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Abstract and Figures

We show that a vector matter-wave soliton in a Bose-Einstein condensate (BEC) loaded into an optical lattice can escape from a trap formed by a parabolic potential, resembling a Hawking emission. The particle-antiparticle pair is emulated by a low-amplitude bright-bright soliton in a two-component BEC with effective masses of opposite signs. It is shown that the parabolic potential leads to a spatial separation of BEC components. One component with chemical potential in a semi-infinite gap exerts periodical oscillations, while the other BEC component, with negative effective mass, escapes from the trap. The mechanism of atom transfer from one BEC component to another by spatially periodic linear coupling term is also discussed.
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Escape of a vector matterwave soliton from
a parabolic trap
Yuliy V Bludov
1,2
and Monica A García-Ñustes
3
1
Department of Physics and Center of Physics, University of Minho, PT-4710-057, Braga, Portugal
2
QuantaLab, University of Minho, PT-4710-057, Braga, Portugal
3
Instituto de Física, Ponticia Universidad Católica de Valparaíso, Avenida Brasil, Valparaíso, Casilla
2950, Chile
E-mail: bludov@sica.uminho.pt
Received 30 December 2016, revised 14 April 2017
Accepted for publication 19 May 2017
Published 12 June 2017
Abstract
We show that a vector matterwave soliton in a BoseEinstein condensate (BEC)loaded into an
optical lattice can escape from a trap formed by a parabolic potential, resembling a Hawking
emission. The particleantiparticle pair is emulated by a low-amplitude brightbright soliton in a
two-component BEC with effective masses of opposite signs. It is shown that the parabolic
potential leads to a spatial separation of BEC components. One component with chemical
potential in a semi-innite gap exerts periodical oscillations, while the other BEC component,
with negative effective mass, escapes from the trap. The mechanism of atom transfer from one
BEC component to another by spatially periodic linear coupling term is also discussed.
Supplementary material for this article is available online
Keywords: BoseEinstein condensate, soliton, optical lattice
(Some gures may appear in colour only in the online journal)
1. Introduction
One of the most prominent features of a BoseEinstein con-
densate (BEC)subjected to external potential is the possibility
for it to be used as almost a perfect test-bench for reproducing a
lot of phenomena from other areas of physics (for review see,
e.g. [1]). Particular attention has been paid to the phenomena
from condensed matter and cosmology. For instance, the
advantage of investigating solid-state phenomena such as Bloch
oscillations [2,3],LandauZener tunneling [4]and Josephson
junction [5,6]in a BEC (instead of proper solid-state structures)
lies in the fact that the periodic external potential provides an
analogue of a perfect crystalline lattice without defects. In the
area of cosmology, an interest in both atomic [713]and
polaritonic [1416]BECs comes from the possibility to use it as
an experimentally attainable system of analogue gravity[17]
a laboratory model for curved-space quantum theory, e.g., black
holes and, in particular, Hawking radiation.
Hawking radiation represents an additional emission
mechanism of particles from a potential well along with
classical escaping by external perturbations [1820]and
quantum tunnelling [20,21].Inasimplied view of this
process, quantum uctuations create a particleantiparticle
pair near to the black hole edge [22,23]. If one of the pair
constituents crosses the event horizon, it never returns, thus
giving rise to the emission from the black hole, which in turn
leads to decreasing of black hole energy and mass (for
review see, e.g., [24]).However,Hawkingemissionfrom
nowadays known astronomic black holes is hard to explore
because of its weak predicted intensity. Charged black hole
amplication of Hawking radiation can take place due to the
resonance in the cavity formed by inner and outer horizons
with subsequent black hole lasing [25,26]. To realize this
idea in a BEC, a variety of different congurations have
been proposed [2731], and later an experimental realization
of lasing from a BEC was reported [32]. It is worth noting
Journal of Physics B: Atomic, Molecular and Optical Physics
J. Phys. B: At. Mol. Opt. Phys. 50 (2017)135004 (9pp)https://doi.org/10.1088/1361-6455/aa7432
0953-4075/17/135004+09$33.00 © 2017 IOP Publishing Ltd Printed in the UK1
... The objective of the present work is to explore a possibility of forming bound states of solitons with opposite signs of the effective masses, which implies that they should also have opposite signs of the self-interaction coefficients (otherwise, bright solitons cannot exist in both components; for this reason, only one component was a soliton in the above-mentioned photonic setting [14], while the other one was treated as a Thomas-Fermi mode). This situation is possible in a two-component atomic BEC loaded in an opticallattice (OL) potential, which may induce the effective mass of either sign (positive for regular solitons, and negative for gap solitons in a finite bandgap [17][18][19][20][21][22][23][24][25]), while the sign of the self-interaction in any component may be switched by means of the Feshbach resonance [26]. It is relevant to mention that the dynamics of a pair of matter-wave solitons with effective masses of opposite signs, loaded in a harmonic-oscillator trapping potential, was studied in recent work [25]. ...
... This situation is possible in a two-component atomic BEC loaded in an opticallattice (OL) potential, which may induce the effective mass of either sign (positive for regular solitons, and negative for gap solitons in a finite bandgap [17][18][19][20][21][22][23][24][25]), while the sign of the self-interaction in any component may be switched by means of the Feshbach resonance [26]. It is relevant to mention that the dynamics of a pair of matter-wave solitons with effective masses of opposite signs, loaded in a harmonic-oscillator trapping potential, was studied in recent work [25]. As a result, the soliton with the positive mass remains trapped, while its counterpart with the negative mass can escape, as the potential is effectively expulsive for it [20]. ...
... and respective changes in Eqs. (25) and (28): ...
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