Slow neutrons and their role to test gravity
Testing Gravity 2015
16.01.2015
Gunther Cronenberg
Dark Matter & Dark Energy Search
•
galaxy rotation problem
• Supernova Ia
• cosmic microwave
background (CMB)
experimental evidence for
Dark Matter (DM) and
Dark Energy (DE)
Planck 2013 results, arXiv:1303.5076
limits of 2 parts in 10' . Furthermore, it has been shown that the gravity acceleration is independent of the composition of matter
within one part in 10".' Thus it may be concluded
that neutrons and protons bound in nuclei experience the same gravitational acceleration within
about 10 "4g/g. On the other hand the behavior
of free particles, atoms, ' neutrons,
electrons, '
and photons" in the earth's gravitational field has
been studied with lower accuracy of about only
one part in 10' or 10'. Among the particles, the
neutron is best suited for a study of the gravitational force in the "quantum limit"" since it may experience the gravity simultaneously while reacting
as a matter wave.
Thus, experiments with freely falling matter
waves may provide a direct proof of the statement
that the action of gravity does not affect the validity of the quantum physical laws for matter waves.
A verification of this fact includes also the verification of the Einstein equivalence principle. On the
other hand, experiments with freely falling neutrons in the "classical" limit, without neutron reactions other than simple detection, are not suitable for verifying the equivalence.
In this note I will report on evaluations of exact
measurements of scattering length for slow neutrons which led to a direct verification of the
equivalence for the neutron in the quantum limit.
within stringent
dependent on and independent of gravity. The
gravity-dependent
measurements were made in the
neutron gravity ref ractometer.
In this device
(see Fig. 1) very slow neutrons are reflected from
liquid mirrors after having fallen a distance h.
By the free fall they gain an energy mgfh in the
direction of gravity. If this energy equals the
potential energy of neutrons inside the mirror
substance (scattering length b, N atoms per cm')
the relation
''
Neutrons & Gravity
""'
First experiments:
• COW (1975): first observation of gravitational shift
for neutrons
m g, h, = 2~5'm. -'Nb
is valid. h, denotes the critical height for total
reflection. Measurements of h, for liquid lead'
and previous experiments" on liquid bismuth
yielded values for the scattering length bf listed
in line 12 of Table I. These quantities were calculated with effective values h,* for the critical
height of
—
Nb& —m, m g&h,*/2vh' =
test equality of inertial and
gravitational mass
II. METHOD AND RESULT
by scattering
measurements
From the length
experimentally (with high accuracy)
ym~
,g,*h2/sv'.
The equivalence fa. ctor y = (m,./m)(gz/g, ) was taken
to be unity. If this assumption is not fulfilled,
Köster (1976):
•
fall" according to
m ain
.
slit
K1 K3 K2 K5
-„t0
"or
9
a
K4
~
beam
0
axis
0
O
Ch
confirmed principle of the universality of free
fall it follows that the gravitational accelerations
mirror
of the free neutron (gz) and of bulk matter, the
0
20
40
100 m
60
80
local value (g, ), are equal. Thus, neutron exFIG. 1. Principle of the neutron gravity refractometer.
which
result
periments
in
value
for
the
a
equiKl, . . . , Kg: slits and stopper for the neutron beam
Colella, R., Overhauser, A., & Werner, S. (1975). Physical Review Letters, 34(23), 1472
=
valence factor
(Ref. 8).
/m)(gz/g, ) provide a test
Koester, L. (1976).Physical
Reviewy D,(m,
14(4),
1F
I
14
907
I
I
I
I
I
I
I
Ultra/Very Cold Neutrons
6.5 m/s
UCN
VCN!
⇡ 1.5nm 15nm
⇠ 50nm Ekin ⇡ (50
Neutron:
• no electric charge
• small polarisability
•
total reflection for even big angles (VCN < 1°)
absorption !
courtesy of C. Plonka
nEDM
UCN/VCN source:
PF2 at ILL
300)neV
(11.6 ± 1.5) · 10 4 fm3
/ 10 19 ↵atom
|dn | < 2.9 ⇥ 10 26 ecm
•
•
50 m/s
Baker, C. A., et al. (2006), Physical Review Letters, 97(13)
UCNs in the gravity field
90°
40
30
20
10
0
40
30
20
10
0
V.I. Luschikov and A.I. Frank, JETP Lett. 28 559 (1978)
V. Nesvizhevsky et al., Nature, 415 297 (2002)
UCNs in the gravity field
Schrödinger eq. with linearized gravity potential
•
' !2 ∂2
$
%% −
+ mgz ""ϕ n ( z ) = Enϕ n ( z )
2
& 2m ∂z
#
& z En #
& z En #
ϕ n ( z ) = an Ai $ − ! + bn Bi $ − !
