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Physical Review A

Quantum phase transitions for two coupled cavities with dipole-interaction atoms

Lei Tan, Yuqing Zhang, Wu‐Ming Liu

Published Dec 6, 2011• 15 citations
Publisher

Abstract

We investigate the quantum phase transitions for two weakly coupled atom-cavity sites. The interatomic dipole-dipole interaction is considered. Our numerical results show that the dipole-dipole interaction is a crucial parameter for the quantum phase transition. For small atom-cavity detuning, the ``superfluid'' becomes more and more obvious with the increase of the dipole-dipole interaction. In addition, the strong dipole-dipole interaction can lead the atomic excitation to be suppressed completely, and only the photonic excitation exists for the ground states. When the atom-cavity detuning is comparable with the dipole-dipole interaction, the dipole-dipole interaction enlarges the positive detunings, which is in favor of exhibiting superfluid photonic states. While for the negative detuning, the dipole-dipole interaction will reduce it, and contribute to the formation of the polaritonic insulator states. The cases for extended models have also been briefly analyzed. We also discuss how to find these novel phenomena in future experiments.

DOI
10.1103/physreva.84.063816

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We investigate the quantum phase transitions for two weakly coupled atom-cavity sites. The interatomic dipole-dipole interaction is considered. Our numerical results show that the dipole-dipole interaction is a crucial parameter for the quantum phase transition. For small atom-cavity detuning, the ``superfluid'' becomes more and more obvious with the increase of the dipole-dipole interaction. In addition, the strong dipole-dipole interaction can lead the atomic excitation to be suppressed completely, and only the photonic excitation exists for the ground states. When the atom-cavity detuning is comparable with the dipole-dipole interaction, the dipole-dipole interaction enlarges the positive detunings, which is in favor of exhibiting superfluid photonic states. While for the negative detuning, the dipole-dipole interaction will reduce it, and contribute to the formation of the polaritonic insulator states. The cases for extended models have also been briefly analyzed. We also discuss how to find these novel phenomena in future experiments.
The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits of exact resonance, large positive and negative detunings are discussed, and four types of the ground states are revealed. Then the phase diagrams of the ground state are plotted by choosing three different "order parameters". We find that the phase space, determined by the combinative action of detuning and the dipole coupling strength, is divided into four regions. This is different from the general Bose-Hubbard model and more richer physics are presented in the two-site coupled cavities system. That is, the insulator region may be polaritonic or atomic and the superfluid region may be polaritonic or photonic in nature.
Summary form only given. The studies of insulator to superfluid transitions in many body systems and their realization in optical lattices have opened great possibilities for simulating many body systems. It is thus interesting to explore which other systems permit such phases and simulations, especially if the problem of accessibility of the individual sites is not present. Particularly arresting will be to find such phases in a system of photons which, by being non-interacting, are unlikely candidates for the studies of many-body phenomena. Here we show that a Mott phase can arise in an array of coupled high Q electromagnetic cavities between which photons can hop, when each cavity is coupled to a single two level system (atom/quantum dot/Cooper pair). In this phase each atom-cavity system has the same integral number of polaritonic (atomic plus photonic) excitations. It occurs for resonant photonic and atomic frequencies when photon blockade provides an effective repulsion between the excitations in each atom-cavity system. Detuning the atomic and photonic frequencies suppresses this repulsion and induces a transition from the Mott phase to a photonic superfluid. We also show that for zero detuning, the system can simulate the dynamics of a spin chain with arbitrary number of excitations and can be used to implement quantum information processing tasks.
Recent studies of quantum phase transitions in coupled atom-cavity arrays have focused on the similarities between such systems and the Bose-Hubbard model. However, the bipartite nature of the atom-cavity systems that make up the array introduces some differences. In order to examine the unique features of the coupled-cavity system, the behavior of a simple two-site model is studied over a wide range of parameters. Four regions are identified, in which the ground state of the system may be classified as a polaritonic insulator, a photonic superfluid, an atomic insulator, or a polaritonic superfluid.
The transmission spectrum of two dipole-coupled atoms interacting with a single-mode optical cavity in the strong coupling regime is investigated theoretically for the lower and higher excitation cases. The dressed states containing the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom system. We find that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weakens them for the negative detuning cases for the lower excitation, which causes the spectrum to exhibit two asymmetric peaks with shifted heights and positions. For the higher excitation cases, the DDI augments the atomic saturation and leads to the deforming of the spectrum. Furthermore, the large DDI can cause the atom and the cavity to decouple, producing a singlet of the normal-mode spectrum.
We compute the energies of the interaction between two atoms placed in the middle of a perfectly reflecting planar cavity, in the weak-coupling nondegenerate regime. Both inhibition and enhancement of the interactions can be obtained by varying the size of the cavity. We derive exact expressions for the dyadic Green's function of the cavity field which mediates the interactions and apply time-dependent quantum perturbation theory in the adiabatic approximation. We provide explicit expressions for the van der Waals potentials of two polarizable atomic dipoles and the electrostatic potential of two induced dipoles. We compute the van der Waals potentials in three different scenarios: two atoms in their ground states, two atoms excited, and two dissimilar atoms with one of them excited. In addition, we calculate the phase-shift rate of the two-atom wave function in each case. The effect of the two-dimensional confinement of the electromagnetic field on the dipole-dipole interactions is analyzed. This effect depends on the atomic polarization. For dipole moments oriented parallel to the cavity plates, both the electrostatic and the van der Waals interactions are exponentially suppressed for values of the cavity width much less than the interatomic distance, whereas for values of the width close to the interatomic distance, the strength of both interactions is higher than their values in the absence of cavity. For dipole moments perpendicular to the plates, the strength of the van der Waals interaction decreases for values of the cavity width close to the interatomic distance, while it increases for values of the width much less than the interatomic distance with respect to its strength in the absence of cavity. We illustrate these effects by computing the dipole-dipole interactions between two alkali atoms in circular Rydberg states.
Bipartite entanglement entropies are calculated for the ground state of the two-excitation subspace in a two-site coupled cavity model. Each region in the phase diagram (atomic insulator, polaritonic insulator, photonic superfluid, and polaritonic superfluid) is found to be characterized by unique entanglement properties. In particular, the polaritonic superfluid region exhibits genuine 4-partite entanglement among the two atoms and two-cavity fields. The difference in entanglement properties between the small- and large-hopping limits provides further evidence that the transitions in the two limits are qualitatively different and that the large-hopping limit cannot be described by a simple Bose-Hubbard-type model.