arXiv subjects

Yajiang Hao

Publications and source records attributed to Yajiang Hao.

At least 37 records · Page 2Linked to original sources

arXiv2012

Dissipation effect in the double-well Bose-Einstein Condensate

Dynamics of the double-well Bose-Einstein condensate subject to energy dissipation is studied by solving a reduced one-dimensional time-dependent Gross-Pitaevskii equation numerically. We first reproduce the phase space diagram of the system without dissipation systematically, and then calculate evolutionary trajectories of dissipated systems. It is clearly shown that the dissipation can drive the system to evolve gradually from the $π$-mode quantum macroscopic self-trapping state, a state with relatively higher energy, to the lowest energy stationary state in which particles distribute equally in the two wells. The average phase and phase distribution in each well are discussed as well. We show that the phase distribution varies slowly in each well but may exhibit abrupt changes near the barrier. This sudden change occurs at the minimum position in particle density profile. We also note that the average phase in each well varies much faster with time than the phase difference between two wells.

cond-mat.quant-gas↗

arXiv2012

Dynamical properties of hard-core anyons in one-dimensional optical lattices

We investigate the dynamical properties of anyons confined in one-dimensional optical lattice combined with a weak harmonic trap using the exact numerical method based on a generalized Jordan-Wigner transformation. The density profiles, momentum distribution, occupation distribution and occupations of the lowest natural orbital are obtained for different statistical parameters. The density profiles of anyons display the same behaviors irrespective of statistical parameter in the full evolving period. While the behaviors dependent on statistical property are shown in the momentum distributions and occupations of natural orbitals.

cond-mat.quant-gas↗

arXiv2012

Density-functional theory for 1D harmonically trapped Bose-Fermi mixture

We present a density-functional theory for the one dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the Local Density Approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for strong enough interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in the Bose density curves reflecting the strong correlation with Fermions. For infinite strong interaction, the ground state energy of the mixture and the total density are consistent with the scenario that all atoms in the mixture are fully fermionized.

cond-mat.quant-gas↗

arXiv2011

The lowest scattering state of one-dimensional Bose gas with attractive interactions

We investigate the lowest scattering state of one-dimensional Bose gas with attractive interactions trapped in a hard wall trap. By solving the Bethe ansatz equation numerically we determine the full energy spectrum and the exact wave function for different attractive interaction parameters. The resultant density distribution, momentum distribution, reduced one body density matrix and two body correlation show that the decreased attractive interaction induces rich density profiles and specific correlation properties in the weakly attractive Bose gas.

cond-mat.quant-gas↗

arXiv2011

Dynamics of Two-Component Bose-Einstein Condensates Coupled with Environment

We investigate the dynamics of an open Bose-Einstein condensate system consisting of two hyperfine states of the same atomic species which are coupled by tunable Raman laser. It is already suggested that the detuning between the laser frequency and transition frequency affect significantly on the dynamics of the pure condensate. Here we show that the detuning effect is suppressed by noise and dissipation caused by the environment. The increase of coherence and purity are also displayed for specific parameters. As a verification to the lowest-order approximation we derive the hierarchy of motion equations in the second-order approximation. It turns out that the former one can describe the dynamical evolution qualitatively for weak noise and dissipation and quantitatively for strong noise and dissipation.

cond-mat.quant-gas↗

arXiv2010

Preparation of stable excited states in an optical lattice via sudden quantum quench

We study how stable excited many-body states of the Bose-Hubbard model, including both the gas-like state for strongly attractive bosons and bound cluster state for repulsive bosons, can be produced with cold bosonic atoms in an one-dimensional optical lattice. Starting from the initial ground states of strongly interacting bosonic systems, we can achieve stable excited states of the systems with opposite interaction strength by suddenly switching the interaction to the opposite limit. By exactly solving dynamics of the Bose-Hubbard model, we demonstrate that the produced excited state can be a very stable dynamic state. This allows the experimental study of excited state properties of ultracold atoms system in optical lattices.

cond-mat.quant-gas↗

arXiv2010

Transition from Tonks-Girardeau gas to super-Tonks-Girardeau gas as an exact many-body dynamics problem

