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Li-Bin Fu

Publications and source records attributed to Li-Bin Fu.

At least 37 records · Page 2Linked to original sources
arXiv2006

Singularity of Berry Connections Inhibits the Accuracy of Adiabatic Approximation

Adiabatic approximation for quantum evolution is investigated quantitatively with addressing its dependence on the Berry connections. We find that, in the adiabatic limit, the adiabatic fidelity may uniformly converge to unit or diverge manifesting the breakdown of adiabatic approximation, depending on the type of the singularity of the Berry connections as the functions of slowly-varying parameter $R$. When the Berry connections have a singularity of $1/R^σ$ type with $σ< 1$, the adiabatic fidelity converges to unit in a power-law; whereas when the singularity index $σ$ is larger than one, adiabatic approximation breaks down. Two-level models are used to substantiate our theory.

quant-ph↗
arXiv2006

Irregular Spin Tunnelling for Spin-1 Bose-Einstein Condensates in a Sweeping Magnetic Field

We investigate the spin tunnelling of spin-1 Bose-Einstein condensates in a linearly sweeping magnetic field with a mean-field treatment. We focus on the two typical alkali Bose atoms $^{87}Rb$ and $^{23}Na$ condensates and study their tunnelling dynamics according to different sweeping rates of external magnetic fields. In the adiabatic (i.e., slowly sweeping) and sudden (i.e., fast sweeping) limits, no tunnelling is observed. For the case of moderate sweeping rates, the tunnelling dynamics is found to be very sensitive on the sweeping rates with showing a chaotic-like tunnelling regime. With magnifying the regime, however, we find interestedly that the plottings become resolvable under a resolution of $10^{-4}$ G/s where the tunnelling probability with respect to the sweeping rate shows a regular periodic-like pattern. Moreover, a conserved quantity standing for the magnetization in experiments is found can dramatically affect the above picture of the spin tunnelling. Theoretically we have given a reasonable interpretation to the above findings and hope our studies would bring more attention to spin tunnelling experimentally.

cond-mat.mes-hall↗
arXiv2006

Quantum Entanglement Manifestation of Transition to Nonlinear Self-trapping for Bose-Einstein Condensates in a Symmetric Double-Well

We investigate the nonlinear self-trapping phenomenon of the Bose-Einstein condensates (BEC) in a symmetric double-well, emphasizing on its behind dynamical phase transition. With increasing the nonlinear parameter depicting the interaction between the degenerate atoms the BEC turns to be self-trapped manifesting an asymmetric distribution of the atomic density profile. Essence of this phenomenon is revealed to be a continuous phase transition and underlying critical behavior is studied analytically and found to follow a logarithm scaling-law. We then go beyond the mean field treatment and extend to discuss the effect of the many-body quantum fluctuation on the transition. It is found that the transition point is shifted and the scaling-law is broken. In particular, the quantum phase transition is accompanied by the change of the entanglement entropy which is found to reach maximum at transition point. Behind physics is revealed.

cond-mat.mes-hall↗
arXiv2006

Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap

We investigate the tunnelling dynamics of Bose-Einstein-Condensates(BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling-law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunnelling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poicaré section method that visualizes the motions of BECs in a reduced phase plane.

cond-mat.other↗
arXiv2006

Collective excitations of a Bose-Einstein condensate in an anharmonic trap

We investigate the collective excitations of a one-dimensional Bose-Einstein condensate (BEC) with repulsive interaction between atoms in a quadratic plus quartic trap. By using the variational approach, the coupled equations of motion for the center-of-mass coordinate of the condensate and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations, which originate from the nonlinear coupling between the two modes, are discussed.

cond-mat.mes-hall↗
arXiv2006

Measurable nonlocal effect of bipartite system during a local cyclic evolution of its subsystem

In this letter, a nonlocal effect for a bipartite system which is induced by a local cyclic evolution of one of its subsystem is suggested. This effect vanishes when the system is at a disentangled pure state but can be observed for some disentangled mixed states. As a paradigm, we study the effect for the system of two qubits in detail. It is interesting that the effect is directly related to the degree of entanglement for pure state of qubit pairs. Furthermore, we suggest a Bell-type experiment to measure this nonlocal effect for qubit pairs.

quant-ph↗
arXiv2006

Landau-Zener Tunnelling in a Nonlinear Three-level System

We present a comprehensive analysis of the Landau-Zener tunnelling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunnelling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of linear case. In particular, the tunnelling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunnelling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunnelling probability when the nonlinear "internal field" resonate with the external field. We also discuss the asymmetry of the tunnelling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.

