In this work, we study the $ U(1)/Z_2 $ Dicke model at a finite $ N $ by using the $ 1/J $ expansion and exact diagonization. This model includes the four standard quantum optics model as its various special limits. The $ 1/J $ expansions is compleme
ntary to the strong coupling expansion used by the authors in arXiv:1512.08581 to study the same model in its dual $ Z_2/U(1) $ representation. We identify 3 regimes of the systems energy levels: the normal, $ U(1) $ and quantum tunneling (QT) regime. The systems energy levels are grouped into doublets which consist of scattering states and Schrodinger Cats with even ( e ) and odd ( o ) parities in the $ U(1) $ and quantum tunneling (QT) regime respectively. In the QT regime, by the WKB method, we find the emergencies of bound states one by one as the interaction strength increases, then investigate a new class of quantum tunneling processes through the instantons between the two bound states in the compact photon phase. It is the Berry phase interference effects in the instanton tunneling event which leads to Schrodinger Cats oscillating with even and odd parities in both ground and higher energy bound states. We map out the energy level evolution from the $ U(1) $ to the QT regime and also discuss some duality relations between the energy levels in the two regimes. We also compute the photon correlation functions, squeezing spectrum, number correlation functions in both regimes which can be measured by various experimental techniques. The combinations of the results achieved here by $ 1/J $ expansion and those in arXiv:1512.08581 by strong coupling method lead to rather complete understandings of the $ U(1)/Z_2 $ Dicke model at a finite $ N $ and any anisotropy parameter $ beta $.
A duality transformation in quantum field theory is usually established first through partition functions. It is always important to explore the dual relations between various correlation functions in the transformation. Here, we explore such a dual
relation to study quantum phases and phase transitions in an extended boson Hubbard model at 1/3 (2/3) filling on a triangular lattice. We develop systematically a simple and effective way to use the vortex degree of freedoms on dual lattices to characterize both the density wave and valence bond symmetry breaking patterns of the boson insulating states in the direct lattices. In addition to a checkerboard charge density wave (X-CDW) and a stripe CDW, we find a novel CDW-VBS phase which has both local CDW and local valence bond solid (VBS) orders. Implications on QMC simulations are addressed. The possible experimental realizations of cold atoms loaded on optical lattices are discussed.
Superfluid has been realized in Helium-4, Helium-3 and ultra-cold atoms. It has been widely used in making high-precision devices and also in cooling various systems. There have been extensive experimental search for possible exciton superfluid (ESF)
in semiconductor electron-hole bilayer (EHBL) systems below liquid Helium temperature. However, exciton superfluid are meta-stable and will eventually decay through emitting photons. Here we study quantum nature of photons emitted from the excitonic superfluid (ESF) phase in the semiconductor EHBL and find that the light emitted from the excitonic superfluid has unique and unusual features not shared by any other atomic or condensed matter systems. We show that the emitted photons along the direction perpendicular to the layer are in a coherent state, those along all tilted directions are in a two modes squeezed state. We determine the two mode squeezing spectra, the angle resolved power spectrum, the line shapes of both the momentum distribution curve (MDC) and the energy distribution curve (EDC). From the two photon correlation functions, we find there are photon bunching, the photo-count statistics is super-Poissonian. We discuss how several important parameters such as the chemical potential, the exciton decay rate, the quasiparticle energy spectrum and the dipole-dipole interaction strength between the excitons in our theory can be extracted from the experimental data and comment on available experimental data on both EDC and MDC.
We construct a quantum Ginsburg-Landau theory to study the quantum phases and transitions in electron hole bilayer system. We propose that in the dilute limit as distance is increased, there is a first order transition from the excitonic superfluid (
ESF) to the excitonic supersolid (ESS) driven by the collapsing of a roton minimum, then a 2nd order transition from the ESS to excitonic normal solid. We show the latter transition is in the same universality class of superfluid to Mott transition in a rigid lattice. We then study novel elementary low energy excitations inside the ESS. We find that there are two supersolidon longitudinal modes (one upper branch and one lower branch) inside the ESS, while the transverse mode in the ESS stays the same as that inside a ENS. We also work out various experimental signatures of these novel elementary excitations by evaluating the Debye-Waller factor, density-density correlation, specific heat and vortex -vertex interactions. For the meta-stable supersolid generated by photon pumping, we show that the angle resolved spectrum is dominated by the macroscopic super-radiance from its superfluid component, even it is just a very small percentage of the the whole system. This fact can be used to detect the metastable ESS state generated by photon pumping by a power spectrum experiment easily and without any ambiguity.
By using a dual vortex method, we study phases such as superfluid, solids, supersolids and quantum phase transitions in a unified scheme in extended boson Hubbard models at and slightly away from half filling on bipartite optical lattices such as hon
eycomb and square lattice. We also map out its global phase diagram at $ T=0 $ of chemical potential versus the ratio of kinetic energy over the interaction. We stress the importance of the self-consistence condition on the saddle point structure of the dual gauge fields in the translational symmetry breaking insulating sides, especially in the charge density wave side. We find that in the translational symmetry breaking side, different kinds of supersolids are generic possible states slightly away from half filling. We propose a new kind of supersolid: valence bond supersolid (VB-SS). In this VB-SS, the density fluctuation at any site is very large indicating its superfluid nature, but the boson kinetic energies on bonds between two sites are given and break the lattice translational symmetries indicating its valence bound nature. Implications on possible future QMC simulations in both bipartite lattices are given. All these phases and phase transitions can be potentially realized in ultra-cold atoms loaded on optical bipartite lattices.
We study elementary low energy excitations inside a supersolid. We find that the coupling between the longitudinal lattice vibration mode and the superfluid mode leads to two longitudinal modes (one upper branch and one lower branch) inside the super
solid, while the transverse modes in the supersolid stay the same as those inside a normal solid. We also work out various experimental signatures of these novel elementary excitations by evaluating the Debye-Waller factor, density-density correlation, vortex loop-vertex loop interactions, specific heat and excess entropy from the vacancies per mole.