% z0 E0 "
% z0 E0 "
•
•
bound, discrete states
Non-equidistant energy levels
bc: ϕ n (0) = 0,
40
30
state
1
energy
#1.41#peV
20
10
0
2
#2.46#peV
3
#3.32#peV
ϕ n (l ) = 0
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2009
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et 67al.7@:
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Cavity
Photon
Bouncing
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>:7 7@: 5:879<5F bL _F>CA@7>L 8K369EFV ZF:: PCA4 1[? 7@:L 3C>> G<>><3 6
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6KK9<JC=67C<5? 65E 3C>> 7@:5 C5;9:6F: 6A6C54 #< >C=C7 7@: B:97C;6>
Abele
et al. K696>>:> 7< 7@: N<77<=
B:><;C7L Nesvizhevsky,
;<=K<5:57? 3: 8F:
65 6NF<9N:9
=C99<9 65E
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ZF::UCN
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Neutron
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detector
F8GD;C:57>L
Collimator
Bottom mirrors
6>7@<8A@ 7@
5:879<5 36
F>C7 CF 9:6>>
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7965F=CFFC<
E<:F 5<7
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et al.,)/&,#
Appl.
Phys. B,
407()-:(&
(1992)
PCA89: +
4$.+$/)/& 9)H.
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"/ "55-&-$/"2
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"/5 6-8) $' &() )/&,#
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4$22-."&$, 4"/V.
7)Nesvizhevsky
"5;%6&)50
et al., Nature, 415 297 (2002)
G. Della Valle et al., PRL, 102 (2009)
Quantum Bouncer
1971,1974
Langhoff, Gibbs
The Quantum Bouncer
1992
Wallis et al.
Trapping Atoms in a
1978
Lushchikov, Frank
Quantum Bouncer with UCN
P.W. Langhoff, Am. J. Phys. 39, 954 (1971)
R. Gibbs, American Journ. o. Phys. 43 25 (1975)
V.I. Luschikov and A.I. Frank, JETP Lett. 28 559 (1978)
*+,
© 2002 Macmillan Magazines
qBounce: Timeline
2009
Jenke et al.
First Gravity Resonance Spectroscopy
2007-2009
Jenke et al.
qBouncer
2012
Cronenberg, TJ, HF, MT et al.
Full 3-part Rabi like setup
2014
Thalhammer, TJ, TR et al.
qBouncer
2010, 2011
Jenke, GC et al.
Axion, Chameleon measurements
H. Filter
Neutron charge





ω pq
!"
B





 


 








 










 




 









FIG. 2: Proposed experimental setup. Region 1: Preparation in a specific quantum state, e.g. state one with polarizer. Reg
2: Application of first π/2-flip. Region 3: Flight path with length L. Region 4: Application of second π/2-flip. Region 5: St
analyzer
T. Jenke et al., NIM A 611 318 (2009)
H. Abele et. al., Nucl. Phys A827, 593c (2009)
V.I. Luschikov and A.I. Frank, JETP Lett. 28 559 (1978)
of the Airy function, Ai(−ϵn ) = 0, due to the boundary
condition ψn (0) = 0.
For zero electric charge of the neutron, the eigenenergies of the quantum bouncer are
En(0)
= ϵn mg z0 (q = 0) ,
(11)
(0)
2. a region, where one applies a π/2 pulse creat
the superposition of the two states, whose ene
difference should be measured,
3. a region, where the phase evolves,
4. a second region to read the relative phase by app
ing a second π/2 pulse, and finally
Quantum Bouncer
step: 60 µm
Rabis method
A magnet
C
scatterer
scatterer
UCN
B magnet
1
neutron mirror
1 → 4
neutron mirror
ω pq
1?
neutron mirror
counter
Gravity Resonance
Spectroscopy
• Rabi
scatterer
scatterer
1 → 4
1
UCN
neutron mirror
neutron mirror
ω pq
E = hν
1 ?
