangled with its center-of- mass motion and teleported to a remote microorganism. Our proposal can be realized with state-of-the-art tech- nologies. The proposed setup is a quantum-limited mag- netic resonance force microscope. Since internal states of an organism contain information, our proposal also pro- vides a scheme for teleporting information or memories between two remote organisms.
基金Supported in part by National Natural Science Foundation of China under Grant No. 11171164
文摘In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11105097,10975075,and 11175089the National Basic Research Program of China under Grant No.2012CB921900the National Research Foundation and Ministry of Education,Singapore under Grant No.WBS:R-710-000-008-271
文摘The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.
