After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in gene...After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in general form. Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities. The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics. A large set of these states do not belong to sub- or to super-Poissonian states but are also not Poissonian states. We illustrate in examples their photon distributions. This shows that the notions of sub- and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment of squeezing and the disentanglement of their operators. Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.展开更多
Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-fi...Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose-Einstein condensation（BEC） occurs if and only if the U（1） symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schroedinger eigenvalue equation and using the self-consistent condition.展开更多
Starting from Wigner’s definition of the function named now after him we systematically develop different representation of this quasiprobability with emphasis on symmetric representations concerning the canonical va...Starting from Wigner’s definition of the function named now after him we systematically develop different representation of this quasiprobability with emphasis on symmetric representations concerning the canonical variables (q,p) of phase space and using the known relation to the parity operator. One of the representations is by means of the Laguerre 2D polynomials which is particularly effective in quantum optics. For the coherent states we show that their Fourier transforms are again coherent states. We calculate the Wigner quasiprobability to the eigenstates of a particle in a square well with infinitely high impenetrable walls which is not smooth in the spatial coordinate and vanishes outside the wall boundaries. It is not well suited for the calculation of expectation values. A great place takes on the calculation of the Wigner quasiprobability for coherent phase states in quantum optics which is essentially new. We show that an unorthodox entire function plays there a role in most formulae which makes all calculations difficult. The Wigner quasiprobability for coherent phase states is calculated and graphically represented but due to the involved unorthodox function it may be considered only as illustration and is not suited for the calculation of expectation values. By another approach via the number representation of the states and using the recently developed summation formula by means of Generalized Eulerian numbers it becomes possible to calculate in approximations with good convergence the basic expectation values, in particular, the basic uncertainties which are additionally represented in graphics. Both considered examples, the square well and the coherent phase states, belong to systems with SU (1,1) symmetry with the same index K=1/2 of unitary irreducible representations.展开更多
We find tight upper bound on the coherence of a superposition of two states in terms of the coherence of the two states constituting the superposition with l1-norm of coherence. Our upper bound is tighter than the one...We find tight upper bound on the coherence of a superposition of two states in terms of the coherence of the two states constituting the superposition with l1-norm of coherence. Our upper bound is tighter than the one presented by Liu, et al. [Quantum Inf. Process. 15(2016) 4209.] We also generalize the results to the case that the superposition is constituted with more than two states in high dimension, and we give the corresponding upper bounds.展开更多
Using unitary transformations, this paper obtains the eigenvalues and the common eigenvector of Hamiltonian and a new-defined generalized angular momentum （Lz） for an electron confined in quantum dots under a unifor...Using unitary transformations, this paper obtains the eigenvalues and the common eigenvector of Hamiltonian and a new-defined generalized angular momentum （Lz） for an electron confined in quantum dots under a uniform magnetic field （UMF） and a static electric field （SEF）. It finds that the eigenvalue of Lz just stands for the expectation value of a usual angular momentum lz in the eigen-state. It first obtains the matrix density for this system via directly calculating a transfer matrix element of operator exp（-βH） in some representations with the technique of integral within an ordered products （IWOP） of operators, rather than via solving a Bloch equation. Because the quadratic homogeneity of potential energy is broken due to the existence of SEF, the virial theorem in statistical physics is not satisfactory for this system, which is confirmed through the calculation of thermal averages of physical quantities.展开更多
An exact quantum treatment reveals that signal and idler photon number operators are not well-behaved dynamical operators for studying photon statistics in parametric amplification/down-conversion processes. Contrary ...An exact quantum treatment reveals that signal and idler photon number operators are not well-behaved dynamical operators for studying photon statistics in parametric amplification/down-conversion processes. Contrary to expectations, the mean signal-idler photon number difference varies with time, while the corresponding signal-idler photon number cross-correlation function is complex and experiences an interference phenomenon driven by the interaction parameters. The intensity operators and related polarization operators of the polarized signal-idler photon pair in positive and negative helicity states are identified as the appropriate operators specifying a conservation law and the dynamical symmetry group (SU(1, 1)) of the parametric amplification process. The conservation of the mean positive and negative helicity photon intensity difference and the purely real positive-negative helicity intensity cross-correlation function correctly account for the simultaneous production of polarized signal and idler photons in positive and negative helicity states.展开更多
We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels： amplitude damping channel, phase damping channel, depolarizing channel and bit flit ...We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels： amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.展开更多
In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l1-norm, the R′enyi α-relative entropy and the Tsallis α-relative ...In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l1-norm, the R′enyi α-relative entropy and the Tsallis α-relative entropy of coherence, respectively. The amplitude damping channel, phase damping channel, depolarizing channel, and flip channels are analytically calculated. It shows that the decohering power of the amplitude damping channel on the x, y, and z basis is equal to each other. The same phenomenon can be seen for the phase damping channel and the flip channels.The cohering power for the phase damping channel and the flip channels on the x, y basis also equals to that on the z basis. However, the cohering and decohering power of the depolarizing channel is independent to the reference basises.And the cohering power of the amplitude damping channel on the x, y basis is different to that on the z basis.展开更多
文摘After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in general form. Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities. The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics. A large set of these states do not belong to sub- or to super-Poissonian states but are also not Poissonian states. We illustrate in examples their photon distributions. This shows that the notions of sub- and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment of squeezing and the disentanglement of their operators. Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.
