of 47
Kaltenbaek et al.
EPJ Quantum Technology
(2016) 3:5
DOI
10.1140/epjqt/s40507-016-0043-7
R E V I E W
Open Access
Macroscopic Quantum Resonators
(MAQRO): 2015 update
Rainer Kaltenbaek
1*
,MarkusAspelmeyer
1
, Peter F Barker
2
, Angelo Bassi
3
,
4
,JamesBateman
5
,
Kai Bongs
6
,SougatoBose
2
, Claus Braxmaier
7
,
8
,
ˇ
Caslav Brukner
1
,
9
, Bruno Christophe
10
, Michael Chwalla
11
,
Pierre-François Cohadon
12
, Adrian Michael Cruise
6
, Catalina Curceanu
13
, Kishan Dholakia
14
, Lajos Diósi
15
,
Klaus Döringshoff
16
,WolfgangErtmer
17
, Jan Gieseler
18
, Norman Gürlebeck
7
, Gerald Hechenblaikner
11
,
19
,
Antoine Heidmann
12
, Sven Herrmann
7
, Sabine Hossenfelder
20
,UlrichJohann
11
, Nikolai Kiesel
1
,
Myungshik Kim
21
, Claus Lämmerzahl
7
, Astrid Lambrecht
12
, Michael Mazilu
14
, Gerard J Milburn
22
,
Holger Müller
23
, Lukas Novotny
18
, Mauro Paternostro
24
,AchimPeters
16
,IgorPikovski
25
,
André Pilan Zanoni
11
,
26
,ErnstMRasel
17
,SergeReynaud
12
, Charles Jess Riedel
27
, Manuel Rodrigues
10
,
Loïc Rondin
18
, Albert Roura
28
, Wolfgang P Schleich
28
,
29
, Jörg Schmiedmayer
30
, Thilo Schuldt
8
,
Keith C Schwab
31
, Martin Tajmar
32
, Guglielmo M Tino
33
, Hendrik Ulbricht
34
, Rupert Ursin
9
and
Vlatko Vedral
35
,
36
*
Correspondence:
rainer.kaltenbaek@univie.ac.at
1
Vienna Center for Quantum
Science and Technology, University
of Vienna, Boltzmanngasse 5,
Vienna, Austria
MAQRO Consortium, names after
first author sorted alphabetically
Full list of author information is
available at the end of the article
Abstract
Do the laws of quantum physics still hold for macroscopic objects - this is at the heart
of Schrödinger’s cat paradox - or do gravitation or yet unknown effects set a limit for
massive particles? What is the fundamental relation between quantum physics and
gravity? Ground-based experiments addressing these questions may soon face
limitations due to limited free-fall times and the quality of vacuum and microgravity.
The proposed mission
Macroscopic Quantum Resonators (MAQRO)
may overcome
these limitations and allow addressing such fundamental questions.
MAQRO
harnesses recent developments in quantum optomechanics, high-mass matter-wave
interferometry as well as state-of-the-art space technology to push macroscopic
quantum experiments towards their ultimate performance limits and to open new
horizons for applying quantum technology in space. The main scientific goal is to
probe the vastly unexplored ‘quantum-classical’ transition for increasingly massive
objects, testing the predictions of quantum theory for objects in a size and mass
regime unachievable in ground-based experiments. The hardware will largely be
based on available space technology. Here, we present the
MAQRO
proposal
submitted in response to the
4th Cosmic Vision call for a medium-sized mission (M4)
in 2014 of the
European Space Agency (ESA)
with a possible launch in 2025, and we
review the progress with respect to the original
MAQRO
proposal for the
3rd Cosmic Vision call for a medium-sized mission (M3)
in 2010. In particular, the
updated proposal overcomes several critical issues of the original proposal by relying
on established experimental techniques from high-mass matter-wave interferometry
and by introducing novel ideas for particle loading and manipulation. Moreover, the
mission design was improved to better fulfill the stringent environmental
requirements for macroscopic quantum experiments.
Keywords:
space; quantum physics; quantum optomechanics; matter waves;
optical trapping; MAQRO
©
2016 Kaltenbaek et al. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, pro-
vided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and
indicate if changes were made.
Kaltenbaek et al.
EPJ Quantum Technology
(2016) 3:5
Page 2 of 47
1 Introduction
MAQRO
is a proposal for a medium-sized space mission to use the unique environment
of deep space in combination with novel technological developments of space and quan-
tum technology to test the foundations of quantum physics. The central idea is to perform
matter-wave interferometry with massive objects (nanospheres of various materials, e.g.,
glass) with masses up to 

