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

@article{Zhang2022QuantumDO,
  title={Quantum dynamics of cold atomic gas with SU(1,1) symmetry},
  author={Jing Zhang and Xiaoying Yang and Chenwei Lv and Shengli Ma and Ren-jie Zhang},
  journal={Physical Review A},
  year={2022}
}
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 Poincar´e disk, a stereographic projection of the upper hyperboloid… 

Figures from this paper

References

SHOWING 1-10 OF 49 REFERENCES

Geometrizing Quantum Dynamics of a Bose-Einstein Condensate.

This work suggests a new geometric framework to coherently control quantum systems and reverse their dynamics using SU(1,1) echoes in the presence of perturbations breaking the SU(2,2) symmetry.

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

This work designs echoes to reverse quantum dynamics of breathers in three-dimensional unitary fermions and two-dimensional bosons and fermion with contact interactions, which are governed by an underlying su(1,1) algebra.

Many-body dynamics with time-dependent interaction

Recent advances in optical Feshbach resonance technique have enabled the experimental investigation of atomic gases with time-dependent interaction. In this work, we study the many-body dynamics of

Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas.

It is shown that the classical SO(2,1) symmetry of a harmonically trapped Fermi gas in two dimensions is broken by quantum effects and the virial theorem for the system and a universal relation for the pressure of a homogeneous gas is derived.

Dynamical Symmetry and Breathers in a Two-Dimensional Bose Gas

A fluid is said to be \emph{scale-invariant} when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale

Pseudospin approach to the dynamics and squeezing of SU(2) and SU(1, 1) coherent states

The semi-classical Dicke model and the ideal parametric amplifier are described by Hamiltonians linear in the SU(2) and SU(1, 1) group generators, respectively. We use the usual pseudospin vector as

Quantum simulation of Unruh radiation

The exploration of quantum phenomena in a curved spacetime is an emerging interdisciplinary area at the interface between general relativity1–4, thermodynamics4–6 and quantum information7,8. One

Observation of Dynamical Super-Efimovian Expansion in a Unitary Fermi Gas.

Observing super Efimovian evolution represents a paradigm in probing universal properties and allows us in a new way to study many-body nonequilibrium dynamics with experiments.

Quantum Anomaly and 2D-3D Crossover in Strongly Interacting Fermi Gases.

The authors' measurements deep in the 2D regime lie above the scale-invariant prediction for a range of interaction strengths providing evidence for the quantum anomaly and signifying the breakdown of an elementary δ-potential model of atomic interactions.

Relaxation Dynamics in the Merging of N Independent Condensates.

A detailed study of the rich out-of-equilibrium dynamics of an adjustable number N of uncorrelated condensates after connecting them in a ring-shaped optical trap and insight into the microscopic mechanism that underlies the smoothening of the phase profile is provided.