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Zhang, Ren

Publications and source records attributed to Zhang, Ren.

5 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantum dynamics of cold atomic gas with SU(1,1) symmetry

Motivated by recent advances in quantum dynamics, we investigate the dynamics of the system with SU(1,1) symmetry. Instead of performing the time-ordered integral for the evolution operator of the time-dependent Hamiltonian, we show that the time evolution operator can be expressed as an SU(1,1) group element. Since the SU(1,1) group describes the “rotation” on a hyperbolic surface, the dynamics can be visualized on a Poincaré disk, a stereographic projection of the upper hyperboloid. As an example, we present the trajectory of the revival of Bose-Einstein condensation and that of the scale-invariant Fermi gas on the Poincaré disk. Further considering quantum gases in an oscillating lattice, we also study the dynamics of the system with time-dependent single-particle dispersion.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Curving the space by non-Hermiticity

Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas these intriguing phenomena have been considered peculiar to non-Hermitian systems, we show that they can be naturally explained by a duality between non-Hermitian models in flat spaces and their counterparts, which could be Hermitian, in curved spaces. For instance, prototypical one-dimensional (1D) chains with uniform chiral tunnelings are equivalent to their duals in two-dimensional (2D) hyperbolic spaces with or without magnetic fields, and non-uniform tunnelings could further tailor local curvatures. Such a duality unfolds deep geometric roots of non-Hermitian phenomena, delivers an unprecedented routine connecting Hermitian and non-Hermitian physics, and gives rise to a theoretical perspective reformulating our understandings of curvatures and distance. In practice, it provides experimentalists with a powerful two-fold application, using non-Hermiticity to engineer curvatures or implementing synthetic curved spaces to explore non-Hermitian quantum physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Efimov-like states and quantum funneling effects on synthetic hyperbolic surfaces

Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures. Here, we point out that discrete synthetic Poincaré half-planes and Poincaré disks, which are created by lattices in flat planes, support infinitely degenerate eigenstates for any nonzero eigenenergies. Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces. Furthermore, all eigenstates are exponentially localized in the hyperbolic coordinates, signifying the first example of quantum funneling effects in Hermitian systems. As such, any initial wave packet travels towards the edge of the Poincaré half-plane or its equivalent on the Poincaré disk, delivering an efficient scheme to harvest light and atoms in two dimensions. Furthermore, our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

SU(1,1) Echoes for Breathers in Quantum Gases

Though the celebrated spin echoes have been widely used to reverse quantum dynamics, they are not applicable to systems whose constituents are beyond the control of the su(2) algebra. In this work, we design echoes to reverse quantum dynamics of breathers in three-dimensional unitary fermions and two-dimensional bosons and fermions with contact interactions, which are governed by an underlying su(1, 1) algebra. Geometrically, SU(1, 1) echoes produce closed trajectories on a single or multiple Poincaré disks and thus could recover any initial states without changing the sign of the Hamiltonian. In particular, the initial shape of a breather determines the superposition of trajectories on multiple Poincaré disks and whether the revival time has period multiplication. Our work provides physicists with a recipe to tailor collective excitations of interacting many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