Download Genovese_cern

Improving interferometers by
quantum light:
is possible testing quantum gravity on
an Optical bench?
Marco Genovese
QFPPP 2014
CERN
This work has been supported by:
• EU Projects: BRISQ2
• John Templeton Foundation
• Italian Minister of Research: FIRB
projects
RBFR10YQ3H
and
RBFR10UAUV; Progetto premiale
P5
• Bank
Foundation: Compagnia di
San Paolo.
INRIM QUANTUM OPTICS GROUP
“Carlo Novero lab” Responsible:
M. Genovese
8 quantum optics labs
5 permanent staff (M.G., G. Brida, I. Degiovanni, M.Gramegna, I.Ruo Berchera)
8 non permanent staff (G.Adenier,A.Avella, A. Meda, G.Giorgi,E.Moreva, F. Piacentini, M.Roncaglia,P.Traina);
1 PhD students (N.Samantaray)
several undergraduate students
G. Brida, I. P.Degiovanni,M.G.,Alice Meda,
E.D. (Lisa) Lopaeva, I. Ruo Berchera
+ undergraduate students
Stefano Olivares (Univ. Milano)
Type-I PDC
Type-II PDC
Photon number correlations in twin beams/ideal case
FAR FIELD
Plane Wave Pump
q=0

q
2 
N s ( x1 )
x1
q
-x1
Two-Mode Entangled State
(squeezed vacuum)
q 
Ni ( x1 )
Two-Mode Photon
number correlation

exp(  za 1a 2  h.c ) 0   cn (q ) nq nq
n 0
N
x
N

x
s(
1)
i(
1)
5
Photon number correlations in twin beams/gaussian pump
Noisy Intensity Pattern, where the
typical scale is the Coherence Area
Gaussian Pump
N s (x)
wp
(2)
N i ( x)
qpump
0q
Relaxation of the phase
matching condition
q
q
0
q
1
2
uncertainty in the propagation
directions of twin photons
2

f 1

2
x
x2 0
x


x
  2
1
 w
2
p
To detect quantum correlation, the detector size
must be larger than the single spatial mode
A
A

