Edge-locking and quantum control in highly polarized spin chains

For an open-boundary spin chain with anisotropic Heisenberg (XXZ) interactions, we present states in which a connected block near the edge is polarized oppositely to the rest of the chain. We show that such blocks can be `locked' to the edge of the spin chain, and that there is a hierarchy of edge-locking effects at various orders of the anisotropy. The phenomenon enables dramatic control of quantum state transmission: the locked block can be freed by flipping a single spin or a few spins.Comment: 4 pages, 4 figure

Fine structures in the spectrum of the open-boundary Heisenberg chain at large anisotropies

At large anisotropies, the spectrum of the Heisenberg XXZ spin chain separates into `bands' with energies largely determined by the number of domain walls. The band structure is richer with open boundary conditions: there are more bands and the bands develop intricate fine structures. We characterize and explain these structures and substructures in the open-boundary chain. The fine structures are explained using degenerate perturbation theory. We also present some dynamical consequences of these sub-band structures, through explicit time evolution of the wavefunction from initial states motivated by the fine structure analysis

Repulsive to attractive interaction quenches of 1D Bose gas in a harmonic trap

We consider quantum quenches of harmonically trapped one-dimensional bosons from repulsive to attractive interactions, and the resulting breathing dynamics of the so-called `super-Tonks-Girardeau' (sTG) state. This state is highly excited compared to the ground state of the attractive gas, and is the lowest eigenstate where the particles are not bound or clustered. We analyze the dynamics from a spectral point of view, identifying the relevant eigenstates of the interacting trapped many-body system, and analyzing the nature of these quantum eigenstates. To obtain explicit eigenspectra, we use Hamiltonians with finite-dimensional Hilbert spaces to approximate the Lieb-Liniger system. We employ two very different approximate approaches: an expansion in a truncated single-particle harmonic-trap basis and a lattice (Bose-Hubbard) model. We show how the breathing frequency, identified with the energy difference between the sTG state and another particular eigenstate, varies with interaction.Comment: 9 pages, 9 figure

Modulated trapping of interacting bosons in one dimension

We investigate the response of harmonically confined bosons with contact interactions (trapped Lieb-Liniger gas) to modulations of the trapping strength. We explain the structure of resonances at a series of driving frequencies, where size oscillations and energy grow exponentially. For strong interactions (Tonks-Girardeau gas), we show the effect of resonant driving on the bosonic momentum distribution. The treatment is `exact' for zero and infinite interactions, where the dynamics is captured by a single-variable ordinary differential equation. For finite interactions the system is no longer exactly solvable. For weak interactions, we show how interactions modify the resonant behavior for weak and strong driving, using a variational approximation which adds interactions to the single-variable description in a controlled way.Comment: 9 pages, 8 figure

Squeezing in the weakly interacting uniform Bose condensate

We investigate the presence of squeezing in the weakly repulsive uniform Bose gas, in both the condensate mode and in the nonzero opposite-momenta mode pairs, using two different variational formulations. We explore the U(1) symmetry breaking and Goldstone's theorem in the context of a squeezed coherent variational wavefunction, and present the associated Ward identity. We show that squeezing of the condensate mode is absent at the mean field Hartree-Fock-Bogoliubov level and emerges as a result of fluctuations about mean field as a finite volume effect, which vanishes in the thermodynamic limit. On the other hand, the squeezing of the excitations about the condensate survives the thermodynamic limit and is interpreted in terms of density-phase variables using a number-conserving formulation of the interacting Bose gas.Comment: 8 pages, 3 figures. Version 2 (Sept'06): expanded discussion

Nonsmooth and level-resolved dynamics illustrated with the tight binding model

We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function \sinc x \equiv \sin x / x. These physical effects appear in many systems with approximately equally spaced spectra, and is also robust for larger-amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven tight-binding model to illustrate these effects, both within and outside the perturbative regime.Comment: Link with the Paley-Wiener theorem and another reference is added; any comment is welcome and will be greatly appreciated

Interaction ramps in a trapped Bose condensate

Non-adiabatic interaction ramps are considered for trapped Bose-Einstein condensates. The deviation from adiabaticity is characterized through the heating or residual energy produced during the ramp. We find that the dependence of the heat on the ramp time is very sensitive to the ramp protocol. We explain features of this dependence through a single-parameter effective description based on the dynamics of the condensate size.Comment: 4 pages, 3 figure

Transition Temperature of Dilute, Weakly Repulsive Bose Gas

Within a quasiparticle framework, we reconsider the issue of computing the Bose-Einstein condensation temperature ($T_c$) in a weakly non-ideal Bose gas. The main result of this and previous investigations is that $T_c$ increases with the scattering length $a$, with the leading dependence being either linear or log-linear in $a$. The calculation of $T_c$ reduces to that of computing the excitation spectrum near the transition. We report two approaches to regularizing the infrared divergence at the transition point. One leads to a $a\sqrt{|\ln{a}|}$-like shift in $T_c$, and the other allows numerical calculations for the shift.Comment: 8 pages, 3 figures, revtex

Breathing mode in the Bose-Hubbard chain with a harmonic trapping potential

We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low energy eigenspectrum of the trapped many-boson system, and study overlaps of the initial state with eigenstates of the quenched Hamiltonian. There is an intermediate interaction regime, between a "free-boson" limit and a "free-fermion" limit, in which the Bose-Hubbard breathing mode frequency approaches the Gross-Pitaevskii prediction. In addition, we present a striking failure of the time-dependent Gutzwiller approximation for describing breathing modes.Comment: 8 pages, 8 figure