光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变

研究了单模光腔中两组分玻色-爱因斯坦凝聚的基态性质和相关的量子相变.通过利用自旋相干态变换将等效赝自旋哈密顿算符对角化并求得基态能量泛函.基态能量泛函对其经典场变量进行变分并取极小值,得到光子数解和相边界曲线.通过稳定性讨论发现系统除了出现正常相和超辐射相之外,还得到了多稳的宏观量子态;受激辐射来自于原子数反转的集体态,单组分的Dicke系统中并没有此现象;受激辐射只能从一组分的原子中产生,而另外的仍保持在普通超辐射状态.通过调整相关的原子-场耦合强度和频率失谐,超辐射和受激辐射态的顺序可以在原子的两个组分之间互换.     

Generation of Entangled Multi-atom Dicke States in Cavity Quantum Electrodynamics

We propose a scheme to generate two-atom maximally entangled state in cavity quantum electrodynamies （QED）. The scheme can 5e extended to generation of entangled multi-atom Dicke states if we control the interaction time of atoms with cavity modes. We use adiabatically state evolution under large atom-cavity detuning, so the scheme is insensitive to atomic spontaneous decay. The influence of cavity decay on fidelity and success probability is discussed.     

Exact results on decoherence and entanglement in a system of N driven atoms and a dissipative cavity mode

We solve the dynamics of an open quantum system where N strongly driven two-level atoms are equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. We predict decoherencefree subspaces for the whole system and the N-qubit subsystem, the monitoring of quantum coherence and purity decay by atomic populations measurements, the conditional generation of atomic multi-partite entangled states and of cavity cat-like states. We show that the dynamics of atoms prepared in states invariant under permutation of any two components remains restricted within the subspace spanned by the completely symmetric Dicke states. We discuss examples and applications in the cases N = 3, 4. An erratum to this article can be found at     

Quantum dots in photonic crystals: From quantum information processing to single photon nonlinear optics

Quantum dots in photonic crystals are interesting both as a testbed for fundamental cavity quantum electrodynamics (QED) experiments and as a platform for quantum and classical information processing. We describe a technique to coherently access the QD-cavity system by resonant light scattering. Among other things, the coherent access enables a giant optical nonlinearity associated with the saturation of a single quantum dot strongly coupled to a photonic crystal cavity. We explore this nonlinearity to implement controlled phase and amplitude modulation between two modes of light at the single photon level—a nonlinearity observed so far only in atomic physics systems. We also measured the photon statistics of the reflected beam at various detunings with the QD/cavity system. These measurements reveal effects such as photon blockade and photon-induced tunneling, for the first time in solid state. These demonstrations lie at the core of a number of proposals for quantum information processing, and could also be employed to build novel devices, such as optical switches controlled at the single photon level.     

Solvable dynamics of N driven two-level atoms coupled to a dissipative cavity mode

We solve exactly the dynamics of N strongly driven two-level atoms equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. Decoherence-free subspaces are predicted for the whole system and the N-qubit subsystem. Multi-partite entangled states and cavity cat-like states can be conditionally generated. The decay of quantum coherence and purity can be monitored by joint measurements on atomic populations. Atoms prepared in states invariant under permutation of any two components evolve within the subspace spanned by the completely symmetric Dicke states. Applications to N = 3, 4 are discussed.     

激光驱动下腔与玻色-爱因斯坦凝聚中的量子相变

Dicke模型中的量子相变在三十多年前已被预言,该模型描述的是N个二能级原子与单模腔场集体耦合的系统.在标准Dicke模型的基础上加入原子光的非线性相互作用和含时外场驱动,使用含时幺正变换和Holstein-Primafoff变换方法从理论上推导出基态能量表达式.并且给出了丰富的相图,而且这些性质最近已有文献从实验上验证.本文主要呈现了非线性相互作用和外场驱动对量子相变的影响.     

Arbitrary state controlled-unitary gate between two remote atomic qubits via adiabatic passage

We generalize the scheme of Lacour et al. [X. Lacour, N. Sangouard, S. Guerin, H.R. Jauslin, Phys. Rev. A 73 (2006) 042321] to the case of nonlocal qubits, which makes the resultant gate suitable for distributed quantum computation. In our scheme, two remote atomic qubits are separately trapped in two distant cavities connected by an optical fiber. Based on adiabatic passage, our scheme is immune to the decoherence due to spontaneous emission and to photon decay from the cavity modes and the fiber mode. Moreover, our scheme can work robustly beyond the Lamb–Dicke limit. It is shown that the minimum fidelity of the resultant gate operation for an arbitrary input state could be over 0.98.     

A New First-Order Phase Transition for an Extended Jaynes–Cummings–Dicke Model with a High-Finesse Optical Cavity in the BEC System<Superscript>†</Superscript>

We present a two-level atomic Bose–Einstein condensate (BEC) with dispersion, which is coupled to a high-finesse optical cavity. We call this model the extended Jaynes–Cummings–Dicke (JC-Dicke) model and introduce an effective Hamiltonian for this system. From the direct product of Heisenberg–Weyl (HW) coherent states for the field and U(2) coherent states for the matter, we obtain the potential energy surface of the system. Within the framework of the mean-field approach, we evaluate the variational energy as the expectation value of the Hamiltonian for the considered state. We investigate numerically the quantum phase transition and the Berry phase for this system. We find the influence of the atom–atom interactions on the quantum phase transition point and obtain a new phase transition occurring when the microwave amplitude changes. Furthermore, we observe that the coherent atoms not only shift the phase transition point but also affect the macroscopic excitations in the superradiant phase.     

