Quantum scars and regular eigenstates in a chaotic spinor condensate (2306.10411v1)
Abstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum, and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system's rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates.
- J. M. Deutsch, Phys. Rev. A 43, 2046 (1991).
- M. Srednicki, Phys. Rev. E 50, 888 (1994), arXiv:cond-mat/9403051 [cond-mat] .
- R. V. Jensen and R. Shankar, Phys. Rev. Lett. 54, 1879 (1985).
- M. Rigol, Phys. Rev. Lett. 103, 100403 (2009).
- R. Nandkishore and D. A. Huse, Annual Review of Condensed Matter Physics 6, 15 (2015).
- N. Shiraishi and T. Mori, Phys. Rev. Lett. 119, 030601 (2017).
- E. J. Heller, The Semiclassical Way to Dynamics and Spectroscopy (Princeton University Press, Princeton, 2018).
- J. Stein and H.-J. Stöckmann, Phys. Rev. Lett. 68, 2867 (1992).
- E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
- T. Mori, Phys. Rev. E 96, 012134 (2017).
- S. Sinha and S. Sinha, Phys. Rev. Lett. 125, 134101 (2020).
- M. Rautenberg and M. Gärttner, Phys. Rev. A 101, 053604 (2020).
- Y. Kawaguchi and M. Ueda, Phys. Rep. 520, 253 (2012).
- D. M. Stamper-Kurn and M. Ueda, Rev. Mod. Phys. 85, 1191 (2013).
- T.-L. Ho, Phys. Rev. Lett. 81, 742 (1998).
- M. V. Berry, J. Phys. A: Math. and Gen. 10, 2083 (1977).
- V. Vedral, Central European Journal of Physics 1, 289 (2003).
- M. Srednicki, J. Phys. A: Math. and Gen. 29, L75 (1996).
- M. Srednicki, J. Phys. A: Math. and Gen. 32, 1163 (1999).
- R. Gati and M. K. Oberthaler, J. Phys. B: At. Mol. and Opt. Phys. 40, R61 (2007).
- P. Gaspard, Chaos, Scattering and Statistical Mechanics, Cambridge Nonlinear Science Series (Cambridge University Press, 1998).
- T. Parker and L. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer New York, 2012).