VOLUME 86, NUMBER 10 PHYSICAL REVIEW LETTERS 5MARCH 2001
Search for Exchange-Antisymmetric States for Spin-0 Particles at the 10
211
Level
D. Mazzotti,
1,2
P. Cancio,
1
G. Giusfredi,
1
M. Inguscio,
2
and P. De Natale
1
1
Istituto Nazionale di Ottica Applicata (INOA), Largo E. Fermi 6, I-50125 Firenze, Italy
2
Istituto Nazionale per la Fisica della Materia (INFM) and European Laboratory for Nonlinear Spectroscopy (LENS),
Largo E. Fermi 2, I-50125 Firenze, Italy
(Received 23 August 2000)
We set a new upper limit of 1.7 3 10
211
to the probability that two spin-0
16
O nuclei are in forbidden
exchange-antisymmetric states, testing the validity of fundamental principles of quantum mechanics. A
newly designed difference-frequency spectrometer is used to look for the existence of these states. The
experimental test was performed by tuning the spectrometer across a molecular transition of
12
C
16
O
2
belonging to the rovibrational band at 4.25 mm, connecting the forbidden states 00
0
0, J 25 and
00
0
1, J 26.
DOI: 10.1103/PhysRevLett.86.1919 PACS numbers: 05.30.Jp, 21.10.Hw, 33.20.–t, 42.62.Fi
Although the symmetrization postulate (SP) constitutes
the basis for a quantum-mechanical description of any sys-
tem of identical particles, the possibility of theories going
beyond the Bose and Fermi statistics, arising from the SP,
has long been recognized [1,2]. More recently, theories al-
lowing small SP violations have been developed, basically
following two different approaches. In the first approach,
trilinear commutation relations are defined instead of the
usual bilinear Bose and Fermi commutators [3], whereas
in the second a slight deformation of the bilinear commu-
tation relations is introduced, using a parameter which can
continuously turn each statistics into the other [4].
At present, no experimental evidence of SP violation
has been demonstrated. The most accurate tests of the SP
were performed on fermions, which must obey the Pauli
exclusion principle (PEP), which is a particular case of the
SP. Ramberg and Snow [5] searched for a PEP-forbidden
electronic transition in a copper strip with electrical cur-
rent flowing through it for hundreds of hours. The negative
result of this experiment was interpreted to give an upper
limit of 1.7 3 10
226
to PEP violation for a many-electron
system. A simpler and more rigorously interpreted two-
fermion system, the helium atom, was investigated by
Deilamian et al. [6]. They adopted a spectroscopic tech-
nique to search for an electronic transition involving a
PEP-forbidden state. This experiment set 5 3 10
26
as a
bound to PEP violation for a two-electron system. An ex-
perimental evidence of SP violation in a system of bosons
is harder to be observed. Nevertheless, some tests were
first proposed [7,8] and then performed, searching for for-
bidden exchange-antisymmetric states in molecules con-
taining two identical
16
O nuclei (spin-0 bosons). Two
independent spectroscopic tests on
16
O
2
set the bound to
a SP violation, respectively, to 5 3 10
27
[9] and 1.3 3
10
26
[10]. The first test on
12
C
16
O
2
, due to the stronger
allowed transitions involved in the measurement, improved
upon the previous ones by more than 2 orders of magni-
tude, setting an upper limit of 2.1 3 10
29
to SP violations
[11]. Recent discussion on the theoretical implications of
these experimental tests can be found in Ref. [12].
The choice of a suitable test molecule/transition both
depends on bare physics and on the availability of a proper
source of coherent radiation at the corresponding wave-
length. From the point of view of the general physi-
cal properties, diatomic homonuclear molecules, such as
16
O
2
, are not the best choice for the test, because of
their lack of active electric dipole transitions in the in-
frared (IR). Higher sensitivity to look for the existence
of exchange-antisymmetric states can be achieved by in-
vestigation of polyatomic molecules containing a pair of
identical bosonic nuclei. Among them the
12
C
16
O
2
mole-
cule is one of the best candidates because its rovibra-
tional IR transitions may have line strengths up to 3.5 3
10
218
cmmolecule. In Ref. [11], the 12
0
1-00
0
0 combi-
nation band of
12
C
16
O
2
around a 2 mm wavelength was
chosen, since it is the strongest that can be reached by
available distributed-feedback diode lasers.
In this Letter, following the original idea of Hilborn
[7], we report on a new sensitive search of the existence
of exchange-antisymmetric states for spin-0 particles,
which was performed by investigating the spectrum of
the 00
0
1-00
0
0 fundamental band of
12
C
16
O
2
around
4.25 mm. This band is about 2000 times stronger than
the 12
0
1-00
0
0, providing us with a higher sensitivity.
The high-sensitivity spectroscopic investigation of this
band was made possible by the recent development of a
difference-frequency radiation source at this wavelength,
with the desired features of wide tunability, narrow
linewidth, and low intensity noise [13]. These features,
in a previous experiment, had also allowed us to observe
low-power saturated-absorption spectra of CO
2
[14].
According to the Born-Oppenheimer approximation,
the total wave function C of a single molecule can be fac-
torized in the form C c
e
c
y
c
r
c
n
, where c
e
, c
y
, c
r
,
and c
n
are the electronic, vibrational, rotational, and
nuclear wave functions, respectively. The ground elec-
tronic and vibrational wave functions of the
12
C
16
O
2
molecule are symmetric in the exchange of the two
16
O
nuclei. Also, the nuclear wave function is symmetric,
since the nuclear spin I
16
O 0. The rotational wave
0031-9007 01 86(10) 1919(4)$15.00 © 2001 The American Physical Society 1919