两个原子与双模腔场的多光子相互作用：场和原子的动力学性质

研究一对偶极相互作用原子与双模量子腔场的多光子相互作用，分析场和原子的动力学性质，给出腔模平均光子数和原子反转度时间演化的解析表达式，考察腔模初态、初场强度以及原子间偶极－偶极相互作用的影响。     

Dynamics of the two-atom Jaynes-Cummings model with nondegenerate two-photon transitions

An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.     

Stability of symmetry breaking states in finite-size Dicke model with photon leakage

We investigate the finite-size Dicke model with photon leakage. It is shown that the symmetry breaking states, which are characterized by non-vanishing $〈\stackrel{?}{a}〉\ne 0$ and correspond to the ground states in the superradiant phase in the thermodynamic limit, are stable, while the eigenstates of the isolated finite-size Dicke Hamiltonian conserve parity symmetry. We introduce and analyze an effective master equation that describes the dynamics of a pair of the symmetry breaking states that are the degenerate lowest energy eigenstates in the superradiant region with photon leakage. It becomes clear that photon leakage is essential to stabilize the symmetry breaking states and to realize the superradiant phase without the thermodynamic limit. Our theoretical analysis provides an alternative interpretation using the finite-size model to explain results from cold atomic experiments showing superradiance with the symmetry breaking in an optical cavity.     

Atomic Wehrl entropy and negativity as entanglement measures for qudit pure states in a trapped ion

We analyze the atomic Wehrl entropy and negativity as compared with concurrence for qudit pure states in a trapped ion. We use the density matrix in calculating the three measures of quantum correlations. We find that a long surviving entangled qudit can be established between the three atomic levels and vibrational modes. We observe three distinct entanglements in response to an increasing Lamb–Dicke parameter.     

Entanglement generated by a Dicke phase transition

We consider A atoms interacting dispersively with two cavity modes. We find that the entanglement between two modes of the electromagnetic field is created in a Dicke phase transition.     

First-Order Quantum Phase Transition for Dicke Model Induced by Atom-Atom Interaction

In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on the extended Dicke model's ground state properties, the mean photon number, the scaled atomic population and the average ground energy are displayed. Using the self-consistent field theory to solve the atom-atom interaction, we discover the system undergoes a first-order quantum phase transition from the normal phase to the superradiant phase, but a famous Dicke-type second-order quantum phase transition without the atom-atom interaction. Meanwhile, the atom-atom interaction makes the phase transition point shift to the lower atom-photon collective coupling strength.     

Detuning effects in the vertical cold-atom micromaser

The quantum theory of the cold atom micromaser including the effects of gravity is established in the general case where the cavity mode and the atomic transition frequencies are detuned. We show that atoms which classically would not reach the interaction region are able to emit a photon inside the cavity. The system turns out to be extremely sensitive to the detuning and in particular to its sign. A method to solve the equations of motion for non resonant atom-field interaction and arbitrary cavity modes is presented.     

Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity

We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-Q cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large quantum state superpositions at the quantum-classical boundary.     

Non-equilibrium dynamical phases of the two-atom Dicke model

In this paper, we investigate the non-equilibrium dynamical phases of the two-atom Dicke model, which can be realized in a two species Bose–Einstein condensate interacting with a single light mode in an optical cavity. Apart from the usual non-equilibrium normal and inverted phases, a non-equilibrium mixed phase is possible which is a combination of normal and inverted phase. A new kind of dynamical phase transition is predicted from non-superradiant mixed phase to the superradiant phase which can be achieved by tuning the two different atom–photon couplings. We also show that a dynamical phase transition from the non-superradiant mixed phase to the superradiant phase is forbidden for certain values of the two atom–photon coupling strengths.     

Vacuum-Induced Abelian and Non-Abelian Gauge Potentials in CavityQuantum Electrodynamics

Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems. In this paper, we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics. It is shown that a non-Abelian gauge potential is achieved only for a single atom, whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble. More importantly, two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted. The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes, which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.     

Dicke Quantum Phase Transition for a Bose-Einstein Condensate in a Two-Mode Optical Cavity

In this paper we mainly discuss the ground state properties of the two-mode Dicke model, which is realized in an ensemble of two-level atoms interacting simultaneously with two quantized cavity fields. We reveal rich phase diagrams and discover the second-order quantum phase transition from the normal phase to the superradiant phase by means of the spin-coherent-state variational method. While the critical phase transition point can be shifted by the detuning of the cavity mode or the atom-field coupling imbalance parameter. The collective atom-field coupling imbalance parameter can make the phase transition point symmetrically shift left or right in the resonance or non-resonance. If the two collective atom-photon coupling strengths are not equal in the resonance, the system may be in different phases, while the phases occupied are completely symmetrical. When one of the coupling constants vanishes or two couplings are equal, the ground-states’s properties and related QPT reduce to that of a standard or an ordinary Dicke model.