Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas

Physical Review A (Impact Factor: 2.81). 07/2009; 80(5). DOI: 10.1103/PhysRevA.80.053616
Source: arXiv


We derive a $1/c$-expansion for the single-particle density matrix of a
strongly interacting time-dependent one-dimensional Bose gas, described by the
Lieb-Liniger model ($c$ denotes the strength of the interaction). The formalism
is derived by expanding Gaudin's Fermi-Bose mapping operator up to $1/c$-terms.
We derive an efficient numerical algorithm for calculating the density matrix
for time-dependent states in the strong coupling limit, which evolve from a
family of initial conditions in the absence of an external potential. We have
applied the formalism to study contraction dynamics of a localized wave packet
upon which a parabolic phase is imprinted initially.

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    ABSTRACT: Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.
    New Journal of Physics 11/2009; 12. DOI:10.1088/1367-2630/12/5/055010 · 3.56 Impact Factor
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    ABSTRACT: We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions). The ground state properties of the gas in the wedge-like trapping potential are calculated in the strongly interacting regime by using Girardeau's Fermi-Bose mapping and the pseudopotential approach in the $1/c$-approximation ($c$ denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an $N$-dimensional Fourier transform as in the case of free expansion.
    Physical Review A 05/2010; 82(2). DOI:10.1103/PhysRevA.82.023606 · 2.81 Impact Factor
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    ABSTRACT: Quantum adiabatic processes—that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian—are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. “Shortcuts to adiabaticity” are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects.
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