An isolated quantum system often shows relaxation to a quasi-stationary state before reaching thermal equilibrium. Such a pre-thermalized state was observed in recent experiments in a one-dimensional Bose gas after it had been coherently split into two. Although the existence of local conserved quantities is usually considered to be the key ingredient of pre-thermalization, the question of whether non-local correlations between the subsystems can influence pre-thermalization of the entire system has remained unanswered. Here we study the dynamics of coherently split one-dimensional Bose gases and find that the initial entanglement combined with energy degeneracy due to parity and translation invariance strongly affects the long-term behaviour of the system. The mechanism of this entanglement pre-thermalization is quite general and not restricted to one-dimensional Bose gases. In view of recent experiments with a small and well-defined number of ultracold atoms, our predictions based on exact few-body calculations could be tested in experiments.
At a glance
- Beweis des ergodensatzes und des H-theorems in der neuen mechanik. Z. Phys. 57, 30–70 (1929).
- Chaos and quantum thermalization. Phys. Rev. E 50, 888–901 (1994).
- From quantum dynamics to the canonical distribution: General picture and a rigorous example. Phys. Rev. Lett. 80, 1373–1376 (1998).
- Entanglement and the foundations of statistical mechanics. Nature Phys. 2, 754–758 (2006). , &
- Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854–858 (2008). , &
- Quantum mechanical evolution towards thermal equilibrium. Phys. Rev. E 79, 061103 (2009). , , &
- Normal typicality and von Neumann’s quantum ergodic theorem. Proc. R. Soc. A 466, 3203–3224 (2010). , , , &
- Exact relaxation dynamics of a localized many-body state in the 1D Bose gas. Phys. Rev. Lett. 108, 110401 (2012). , , &
- A quantum Newton’s cradle. Nature 440, 900–903 (2006). , &
- Non-equilibrium coherence dynamics in one-dimensional Bose gases. Nature 449, 324–327 (2007). , , , &
- Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas. Nature Phys. 8, 325–330 (2012). et al.
- Prethermalization. Phys. Rev. Lett. 93, 142002 (2004). , &
- Relaxation and prethermalization in an isolated quantum system. Science 337, 1318–1322 (2012). et al.
- Local emergence of thermal correlations in an isolated quantum many-body system. Nature Phys. 9, 640–643 (2013). , , , &
- Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems. Phys. Rev. B 84, 054304 (2011). , &
- Relaxation timescales and decay of correlations in a long-range interacting quantum simulator. New J. Phys. 15, 083007 (2013). , , &
- Thermalization after an interaction quench in the Hubbard model. Phys. Rev. Lett. 103, 056403 (2009). , &
- Quench dynamics of the interacting Bose gas in one dimension. Phys. Rev. Lett. 109, 115304 (2012). &
- Interaction quenches in the one-dimensional Bose gas. Phys. Rev. B 88, 205131 (2013). , , , &
- Analytic results for a quantum quench from free to hard-core one-dimensional Bosons. Phys. Rev. A 89, 013609 (2014). , &
- Solution for an interaction quench in the Lieb–Liniger Bose gas. Phys. Rev. A 89, 033601 (2014). , , &
- Quench between a Mott insulator and a Lieb–Liniger liquid. Phys. Rev. A 90, 043626 (2014). &
- Effective thermal dynamics following a quantum quench in a spin chain. Phys. Rev. Lett. 102, 127204 (2009). , , &
- Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior. Phys. Rev. B 82, 144302 (2010). , , , &
- Quantum quench in the transverse-field Ising chain. Phys. Rev. Lett. 106, 227203 (2011). , &
- Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators. J. Stat. Mech. 2012, P07016 (2012). , &
- Quantum quenches in the transverse field Ising chain: II. Stationary state properties. J. Stat. Mech. 2012, P07022 (2012). , &
- Relaxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core Bosons. Phys. Rev. Lett. 98, 050405 (2007). , , &
- Generalized thermalization in an integrable lattice system. Phys. Rev. Lett. 106, 140405 (2011). , &
- Infinite-time average of local fields in an integrable quantum field theory after a quantum quench. Phys. Rev. Lett. 111, 100401 (2013).
- Validity of the GGE for quantum quenches from interacting to noninteracting models. J. Stat. Mech. 2014, P07024 (2014). &
- Generalized Gibbs ensembles for quantum field theories. Phys. Rev. A 91, 051602(R) (2015). , &
- Deterministic preparation of a tunable few-fermion system. Science 332, 336–338 (2011). et al.
- Fermionization of two distinguishable fermions. Phys. Rev. Lett. 108, 075303 (2012). et al.
- Ramsey interference in one-dimensional systems: The full distribution function of fringe contrast as a probe of many-body dynamics. Phys. Rev. Lett. 104, 255302 (2010). et al.
- The dynamics and prethermalization of one-dimensional quantum systems probed through the full distributions of quantum noise. New J. Phys. 13, 073018 (2011). , , &
- Exact analysis of an interacting Bose gas. I. The general solution and the ground state. Phys. Rev. 130, 1605–1616 (1963). &
- One-particle dynamical correlations in the one-dimensional Bose gas. J. Stat. Mech. 2007, P01008 (2007). , &
- 1983). La fonction d’onde de Bethe (Masson,
- Calculation of norms of Bethe wave functions. Commun. Math. Phys. 86, 391–418 (1982).
- Calculation of scalar products of wave functions and form factors in the framework of the algebraic Bethe ansatz. Teor. Mat. Fiz. 79, 502–508 (1989).
- Nonequal-time current correlation function in a one-dimensional Bose gas. Teor. Mat. Fiz. 82, 273–282 (1990).
- Foundation of statistical mechanics under experimentally realistic conditions. Phys. Rev. Lett. 101, 190403 (2008).
- Equilibration of quantum systems and subsystems. New J. Phys. 13, 053009 (2011).
- Reduced density matrix after a quantum quench. Phys. Rev. B 87, 245107 (2013). &
- Atomic scattering in the presence of an external confinement and a gas of impenetrable Bosons. Phys. Rev. Lett. 81, 938–941 (1998).
- Breakdown of thermalization in finite one-dimensional systems. Phys. Rev. Lett. 103, 100403 (2009).
- Time evolution of local observables after quenching to an integrable model. Phys. Rev. Lett. 110, 257203 (2013). &
- Correlations after quantum quenches in the XXZ spin chain: Failure of the generalized Gibbs ensemble. Phys. Rev. Lett. 113, 117203 (2014). et al.
- http://arXiv.org/abs/1505.03080 (2015). , & Relaxation dynamics of local observables in integrable systems. Preprint at
- Supplementary information (790,801 KB)