P HYSICAL R EVIEW
LETTERS
VOLUME 78 2 JUNE 1997 NUMBER 22
Transition from Phase Locking to the Interference of Independent Bose Condensates:
Theory versus Experiment
A. Röhrl, M. Naraschewski, A. Schenzle, and H. Wallis
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
and Sektion Physik, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
(Received 28 February 1997)
The macroscopic interference of two Bose condensates released from a double minimum potential has
been demonstrated recently [M. R. Andrews et al., Science 275, 637 (1997)]. In this Letter we show
the excellent agreement between those experiments and theoretical predictions based on the nonlinear
Schrödinger equation. In addition, the transition from interference of coupled condensates, comparable
with the Josephson effect in superconductors, to the interference of independent Bose condensates is
studied. [S0031-9007(97)03260-2]
PACS numbers: 03.75.Fi, 05.30.Jp
The recent experimental breakthrough to Bose-Einstein
condensation with small numbers of atoms collected in
magnetic traps [1–4] has now culminated in the demon-
stration of the macroscopic coherence of Bose conden-
sates [5]. The interference of two condensates released
from a divided magnetic trap has provided compelling evi-
dence for the intrinsic coherence of the many-atom ground
state in the trap. This observation is closely related to the
Josephson effect in superconductors. Quantum interfer-
ence of many particles suggests a classical interpretation of
the matter wave, resembling the classical limit of electro-
magnetic fields. Such a description using a macroscopic
wave function with a definite, stable phase implies bro-
ken gauge symmetry. Hence the production of a coher-
ent particle beam also amounts to the first demonstration
of a pulsed “atom laser”—a milestone for the further de-
velopment of atom optics, atom interferometry, and atom
lithography.
The experiment reported in [5] illuminates two aspects
of broken gauge symmetry. First, it proves the coherence
properties of a single Bose condensate by the interference
with a second one. In this Letter we will confirm the coher-
ence of the condensate wave function by a detailed com-
parison between the measured condensate dynamics and its
theoretical description in terms of a nonlinear Schrödinger
equation [6]. Second, it enables one to study the transi-
tion from independent to coupled Bose condensates, since
in the current experimental setup the separation between
the condensates can be varied. For large separation the
interference of initially independent condensates is stud-
ied; for small separation the initial condensates merge, and
the situation can be regarded as an analog of a Josephson
junction.
The broken gauge symmetry of a classical field implies
that an interference pattern created by independent Bose
condensates must depend on an arbitrary relative phase
between the condensates. This phase varies randomly
between different experimental runs to ensure the gauge
symmetry of the ensemble, but not during a single run.
Such a view has been confirmed by a detailed analysis of
correlation functions [7,8]. The postulated variation of the
interference pattern between different runs would reveal
the spontaneous aspect of broken symmetry.
In contrast, if the external potential and the repul-
sive self-interaction lead to a non-negligible overlap
between the two condensates, tunneling occurs and the
condensates are no longer independent. Instead the
system possesses a nondegenerate ground state, which
for small coupling can be approximated by a well-
defined coherent superposition of the two previously
independent condensate wave functions. Since only
this combined ground state is macroscopically occupied,
0031-9007 97 78(22) 4143(4)$10.00 © 1997 The American Physical Society 4143