Abstract
We present a comparative analysis on the evolution of two coupled bosonic many-body quantum systems. Considering photons in two coupled cavities and bosonic atoms in a double-well potential, the effect of the boson-boson interaction on the spectral properties and the dynamical behavior is studied. In particular, we analyze the evolution of a Fock state to a N00N state, which is a superposition of two complementary Fock states. Such an entangled state appears in the evolution only if tunneling and many-body interaction are balanced.
Highlights
The dynamics of isolated many-body quantum systems has been a subject of intense research in atomic physics during recent years, in experiment [1] as well as in theory [2]
Bosonic atoms are prepared in a Fock state, where a definite number of atoms are localized in deep optical potential wells
We have considered a pair of optical cavities, where the photons in each cavity couple to a two-level atom
Summary
The dynamics of isolated many-body quantum systems has been a subject of intense research in atomic physics during recent years, in experiment [1] as well as in theory [2]. The experimental preparation of Fock states in a optical cavity has been achieved recently [16, 17] This is a crucial step towards a systematic study of correlated many-body systems with photonic states. The photons can tunnel between the two optical cavities, leading to a quantum evolution of the initial Fock state |N, 0 within the Hilbert space that is spanned by the eigenstates of the Hamiltonian of the new system. This new Hamiltonian can be approximated, for instance, by the Hubbard Hamiltonian, as suggested recently by several groups [21,22,23,24].
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