We investigate transition of a one-dimensional interacting Bose gas from a strongly repulsive regime to a strongly attractive regime, where a stable highly excited state known as the super Tonks-Girardeau gas was experimentally realized very recently. By solving exact dynamics of the integrable Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a very stable dynamic state. Furthermore we calculate the breathing mode of the super Tonks-Girardeau gas which is found to be in good agreement with experimental observation. Our results show that the highly excited super Tonks-Girardeau gas phase can be well understood from the fundamental theory of the solvable Bose gas.

cond-mat.quant-gas↗

arXiv2009

Bose-Fermi mixture in one-dimensional optical lattices with hard-core interactions

We study a mixture of $N_{b}$ bosons with point hard-core boson-boson interactions and $N_{f}$ noninteracting spinless fermions with point hard-core boson-fermion interactions in 1D optical lattice with external harmonic confine potential. Using an extended Jordan-Winger transformation (JWT) which maps the hard-core Bose-Fermi mixture into two component noninteracting spinless fermions with hard-core interactions between them, we get the ground states of the system. Then we determine in details the one particle density matrix, density profile, momentum distribution, the natural orbitals and their occupations based on the constructed ground state wavefunctions. We also discuss the ground state properties of the system with large but finite interactions which lead to the lift of ground degeneracy. Our results show that, although the total density profile is almost not affected, the distributions for bosons and fermions strongly depend on the relative strengthes of boson-boson interactions and boson-fermion interactions.

cond-mat.quant-gas↗

arXiv2009

Ground-state properties of hard-core anyons in one-dimensional optical lattices

We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit ($χ=1$) and Fermi limit ($χ=0$) the momentum distributions are symmetric but in between they are asymmetric. It turns out that the origin of asymmetry comes from the fractional statistics that anyons obey. The occupation distribution and the modulus of natural orbitals show crossover behaviours from the Bose limit to the Fermi limit.

cond-mat.str-el↗

arXiv2009

Quantum entanglement of particles on a ring with fractional statistics

In this paper we investigate the von Neumann entropy in the ground state of one-dimensional anyonic systems with the repulsive interaction. Based on the Bethe-ansatz method, the entanglement properties for the arbitrary statistical parameter ($0\leqκ\leq1$) are obtained from the one-particle reduced density matrix in the full interacting regime. It is shown that the entanglement entropy increases with the increase in the interaction strength and statistical parameter. The statistic parameter affects the entanglement properties from two aspects: renormalizing of the effective interaction strength and introducing an additional anyonic phase. We also evaluate the entanglement entropy of hard-core anyons for different statistical parameters in order to clarify solely the effect induced by the anyonic phase.

quant-ph↗

arXiv2009

Density-functional theory of two-component Bose gases in one-dimensional harmonic traps

We investigate the ground-state properties of two-component Bose gases confined in one-dimensional harmonic traps in the scheme of density-functional theory. The density-functional calculations employ a Bethe-ansatz-based local-density approximation for the correlation energy, which accounts for the correlation effect properly in the full physical regime. For the binary Bose mixture with spin-independent interaction, the homogeneous reference system is exactly solvable by the Bethe-ansatz method. Within the local-density approximation, we determine the density distribution of each component and study its evolution from Bose distributions to Fermi-like distribution with the increase in interaction. For the binary mixture of Tonks-Girardeau gases with a tunable inter-species repulsion, with a generalized Bose-Fermi transformation we show that the Bose mixture can be mapped into a two-component Fermi gas, which corresponds to exact soluble Yang-Gaudin model for the homogeneous system. Based on the ground-state energy function of the Yang-Gaudin model, the ground-state density distributions are calculated for various inter-species interactions. It is shown that with the increase in inter-species interaction, the system exhibits composite-fermionization crossover.

cond-mat.str-el↗

arXiv2009

Ground-state properties of interacting two-component Bose gases in a hard-wall trap

We investigate ground-state properties of interacting two-component Bose gases in a hard-wall trap using both the Bethe ansatz and exact numerical diagonalization method. For equal intra- and inter-atomic interaction, the system is exactly solvable. Thus the exact ground state wavefunction and density distributions for the whole interacting regime can be obtained from the Bethe ansatz solutions. Since the ground state is a degenerate state with total spin S=N/2, the total density distribution are same for each degenerate state. The total density distribution evolves from a Gauss-like Bose distribution to a Fermi-like one as the repulsive interaction increases. The distribution of each component is N_i/N of the total density distribution. This is approximately true even in the experimental situation. In addition the numerical results show that with the increase of interspecies interaction the distributions of two Tonks-Girardeau gases exhibit composite fermionization crossover with each component developing N peaks in the strongly interacting regime.

