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Register a new userReply to arXiv:1002.4366, Comment on `Motion of an impurity in an ultracold quasi-one-dimensional gas of hard-core bosons`, by S. Giraud and R. Combescot
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Added by
Marvin D. Girardeau
Publication date
2010
fields
Physics
and research's language is
English
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In their Comment [1] Giraud and Combescot point out that the contribution to the impurity-boson distribution function $rho_{bi}(x-y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but nevertheless our results for $rho_{bi}$ are highly accurate for large impurity-boson mass ratio $m_i/m$ and remain qualitatively correct for all values of $m_i/m$ and all values of the boson-impurity coupling constant.
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Very recently Girardeau and Minguzzi [arXiv:0807.3366v2, Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they deal with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial step is erroneous, contradicting both physical intuition and known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.
The low-lying eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaron-like composite object consisting of the impurity clothed by a co-moving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio $m_i/m$ unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact solution for arbitrary $m_i/m$ and impurity-boson interaction strength.
Using the exact $N$-particle ground state wave function for a one-dimensional gas of hard-core bosons in a harmonic trap we develop an algorithm to compute the reduced single-particle density matrix and corresponding momentum distribution. Accurate numerical results are presented for up to N=8 particles, and the momentum distributions are compared to a recent analytic approximation.
By means of time-dependent density-matrix renormalization-group (TDMRG) we are able to follow the real-time dynamics of a single impurity embedded in a one-dimensional bath of interacting bosons. We focus on the impurity breathing mode, which is found to be well-described by a single oscillation frequency and a damping rate. If the impurity is very weakly coupled to the bath, a Luttinger-liquid description is valid and the impurity suffers an Abraham-Lorentz radiation-reaction friction. For a large portion of the explored parameter space, the TDMRG results fall well beyond the Luttinger-liquid paradigm.
We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi one dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent Hartree method for bosons, a numerical exact approach to simulate quantum many-body dynamics. In particular, we are interested in the scenario by which the ion is so strongly trapped that its motion can be effectively neglected. This enables us to focus on the atomic ensemble only. With the development of a model potential for the atom-ion interaction, we are able to numerically obtain the exact many-body ground state of the atomic ensemble in the presence of an ion. We analyse the influence of the atom number and the atom-atom interaction on the ground state properties. Interestingly, for weakly interacting atoms, we find that the ion impedes the transition from the ideal gas behaviour to the Thomas-Fermi limit. Furthermore, we show that this effect can be exploited to infer the presence of the ion both in the momentum distribution of the atomic cloud and by observing the interference fringes occurring during an expansion of the quantum gas. In the strong interacting regime, the ion modifies the fragmentation process in dependence of the atom number parity which allows a clear identification of the latter in expansion experiments. Hence, we propose in both regimes experimentally viable strategies to assess the impact of the ion on the many-body state of the atomic gas. This study serves as the first building block for systematically investigate many-body physics of such hybrid system.
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