In quantum interferometry, it is vital to control and utilize nonlinear interactions for the achievement of high-precision measurements. Due to their long coherence time and high controllability, ultracold atoms inclu...In quantum interferometry, it is vital to control and utilize nonlinear interactions for the achievement of high-precision measurements. Due to their long coherence time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for quantum interferometry. Here, we review recent progress in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on nonlinear phenomena induced by atom-atom interactions, and how to control and utilize these nonlinear phenomena. With a mean-field description, due to atom-atom interactions, matter-wave solitons appear in the interference patterns, and macroscopic quantum self-trapping exists in Bose-Josephson junctions. With a many-body description, atom-atom in- teractions can generate non-classical entanglement, which can be utilized to achieve high-precision measurements beyond the standard quantum limit.展开更多
We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitae...We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitaevskii equations are developed to study the nonlinear dynamics of BoseEinstein condensates. Analytically, we present the integrable conditions for the Gross Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose Einstein condensates.展开更多
We use the methodology of A. D. Linde to model the probability of obtaining a cosmological constant which is in turn affected by scaling arguments for a Bose Einstein gravitational condensate as given by Chavanis, in ...We use the methodology of A. D. Linde to model the probability of obtaining a cosmological constant which is in turn affected by scaling arguments for a Bose Einstein gravitational condensate as given by Chavanis, in 2015. The net result, is that the scaling argument so provided allows for a gravitational constant commensurate with the size of the Universe, using arguments which appear to be simple but which give, if one has the conditions for modeling the Universe as a “black hole” virtually 100 % chance for the cosmological constant arising.展开更多
The nonlinear lattice - a new and nonlinear class of periodic potentials - was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional （2D） solitons ag...The nonlinear lattice - a new and nonlinear class of periodic potentials - was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional （2D） solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting - the cubic and quintic model - by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully ＂nonlinear quasi-crystal＂. A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov-Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode -- the fundamental and vortex solitons -- are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting （cubic-quintic model） is in the framework of the Gross-Pitaevskii equation or nonlinear Schr6dinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.展开更多
We review our recent experimental realization and investigation of a spin orbit （SO） coupled Bose Einstein condensate （BEC） and quantum degenerate Fermi gas. By using two counter-propagathlg Ranlan lasers and cont...We review our recent experimental realization and investigation of a spin orbit （SO） coupled Bose Einstein condensate （BEC） and quantum degenerate Fermi gas. By using two counter-propagathlg Ranlan lasers and controlling the different frequency of two R,aman lasers to engineer the atom light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We, observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as halhnarks of SO coupling in a Fermi gas. To clearly reveal the, property of SO coupling Fermi gas, we also study the momentmn-resolved radio-frequency spectroscopy which characterizes the energy momentum dispersion and spin composition of the quantum states. We observe the change of errmion surfaces in different helieity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracoht Fermi gas.展开更多
Taking into account both gain/loss and time-dependent atomic scattering length, this paper analytically derives an exact bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive par...Taking into account both gain/loss and time-dependent atomic scattering length, this paper analytically derives an exact bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive parabolic potential. Due to the balance of the scattering length and gain/loss, the bright solitary wave is shown to have constant amplitude. Especially, it is found that the bright solitary wave is accelerated by expulsive force, whose velocity can be modulated by changing the axial and transverse angular frequencies. The results are in good agreement with the experimental observations by Khaykovich et al （2002 Science 296 1290）.展开更多
This paper reports an experiment of creating Bose-Einstein condensate （BEC） on an atom chip. The chip-based Z-wire current with a homogeneous bias magnetic field creates a tight magnetic trap, which allows for a fas...This paper reports an experiment of creating Bose-Einstein condensate （BEC） on an atom chip. The chip-based Z-wire current with a homogeneous bias magnetic field creates a tight magnetic trap, which allows for a fast production of BEC. After a 4.17-s forced radio frequency evaporative cooling, a condensate with about 3000 atoms appears. The transition temperature is about 300 nK. This compact system is quite robust, allowing for versatile extensions and further studying of BEC.展开更多
The tunneling effect of Bose-Einstein condensate （BEC） in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunnel...The tunneling effect of Bose-Einstein condensate （BEC） in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.展开更多
We propose that the exotic meson tetraquark u<sub>d</sub>~</sup>dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition ...We propose that the exotic meson tetraquark u<sub>d</sub>~</sup>dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, d<sub>d</sub>~</sup> and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The u<sub>d</sub>~</sup>dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũd<sub>d</sub>~</sup> for the electrons and u<sub>d</sub>~</sup>d<sub>d</sub>~</sup> for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state u<sub>d</sub>~</sup>dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.展开更多
文摘In quantum interferometry, it is vital to control and utilize nonlinear interactions for the achievement of high-precision measurements. Due to their long coherence time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for quantum interferometry. Here, we review recent progress in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on nonlinear phenomena induced by atom-atom interactions, and how to control and utilize these nonlinear phenomena. With a mean-field description, due to atom-atom interactions, matter-wave solitons appear in the interference patterns, and macroscopic quantum self-trapping exists in Bose-Josephson junctions. With a many-body description, atom-atom in- teractions can generate non-classical entanglement, which can be utilized to achieve high-precision measurements beyond the standard quantum limit.