counter
neutron mirror
Transm
1.0
0.8
0.6
transitions induced by
mechanical oscillations or
magnetic fields
0.4
0.2
f [Hz]
300 400 500 600 700 800
Gravity Resonance
Spectroscopy
• Rabi (2012)
scatterer
scatterer
1
UCN
neutron mirror
1 → 4
1 ?
neutron mirror
ω pq
neutron mirror
• First realisation (2009, 2010)
scatterer
UCN
ω pq
counter
neutron mirror
ω pq
T. Jenke et al.: “Realization of a gravity-resonance-spectroscopy technique” Nature Physics 7, 468–472
(2011)
counter
symmetry. The non-observation of an nEDM at current sensitivity levels constrains the CP violating term (θ-term) in the
Lagrangian of the strong interaction to be nine orders of magnitude smaller than naturally expected [7]. This fact is known as
the strong CP problem and a solution to it was proposed in [8],
where the spontaneously broken Peccei-Quinn symmetry was
introduced.
A new pseudoscalar boson emerges from this symmetry, the
axion [9, 10]. An intrinsic feature of the Peccei-Quinn model
is a fixed relation between mass and interaction strength of the
axion. The originally assumed symmetry breaking scale (corresponding to the electroweak scale) was ruled out, leaving only
higher energy scales possible. For the axion one thus expects
a small mass and a feeble interaction with other particles. The
possible mass of the axion is constrained by cosmology and
astro-particle physics measurements to the so-called axion window [11].
A short range spin-dependent interaction which could be mediated by an axion was proposed in [12]. There, three classes
of interactions were presented, involving either g2S -, gS gP -, or
g2P -couplings, whereas gS gP -couplings are considered of particular interest, since they violate CP symmetry. A gS gP -coupling
diagram is shown in Fig. 1 (a) and takes place between an unpolarized particle Ψ (where unpolarized means randomly pos p
larized with respect to any quantization axis) and a polarized
particle Φ⋄ . The symbol ⋄ is used to denote properties of the
particle interacting at the pseudoscalar vertex with a strength
proportional to the coupling constant g⋄P of the particle Φ⋄ . The
potential caused by such a gS g⋄P -coupling between an unpolarized particle and a polarized particle with mass m⋄ and spin σ⋄
is derived as [12]:
!
"
2
1 −r/λ
1
(!c)
⋄
(
σ̂
·
r̂)
+
e ,
(2)
V(r) = gS g⋄P
rλ r2
8πm⋄ c2
Axions
•
•
Our measurement with ultracold neutrons is part
sitive to axion-like particles with a mass in the rang
10 meV to 100 meV coupling to fermions. It also
mass range targeted by helioscopes such as CAST
would be sensitive to axion-like particles coupling
spin-mass coupling
scalar-pseudoscalar coupling
Introduced to solve problem on CP-violation in strong
Figure 1: (a) Interaction diagram of a scalar-pseudoscalar co
interactions
particles Ψ and Φ . Ψ is unpolarized and interacts at the scalar
Candidates for dark matter
⋄
coupling constant gS , whereas Φ⋄ is polarized and interacts at t
vertex with the coupling constant g⋄P . The total interaction stre
tional to the product gS g⋄P . (b) A polarized neutron n with spin
an unpolarized nucleon N at distance r within bulk matter shap
thickness d. A view of the ϱ-z plane in a cylindrical coordinate
is shown.
✓
◆
!·!
1
n
1
!
r/
V ( r ) = ~g g
+ 2 e
8⇡mc
r r 3. The measurement with the nEDM apparatus
Also search for Axion-like particles (ALPs)
⋄
Spin-polarized ultracold neutrons of energies be
are confined in a cylindrical storage chamber with
height H=12 cm, and inner diameter ø=47 cm at t
the nEDM apparatus. A vertical magnetic hold
∼1 µT is applied. The UCN spins precess for 1
precession frequency is inferred using Ramsey’s
The spins of polarized 199 Hg atoms precess simul
the same volume allowing to correct the Larmor pr
quency of the neutrons for magnetic field fluctuatio
Neutrons
ecific symmetry breaking scale. Thus, no sigt (i.e. comparable to experimental sensitivity
can be deduced from current EDM limits [16]
Search
for
Axions
eneric boson being the interaction mediator.