cond-mat.mes-hall↗
arXiv2005

Periodic Modulation Effect on Self-Trapping of Two weakly coupled Bose-Einstein Condensates

With phase space analysis approach, we investigate thoroughly the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BEC) in a symmetric double-well potential. We identify two kinds of self-trapping by their different relative phase behavior. With applying a periodic modulation on the energy bias of the system we find the occurrence of the self-trapping can be controlled, saying, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high and low frequency modulations. For an intermediate frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affects the tunnelling dynamics and demonstrate many novel phenomena. Finally, we study the effects of many-body quantum fluctuation on self-trapping and discuss the possible experimental realization of the model.

cond-mat.mes-hall↗
arXiv2005

Topology hidden behind the breakdown of adiabaticity

For classical Hamiltonian systems, the adiabatic condition may fail at some critical points. However, the breakdown of the adiabatic condition does not always make the adiabatic evolution be destroyed. In this paper, we suggest a supplemental condition of the adiabatic evolution for the fixed points of classical Hamiltonian systems when the adiabatic condition breaks down at the critical points. As an example, we investigate the adiabatic evolution of the fixed points of a classical Hamiltonian system which has a number of applications.

physics.class-ph↗
arXiv2004

Maximal violation of Clauser-Horne-Shimony-Holt inequality for four-level systems

Clauser-Horne-Shimony-Holt inequality for bipartite systems of 4-dimension is studied in detail by employing the unbiased eight-port beam splitters measurements. The uniform formulae for the maximum and minimum values of this inequality for such measurements are obtained. Based on these formulae, we show that an optimal non-maximally entangled state is about 6% more resistant to noise than the maximally entangled one. We also give the optimal state and the optimal angles which are important for experimental realization.

quant-ph↗
arXiv2004

Landau-Zener tunneling with many-body quantum effects in crystals of molecular magnets

We present a quantum interpretation of the heights in hysteresis of $Fe_{8}$ molecule at lower temperatures by treating the crystal as an Ising spin system with the dipolar interaction between spins. Then we apply it to two limit cases : rapid and adiabatic regions. Our theoretical analysis is in agreement with the experimental observation in these regions, which indicates that the steps in hysteresis loops of magnetization of Fe$_{8}$ at lower temperatures show a pure quantum process.

cond-mat.other↗
arXiv2004

Geometric Phases for Mixed States during Cyclic Evolutions

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85}, 2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states.

quant-ph↗
arXiv2004

General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two-dimension. This inequality is optimal in the same sense as the CHSH inequality for two dimensional systems, namely, the maximal amount by which the inequality is violated consists with the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].

quant-ph↗
arXiv2003

Maximal violation of Clauser-Horne-Shimony-Holt inequality for two qutrits

Bell-Clauser-Horne-Shimony-Holt inequality (in terms of correlation functions) of two qutrits is studied in detail by employing tritter measurements. A uniform formula for the maximum value of this inequality for tritter measurements is obtained. Based on this formula, we show that non-maximally entangled states violate the Bell-CHSH inequality more strongly than the maximally entangled one. This result is consistent with what was obtained by Ac{í}n {\it et al} [Phys. Rev. A {\bf 65}, 052325 (2002)] using the Bell-Clauser-Horne inequality (in terms of probabilities).

quant-ph↗
arXiv2002

Critical onset in coherent oscillations between two weakly coupled Bose-Einstein condensates

The Josephson effects in two weakly linked Bose-Einstein condensates have been studied recently. In this letter, we study the equations derived by Giovanazzi et. al. [Phys. Rev. Lett. 84, 4521 (2000)] focusing on the effects of the initial acceleration and the velocity of the barrier on the ``dc'' current. We find that the dc current has lifetime which critically depends on the moving velocity of the barrier. Moreover, the influence of the initial acceleration is also investigated and found to be crucial for the experimental realization of the effects.

cond-mat↗
arXiv2002

The configuration of a topological current and physical structure: an application and paradigmatic evidence

In the $ϕ$-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between different structures happens at the bifurcation point of the topological current. In a self-interaction two-level system, the change of topological particles corresponds to change of energy levels.

physics.gen-ph↗
arXiv2001

Understanding Quantum Entanglement of Bipartite System Based on Bell Inequality

We present an alternative definition of quantum entanglement for bipartite system based on Bell inequality and operators' noncommutativity. A state is said to be entangled, if the maximum of CHSH expectation value $F_{\max}$ is obtain by noncommutative measures on each particle of the bipartite system; otherwise, the state is a disentangled state. A uniform measure quantifying the degree of entanglement for any state of the bipartite system is also proposed.

quant-ph↗