Sauter-Schwinger-like tunneling in tilted Bose-Hubbard lattices in the Mott phase

Abstract

We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations. Introduction. There are many striking analogies between apparently very different areas in physics, which help us to unify our understanding of nature -as R. Feynman said: The same equations have the same solutions. In this Letter, we establish such a quantitative analogy between high-field science and ultra-cold atoms in optical lattices. The Sauter-Schwinger effect [1][2][3] predicts that an extremely strong electric field may create electronpositron pairs out of the QED vacuum. As an intuitive picture, one can envisage this effect as tunneling of an electron from the Dirac sea into the positive continuum, leaving behind a hole (i.e., positron), see Fig. 1. Unfortunately, this prediction has not been experimentally verified yet since it is hard to generate sufficiently strong electric fields in large enough space-time regions. As we shall demonstrate below, the same equations govern particlehole pair creation in a Mott insulator via tunneling due to a small potential gradient. The Mott insulator state we are considering can be generated by bosonic atoms in an optical lattice [4,5] for example, which repel each other and thereby become effectively pinned to the lattice sites (zero mobility). The benefits of this quantitative analogy are two-fold. On the one hand, we can apply our knowledge of the Sauter-Schwinger effect [1, 2] to atoms in optical lattices and understand them better in this way. On the other hand, atoms in optical lattices may provide (via this analogy) an experimental approach to the so far unobserved Sauter-Schwinger effect.

Large-coordination-number expansion of a lattice Bose gas at finite temperature

“…It was found that the results are in good agreement with rigorous high-temperature and low-temperature expansions [36]. A related approximation method was previously applied to investigate the dynamics of lattice site correlations after a quantum quench [39][40][41] and particlehole pair creation in tilted optical lattices [42]. The 1/Zexpansion is valid for all values of the interaction energy and the hopping energy.…”

“…From the partition function we obtained local quantities such as the on-site probabilities p n as well as the non-local thermal correlations b † µbν . It should be noted that, in the limit of vanishing temperature, the correlation functions b † µbν as well as the occupation probabilities can also be obtained from 1/Zhierarchy that describes the dynamics of lattice site correlations [39,42]. …”

Ultracold bosons with short-range interaction in regular optical lattices

“…An alternative approach was recently suggested in Refs. [401,404,405,511] which deals with the dynamical equations for the reduced density matrices of different number of lattice sites. However, the full theoretical description of sufficiently large systems in the whole parameter range and for arbitrarily long times is still not reached.…”

“…In such a description, excitations in the Bragg process are created as particle-hole pairs [383,401,402]. However, the latter appears to be of the second order in the inverse of coordination number Z = 2d [401,[403][404][405] and, therefore, is not taken into account by the standard Gutzwiller ansatz.…”

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

“…The results (86), (87), and (91) can also be obtained via other approaches, such as the spin density wave ansatz [101] (which is related to dynamical mean field theory according to Ref. [102]).…”