Laser-Manipulating Macroscopic Quantum States of a Bose-Einstein Condensate Held in a Kronig-Penny Potential

We investigate the boundary vaJue problem （BVP） of a quasi-one-dimensional Gross-Pitaevskii equation with the Kronig-Penney potential （KPP） of period d, which governs a repulsive Bose-Einstein condensate. Under the zero and periodic boundary conditions, we show how to determine n exact stationary eigenstates {Rn} corresponding to different chemical potentials {μn} from the known solutions of the system. The n-th eigenstate P~ is the Jacobian elliptic function with period 2din for n = 1,2,…, and with zero points containing the potential barrier positions. So Rn is differentiable at any spatial point and R2 describes n complete wave-packets in each period of the KPP. It is revealed that one can use a laser pulse modeled by a 5 potential at site xi to manipulate the transitions from the states of {Rn} with zero Point x≠xi to the states of {Rn＇} with zero Point x= Xi. The results suggest an experimental scheme for applying BEC to test the BVP and to observe the macroscopic quantum transitions.

Macroscopic Quantum Coherence in Antiferromagnetic Molecular Magnets

The macroscopic quantum coherence in a biaxial antiferromagnetic molecular magnet in the presence of magnetic field acting parallel to its hard anisotropy axis is studied within the two-sublattice model. On the basis of instanton technique in the spin-coherent-state path-integral representation, both the rigorous Wentzel-Kramers-Brillouin exponent and pre-exponential factor for the ground-state tunnel splitting are obtained. We find that the quantum fluctuations around the classical paths can not only induce a new quantum phase previously reported by Chiolero and Loss (Phys. Rev. Lett. 80 (1998) 169), but also have great influence on the intensity of the ground-state tunnel splitting. Those features clearly have no analogue in the ferromagnetic molecular magnets. We suggest that they may be the universal behaviors in all antiferromagnetic molecular magnets. The analytical results are complemented by exact diagonalization calculation.

Macroscopic Quantum Coherence in an Antiferromagnetic Spin Chain with Biaxial Anisotropy

Instanton configurations of （1＋1）-dimensions in an antiferromagnetic biaxial-anisotropy-spin-chain are obtained explicitly in the strong anisotropy limit, which interpolate between degenerate equilibrium orientations of the Neel vector along easy axis and are seen to be responsible for quantum tunneling. Macroscopic quantum coherence of the domain walls is demonstrated in terms of the instantons.

Enhancement of feasibility of macroscopic quantum superposition state with the quantum Rabi-Stark model

We propose an efficient scheme to generate a macroscopical quantum superposition state with a cavity optomechanical system,which is composed of a quantum Rabi-Stark model coupling to a mechanical oscillator.In a low-energy subspace of the Rabi-Stark model,the dressed states and then the effective Hamiltonian of the system are given.Due to the coupling of the mechanical oscillator and the atom-cavity system,if the initial state of the atom-cavity system is one of the dressed states,the mechanical oscillator will evolve into a corresponding coherent state.Thus,if the initial state of the atom-cavity system is a superposition of two dressed states,a coherent state superposition of the mechanical oscillator can be generated.The quantum coherence and their distinguishable properties of the two coherent states are exhibited by Wigner distribution.We show that the Stark term can enhance significantly the feasibility and quantum coherence of the generated macroscopic quantum superposition state of the oscillator.

Macroscopic Quantum Tunneling and Coherence of the Néel Vector in Small Antiferromagnets

The tunneling behavior of the Néel vector out of metastable easy directions or between degenerate easy directions is studied for a small single\|domain antiferromagnetic particle at low temperature. The quantum tunneling rates for these processes are evaluated for two examples of macroscopic quantum tunneling and one example of macroscopic quantum coherence. The calculations are performed by using the two sublattice model and the instanton method in the spin coherent state path integral. Quantum interference or the spin parity effect is also discussed for each case.

Macroscopic Quantum Phenomena and Topological Phase Interference Effects in Single-Domain Magnets

The tunneling of macroscopic object is one of the most fascinating phenomena in condensed matter physics. During the last decade, the problem of quantum tunneling of magnetization in nanometer-scale magnets has attracted a great deal of theoretical and experimental interest. A review of recent theoretical research of the macroscopic quantum phenomena in nanometer-scale single-domain magnets is presented in this paper. It includes macroscopic quantum tunneling (MQT) and coherence (MQC) in single-domain magnetic particles, the topological phase interference or spin-parity effects, and tunneling of magnetization in an arbitrarily directed magnetic field. The general formulas are shown to evaluate the tunneling rate and the tunneling level splitting for single-domain AFM particles. A nontrivial generalization of Kramers degeneracy for double-well system is provided to coherently spin tunneling for spin systems with m-fold rotational symmetry. The effects induced by the external magnetic field have been studied, where the field is along the easy, medium, hard axis, or arbitrary direction.