基金Acknowledgements We would like to express our sincere thanks to Z. X. Liangang L. Wu for their original works and figures. This work was supported by the NatiorLM Natural Science Foundation of China （Grant Nos. 10874235, 10934010, and 60978019）, the National Key Basic Research Special Foundation of China （Grant Nos. 2009CB930701, 2010CB922904, and 2011CB921500）.
文摘We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitaevskii equations are developed to study the nonlinear dynamics of BoseEinstein condensates. Analytically, we present the integrable conditions for the Gross Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose Einstein condensates.
文摘We use the methodology of A. D. Linde to model the probability of obtaining a cosmological constant which is in turn affected by scaling arguments for a Bose Einstein gravitational condensate as given by Chavanis, in 2015. The net result, is that the scaling argument so provided allows for a gravitational constant commensurate with the size of the Universe, using arguments which appear to be simple but which give, if one has the conditions for modeling the Universe as a “black hole” virtually 100 % chance for the cosmological constant arising.
文摘The nonlinear lattice - a new and nonlinear class of periodic potentials - was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional （2D） solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting - the cubic and quintic model - by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully ＂nonlinear quasi-crystal＂. A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov-Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode -- the fundamental and vortex solitons -- are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting （cubic-quintic model） is in the framework of the Gross-Pitaevskii equation or nonlinear Schr6dinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.
基金Acknowledgements This work was supported by the National Basic Research Program of China （Grant No. 2011CB921601）, the National Natural Science Foundation of China （NSFC, Grant No. 11234008）, NSFC Project for Excellent Research Team （Grant No. 61121064）, and Doctoral Program Foundation of the Ministry of Education China （Grant No. 20111401130001）.
文摘We review our recent experimental realization and investigation of a spin orbit （SO） coupled Bose Einstein condensate （BEC） and quantum degenerate Fermi gas. By using two counter-propagathlg Ranlan lasers and controlling the different frequency of two R,aman lasers to engineer the atom light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We, observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as halhnarks of SO coupling in a Fermi gas. To clearly reveal the, property of SO coupling Fermi gas, we also study the momentmn-resolved radio-frequency spectroscopy which characterizes the energy momentum dispersion and spin composition of the quantum states. We observe the change of errmion surfaces in different helieity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracoht Fermi gas.
基金supported by the National Natural Science Foundation of China(Grant Nos 10674070 and 10674113)the Program for New Century Excellent Talents in University of China(NCET-06-0707)+2 种基金the Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No 200726)the Natural Science Foundation of Hunan Province of China(Grant No 006JJ50006)the Program for Changjiang Scholars and Innovative Team in University of China(Grant No IRT0534)
文摘Taking into account both gain/loss and time-dependent atomic scattering length, this paper analytically derives an exact bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive parabolic potential. Due to the balance of the scattering length and gain/loss, the bright solitary wave is shown to have constant amplitude. Especially, it is found that the bright solitary wave is accelerated by expulsive force, whose velocity can be modulated by changing the axial and transverse angular frequencies. The results are in good agreement with the experimental observations by Khaykovich et al （2002 Science 296 1290）.
基金Project supported by the National Basic Research Program of China (Grant No 2006CB921202)the Science Foundation of the Ministry of Science and Technology of China (Grant No 2006CB921A03)
文摘This paper reports an experiment of creating Bose-Einstein condensate （BEC） on an atom chip. The chip-based Z-wire current with a homogeneous bias magnetic field creates a tight magnetic trap, which allows for a fast production of BEC. After a 4.17-s forced radio frequency evaporative cooling, a condensate with about 3000 atoms appears. The transition temperature is about 300 nK. This compact system is quite robust, allowing for versatile extensions and further studying of BEC.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10974068)
文摘The tunneling effect of Bose-Einstein condensate （BEC） in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.
文摘We propose that the exotic meson tetraquark u<sub>d</sub>~</sup>dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, d<sub>d</sub>~</sup> and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The u<sub>d</sub>~</sup>dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũd<sub>d</sub>~</sup> for the electrons and u<sub>d</sub>~</sup>d<sub>d</sub>~</sup> for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state u<sub>d</sub>~</sup>dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.
