For atoms in external electric fields,the hyperpolarizabilities are the coefficients describing the nonlinear interactions contributing to the induced energies at the fourth power of the applied electric fields.Accura...For atoms in external electric fields,the hyperpolarizabilities are the coefficients describing the nonlinear interactions contributing to the induced energies at the fourth power of the applied electric fields.Accurate evaluations of these coefficients for various systems are crucial for improving precision in advanced atom-based optical lattice clocks and for estimating field-induced effects in atoms for quantum information applications.However,there is a notable scarcity of research on atomic hyperpolarizabilities,especially in the relativistic realm.Our work addresses this gap by establishing a novel set of alternative formulas for the hyperpolarizability based on the fourth-order perturbation theory.These formulas offer a more reasonable regrouping of scalar and tensor components compared to previous formulas,thereby enhancing their correctness and applicability.To validate our formulas,we perform the calculations for the ground and low-lying excited pure states of few-electron atoms H,Li,and Be^(+).The highly accurate results obtained for the H atom could serve as benchmarks for further development of other theoretical methods.展开更多
We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because o...We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12174402 and 12393821)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant Nos.XDB0920100 and XDB0920101)+2 种基金the Nature Science Foundation of Hubei Province(Grant Nos.2019CFA058 and 2022CFA013)supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)supported in part by NSF grant PHY-2116679.All the calculations are finished on the APM-Theoretical Computing Cluster(APMTCC)。
文摘For atoms in external electric fields,the hyperpolarizabilities are the coefficients describing the nonlinear interactions contributing to the induced energies at the fourth power of the applied electric fields.Accurate evaluations of these coefficients for various systems are crucial for improving precision in advanced atom-based optical lattice clocks and for estimating field-induced effects in atoms for quantum information applications.However,there is a notable scarcity of research on atomic hyperpolarizabilities,especially in the relativistic realm.Our work addresses this gap by establishing a novel set of alternative formulas for the hyperpolarizability based on the fourth-order perturbation theory.These formulas offer a more reasonable regrouping of scalar and tensor components compared to previous formulas,thereby enhancing their correctness and applicability.To validate our formulas,we perform the calculations for the ground and low-lying excited pure states of few-electron atoms H,Li,and Be^(+).The highly accurate results obtained for the H atom could serve as benchmarks for further development of other theoretical methods.
文摘We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.