Quantum Nucleation of Antiferromagnetic Bubbles with Tetragonal and Hexagonal Symmetries

We study the quantum nucleation in a nanometer-scale antiferromagnet placed in a magnetic field at an arbitrary angle. We consider the magnetocrystalline anisotropy with tetragonal symmetry and that with hexagonal symmetry, respectively. Different structures of the tunneling barriers can be generated by the magnitude and the orientation of the magnetic field. We use the instanton method in the spin-coherent-state path-integral representation to calculate the dependence of the rate of quantum nucleation and the crossover temperature on the orientation and strength of the field for bulk solids and two-dimensional films of antiferromagnets, respectively. We find that the rate of quantum nucleation and the crossover temperature from thermal-to-quantum transitions depend on the orientation and strength of the external magnetic field distinctly, which can be tested by use of existing experimental techniques.

Fabrication of high-quality submicron Nb/Al-AlO_x/Nb tunnel junctions

Nb/Al-AlOx/Nb tunnel junctions are often used in the studies of macroscopic quantum phenomena and superconducting qubit applications of the Josephson devices. In this work, we describe a convenient and reliable process using electron beam lithography for the fabrication of high-quality, submicron-sized Nb/Al-AlOx/Nb Josephson junctions. The technique follows the well-known selective Nb etching process and produces high-quality junctions with Vm=100 mV at 2.3 K for the typical critical current density of 2.2 kA/cm^2, which can be adjusted by controlling the oxygen pressure and oxidation time during the formation of the tunnelling barrier. We present the results of the temperature dependence of the sub-gap current and in-plane magnetic-field dependence of the critical current, and compare them with the theoretical predictions.

Nb/Al-AlO_x/Nb junctions with controllable critical current density for qubit application

Nb/Al-AlOx/Nb tunnel junctions with controllable critical current density Jc are fabricated using the standard selective Nb etching process. Tunnel barriers are formed in different oxygen exposure conditions （oxygen pressure P and oxidation time t）, giving rise to Jc ranging from 100A/cm^2 to above 2000A/cm^2. Jc shows a familiar linear dependence on P×t in logarithmic scales. We calculate the energy levels of the phase- and flux-type qubits using the achievable junction parameters and show that the fabricated Nb/Al-AlOx/Nb tunnel junctions can be used conveniently for quantum computation applications in the future.

The connection between meridians and physiological functions:A quantum principle

In the long history of traditional Chinese medicine(TCM),meridians play essential roles as the critical network to regulate the normal physiological functions of the human body.They are regarded to be the channels connecting the internal organs with the body surface and various parts of the body.Although there are many studies and doctrines trying to reveal the nature of meridians for their validation in TCM,the mechanism underlying the meridians remains unclear.Herein,based on our macroscopic quantum state concept of ion channels(i.e.,sub-nanometer scale channels),we propose a quantum principle of meridians.The acupoints and organ symptom are in a macroscopic coherence state of the ion channels in meridians.By applying TCM treatments(e.g.,TCM massage,acupuncture,moxibustion,and electroacupuncture)on the acupoint,the corresponding organ symptom could be well regulated with help of quantum meridian state.

Determination of Relaxation Time of a Josephson Tunnel Junction

We propose a non-stationary method to measure the energy relaxation time of Josephson tunnel junctions from microwave enhanced escape phenomena. Compared with the previous methods, our method possesses simple and accurate features. Moreover, having determined the energy relaxation time, we can further obtain the coupling strength between the microwave source and the junction by changing the microwave power.

Effects of Arbitrarily Directed Field on Spin Phase Oscillations in Biaxial Molecular Magnets

Quantum phase interference and spin-parity effects are studied in biaxial molecular magnets in a magnetic field at an arbitrarily directed angle. The calculations of the ground-state tunnel splitting are performed on the basis of the instanton technique in the spin-coherent-state path-integral representation, and complemented by exactly numerical diagonalization. Both the Wentzel–Kramers–Brillouin exponent and the pre-exponential factor are obtained for the entire region of the direction of the field. Our results show that the tunnel splitting oscillates with the field for the small field angle, while for the large field angle the oscillation is completely suppressed. This distinct angular dependence, together with the dependence of the tunnel splitting on the field strength, provides an independent test for spin-parity effects in biaxial molecular magnets. The analytical results for the molecular magnet are found to be in good agreement with the numerical simulations, which suggests that even the molecular magnet with total spin is large enough to be treated as a giant spin system.