cond-mat.str-el↗

arXiv2008

Ground-state properties of one-dimensional anyon gases

We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant ($0\leq c\leq \infty$) and statistics parameter ($0\leq κ\leq π$). It is shown that the density of state in quasi-momentum $k$ space and the ground state energy are determined by the renormalized coupling constant $c'$. The effect induced by the statistics parameter $κ$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $κ$ deviates from 0 (Bose statistics) and $π$ (Fermi statistics) for any coupling constant $c$. The momentum distribution evolves from a Bose distribution to a Fermi one as $κ$ varies from 0 to $π$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the non-diagonal element of reduced density matrix, which is an odd function of $κ$. The peak at positive momentum will shift to negative momentum if $κ$ is negative.

cond-mat.str-el↗

arXiv2008

Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap

We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the ground-state density distributions in the whole interaction regime for different atomic number ratio, intra- and inter-atomic interactions. For the case with equal intra- and inter-atomic interactions, our results clearly display the evolution of density distributions from a Bose condensate distribution to a Fermi-like distribution with the increase of the repulsive interaction. Particularly, we compare our result in the strong interaction regime to the exact result in the infinitely repulsive limit which can be obtained by a generalized Bose-Fermi mapping. We also discuss the general case with different intra- and inter-atomic interactions and show the rich configurations of the density profiles.

cond-mat.str-el↗

arXiv2008

Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split

We carry out a detailed examination of the ground state property of few-boson system in a one-dimensional hard wall potential with a $δ-$ split in the center. In the Tonks-Girardeau limit with infinite repulsion between particles, we use the Bose-Fermi mapping to construct the exact $N-$ particle ground state wavefunction which allows us to study the correlation properties accurately. For the general case with finite inter-particle interaction, the exact diagonalization method is exploited to study the ground-state density distribution, occupation number distribution, and momentum distribution for variable interaction strengths and barrier heights. The secondary peaks in the momentum distribution reveal the interference between particles on the two sides of the split, which is more prominent for large barrier strength and small interaction strength.

cond-mat.str-el↗

arXiv2008

Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition

The notion of fidelity in quantum information science has been recently applied to analyze quantum phase transitions from the viewpoint of the ground state (GS) overlap for various many-body systems. In this work, we unveil the intrinsic relation between the GS fidelity and the derivatives of GS energy and find that they play equivalent role in identifying the quantum phase transition. The general connection between the two approaches enables us to understand the different singularity and scaling behaviors of fidelity exhibited in various systems on general grounds. Our general conclusions are illustrated via several quantum spin models which exhibit different kinds of QPTs.

cond-mat.other↗

arXiv2008

Quantum dynamics of repulsively bound atom pairs in the Bose-Hubbard model

We investigate the quantum dynamics of repulsively bound atom pairs in an optical lattice described by the periodic Bose-Hubbard model both analytically and numerically. In the strongly repulsive limit, we analytically study the dynamical problem by the perturbation method with the hopping terms treated as a perturbation. For a finite-size system, we numerically solve the dynamic problem in the whole regime of interaction by the exact diagonalization method. Our results show that the initially prepared atom pairs are dynamically stable and the dissociation of atom pairs is greatly suppressed when the strength of the on-site interaction is much greater than the tunneling amplitude, i.e., the strongly repulsive interaction induces a self-localization phenomenon of the atom pairs.

cond-mat.other↗

arXiv2007

One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap

We investigate the ground state of the one-dimensional fermionic system enclosed in a hard-wall trap with attractive contact p-wave interactions. Based on the Bethe ansatz method, the explicit wave function is derived by numerically solving the Bethe ansatz equations for the full physical regimes ($-\infty \leq c_F\leq 0$). With the exact wave function some quantities which are important in many-body physics are obtained, including the one-body density matrix and the momentum distribution of the ground state for finite system. It is shown that the shell structure of the density profiles disappears with the increase of the interaction and in the fermionic Tonks-Girardeau (FTG) limit the density distribution shows the same behavior as that of an ideal Bose gas. However the one-body density matrix and the momentum distribution exhibit completely different structures compared with their bosonic counterparts.

cond-mat.other↗