ent with ultracold neutrons is particularly sene particles
a mass intothe
rangefor
of roughly
Setupwith
is sensitive
axions
eV coupling to fermions. It also matches the
ed by helioscopes
CAST (10µeV..1eV)
[17] which
0.2µm suchas2cm
e to axion-like particles coupling to photons.
ion diagram
of a scalar-pseudoscalar coupling between
Afach, S., et al. (2014). arxiv:1412.3679
K. Nakamura et al. (Particle Data Group), JPG 37, 075021
is unpolarized and interacts at the scalar vertex with the
result was obtained for the case of an ideal
) but remains valid at room temperature
essure of 10−4 mbar. We calculate bounds
g constant β by comparing the transition
h their theoretical values, which are propormatrix elements νkj − νtheo
kj ∼ βðhkjΦjki−
he corresponding data analysis, the fit
Applying
magnetic
field
•
Earth’s acceleration was fixed at the local
5 m=s•2 , while
all othereffect
parameters
were
Measuring
for each
acted confidence intervals for limits on the
nd n are given in Fig. 3. The experiment is
at 2 ≤ n ≤ 4 (visible only on a linear scale
2
The neutron spin polarization is analyzed by our modifi
detector described above. A hypothetical spin-depende
force would change the transition frequencies. This shift
obtained by reversing the direction of both the applied gui
field as well as the detector field and by measuring t
difference in the count rates at the two steep slopes
the three-level resonance j1i↔j2i↔j3i. We do not obser
any significant frequency shift. A fit of the strength gs
and range λ together with all other
lea
Spinparameters
Up
spin
(at 95% C.L.) to an upper limit on the axion interacti
Spin Down
strength as shown in Fig. 4. For example, at λ ¼ 20 μm,
Search for Axions & ALPs
12
13
scatterer
ω pq
!"
B
this work
GRS UCN
counter
neutron mirror
ω pq
Log10 gs g p
atomic physics
14
15
n
5.5
8
10
nline). Exclusion plot for chameleon fields
level). Our newly derived limits (solid line)
A
A
5.0
Log10
5th force tests
6
GRS this work
16
6.0
4
B
4.5
4.0
m
FIG. 4 (color online). Limits on the pseudoscalar coupling
axions (95% confidence level). Our limit for a repulsive (attra
Jenke, T., Cronenberg, G., et al. Phys. Rev. Lett., 112, 151105. (2014)
tive) coupling is shown in a solid (dashed) line marked w
A þ ðA−Þ. The limits are a factor of 30 more precise than t
L. Filter
Chameleons
•
Dark energy candidate
mechanism suppresses in vicinity of masses#
massless scalar field, hidden at laboratory scales
Ve↵ (') = V ( ) +
MPl
'⇢
Ratra-Peebles model (n > 0):
4+n
⇤
4
V (') = ⇤ +
'n
leads to screening effects
Khoury, J., & Weltman, A. (2004). Chameleon cosmology. Physical Review D, 69(4)
P. Brax, G. Pignol, Phys. Rev. Lett. 107, 111301 (2011)
n=3
80
Veff (ϕ)
V(ϕ)
60
Veff
•
ρ eβϕ/MPl
40
20
0
0.2
0.4
0.6
0.8
ϕ
Self interaction
1.0
1.2
1.4
Interaction
with matter
Ref. [26]. This result was obtained for the case of an ideal
vacuum (ρ ¼ 0) but remains valid at room temperature
and vacuum pressure of 10−4 mbar. We calculate bounds
on the coupling constant β by comparing the transition
frequencies with their theoretical values, which are proportional to the matrix elements νkj − νtheo
kj ∼ βðhkjΦjki−
hjjΦjjiÞ. In the corresponding data analysis, the fit
parameter for Earth’s acceleration was fixed at the local
value g ¼ 9.805 m=s2 , while all 2other parameters were
2+n
E
=
h
|
(z⇤)
| nfor
i limits on the
Chameleon shifts energy of state: varied. The n
n
extracted confidence
intervals
2
parameters
β and n are given in Fig. 3. The experiment is
◆ 2+n
✓
m
2 + n most sensitive at 2 ≤ n ≤ 4 (visible only on a linear scale
p z⇤
V (z) = mgz +
⇤~c
Chameleon fields
M Pl
2
15
1.0
atomic physics
0.6
0.4
0.2
0.0
300
GRS this work
10
Log10
transmission
0.8
no chameleon
5
n=2, Log10 [β]=7.4
400
500
600
700
5th force tests
0
800
Hz
2
P.#Brax,#G.#Pignol,#Phys.#Rev.#Lett.#107,#111301#(2011)#
A.N.#Ivanov#et#al.,#(2013).#Physical#Review#D,#87(10),#105013.#
FIG. 3
Jenke,#T.,#Cronenberg,#G.,#et#al.#Phys.#Rev.#Lett.,#112,#151105.#(2014)
4
n
6
8
10
(color online). Exclusion plot for chameleon fields
(95% confidence level). Our newly derived limits (solid line)
are 5 orders of magnitude lower than the upper bound from
Lloyd interferometer
L
L0
very cold neutrons 10 nm, 40 m/s shielding
in realization by Filter, Masahiro, Oda et al.
