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Register a new userMultiple-scale approach for the expansion scaling of superfluid quantum gases
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We present a general method, based on a multiple-scale approach, for deriving the perturbative solutions of the scaling equations governing the expansion of superfluid ultracold quantum gases released from elongated harmonic traps. We discuss how to treat the secular terms appearing in the usual naive expansion in the trap asymmetry parameter epsilon, and calculate the next-to-leading correction for the asymptotic aspect ratio, with significant improvement over the previous proposals.
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Scale invariance emerges and plays an important role in strongly correlated many-body systems such as critical regimes nearby phase transitions and the unitary Fermi gases. Discrete scaling symmetry also manifests itself in quantum few-body systems such as the Efimov effect. Here we report both theoretical predication and experimental observation of a novel type expansion dynamics for scale invariant quantum gases. When the frequency of the harmonic trap holding the gas decreases continuously as the inverse of time $t$, surprisingly, the expansion of cloud size exhibits a sequence of plateaus. Remarkably, the locations of these plateaus obey a discrete geometric scaling law with a controllable scale factor and the entire expansion dynamics is governed by a log-periodic function. This striking expansion of quantum Fermi gases shares similar scaling laws and same mathematical description as the Efimov effect. Our work demonstrates the first expansion dynamics of a quantum many-body system with the temporal discrete scaling symmetry, which reveals the underlying spatial continuous scaling symmetry of the many-body system.
We present a novel approach to modeling dynamics of trapped, degenerate, weakly interacting Bose gases beyond the mean field limit. We transform a many-body problem to the interaction representation with respect to a suitably chosen part of the Hamiltonian and only then apply a multimode coherent-state ansatz. The obtained equations are almost as simple as the Gross--Pitaevskii equation, but our approach captures essential features of the quantum dynamics such as the collapse of coherence.
We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating between the noninteracting and the Thomas-Fermi limits. This allows us to implement a frictionless quench by engineering inversely the smooth trap frequency, as compared to the two-jump trajectory. Our result is beneficial to design the shortcut-to-adiabaticity expansion of trapped Bose gases for arbitrary values of interaction, and can be directly extended to the three-dimensional case.
Recent studies of quantum circuit models have theoretically shown that frequent measurements induce a transition in a quantum many-body system, which is characterized by the change of the scaling law of the entanglement entropy from a volume law to an area law. In order to propose a way for experimentally observing this measurement-induced transition, we present numerical analyses using matrix-product states on quench dynamics of a dissipative Bose-Hubbard model with controllable two-body losses, which has been realized in recent experiments with ultracold atoms. We find that when the strength of dissipation increases, there occurs a measurement-induced transition from volume-law scaling to area-law scaling with a logarithmic correction in a region of relatively small dissipation. We also find that the strong dissipation leads to a revival of the volume-law scaling due to a continuous quantum Zeno effect. We show that dynamics starting with the area-law states exhibits the breaking of ergodicity, which can be used in experiments for distinguishing them from the volume-law states.
In this paper, we study the dynamics of the Bose-Hubbard model with the nearest-neighbor repulsion by using time-dependent Gutzwiller methods. Near the unit filling, the phase diagram of the model contains density wave (DW), supersolid (SS) and superfluid (SF). The three phases are separated by two second-order phase transitions. We study slow-quench dynamics by varying the hopping parameter in the Hamiltonian as a function of time. In the phase transitions from the DW to SS and from the DW to SF, we focus on how the SF order forms and study scaling laws of the SF correlation length, vortex density, etc. The results are compared with the Kibble-Zurek scaling. On the other hand from the SF to DW, we study how the DW order evolves with generation of the domain walls and vortices. Measurement of first-order SF coherence reveals interesting behavior in the DW regime.
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