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Scientific Reports

Single-impurity-induced Dicke quantum phase transition in a cavity-Bose-Einstein condensate

Ji-Bing Yuan, Wangjun Lu, Ya‐Ju Song, Le‐Man Kuang

Published Aug 1, 2017• 19 citations
Publisher

Abstract

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 induce Dicke 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).

DOI
10.1038/s41598-017-07899-x

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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 induce Dicke 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).
We present a new generalized Dicke model, an impurity-doped Dicke model (IDDM), by the use of an impurity-doped cavity-Bose-Einstein condensate. It is shown that the impurity atom can induce Dicke quantum phase transition (QPT) from the normal phase to superradiant phase at a critic value of the impurity population. It is found that the IDDM exhibits continuous Dicke QPT with an infinite number of critical points, which is significantly different from that observed in the standard Dicke model with only one critical point. It is revealed that the impurity-induced Dicke QPT can happen in an arbitrary coupling regime of the cavity field and atoms while the Dicke QPT in the standard Dicke model occurs only in the strong coupling regime of the cavity field and atoms. This opens a way to observe the Dicke QPT in the intermediate and even weak coupling regime of the cavity field and atoms.
We study Einstein-Podolsky-Rosen (EPR) steering properties of quantum phases in the generalized Dicke model (GDM) generated by a cavity Bose-Einstein condensate (BEC) doped with a single impurity. It is shown that the normal and superradiant phases of the GDM exhibit much rich EPR steerability. In the normal phase, there exist one-way EPR steering from the cavity field (condensed atoms) to condensed atoms (the cavity field). In the superradiant phase, there is either one-way or two-way EPR steering for the cavity field and condensed atoms. It is found that the single impurity can act as a single-atom switch of the EPR steering to control the steering direction of one-way EPR steering and the transition between one-way and two-way EPR steering through switching on or off the impurity-BEC coupling. It is proved that the EPR steering parameters can witness the quantum phase transition (QPT) occurrence through the sudden change of the EPR steering parameters at the critical point of the QPT. Our results open a new way to manipulate macroscopic EPR steering and witness the QPT between the normal phase and the superradiant phase in the GDM through a microscopic impurity atom.
Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.
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.
When an atomic ensemble is coupled with a cavity field governed by the well-known Dicke model , an important quantum phase transition (QPT) from the normal phase to the superradiant phase occurs, which was predicted more than 30 years ago. In this paper, both the atom-photon nonlinear interaction and the driving field are added to the Dicke's Hamiltonian. With the method of Holstein-Primafoff transformation, the ground state energy is given by the theoretical calculation, and the rich phase figures are presented. Meanwhile, these properties are observed experimentally. We mainly dicuss the effects of the atom-photon nonlinear interaction and the driving field on QPT.