We present a new generalized Dicke model, an impurity-doped Dicke model (IDDM), by the use of an impurity-doped cavity-Bose-Einstein condensate (BEC). It is shown that the impurity atom can induceDicke quantum phase transition (QPT) from the normal phase to superradiant phase at a critic value of the impurity population. It is found that the impurity-induced Dicke QPT can happen in an arbitrary field-atom coupling regime while the Dicke QPT in the standard Dicke model occurs only in the strong coupling regime of the cavity field and atoms. This opens the possibility to realize the control of quantum properties of a macroscopic-quantum system (BEC) by using a microscopic quantum system (a single impurity atom).In recent years ultracold atoms in optical cavities have revealed themselves as attractive new systems for studying strongly-interacting quantum many-body theories. Their high degree of tunability makes them especially attractive for this purpose. One example, which has been extensively studied theoretically and experimentally, is the Dicke quantum phase transition (QPT) from the normal phase to the superradiant phase with a Bose-Einstein condensate (BEC) in an optical cavity 1-10 . The Dicke model 11 describes a large number of two-level atoms interacting with a single cavity field mode, and predicts the existence of the Dicke QPT 10, 12-15 from the normal phase to the superradiant phase. However, it is very hard to observe the Dicke QPT in the standard Dicke model, since the critical collective atom-field coupling strength needs to be of the same order as the energy separation between the two atomic levels. Fortunately, strong collective atom-field coupling has realized experimentally in a BEC coupling with a ultrahigh-finesse cavity filed 16,17 . C. Emary and T. Brandes 18 first indicated that the Dicke model exhibits a zero-temperature QPT from the normal phase to the superradiant phase in the thermodynamic limit. Then, D. Nagy et al. 4 pointed out that the Dicke QPT from the normal to the superradiant phase corresponds to the self-organization of atoms from the homogeneous into a periodically patterned distribution. Soon after this, the Dicke QPT was experimentally observed in the sense of the self-organization of atoms by using the cavity-BEC system 2 . In the Dicke QPT experimental realization 2 , the normal phase corresponds to the BEC being in the ground state associated with vacuum cavity field state while both the BEC and cavity field have collective excitations in the super-radiant phase. A few extended Dicke models 9,19 have been proposed to reveal rich phase diagrams and exotic QPTs, which are different from those in the original Dicke model. Impurities in a BEC have motivated the investigation of a wide range of phenomena [20][21][22][23][24][25][26][27][28][29][30][31][32][33] . For instance, a single impurity can probe superfluidity 20,21 . A neutral impurity can self-localize in BECs 22-25 , and can be dressed into a quasiparticle, the Bose polaron [26][27][28][29][30] and the soliton for ...

No abstract

We investigate nonlinear Dicke quantum phase transition (QPT) induced by inter-atomic nonlinear interaction and its quantum witness in a cavity-Bose–Einstein-condensate (BEC) system. It is shown that inter-atomic nonlinear interaction in a cavity BEC system can induce first-order Dicke QPT. It is found that this nonlinear Dicke QPT can happen in an arbitrary coupling regime of the cavity and atoms. It is demonstrated that the quantum speed limit time can witness the Dicke QPT through its sudden change at the critical point of the QPT.