We consider the derivative nonlinear Schrodinger equation with constant potential as a model for wave propagation on a discrete nonlinear transmission line. This equation can be derived in the small amplitude and long wavelength limit using the standard reductive perturbation method and complex expansion. We construct some exact soliton and elliptic solutions of the mentioned equation by perturbation of its Stokes wave solutions. We find that for some values of the coefficients of the equation and for some parameters of solutions, the graphical representations show some kinds of symmetries such as mirror symmetry and rotational symmetry.

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Exact solutions of the derivative nonlinear Schrödinger equation for a nonlinear transmission line.

Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field

Bose–Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally relevant optical traps. The nonlinearity, which is proportional to both the number of atoms and the interaction strength, can transform bound states into quasi-bound ones. The latter have a finite lifetime due to tunnelling through the barriers at the borders of the well. We predict the lifetime and stability properties for repulsive and attractive condensates in one, two and three dimensions, for both the ground state and excited soliton and vortex states. We show, via a combination of the variational and WKB approximations, that macroscopic quantum tunnelling in such systems can be observed on time scales of 10 ms to 10 s.

http://iopscience.iop.org/article/10.1088/0953-4075/38/17/012/pdf

Macroscopic quantum tunnelling of Bose–Einstein condensates in a finite potential well

Magnetic solitons in spinor Bose-Einstein condensates confined in a one-dimensional optical lattice are studied by the Holstein-Primakoff transformation method. It is shown that due to the long-range light-induced and static magnetic dipole-dipole interactions, there exist different types of magnetic solitary excitations in different parameter regions. Compared to conventional solid-state materials, the parameters of this type of magnetic solitons in an optical lattice can be easily tuned by the above dipole-dipole interactions, which are highly controllable in experiments.

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Magnetic solitons of spinor Bose-Einstein condensates in an optical lattice

A resonator integrated optic gyro (RIOG) employing trapezoidal phase modulation (TZPM) technique is proposed, analyzed, and demonstrated for the first time. This technique can provide more information about the whole gyro system without complicating the light circuit structure, making it possible to compensate the gyro output in real time. The experimental results of the RIOG prototype show that the standard deviation is greatly reduced after compensation, which proves the viability and effectiveness of the TZPM technique. A bias stability of 0.09 deg/s with an integration time of 10 s over 3000 s is achieved, which is, to our knowledge, the best long-term performance that ever been reported in a RIOG based on a silica waveguide ring resonator.

Resonator integrated optic gyro employing trapezoidal phase modulation technique

We investigate the quantum tunneling of Bose-Einstein condensates in optical lattices under gravity in the "Wannier-Stark localization" regime and "Landau-Zener tunneling" regime. Our results agree with experimental data [B. P. Anderson et al., Science 282, 1686 (1998); F. S. Cataliotti et al., Science 293, 843 (2001)]. We obtain the total decay rate which is valid over the entire range of temperatures, and show how it reduces to the appropriate results for the classical thermal activation at high temperatures, the thermally assisted tunneling at intermediate temperatures, and the pure quantum tunneling at low temperatures. We design an experimental protocol to observe this new phenomenon in further experiments.

/pdf/quantum-tunneling-of-bose-einstein-condensates-in-optical-1rpkdajnyx.pdf

W. M. Zheng

Papers

Quantum tunneling of Bose-Einstein condensates in optical lattices under gravity.