atomic mass units (amus)
. Novel techniques from quantum
optomechanics with optically trapped particles are proposed to be used to prepare test
particles for these matter-wave interference experiments. The proposal was first submit-
ted in response to the  ‘M’ call of the
ESA
for a medium-sized space mission in
ESA
’s
Cosmic Vision program. The original proposal later was published in Ref. [
].
Since this original proposal, significant progress was made in terms of technology de-
velopment and in refining the details of the scientific instrument (also see Section
).
A detailed technological study was performed under contract with
ESA
[
], and sev-
eral studies were performed with respect to the thermal design of the instrument [
,
]. In a series of experiments, various groups demonstrated feed-back cooling [
,
]and
side-band cooling of optically trapped particles [
]. A study on loading mechanisms of
nano- and microparticles for quantum experiments in space was performed under con-
tract with
ESA
[

], and experiments reported progress on loading, manipulating and
keeping particles in optical traps even at high vacuum [


]. Optomechanical cooling
close to the quantum ground state has been demonstrated for a variety of architectures
[


] and seems to be within reach for optically trapped particles [
]. A collaboration
of the University of Vienna, the University of Bremen and Airbus Defence & Space, suc-
cessfully implemented a high-finesse, adhesively bonded optical cavity using space-proof
glue and
ultra-low-expansion (ULE)
material [

]. The same technology is currently in
use to implement a high-finesse test cavity with the same specifications as needed for
MAQRO
. Based on recent theoretical studies [

], the design of
MAQRO
was adapted for
preparing macroscopic superpositions with state-of-the-art non-linear-optics and laser
technology [

] also benefiting from recent advances in the single-mode transmission of
deep
ultra violet (UV)
light [

]. In this way, a central drawback of the initial
MAQRO
proposal (the need for low power, extremely short-wavelength light) could be resolved.
Moreover,
LISA Pathfinder (LPF)
was successfully launched in December  - a tech-
nology demonstrator for the
Laser Interferometer Space Antenna (LISA)
mission, which
served as model for the proposed spacecraft, launcher and orbit of
MAQRO
.Bynow,the
MAQRO
consortium, founded in , consists of  groups from  countries around the
world demonstrating the growing support within the scientific community.
Here, we present an update of the
MAQRO
proposal submitted in  in response to
a new Cosmic Vision call of
ESA
for a medium-sized mission. This update takes into ac-
count the novel developments highlighted above and proposes additional improvements
to the mission design and the scientific instrument of
MAQRO
. A central goal is to address
and overcome potentially critical issues regarding the readiness of core technologies for
MAQRO
and to provide realistic concepts for further technology development. Our work
presents a new benchmark and a review of relevant work towards a ground-breaking mis-
sion that will act as a technology pathfinder for novel, macroscopic quantum technology
and quantum optomechanics in space.
Kaltenbaek et al.
EPJ Quantum Technology
(2016) 3:5
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2Outline
This paper presents an updated version of the mission proposal
MAQRO
and the progress
in defining that proposal and to demonstrate key technologies since the original mission
proposal. We will begin in Section
by giving the central motivation for
MAQRO
and the
reasons for performing these experiments in space (the ‘case for space’). In Section
,we
will outline the relation of
MAQRO
to past and future space missions. Section
defines
the requirements that have to be met in order to achieve the scientific goals of the mission.
These form the basis for deriving the technical requirements that have to be fulfilled by the
scientific instrument of
MAQRO
, which will be described in Section
.InSection
,we
will describe the outline of the mission itself like orbit requirements and mission phases,
and we will summarize the progress and changes with respect to the original mission pro-
posal in Section
.Finally,Section

