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Escape of a vector matter–wave 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, Pontiﬁcia Universidad Católica de Valparaíso, Avenida Brasil, Valparaíso, Casilla

2950, Chile

E-mail: bludov@ﬁsica.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 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.

Supplementary material for this article is available online

Keywords: Bose–Einstein condensate, soliton, optical lattice

(Some ﬁgures may appear in colour only in the online journal)

1. Introduction

One of the most prominent features of a Bose–Einstein 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],Landau–Zener 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 [7–13]and

polaritonic [14–16]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 [18–20]and

quantum tunnelling [20,21].Inasimpliﬁed view of this

process, quantum ﬂuctuations create a particle–antiparticle

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

ampliﬁcation 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 conﬁgurations have

been proposed [27–31], 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