Physics Letters B 785 (2018) 498–505
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Potential tests of the generalized uncertainty principle in the advanced
LIGO experiment
Pasquale Bosso
a,b,c,∗
, Saurya Das
a
, Robert B. Mann
d,e
a
Theoretical Physics Group and Quantum Alberta, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4, Canada
b
Fakultät für Physik, Bielefeld University, D-33501 Bielefeld, Germany
c
Departamento de Física, División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, León, Guanajuato, 37150, Mexico
d
Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
e
Perimeter Institute, 31 Caroline St. N., Waterloo, Ontario, N2L 2Y5, Canada
a r t i c l e i n f o a b s t r a c t
Article history:
Received
28 June 2018
Received
in revised form 24 July 2018
Accepted
9 August 2018
Available
online 6 September 2018
Editor:
M. Cveti
ˇ
c
The generalized uncertainty principle and a minimum measurable length arise in various theories
of gravity and predict Planck-scale modifications of the canonical position-momentum commutation
relation. Postulating a similar modified commutator between the canonical variables of the electromag-
netic
field in quantum optics, we compute Planck-scale corrections to the radiation pressure noise and
shot noise of Michelson–Morley interferometers, with particular attention to gravity wave detectors such
as LIGO. We show that advanced LIGO is potentially sensitive enough to observe Planck-scale effects
and thereby indirectly a minimal length. We also propose estimates for the bounds on quantum gravity
parameters from current and future advanced LIGO experiments.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Current theories of Quantum Gravity, as well as gedanken ex-
periments
in black hole physics, predict the existence of a minimal
length [1–8]. This is in contrast to the Heisenberg Principle, which
allows for arbitrarily small uncertainties in position measurement
for a quantum system. However, this minimal length is expected to
be of the order of Planck length,
Pl
∼10
−35
m, well outside the
sensitivity of any direct observation. Furthermore, quantum grav-
ity
phenomenology incorporating the so-called Generalized Uncer-
tainty
Principle (GUP), have showed the possibility of indirectly
testing Planck-scale effects and those of such a minimal length in
low-energy quantum systems [9–13]. GUP, consisting of a modified
commutation relation between position and momentum assumes
the following form for a one dimensional system
[q, p]=i
¯
h
1 −2δγ p + (δ
2
+3)γ
2
p
2
,
(1)
where
γ =
1
M
Pl
c
, (2)
*
Corresponding author.
E-mail
addresses: pasquale.bosso@uleth.ca (P. Bosso), saurya.das@uleth.ca
(S. Das),
rbmann@uwaterloo.ca (R.B. Mann).
M
Pl
being the Planck mass and c the speed of light. The GUP alge-
bra
(1) consists of two independent parameters, one for the linear
and one for the quadratic term, which for example, can be thought
of as δγ and (δ
2
+3)γ
2
. We parametrized the algebra with three
constants γ , δ, and such that in subsequent perturbation theory
only γ appears as the perturbation parameter. This model is equiv-
alent
to the models in [9] and [11]with the choice δ = 0, = γ
2
0
/3
and
δ =
√
=γ
0
, respectively, where γ
0
∼1.
In this paper we study the implications of this model on various
types of noise in LIGO interferometers, chosen because they have
the highest spatial sensitivity [14,15]. Previous investigations have
already considered interferometric detectors, like LIGO, Virgo, and
LISA, as instruments to probe the quantum nature of spacetime
[16,17]. However, as we shall show, the proposed use of squeezed
light to further increase their resolution further enhances GUP
effects. Our recent work investigated implications of GUP on co-
herent
and squeezed states of a quantum harmonic oscillator [18].
Some of the techniques used in that paper were also extended to
more general perturbations of the harmonic oscillator in [19]. In
this paper, we apply the above techniques to the optical field in
a Michelson–Morley interferometer. This is motivated by the fact
that the electromagnetic field can be written as a collection of
quantum harmonic oscillators, and the Hamiltonian for the pho-
ton
field can be written as well in terms of harmonic oscillator
Hamiltonians. It is worth noting that we do not consider the GUP
for the mechanical part of the interferometers, i.e. the end mirrors,
https://doi.org/10.1016/j.physletb.2018.08.061
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.