ABSTRACT
Albert Benseny,a Joan Baguda`,a Xavier Oriols,b Gerhard Birkl,c
Atomtronics is one of the foremost bottom-top approaches to quan-
tum information science, where neutral atoms in optical, magnetic,
and electric potentials form the building blocks of coherent diode
and transistor-like devices. In this context, we discuss in this chapter
an efficient and robust technique to coherently transport a single
neutral atom, a single hole, or even a Bose-Einstein condensate
(BEC) between the two extreme traps of a triple-well optical
potential. Solving the corresponding quantum dynamics in terms
of Bohmian trajectories, we investigate this adiabatic transport
process and present a very counterintuitive effect: by slowing down
the total time duration of the transport process, it is possible
to achieve sudden particle accelerations yielding ultrahigh atomic
velocities.a
3.1 Introduction 191
3.1.1 Atomtronics 191
3.1.2 Three-level atom optics 192
3.1.3 Adiabatic transport with trajectories 195
3.2 Physical System: Neutral Atoms in Optical Microtraps 198
3.2.1 One-dimensional Hamiltonian 200
3.3 Adiabatic Transport of a Single Atom 201
3.3.1 The matter wave STIRAP paradox with Bohmian
trajectories 201
3.3.2 Velocities and accelerations of Bohmian
trajectories 202
3.4 Adiabatic Transport of a Single Hole 206
3.4.1 Hole transfer as an array-cleaning technique 206
3.4.2 Adiabatic transport of a hole in an array of three
traps 208
3.4.2.1 Three-level approximation description 208
3.4.2.2 Numerical simulations 210
3.4.3 Hole transport fidelity 212
3.4.4 Bohmian trajectories for the hole transport 213
3.4.5 Atomtronics with holes 215
3.4.5.1 Single hole diode 215
3.4.5.2 Single-hole transistor 217
3.5 Adiabatic Transport of a Bose-Einstein Condensate 219
3.5.1 Madelung hydrodynamic formulation 222
3.5.2 Numerical simulations 223
3.6 Conclusions 227
Electronics is the branch of science and technology that deals with
the controlled flow of electrons. Most of today’s electronic devices
use semiconductor diodes and transistors to manipulate electronic
current. Notably, the miniaturization of these devices is getting
closer and closer to the single atom scale, reaching the limit of
Moore’s law [1].a Nowadays, the electronics top-bottom approach is
crossing the frontier between the classical and the quantum realm,
where quantum effects such as quantum tunneling and quantum
correlations, that is, entanglement, are unavoidable. In particular,
the transition from the classical to the quantum world constitutes
one of the physical scenarios where the Bohmian formulation can
give more insight into the underlying physics. See chapter 1 for a
detailed discussion of these aspects and chapter 6 for a particular
application of Bohmian trajectories to quantum electronic devices.