presents conclusions and outlook.
3 Motivation
In the following subsections, we will present the central motivation for
MAQRO
and the
reasons why the experiments to be performed by
MAQRO
have to be carried out in space.
3.1 What are the fundamental physical laws of the universe?
The laws of quantum physics challenge our understanding of the nature of physical re-
ality and of space-time, suggesting the necessity of radical revisions of their underlying
concepts. Experimental tests of quantum phenomena, such as quantum superpositions
involving massive macroscopic objects, provide novel insights into those fundamental
questions.
MAQRO
allows entering a new parameter regime of macroscopic quantum
physics addressing some of the most important questions in our current understanding of
the basic laws of gravity and of quantum physics of macroscopic bodies.
3.2 Fundamental science and technology pathfinder
The main scientific objective of
MAQRO
is to test the predictions of quantum theory
in a hitherto inaccessible regime of quantum superpositions of macroscopic objects that
contain up to 

atoms. This is achieved by combining techniques from quantum op-
tomechanics, matter-wave interferometry and from optical trapping of dielectric particles.
MAQRO
will test quantum physics in a parameter regime orders of magnitude beyond
existing ground-based experimental tests - a realm where alternative theoretical models
predict noticeable deviations from the laws of quantum physics [


]. These models
have been suggested to harmonize the paradoxical quantum phenomena both with the
classical macroscopic world [


] and with notions of Minkowski space-time [


].
MAQRO
will, therefore, enable a direct investi
gation of the underlying nature of quan-
tum reality and space-time, and it may pave the way towards testing the ultimate limit of
matter-wave interference posed by space-time fluctuations [

,

]. Recent works showed
that
MAQRO
might even allow testing certain models of dark matter [

,

]. In contrast
to collapse models, even standard quantum theory, in the presence of gravitation, predicts
decoherence for spatially extended, massive superpositions [

,

]. While this is not ap-
plicable in a microgravity setting, ground-based tests in this direction may benefit from
the technology development necessary for
MAQRO
.
By pushing the limits of state-of-the-art experiments and by harnessing the space
environment for achieving the requirements of high-precision quantum experiments,
Kaltenbaek et al.
EPJ Quantum Technology
(2016) 3:5
Page 4 of 47
MAQRO
may prove a pathfinder for quantum technology in space. For example, quantum
optomechanics is already proving a useful tool in high-precision experiments on Earth
[

].
MAQRO
may open the door for using such technology in future space missions.
3.3 Why space?
In ground-based experiments, the ultimate limitations for observing macroscopic quan-
tum superpositions are vibrations, gravitational field-gradients, and decoherence through
interaction with the environment. Such interactions comprise, e.g., collisions with back-
ground gas as well as scattering, emission and absorption of blackbody radiation. The
spacecraft design of
MAQRO
allows operating the experimental platform in an environ-
ment offering a unique combination of microgravity (


–
g), low pressure (


–
Pa)
and low temperature (

 K). This allows sufficiently suppressing quantum decoherence
for the effects of alternative theoretical models to become experimentally accessible, and
to observe the evolution of macroscopic superpositions over free-fall times of about  s.
The main reasons for performing
MAQRO
inspacearetherequiredqualityofthemi-
crogravity environment (


–
g), the long free-fall times ( s), the high number of data
points required (up to

per measurement run), and the combination of low pressure
(


–
Pa) and low temperature (

 K) while having full optical access. These condi-
tions cannot be fulfilled with ground-based experiments.
4 MAQRO with respect to other missions
For
MAQRO
as well as for any other space mission, it is essential to see it in context with
successful missions in the past as well as in context with future missions
MAQRO
may
share common requirements with. With respect to earlier missions,
MAQRO
can benefit
from technological heritage, which could significantly reduce mission costs. In the case of
future missions, if the parameters of other missions are compatible with the requirements
of
MAQRO
, it could be possible to combine the
MAQRO
scientific instrument with other
instruments on a combined mission. This would significantly cut costs in terms of launch
and mission operation.
4.1 Technological heritage for MAQRO
MAQRO
benefits from recent developments in space technology. In particular,
MAQRO
relies on technological heritage from
LPF
[

], the scientific instrument of
LPF
,which
is called
LISA Technology Package (LTP)
[

