Dynamics of geometric phase for composite quantum system under nonlocal unitary transformation: a case study of dimer system

In this paper, we explore the dynamical properties of geometric phase for a composite quantum system under the nonlocal unitary evolution. As an illustrative example, the analytical expressions of geometric phase are derived for the dimer system. We find that geometric phase presents some interesting properties with coupling strengths (corresponding to nonlocal unitary evolution), such as dynamical oscillation behavior with time evolution, monotonicity, symmetry, etc. We show that the geometric phase and entanglement have the same period for some conditions. Moreover, we discuss geometric phase of the whole system and its subsystems. Our investigations show that geometric phase can reflect some inherent properties of the system: it signals a transition from self-trapping to delocalization.     

Interaction of a Three-Level Atom and Field in a Squeezed Vacuum State with Added Photons: Quantum Phase and Nonclassical Properties

We present a detail study of the evolution of nonlocal correlations of an interacting quantum system comprising a three-level atom and a field mode initially prepared in a squeezed vacuum state with added photons. We compare the dynamical behavior of the quantum phase and entanglement by varying the number of photons added to the squeezed vacuum state. Furthermore, we examine the influence of the added-photon number and the squeeze parameter on the dynamical behavior of entanglement, quantum phase, and nonclassical properties of the field. Moreover, we explore the link between the quantum phase and the nonlocal correlation. Finally, we introduce an effective method to generate and maintain a high level of entanglement for this quantum system based on precise parameter ranges.     

Fisher information due to a phase noisy laser under non-Markovian environment

More recently, K. Berrada [Annals of Physics 340 (2014) 60-69] [1] studied the geometric phase of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system, and collapse and revival phenomena were found for large class of states. In this paper, using this noise effect, we study the quantum fisher information (QFI) for a two-level atom system driven by a phase noise laser under non-Markovian dynamics. A new quantity, called QFI flow is used to characterize the damping effect and unveil a fundamental connection between non-Markovian behavior and dynamics of system–environment correlations under phase noise laser. It is shown that QFI flow has disappeared suddenly followed by a sudden birth depending on the kind of the environment damping. QFI flow provides an indicator to characterize the dissipative quantum system’s decoherence by analyzing the behavior of the dynamical non-Markovian coefficients.     

Collapse–revival of quantum discord and entanglement

In this paper the correlations dynamics of two atoms in the case of a micromaser-type system is investigated. Our results predict certain quasi-periodic collapse and revival phenomena for quantum discord and entanglement when the field is in Fock state and the two atoms are initially in maximally mixed state, which is a special separable state. Our calculations also show that the oscillations of the time evolution of both quantum discord and entanglement are almost in phase and they both have similar evolution behavior in some time range. The fact reveals the consistency of quantum discord and entanglement in some dynamical aspects.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases

We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.     

On the asymptotic behavior of dynamical maps for a finite quantum system

We give some remarks on the dynamical evolution (also nonlinear) of finite quantum system. We are interested int-asymptotic behavior of density matrices in the Liouville space formalism and we show that for nonlinear dynamical semigroups, as well as for the dynamical maps that do not form semigroups, the stationary time evolution may be attained for finite time in contrast to the motion generated by the linear dynamical semigroup. Recently the problem of constructing a nonlinear analog of quantum mechanics with nonlinear wave equation playing the role of the Schrödinger equation has been investigated by some authors; see for example Mielnik (1974), Bergmann (1968). Our work is related to this investigation and gives a characteristic feature of the nonlinear time evolution.     

Effects of Initial Correlation and Quantum Coherence on the Energy Transfer,Purity and Entanglement

We investigate the influences of the initial correlation and quantum coherence on a bipartite dissipative system which is modeled by two two-level quantum emitters driven by an external laser field. It is shown that the initial correlation can enhance or suppress the dynamical evolution of the energy transfer quantified by the excited-state population and the information flow between the two emitters characterized by the purity. We also present the degree of the influence of the initial correlation that is determined by the quantum coherence induced by a relative phase. By introducing Bloch sphere, we illustrate the relation between the energy transfer and the purity. In addition, a scheme for generating maximally entangled steady state is proposed.     

