Abstract
We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis–Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya’s enumeration theorem.
Highlights
Coupled light-matter systems are at the heart of much of the effort in modern atomic and optical physics with applications ranging from quantum information processing to quantum simulations.In this context, the use of cavities plays a prominent role as the strong confinement of the electromagnetic field implies strong interaction with matter coupled to the cavity modes
Before presenting the results and in order to get a deeper insight in the structure of the spin Hamiltonians emergent in cavity arrays, we study the properties of the ground states from the group and graph theory perspective
In this work we have analysed the ground states of a cavity array where each intersection of cavity modes is occupied by a single atom
Summary
Jirí Minár1̌ ,2,3, Şebnem Güneş Söyler, Pietro Rotondo and Igor Lesanovsky. Keywords: cavity arrays, ground states of spin systems, frustrated spin models, quantum Monte Carlo, Dicke, Jaynes–Cummings, Tavis– Cummings models. Original content from this work may be used under the terms of the Creative Abstract. In one-dimension we provide an exact analytical solution. In two-dimensions, we the work, journal citation and DOI. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya’s enumeration theorem
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