], and on technologies from other mis-
sions like Gaia [

],
Gravity field and steady-state Ocean Circulation Explorer (GOCE)
[

,

], Microscope [

,

], the
Gravity Recovery and Climate Experiment (GRACE)
follow-on mission [

,

]andthe
James Webb Space Telescope (JWST)
[

]. The space-
craft, launcher, ground segment and orbit (
Sun-Earth Lagrange Point  (L)
/
Sun-Earth
Lagrange Point  (L)
) are identical to
LPF
.
The most apparent modifications with respect to the
LPF
design are an external, pas-
sively cooled optical instrument thermally shielded from the spacecraft, and the use of two
capacitive inertial sensors from ONERA technology. In addition, the propulsion system
will be mounted differently to achieve the required low vacuum level at the external sub-
system, and to achieve low thruster noise in one spatial direction. The additional optical
instruments and the external platform will reach the
Technological Readiness Level (TRL)
technology validated in relevant environment (TRL )
’ at the start of the BCD phases. For
Kaltenbaek et al.
EPJ Quantum Technology
(2016) 3:5
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all other elements, we assume the
TRLs
to range from ‘
technology demonstrated in
rele-
vant
environment (TRL )
’to‘
actual system proven in operational environment (TRL )
because of heritage from
LPF
and other missions.
4.2 Alternative mission scenarios
Implicit strengths of
MAQRO
are its relatively low weight and power consumption such
that
MAQRO
’s scientific instrument can, in principle, be combined on the same spacecraft
with other missions that have similar requirements in precision and orbit. An example
could be sun-observation instruments benefiting from an
L
orbit. Another example could
be a combination with the ASTROD I mission or similar mission concepts fulfilling the
orbit requirements of
MAQRO
.
5 Scientific objectives
Do the laws of quantum physics remain applicable without modification even up to the
macroscopic level? This question lies at the heart of Schrödinger’s famous gedankenexper-
iment (thought experiment) of a dead-and-alive cat [

]. Matter-wave experiments have
confirmed the predictions of quantum physics from the microscopic level of electrons [

,

], atoms and small molecules [

]uptomassivemoleculeswithupto
amu
[

]. Still,
experiments are orders of magnitude from where alternative theories predict deviations
from quantum physics [

,

].
Using ever more massive test particles on Earth may soon face principal limitations
because of the limited free-fall times as well as the limited quality of microgravity en-
vironments achievable on Earth. Currently, it is assumed that this limit will be reached
for interferometric experiments with particles in the mass range between 
amu
and

amu
[

]. These limitations may be overcome by harnessing space as an experimental
environment for high-mass matter-wave interferometry [
].Atthesametime,quantum
optomechanics provides novel tools for quantum-state preparation and high-sensitivity
measurements [

]. The mission proposal
MAQRO
combines these aspects in order to
test the foundations of quantum physics in a parameter regime many orders of magnitude
beyond current ground-based experiments, in particular, for particle masses in the range
between 
amu
and 

amu
.Thisway,
MAQRO
will not only significantly extend the
parameter range over which quantum physics can be tested. It will also allow for decisive
tests of a number of alternative theories, denoted as ‘collapse models’ predicting notable
deviations from the predictions of quantum theory within the parameter regime tested.
An important feature of
MAQRO
is that the parameter range covered has some overlap
withexperimentsthatshouldbeachievableongroundevenbeforeapossiblelaunchof
MAQRO
. This allows cross-checking the performance of
MAQRO
andtoprovideafail-
safe in case the predictions of quantum physics should fail already for masses between

amu
and 
amu
.Inthiscase,
MAQRO
would not allow for observing matter-wave
interference due to the presence of strong, non-quantum decoherence. For this reason, the
MAQRO
instrument is designed for allowing three modes of operation for testing quan-
tum physics over a wide parameter range - even in the presence of strong decoherence:
Non-interferometric tests of collapse models.
The stochastic momentum transfer in
collapse models can lead to heating of the center-of-mass motion of trapped
nanospheres [

,

]. This can, in principle, be observed by comparing the measured
noise spectra with theoretical predictions [

].
Kaltenbaek et al.
EPJ Quantum Technology
(2016) 3:5
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Deviations from quantum physics in wave-packet expansion.
As in the
frequency-based non-interferometric approach above, this method is based on the
stochastic momentum transfer due to collapse mechanisms. In particular, the
momentum transfer leads to a random walk resulting in an increased rate for the
expansion of wave packets [

