Abstract
We investigate the interplay of superradiant phase transition (SPT) and energy band physics in an extended Dicke-Hubbard lattice whose unit cell consists of a Dicke model coupled to an atomless cavity. We found in such a periodic lattice the critical point that occurs in a single Dicke model becomes a critical region that is periodically changing with the wavenumber $k$. In the weak-coupling normal phase of the system we observed a flat band and its corresponding localization that can be controlled by the ground-state SPT. Our work builds the connection between flat band physics and SPT, which may fundamentally broaden the regimes of many-body theory and quantum optics.
Highlights
The quantum phase transition (QPT), driven by quantum fluctuations in many-body systems, is one of the most fundamental and significant concepts in physics since it can offer the important resources for quantum metrology [1,2,3] and quantum sensing [4,5,6]
We establish a connection between quantum phase transitions (QPTs) and energy band theory in an extended Dicke-Hubbard lattice, where the periodical critical curves modulated by wave number k leads to rich equilibrium dynamics
We have investigated the quantum critical and energyband properties of an extended Dicke-Hubbard lattice and established the connection between the flat band and the superradiant phase transition
Summary
The quantum phase transition (QPT), driven by quantum fluctuations in many-body systems, is one of the most fundamental and significant concepts in physics since it can offer the important resources for quantum metrology [1,2,3] and quantum sensing [4,5,6]. We established the connection between the flat band and the QPT from the normal phase to the superradiant phase in an extended Dicke-Hubbard lattice, i.e., a series of Dicke models [31] coupled together through a set of atomless cavities. This extended model can be implemented in hybrid superconducting circuits [32,33,34,35,36,37,38], in which a twolevel ensemble (e.g., NV center spins) is doped in every other cavity [see Fig. 1(b)]. Either of them can destroy the destructive interference of the lattice and, lead to the disappearance of the flat band
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