Atomic population oscillations between two coupled Bose-Einstein condensates with time-dependent nonlinear interaction

The atomic population oscillations between two Bose-Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system＇s steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping （MQST）. In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.

Phase escape of current-biased Josephson junctions

Switching current distributions of an Nb/Al-AlO2/Nb Josephson junction are measured in a temperature range from 25 mK to 800 mK. We analyse the phase escape properties by using the theory of Larkin and Ovchinnikov （LO） which takes discrete energy levels into account. Our results show that the phase escape can be well described by the LO approach for temperatures near and below the crossover from thermal activation to macroscopic quantum tunneling. These results are helpful for further study of macroscopic quantum phenomena in Josephson junctions where discrete energy levels need to be considered.

The effect of doped ions on single-molecule magnets of the Mn_(12)-Ac family

This paper investigates the single-molecule magnets of pure and Cr/Fe-doped Mn12-Ac. The components of the mixed crystals are identified by AC susceptibility technique. The ground-state spin and anisotropy parameters of doped Mn12-Ac are obtained： （i） MnllCr-Ac （S=19/2, D=0.62K, B=0.0009K, A=63K）, and （ii） Mn11Fe-Ac （S=21/2, D=0.39 K, B=0.001 K, △=55 K）. The single-ion origin of the magnetic anisotropy is discussed.

Quantum dynamics of an impurity-doped Bose–Einstein condensate system

We study the quantum dynamics of an impurity-doped Bose–Einstein condensate(BEC) system.We show how to generate the macroscopic quantum superposition states(MQSSs) of the BEC by the use of projective measurements on impurity atoms. It is found that the nonclassicality of MQSSs can be manipulated by changing the number of the impurities and their interaction with the BEC. It is shown that the BEC matter-wave field exhibits a collapse and revival phenomenon which reveals the quantum nature of the BEC matter-wave field. We investigate the micro-macro entanglement between the impurities and the BEC, and find enhancement of the micro-macro entanglement induced by the initial quantum coherence of the impurity atoms.

Preparation of Macroscopic Entangled Coherent States in Nitrogen-Vacancy Centers Ensembles Coupled to a Superconducting Flux Qubit

We propose a potentially practical scheme for creating macroscopic entangled coherent state between two separate nitrogen-vacancy center spin ensembles placed near a superconducting flux qubit. Through the collective magnetic coupling and the in situ tunability of the flux qubit, the arbitrary entangled coherent states of spin ensembles can be achieved with high success possibilities under the influence from decoherence of the flux qubit and spin ensembles.The experimental feasibility and challenge are justified using currently available technology.

Levitated optomechanics:From single to many-body physics

The levitated optomechanics,because of its ultra-high mechanical Q>1010,is considered to be one of the best testbeds for macroscopic quantum superpostions.In this perspective,we give a brief review on the development of the levitated optomechanics,focusing on the macroscopic quantum phenomena,and the applications in quantum precision measurement.The levitated nanodiamond with built-in nitrogen-vacancy centers is discussed as an example.Finally,we discuss the future dirctions of the levtated optomechanics,such as the space-based experiments,the arrays of levitated optomechanics and applications in quantum simulation.

Population dynamics of ultra-cold atoms interacting with radiation fields in the presence of inter-atomic collisions

We investigate the dynamics of a system that consists of ultra-cold three-level atoms interacting with radiation fields.We derive the analytical expressions for the population dynamics of the system,particularly,in the presence and absence of nonlinear collisions by considering the rotating wave approximation(RWA).We also reanalyze the dynamics of the system beyond RWA and obtain the state vector of the system to study and compare the time behavior of population inversion.Our results show that the system undergoes two pure quantum phenomena,i.e.,the collapse-revival and macroscopic quantum self-trapping due to nonlinear collisional interactions.The occurrence of such phenomena strongly depends on the number of atoms in the system and also the ratio of interaction strengths in the considered system.Finally,we show that the result of the perturbed time evolution operator up to the second-order is in agreement with the numerical solution of the Schrodinger equation.The results presented in the paper may be useful for the design of devices that produce a coherent beam of bosonic atoms known as an atom laser.

Tunneling and Self-Trapping of Superfluid Fermi Gases in BCS-BEC Crossover

We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer （BCS） superfluid to Bose-Einstein condensates （BEC）. Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the ease of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.