基金0ne of author （Huang H B） was partially supported by the Natural Science Foundation of Jiangsu province, China （Grant No BK2005062）.Acknowledgement We thank Professor Tian G S for discussion
文摘Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose-Einstein condensation（BEC） occurs if and only if the U（1） symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schroedinger eigenvalue equation and using the self-consistent condition.
文摘Starting from Wigner’s definition of the function named now after him we systematically develop different representation of this quasiprobability with emphasis on symmetric representations concerning the canonical variables (q,p) of phase space and using the known relation to the parity operator. One of the representations is by means of the Laguerre 2D polynomials which is particularly effective in quantum optics. For the coherent states we show that their Fourier transforms are again coherent states. We calculate the Wigner quasiprobability to the eigenstates of a particle in a square well with infinitely high impenetrable walls which is not smooth in the spatial coordinate and vanishes outside the wall boundaries. It is not well suited for the calculation of expectation values. A great place takes on the calculation of the Wigner quasiprobability for coherent phase states in quantum optics which is essentially new. We show that an unorthodox entire function plays there a role in most formulae which makes all calculations difficult. The Wigner quasiprobability for coherent phase states is calculated and graphically represented but due to the involved unorthodox function it may be considered only as illustration and is not suited for the calculation of expectation values. By another approach via the number representation of the states and using the recently developed summation formula by means of Generalized Eulerian numbers it becomes possible to calculate in approximations with good convergence the basic expectation values, in particular, the basic uncertainties which are additionally represented in graphics. Both considered examples, the square well and the coherent phase states, belong to systems with SU (1,1) symmetry with the same index K=1/2 of unitary irreducible representations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61671280,11771009,and 11847101the Natural Science Basic Research Plan in Shaanxi Province of China under Grant No.2017KJXX-92+1 种基金the Fundamental Research Funds for the Central Universities under Grant No.GK201902007the Funded Projects for the Academic Leaders and Academic Backbones,Shaanxi Normal University under Grant No.16QNGG013
文摘We find tight upper bound on the coherence of a superposition of two states in terms of the coherence of the two states constituting the superposition with l1-norm of coherence. Our upper bound is tighter than the one presented by Liu, et al. [Quantum Inf. Process. 15(2016) 4209.] We also generalize the results to the case that the superposition is constituted with more than two states in high dimension, and we give the corresponding upper bounds.
文摘Using unitary transformations, this paper obtains the eigenvalues and the common eigenvector of Hamiltonian and a new-defined generalized angular momentum （Lz） for an electron confined in quantum dots under a uniform magnetic field （UMF） and a static electric field （SEF）. It finds that the eigenvalue of Lz just stands for the expectation value of a usual angular momentum lz in the eigen-state. It first obtains the matrix density for this system via directly calculating a transfer matrix element of operator exp（-βH） in some representations with the technique of integral within an ordered products （IWOP） of operators, rather than via solving a Bloch equation. Because the quadratic homogeneity of potential energy is broken due to the existence of SEF, the virial theorem in statistical physics is not satisfactory for this system, which is confirmed through the calculation of thermal averages of physical quantities.
文摘An exact quantum treatment reveals that signal and idler photon number operators are not well-behaved dynamical operators for studying photon statistics in parametric amplification/down-conversion processes. Contrary to expectations, the mean signal-idler photon number difference varies with time, while the corresponding signal-idler photon number cross-correlation function is complex and experiences an interference phenomenon driven by the interaction parameters. The intensity operators and related polarization operators of the polarized signal-idler photon pair in positive and negative helicity states are identified as the appropriate operators specifying a conservation law and the dynamical symmetry group (SU(1, 1)) of the parametric amplification process. The conservation of the mean positive and negative helicity photon intensity difference and the purely real positive-negative helicity intensity cross-correlation function correctly account for the simultaneous production of polarized signal and idler photons in positive and negative helicity states.
文摘We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels： amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11271237,11671244the Higher School Doctoral Subject Foundation of Ministry of Education of China under Grant No.20130202110001the Central Universities under Grants Nos.2016TS060 and 2016CBY003
文摘In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l1-norm, the R′enyi α-relative entropy and the Tsallis α-relative entropy of coherence, respectively. The amplitude damping channel, phase damping channel, depolarizing channel, and flip channels are analytically calculated. It shows that the decohering power of the amplitude damping channel on the x, y, and z basis is equal to each other. The same phenomenon can be seen for the phase damping channel and the flip channels.The cohering power for the phase damping channel and the flip channels on the x, y basis also equals to that on the z basis. However, the cohering and decohering power of the depolarizing channel is independent to the reference basises.And the cohering power of the amplitude damping channel on the x, y basis is different to that on the z basis.
