Abstract: Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases. However, so far, how to detect these quantum phases effectively remains an outstanding challenge. Here, we show that the optical Bragg scattering of cold atoms loaded on optical lattices can be used to detect many quantum phases, which include not only the conventional superfluid and Mott insulating phases, but also other important phases, such as various kinds of charge density wave (CDW), valence bond solid (VBS), CDW supersolid (CDW-SS) and Valence bond supersolid (VB-SS).
Notes: Ye, Jinwu Zhang, J. M. Liu, W. M. Zhang, Keye Li, Yan Zhang, Weiping
Abstract: We study quench dynamics of the Bose-Hubbard model by exact diagonalization. Initially, the system is at thermal equilibrium and of a finite temperature. The system is then quenched by changing the on-site interaction strength U suddenly. Both the single-quench and double-quench scenarios are considered. In the former case, the time-averaged density matrix and the real-time evolution are investigated. It is found that though the system thermalizes only in a very narrow range of the quenched value of U, it does equilibrate or relax well into a much larger range. Most importantly, it is proven that this is guaranteed for some typical observables in the thermodynamic limit. In order to test whether it is possible to distinguish the unitarily evolving density matrix from the time-averaged (thus time-independent), fully decohered density matrix, a second quench is considered. It turns out that the answer is affirmative or negative depending on whether the intermediate value of U is zero or not.
Abstract: We point out that in higher dimensions, in contrast to the one-dimensional case considered usually, Bloch oscillation driven by a static force can induce transport of the wave packet. The wave packet oscillates constantly, but on a larger time scale it drifts at a constantly velocity permanently. As a noteworthy feature, the net transport in the long run is always normal to the external force and thus controlled by it. We verify this prediction numerically and discuss its experimental realization both with cold atoms in optical lattices and with two-dimensional photonic lattices.
Abstract: We take the Bose-Hubbard model to illustrate exact diagonalization techniques in a pedagogical way. We follow the route of first generating all the basis vectors, then setting up the Hamiltonian matrix with respect to this basis and finally using the Lanczos algorithm to solve low lying eigenstates and eigenvalues. Emphasis is placed on how to enumerate all the basis vectors and how to use the hashing trick to set up the Hamiltonian matrix or matrices corresponding to other quantities. Although our route is not necessarily the most efficient one in practice, the techniques and ideas introduced are quite general and may find use in many other problems.
Abstract: We propose to probe the quantum ground state of a spin-1 Bose-Einstein condensate with the transmission spectra of an optical cavity. By choosing a circularly polarized cavity mode with an appropriate frequency, we can realize coupling between the cavity mode and the magnetization of the condensate. The cavity transmission spectra then contain information of the magnetization statistics of the condensate and thus can be used to distinguish the ferromagnetic and antiferromagnetic quantum ground states. This technique may also be useful for continuous observation of the spin dynamics of a spinor Bose-Einstein condensate.
Notes: Zhang, J. M. Cui, S. Jing, H. Zhou, D. L. Liu, W. M.
Abstract: We investigate the nonlinear dynamics of a combined system which is composed of a cigar-shaped Bose-Einstein condensate and an optical cavity with the two sides coupled dispersively. This system is characterized by the cavity-induced nonlinearity; after integrating out the fast degree of freedom of the cavity mode, the potential felt by the condensate depends on the condensate itself. Adopting a discrete-mode approximation for the condensate, we map out the steady configurations of the system. It is found that due to the nonlinearity of the system, the nonlinear levels of the system may fold up in some parameter regimes. That will lead to the breakdown of adiabatic evolution of the system. Analysis of the dynamical stability of the steady states indicates that the same level structure also results in optical bistability.
Notes: Zhang, J. M. Cui, F. C. Zhou, D. L. Liu, W. M.
Abstract: We study the mean-field dynamics of a Bose Josephson junction which is dispersively coupled to a single mode of a high-finesse optical cavity. An effective classical Hamiltonian for the Bose Josephson junction is derived, and its dynamics is studied from the perspective of a phase portrait. It is shown that the strong condensate-field interplay does alter the dynamics of the Bose Josephson junction drastically. The possibility of coherent manipulating and in situ observation of the dynamics of the Bose Josephson junction is discussed.
Abstract: We investigate the interplay dynamics of a cavity QED system, where the two-level atoms are trapped in a double-well potential, and the cavity mode, with a frequency largely detuned from the atomic level splitting, is driven by a probe laser. The interaction between the center-of-mass motion of the atoms and the cavity mode is induced by the position-dependent atom-field coupling. The dynamics of the system is characterized by two distinct time scales, the inverse of the atomic interwell tunneling rate and the inverse of the cavity loss rate. The system shows drastically different (quasi) steady behaviors in the short- and long-time intervals, and the detection of the statistics of atom number distribution from the transmission spectra is available only in the short-time interval.