,

,

].
High-mass matter-wave interferometry.
This central experiment of
MAQRO
is based
on the original
M
proposal [
]. It has been adapted for harnessing the successful
technique of Talbot-Lau interferometry, which currently holds the mass record for
matter-wave interferometry [

]. The goal is to observe matter-wave interferometry
with particles of varying size and mass, comparing the interference visibility the
predictions of quantum theory and the predictions of alternative theoretical models.
In particular, the non-interferometric tests and observing wave-packet expansion will
allow for performing tests in the presence of comparatively strong decoherence mech-
anisms. If these two tests show agreement with the predictions of quantum physics,
MAQRO
’s scientific instrument can then be used for performing matter-wave interfer-
ometry to test for smaller deviations from quantum physics.
5.1 Non-interferometric tests of quantum physics
The vast majority of the proposals for the test of collapse models put forward so far is
based on interferometric approaches in which massive systems are prepared in large spa-
tial quantum superposition states. In order for such tests to be effective, the superposition
has to be sufficiently stable in time to allow for the performance of the necessary mea-
surements. Needless to say, these are extremely demanding requirements from a practical
viewpoint. Matter-wave interferometry and cavity quantum optomechanics are generally
considered as potentially winning technological platforms in this context, and consider-
able efforts have been made towards the development of suitable experimental configu-
rations using levitated spheres or gas-phase molecular or metallic-cluster beams. Alter-
natively, one might adopt a radically different approach and think of non-interferometric
strategies to achieve the goal of a successful test.
MAQRO
offers the opportunity for exploring one such possibility by addressing the in-
fluences that collapse models (or in general, any non-linear effect on quantum systems)
have on the spectrum of light interacting with a radiation-pressure-driven mechanical os-
cillator in a cavity-optomechanics setting. The overarching goal of this part of
MAQRO
is to affirm and consolidate novel approaches to the revelation of deviations from stan-
dard quantum mechanics in ways that are experimentally viable and open up unforeseen
perspectives in the quest at the center of the
MAQRO
endeavors.
A benchmark in this sense will be provided by the assessment of the
continuous
sponta-
neous
localization (CSL)
model through a non-interferometric approach. In particular, we
will take advantage of the fact that the inclusion of the
CSL
mechanism in the dynamics
of a harmonic oscillator results in an extra line-broadening effect that can be made visible
from its density noise spectrum. By bypassing the necessity of preparing, manipulating,
and sustaining the quantum superposition state of a massive object, the proposed scheme
would be helpful in bringing the goal of observing collapse-induced effects closer to the
current experimental capabilities.
Kaltenbaek et al.
EPJ Quantum Technology
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The equation of motion of the optomechanical system (regardless of its embodiment)
in the presence of the
CSL
mechanism can be cast in the form given in Equation (
)
t
ˆ
O
=
i

[
ˆ
H
,
ˆ
O
]+
i

[
ˆ
V
t
,
ˆ
O
]+
ˆ
N
,()
where
ˆ
O
is an operator of the system,
ˆ
H
is the Hamiltonian of the mechanical oscillator
coupled to the cavity light field,
ˆ
N
embodies all the relevant sources of quantum noise
affecting the system, and
ˆ
V
t
is a stochastic linear potential (linked directly to the position
of the harmonic oscillator) that accounts for the effective action of the
CSL
mechanism
[

]. It can be shown that such a potential is zero-mean and delta-correlated, and thus em-
bodies a source of white noise that adds up to the relevant noise mechanisms affecting the
optomechanical system, namely the damping of the optical cavity and the Brownian mo-
tion (occurring at temperature
T
) of the mechanical oscillator. A lengthy calculation based
on the study, in the frequency domain, of the fluctuation operators of both the optical and
mechanical system, leads to the following expression for the density noise spectrum of the
mechanical system’s position fluctuation:
S
(
ω
)=
α
s

κχ
(

+
κ
+
ω
)+

m
ω
[(

+
κ
ω
)
+
κ
ω
][
γ
m
coth(
βω
)+
Y
]
|
α
s


χ
+
m
(
ω
ω
m
–i
γ
m
ω
)[

+(
κ
+i
ω
)
]
|
,
where
α
s
is the steady-state amplitude of the cavity field,
κ
is the cavity damping rate,
χ
is
the optomechanical coupling rate.