共同环境中三原子间纠缠演化特性研究

研究了三个二能级原子与共同热库发生相互作用的系统纠缠动力学演化. 采用三体负本征值来描述系统间纠缠, 通过数值计算分析了初始状态和原子间偶极-偶极相互作用对系统间纠缠演化的影响. 结果表明, 初始状态的原子相位可以控制量子干涉现象; 长时间演化下原子的激发态布居出现俘获现象; 通过调节偶极-偶极相互作用强度, 可以提升三原子间纠缠.     

Conditional quantum phase gate between two 3-state atoms

We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data bus. In addition, it requires only common addressing of the two atoms by external laser fields.     

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.     

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The dynamics of cold atoms in conservative optical lattices obviously depends on the geometry of the lattice. But very similar lattices may lead to deeply different dynamics. In a 2D optical lattice with a square mesh, it is expected that the coupling between the degrees of freedom leads to chaotic motions. However, in some conditions, chaos remains marginal. The aim of this paper is to understand the dynamical mechanisms inhibiting the appearance of chaos in such a case. As the quantum dynamics of a system is defined as a function of its classical dynamics – e.g. quantum chaos is defined as the quantum regime of a system whose classical dynamics is chaotic – we focus here on the dynamical regimes of classical atoms inside a well. We show that when chaos is inhibited, the motions in the two directions of space are frequency locked in most of the phase space, for most of the parameters of the lattice and atoms. This synchronization, not as strict as that of a dissipative system, is nevertheless a mechanism powerful enough to explain that chaos cannot appear in such conditions.     

Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.     

Quantum interferences in cooperative Dicke emission from spatial variation of the laser phase

We report the generation of a new quantum interference effect in spontaneous emission from a resonantly driven system of two identical two-level atoms due to the spatial variation of the laser phase at the positions of the atoms. This interference affects significantly the spectral features of the emitted radiation and the quantum entanglement in the system. The interference leads to dynamic coupling of the populations and coherences in a basis, determined by the laser phase and represents a kind of vacuum mediated superexchange between the symmetric and antisymmetric states.     

Quantum speed limit for a three-qubit system in spin-chain environment with multisite interaction

We study the relationship between the quantum speed limit (QSL) time of a three-qubit system, and the quantum phase transitions (QPTs) of a spin-chain environment with the three-spin interaction. We find that the three-spin interaction can effectively manipulate the critical value of the QSL time. It makes the QSL time mark more clearly the quantum phase transition of the one-dimensional spin-chain models, especially the XX model. The dynamical evolution of the QSL time presents a periodic behavior in quantum-critical environment, whereas the three-spin interaction and external magnetic field can destroy this periodicity.     

Probing Nonclassicality of Two-Mode SU(2) Generator Based on Quantum Fisher Information

Nonclassicality is an essential but still open question in quantum mechanics. Here, utilizing the maximum value of quantum Fisher information, we suggest a new version of the nonclassical criterion for SU(2) generator realized by two bosonic modes. As an application of the criterion, the system of two coupled nonlinear nanomechanical resonators is considered. And the nonclassicality of the phonon state in the dynamical evolution is explored. The system has a dynamical phase transition from the tunnelling phase to the self-trapping phase by tuning the coupling strength. It is found that for the tunnelling phase, the phonon state is nonclassical in the full time evolution. And for the self-trapping phase, the evolved phonon state is still nonclassical in the full time with a relatively large coupling strength, while it is nonclassical i n the most of time (but not all) with a small coupling strength. Quantum coherence has distinct different behaviors in the two phases.     

Molecular dynamics study of the stability of a carbon nanotube atop a catalytic nanoparticle

The effect of spontaneously generated coherence (SGC) on the quantum heat engine (QHE) consisting of a laser system is studied in terms of its dynamical evolution and the generation of coherences. The QHE is coupled to the two thermal photon reservoirs, a squeezed thermal bath as well as to a cavity mode. The coherence associated with the transition interacting with squeezed reservoir and the average thermal photon number of the hot (as well as cold) reservoir shows a non monotonous behavior between them. The dynamics along with generated coherences of the system and the laser power emitted depend sensitively on the hot, cold and squeezed reservoir parameters.     

QUANTUM STATISTICS OF AN ATOM LASER IN THE PRESENCE OF A STRONG INPUT LIGHT

Within the framework of quantum dynamical theory, we present a new method to control the quantum statistics of an atom laser by applying a powerful input light. Differing from the case in the rotating wave approximation, the non-classical properties can appear in the output atom laser beam with the evolution of time. By choosing a suitable phase of the input light, it is capable of realizing a steady and brighter output of coherent atom laser.