Generating two-dimensional quantum gases with high stability

Quantum gas microscopy has enabled the study on intriguing properties of ultracold atoms in optical lattices.It provides the cutting-edge technology for manipulating quantum many-body systems.In such experiments,atoms have to be prepared into a two-dimensional(2D)system for being resolved by microscopes with limited depth of focus.Here we report an experiment on slicing a single layer of the atoms trapped in a few layers of pancake-shaped optical traps to create a 2D system.This technique is implemented with a microwave“knife”,i.e.,a microwave field with a frequency defined by the resonant condition with the Zeeman-shifted atomic levels related to a gradient magnetic field.It is crucial to keep a stable preparation of the desired layer to create the 2D quantum gas for future experimental applications.To achieve this,the most important point is to provide a gradient magnetic field with low noises and slow drift in combination with a properly optimized microwave pulse.Monitoring the electric current source and the environmental magnetic field,we applied an actively stabilizing circuit and realized a field drift of 0.042(3)mG/hour.This guarantees creating the single layer of atoms with an efficiency of 99.92(3)%while atoms are hardly seen in other layers within 48 hours,satisfying future experimental demands on studying quantum many-body physics.

Universal dynamic scaling and Contact dynamics in quenched quantum gases

Recently universal dynamic scaling is observed in several systems,which exhibit a spatiotemporal self-similar scaling behavior,analogous to the spatial scaling near phase transition.The latter one arises from the emergent continuous scaling symmetry.Motivated by this,we investigate the possible relation between the scaling dynamics and the continuous scaling symmetry in this paper.We derive a theorem that the scaling invariance of the quenched Hamiltonian and the initial density matrix can lead to the universal dynamic scaling.It is further demonstrated both in a two-body system analytically and in a many-body system numerically.For the latter one,we calculate the dynamics of quantum gases quenched from the zero interaction to a finite interaction via the non-equilibrium high-temperature virial expansion.A dynamic scaling of the momentum distribution appears in certain momentum-time windows at unitarity as well as in the weak interacting limit.Remarkably,this universal scaling dynamics persists approximately with smaller scaling exponents even if the scaling symmetry is fairly broken.Our findings may offer a new perspective to interpret the related experiments.We also study the Contact dynamics in the BEC−BCS crossover.Surprisingly,the half-way time displays a maximum near unitarity while some damping oscillations occur on the BEC side due to the dimer state,which can be used to detect possible two-body bound states in experiments.

Magnetic lattices for ultracold atoms and degenerate quantum gases

We review recent developments in the use of magnetic lattices as a complementary tool to optical lattices for trapping periodic arrays of ultracold atoms and degenerate quantum gases. Recent advances include the realisation of Bose–Einstein condensation in multiple sites of a magnetic lattice of one-dimensional microtraps, the trapping of ultracold atoms in square and triangular magnetic lattices,and the fabrication of magnetic lattice structures with submicron period suitable for quantum tunnelling experiments.Finally, we describe a proposal to utilise long-range interacting Rydberg atoms in a large spacing magnetic lattice to create interactions between atoms on neighbouring sites.

Quantum Phase Transition of the Bosonic Atoms near the Feshbach Resonance in an Optical Lattice

The quantum phase transition from the Mott insulator to the superfluid phases of the bosonic atoms trapped in an optical lattice, in which the on-site interaction carl be tuned by a Feshbach resonance, is investigated by a variational approach within mean-field theory. We derive an extended Bos^Hubbard model to describe this ultracold atomic system. By theoretical calculation and analysis, the phase diagram is shown clearly, and we find an exciting and novel phenomenon that is the appearance of the Mort insulator-sea （MI-sea）. Meanwhile, the experimental feasibility of observing the MI-sea is discussed by analyzing the published data related to the Fashbaeh resonance at present. Finally, the potential application of the MI-sea for quantum information processing and quantum computation is also discussed in detail

Single-particle spectroscopies of p-wave and d-wave interacting Bose gases in normal phase

Motivated by experiments with interacting quantum gases across high partial wave resonance,we investigate the thermodynamic properties and single-particle spectra of Bose gases in normal phase for different interaction strengths for both p-and d-wave interactions.The equation of state,contact density,momentum distributions and self-energies of single-particle Green’s functions are obtained in the spirit of ladder diagram approximations.The radio-frequency(RF)spectrum,as an important experimental approach for detecting Feshbach molecules or the interaction effect,is calculated at different temperatures.A reversed temperature dependence on the Bose–Einstein condensation side and Bardeen–Cooper–Schrieffer side is identified for both p-and d-wave interactions.An estimate for the signal of RF spectra under typical experimental conditions is also provided.

Interference Pattern of Density-Density Correlation for Incoherent Atoms with Vortices Released from an Optical Lattice

For a series of incoherent condensate atomic clouds with vortices （an orbital angular momentum） released from an optical lattice, the density-density correlation function of this freely expanding ultracold gases is theoretically investigated. It is shown that the nonzero angular momentum of the atoms has an important effect on the fringe pattern of density-density correlation. Particularly, for a short expansion time, even the rotation direction of the atoms could have an observable effect on the fringe pattern. Observation of this specific fringe pattern would constitute experimental evidence for the presence of a vortex in an atomic condensate.

Ground State of Fermions in a 1D Trap with δ Function Interaction

The ground state of fermions in a 1D trap with δ function interaction is studied mathematically with group theory ideas.

Spinless Bosons in a 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction I： General Theory

In these two papers, we solve the N body 1D harmonically trapped spinless Boson problem with repulsive δ function interaction in the limit N→∞. The general theory is given in paper I and the numerical solutions will be given in paper II.

Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.

Ground State Density Distribution of Bose-Fermi Mixture in a One-Dimensional Harmonic Trap

By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state en- ergy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between finite. While in the infinite interaction limit both distributions and phase separation disappears. two components when the interaction is strong enough but bosons and fermions display the completely same Fermi-like

Statistical Interaction Term of One-Dimensional Anyon Models

A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.

Statistical Mechanical Entropy of a （4 ＋ n）-Dimensional Static Spherically Symmetric Black Hole

Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.