1
det
ection
coherence
[Brambilla et al. Phys Rev A 69, 023802 (2004)].
6
Quantum sensing with twin beams
Sub shot noise imaging
[G.Brida,M.G.,I.Ruo Berchera, Nature Photonics 4 (10) 227
G.Brida,M.G.,A.Meda,,I.Ruo Berchera,PRA 83 (2011) 033811]
1.000
0.500
(N=10)
(N=100)
0.010
0.005
0.001
0
0.1
Perr
Perr
0.100
0.050
0.001
10
5
10
7
0
10000
Nb
10 000
Nb
20 000
20 000
Phase measurements can be improved
by using entangled states as N00N
states
-
Can quantum correlations of twin
beams find application in
interferometry?
-
Application to interferometry
 The dream of building a theory unifying general relativity and quantum
mechanics, the so called quantum gravity has been a key element in
theoretical physics research for the last 60 years.
 A HUGE theoretical work: string theory, loop gravity, ….
 However, for many years no testable prediction emerged from these
studies. In the last few years this common wisdom was challenged: a first
series of testable proposals concerned photons propagating on
cosmological distances [AmelinoCamelia et al.], with the problem of
extracting QG effects from a limited (uncontrollable) observational sample
affected by various propagation effects.
Several QG theories (string theories, holographic theory,
heuristic arguments from black holes,…) predict noncommutativity of position variables at Planck scale
Sort of space-time uncertainty principle (L= radial separation)
 Recently, effects in interferometers connected to non-commutativity of position
variables in different directions were considered both for cavities with
microresonators [Pikovsky et al.] and two coupled interferometers the so called
``holometer'‘ [Hogan]. In particular this last idea led to the planning of a double
40m interferometer at Fermilab
 Here we show how the use of photon number correlations in twin beams
can largely improve the sensibility of this interferometer
1
2
Holographic Noise (HN) and interferometry
Two Interferometers
Single Interferometer
(┴)
time
(‖)
M1
M2
BS
«Overlapping» spacetime volume
«Separated» spacetime volume
HOLOMETER : principle of operation
•
Evaluate the cross-correlation between two equal Michelson interferometers
occupying the same space-time volume (‖ conf.)
•
HNs are correlated while Shot Noises are uncorrelated vanishing over a long
integration time
•
Control measurement can be performed «turned off»
separating the space-time volumes ( ┴ conf.)
HN correlation just by
Holographic Noise (HN) and interferometry
G. Hogan, Phys. Rev. D 85, 064007 (2012).
G. Hogan, Arxiv: 1204.5948
Quantum light in the Holometer
Squeezed light in gravitational wave detectors!!
A sub-shot-noise PS measurement in a single interferometer (e.g. gravitational wave
detector) was suggested exploiting squeezed light
Caves, PRD 23, 1693 (1981)
Kimble et al., PRD 65, 022002 (2001)
Long Story and huge literature…
and recently realized at Geo 600 and Ligo
R. Schnabel et al., Nature Commun. 1, 121 (2010)
Ligo, Nature Phys. 7, 962 (2011)
1
7
The Model
«Overlapping
spacetime»
(‖)
•
•
«separated
spacetime»
(┴)
d
d
1
8
The Model
«Overlapping
spacetime»
(‖)
•
•
«separated
spacetime»
(┴)
d
d
Quantum EV
The Model
«Overlapping
spacetime»
(‖)
•
•
«separated
spacetime»
(┴)
d
d
P.D.F of the phases due to HN
Quantum EV
The Model
«Overlapping
spacetime»
•
•
Phase Covariance
(‖)
«separated
spacetime»
(┴)
The Model
Phases covariance uncertainty:
The Model
Phases covariance uncertainty:
linearization
0-th order
-
0-th order independent from phase fluctuations (i.e. HN)
0-th order Photon noise (shot-noise level in the classical @Fermilab Holometer )
IQIS2013,
24-26 September 2013, Como
The Model
Phases covariance uncertainty:
linearization
0-th order
-
2-nd order
0-th order independent from phase fluctuations (i.e. HN)
0-th order Photon noise (shot-noise level in the classical @Fermilab Holometer )
2-nd order phase dependent (Radiation pressure effect etc..)
0-th order contribution to phase
covariance uncertainty:
The Model
Phases covariance uncertainty:
linearization
0-th order
-
2-nd order
0-th order independent from phase fluctuations (i.e. HN)
0-th order Photon noise (shot-noise level in the classical @Fermilab Holometer )
2-nd order phase dependent (Radiation pressure effect etc..)
0-th order contribution to phase
covariance uncertainty:
d
d
d
d
d
d
d
d
PRL 110, 213601 (2013)
Results ideal case (no losses, no radiation pressure)
In the ideal case of absence of losses:
µ mean photon number of coherent state
 mean photon number of squeezed state
µ >>  >> 1
Results for moderate quantum resources
1.00
0.50
0.20
0.10
0.05
0.02
CL
SQ
PN
+RP
PN
+RP
PN
TWB
+RP
Quantum
Enhancement
Uncertainty
0.90 0.92 0.94 0.96 0.98 1.00
fRP 
photons momentum
Results for strong quantum resources
5.00
1.00
0.50
CL= Shot Noise Level
Ph+RP
TWB
Ph+RP
Ph
0.10
Ph
SQ
0.05
1021 1022 1023 1024 1025
Role of the entanglement
3
0
Role of the entanglement
Is Entanglement related to the TWB quantum enhanchement?
Neg
Sens
10
8
6
4
2
2.5
2.0
1.5
1.0
0.5
0.5 1.0 1.5 2.0 2.5 3.0
0.5 1.0 1.5 2.0 2.5 3.0
Indeed a clear role of entanglement, measured by negativity, is demonstrated.
This is due to the fact that the scheme requires not only perfect photon number
correlation, but also a defined phase of the TWB for a coherent interference with
the classical coherent field at the Beam Splitter.
Regimes of interests for a real experiment
1.00
0.70
0.50
For real life losses, in terms of
absolute sensitivity, the most
promising setup is still by far the
double squeezing.
CL
TWB
0.30
0.20
0.15
0.10
SQxSQ
0.1
0.2
0.5
1.0
2.0
5.0
10.0
U m 2 Hz
1 10 39
5 10 40
2
1
5
2
1
10
10
10
10
10
Shot noise
40
40
41
HN (40m arms)
SQxSQ
41
41
1
10
100
1000
104
meas s
CONCLUSIONS
 We studied for the first time the use of quantum light in coupled interferometers
 This is of extreme interest for the new developments of fundamental physics (testing
holographic principle, quantum gravity ecc..)
 Quantum light enhance the sensitivity of the Holometer below the “Shot-Noise” limit
•
Squeezed light provides an enhancement of the order of the mean number of photon of
the squeezed light
•
Twin-Beam provides a complete suppression of the shot-noise contribution (0!!!!)
•
Losses (effectively) affect this enhancement
•
Radiation pressure is not an problem (for affordable light power level)
PRL 110, 213601 (2013)