Periodically and quasi-periodically driven dynamics of Bose-Einstein  condensates

Zhang, Pengfei; Gu, Yingfei

doi:10.21468/scipostphys.9.5.079

Cited by 13 publications

(6 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, periodic points in the CFT description may prove to be robust to higher excitations, or the latter may be taken into account by other means. Our approach is also suitable for numerical implementations, and we hope that it can be adapted or serve as inspiration for a wide range of other Floquet systems, e.g., for driven Bose-Einstein condensates [45][46][47] or fields in modulated cavities [48].…”

Section: Example W(ξ ) Parametersmentioning

confidence: 99%

Geometric approach to inhomogeneous Floquet systems

Lapierre

Moosavi

2021

Phys. Rev. B

View full text Add to dashboard Cite

We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical systems on the circle that we establish and use to prove existence of (non)heating phases characterized by the (absence) presence of fixed or higher-periodic points of coordinate transformations encoding the time evolution: Heating corresponds to energy and excitations concentrating exponentially fast at unstable such points while nonheating to pseudoperiodic motion. We show that the heating rate (serving as the order parameter for transitions between these two) can have cusps, even within the overall heating phase, and that there is a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. Our geometric approach generalizes previous results for a subfamily of similar systems that used only the sl(2) algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it has wider applicability, even beyond conformal field theory.

show abstract

Section: Example W(ξ ) Parametersmentioning

confidence: 99%

Geometric approach to inhomogeneous Floquet systems

Lapierre

Moosavi

2021

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Novel phases that have no equilibrium analog have been proposed and partly realized experimentally, such as Floquet topological phases [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and time crystals [15][16][17][18][19][20][21][22]. Non-equilibrium phenomena, including localization-thermalization transitions, prethermalization, dynamical localization, dynamical Casimir effect, are analyzed using models with periodic drivings [23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

Wen

Vishwanath

et al. 2022

SciPost Phys.

View full text Add to dashboard Cite

In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven (1+1)(1+1) dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium quantum dynamics. The sequence of driving Hamiltonians is drawn from an independent and identically distributed random ensemble. At each driving step, the deformed Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength and therefore induces a Möbius transformation on the complex coordinates. The non-equilibrium dynamics is then determined by the corresponding sequence of Möbius transformations, from which the Lyapunov exponent \lambda_LλL is defined. We use Furstenberg’s theorem to classify the dynamical phases and show that except for a few exceptional points that do not satisfy Furstenberg’s criteria, the random drivings always lead to a heating phase with the total energy growing exponentially in the number of driving steps nn and the subsystem entanglement entropy growing linearly in nn with a slope proportional to central charge cc and the Lyapunov exponent \lambda_LλL. On the contrary, the subsystem entanglement entropy at an exceptional point could grow as \sqrt{n}n while the total energy remains to grow exponentially. In addition, we show that the distributions of the operator evolution and the energy density peaks are also useful characterizations to distinguish the heating phase from the exceptional points: the heating phase has both distributions to be continuous, while the exceptional points could support finite convex combinations of Dirac measures depending on their specific type. In the end, we compare the field theory results with the lattice model calculations for both the entanglement and energy evolution and find remarkably good agreement.

show abstract

“…With the aid of this geometric picture, the quantum dynamics can be visualized on the Poincaré disk, a stereographic projection of upper hyperboloid, which provides a straightforward intuition of the quantum dynamics of a manybody system. The studies on the dynamics of BEC and the breathing mode in quantum gas are underpinned by the SU (1, 1) group [18][19][20][21][22][23][24][25][26][27][28] and the corresponding geometric visualization [29,30]. As such, it is natural to generalize the geometric visualization to more systems, the dynamics of which are governed by the SU (1, 1) group.…”

Section: Introductionmentioning

confidence: 99%

Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry

Zhang,

Yang,

et al. 2022

Preprint

View full text Add to dashboard Cite

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 the quantum gas in the oscillating lattice, we also study the dynamics of the system with time-dependent singleparticle dispersion. Our results are hopefully to be checked in current experiments.

show abstract

Periodically and quasi-periodically driven dynamics of Bose-Einstein condensates

Cited by 13 publications

References 41 publications

Geometric approach to inhomogeneous Floquet systems

Geometric approach to inhomogeneous Floquet systems

Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry

Contact Info

Product

Resources

About