collimation
L
M1
Lloyd =
neutron
2a
mirror
M2
neutron
beam
S2
S1
detector
200
section 2
section 1
Neutronen @  D
150
N
100
50
0
3.9
Simulated#MC#data
4.0
4.1
Detekto rkoordinate @ m m D
4.2
4.3
Roman Gergen
Pokotilovski,#Y.#N.#(2011).#JETP#Letters,#94(6),#413–417
V1
V2
M
V4
turbo- V5
molecular
pump
air
prepump
He
Slow neutrons
⇡ 3Å
•
R We will calculate the chameleon bubble integral
’ðxÞdx and show that it can be suppressed when introducing a gas at moderate pressure in the sample cell. The
chameleon profile ’ðxÞ in the sample cell satisfies the 1D
chameleon equation,
−10
beam
at side
20
0
10
x [mm]
20
0
−20
−10
II
0air 10
x [mm]
chamber
positions:
PHYSICAL REVIEW D 88, 083004 (2013)
5
8
4
n II
7
k II
h II
−20
vacuum
20
g II
d II
a II
I
I
I
air
I
I
I
94 mm
40 mm
6
2
y [mm]
O detector
I
3
1
5
0
4
-1
3
incident
beam
-2
-3
-4
1
-5
-5
0
-4
-3
-2
-1
0
1
x [mm]
2
3
4
5
(12)
where $ is the mass density of the gas inside the sample
cell. We will assume the boundary condition ’ð$RÞ ¼
’ðRÞ ¼ 0, which proves to be valid when ’c & ’0 where
’c is the field value inside the plate bulk and ’0 ¼ ’ð0Þ is
the maximum of the field in the sample cell.
represented the field profile in 2D obtained numerically in
Fig. 6 when the transverse dimension of the chamber is
finite. We find that bubbles still form in this geometry.
Let us now elaborate in the case $ > 0. First we trans-
50 mm
4mm
2
FIG. 6 (color online). The chameleon profile ’=! in 2D in a
square box calculated for n ¼ 2.
d2 ’
!
¼ V 0 ð’Þ þ
$;
2
MPl
dx
0
beam
at side
path
−10path
beam
at center
movable
10
n=4
PROBING STRONGLY COUPLED CHAMELEONS WITH SLOW . . .
spacial profile measured
density dependence
30
n=2
n=3
neutrons wavelength
•
40
n=1
H detector
10
interferometer
(a)
y [mm]
φ /Λ
−20
neutron beam as shown in Fig 4. We will assume that the
transverse dimension of the cell is infinite and denote the
distance between the plates by 2R. For numerical studies
we will set 2R ¼ 1 cm as in the experiment performed at
NIST [13]. When the cell is filled by no gas, i.e. in vacuum,
a chameleon bubblelike profile ’ðxÞ, $R < x < R, will
appear in the cell, inducing the potential !m=MPl ’ðxÞ
for the neutrons. One can then show (see e.g. [14]) that
the phase shift due to the chameleon bubble is given by
m ZR
m
"# ¼ 2
!
’ðxÞdx:
(11)
kℏ $R MPl
20
(d)
(c)
interferometric setup
S18 at ILL
realized by Th. Potocar /
T. Jenke & collaborators
chamber
phase flag
(b)
V3
V1
Brax,#P.,#Pignol,#G.,#&#Roulier,#D.#(2013).#Physical#Review#D,#88(8),#083004
prepump
pressure
gauge
V2
V4
turbo- V5
molecular
pump
air
M
leak
valve
He
chamber
Kevin Mitsch
Peter Geltenbort
Jason Jung
Hanno Filter
Martin Thalhammer
Tobias Jenke
G. C.
Hartmut Abele