is the detuning between the cavity field and an exter-
nal pump,
m
is the mass of the mechanical oscillator,
γ
m
is the mechanical damping rate,
ω
m
is the mechanical frequency, and
β
is the inverse temperature of the system. Finally,
we have introduced:
Y
=
λ

m
ω
m
,()
where
λ
is the
CSL
coefficient. In our numerical simulations of the observability of the
effects, we have used the value of such parameter achieved by assuming Adler’s estimate
of the
CSL
mechanism’s strength. Quite evidently, the
CSL
mechanism enters into the
expression of the density noise spectrum as an extra thermal-like line broadening contri-
bution. While being formally rather appealing, this elegant result also suggests the strategy
to implement in order to observe the collapse model itself, and identifies the challenges
that have to be faced, namely a cold enough mechanical system that lets the
Y
-dependent
term dominate over the temperature-determined one. Our numerical estimate shows that,
indeed, it is possible to pinpoint the effects of the
CSL
contribution in a parameter regime
currently available in optomechanical labs. Figure
shows a typical result achieved by us-
ing the parameters stated in Ref. [

].
At the present state, this non-interferometric approach has not been investigated in suf-
ficient detail in the context of
MAQRO
. While this does not impede the main science
goals of
MAQRO
, we plan nevertheless to investigate this non-interferometric method
more closely during the study phase of
MAQRO
. It may offer the attractive possibility to
supplement the results of the other two experiments (Sections
.
and
.
).
Kaltenbaek et al.
EPJ Quantum Technology
(2016) 3:5
Page 8 of 47
Figure 1 Broadening of noise power spectra.
Comparison between the density noise spectrum of
the mechanical position fluctuation operators with
(solid red line) and without (dashed black line) the
influence of the CSL mechanism obtained using
Adler’s estimate of the CSL coupling strength and a
mechanical oscillator of 15 ng. The inset shows an
analogous study for
m
= 150 ng (figure from
Ref. [
56
]).
5.2 Deviations from quantum physics in wave-packet expansion
Most forms of decoherence can be described as resulting from the interaction of a quan-
tum system with its environment [

]. Examples are elastic and inelastic scattering as
well as emission of massive particles or radiation [

]. All of these interactions result in
a change of momentum, eventually leading to dephasing and decoherence of quantum
states. In a paper by Collett and Pearle [

], it was shown that decoherence mechanisms
assumed in collapse models also lead to momentum transfer. That means, even in the ab-
sence of standard decoherence mechanisms, collapse models may result in a random walk
due to stochastic momentum transfer. This random walk can, in principle, be observed
when comparing the expansion rate of a quantum wave packet with the predictions of
quantum theory as well as with the predictions of alternative models. Apart from the orig-
inal suggestion for such an experiment [

], there have also been more recent suggestions
to observe this effect using free-falling or optically trapped, dielectric particles [

,

].
Even if there is no decoherence, the width of a quantum wave packet will expand over
time according to the Schrödinger equation. The square of the width of the wave packet
w
s
(
t
)
evolves according to the following relation:
w
s
(
t
)
=
ˆ
x
(
t
)
s
=
ˆ
x
()
+
t
m
ˆ
p
()
.()
Here, the subscript ‘
s
’ denotes evolution according to Schrödinger’s equation,
m
is the
mass of the particle, the angular brackets denote the expectation value for a given quantum
state,
ˆ
x
denotes the position operator, and
ˆ
p
denotes the momentum operator. Equation (
)
relates the width of the wave packet at time
t
with the initial width of the wave packet and
the initial width of the momentum distribution.
In the presence of decoherence, the width of the wave packet increases more quickly:
w
(
t
)
=
ˆ
x
(
t
)
=
w
s
(
t
)
+

m
t
.()
Here,
is a parameter governing the strength of decoherence mechanisms. The width of
the wave packet is not an observable - it has to be inferred from the statistical distribution
of many measurements [

]. If we assume that we perform
N
measurements of the particle
position and if the result of the
j
th measurement is
x
j
,forlarge
N
, the width of the wave
packet can be approximated as:
w
=
N
–
N
j
=
x
j
.()