hong ou mandel experiment with atoms
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Hong Ou Mandel experiment with atoms
Chris WestbrookLaboratoire Charles Fabry, Palaiseau
FRISNO 13, Aussois 18 march 2015
BEC on an MCP
2 particles at a beam splitter
1 particle at each input → 4 possibilities:
both transmitted
both reflected
d
ca
b
both in c both in d
2 particles at a beam splitter
1 particle at each input → 4 possibilities:
both transmitted
both reflected
d
ca
b
both in c both in d
Hong Ou Mandel effect: only 2 possibilities
Hong, Ou and Mandel PRL 59, 2044 (1987)
d
c
〈nc〉 = 〈nd〉 ≠ 0
〈ncnd〉 ≈ 0
“HOM dip” as a function of the overlap between the two arms.
d
ca
b
2 classical wave packets
Ic
Id
𝜙
d
ca
b
2 classical wave packets
Ic
Id
0.0 0.5 1.0 1.5 2.0
0.51.01.52.0
0 π 𝜙
IcId
𝜙
d
ca
b
2 classical wave packets
Ic
Id
0.0 0.5 1.0 1.5 2.0
0.51.01.52.0
0 π 𝜙
IcId
𝜙
correlation function:
g(2)cd = = 1/2 overlapped
g(2)cd =1 not overlapped (detector slower than pulse)
〈Ic Id〉𝜙
〈Ic〉𝜙〈Id〉𝜙 pulse delay
1
0.5
2 quantum fields at a beam splitter
1 particle at each input → 4 QM amplitudes:
both transmitted
both reflected
d
ca
b
2 quantum fields at a beam splitter
1 particle at each input → 4 QM amplitudes:
both transmitted
both reflected
d
ca
b
G(2)cd = 〈ncnd〉 = 0two particle interference has no classical analog
§ 1, 1\a,b = a† b†• 0, 0] = 12Ic† + d†M I-c† + d†M• 0, 0]
= 12I-c†2 + d†2 + c† d† - d† c†M• 0, 0]
= 12H -§ 2, 0\c,d +§ 0, 2\c,d )
Why do it?
Santori et al. “Indistinguishable photons from a single-photon device” Nature, 2002 (one quantum dot)
Beugnon et al. “Quantum interference between two single photons emitted by independently trapped atoms” Nature, 2005
It’s cool...Tests single photon sourcesMetrology with twin Fock states
How to do it with atoms
Essential features
photon coincidence counting → He*, MCP
source of photon pairs → 4 wave mixing
mirrors, beam splitter → Bragg diffraction
spatial, spectral filters → MCP
Get a good team
Pierre Dussarat Almazbek ImanalievMarc Cheneau
Denis BoironC I W Raphael LopesAlain Aspect
Metastable Helium, He*
Lifetimes:23S1: 8000 s23PJ: 100 ns
4He (no nuclear spin)
deexcitation enables electronic detection: He*→He+ + e-
microchannel plate and delay line anode spatial resolution ~250 µmq.e. > 25%
23S1
21S0
11S0
23P0,1,2
1083 nm
E (eV)
0
19.8
20.6
24.6
“Time of flight” observation
5×104 detectors in // record x,y,t for every detected atomget velocity distribution and correlation functions
trap
detector
46 cm
there is also a laser trap
“Time of flight” observation
5×104 detectors in // record x,y,t for every detected atomget velocity distribution and correlation functions
trap
detector
46 cm
there is also a laser trap
Pair production: 4 wave mixing in a latticedynamical instability: 2 k0 → k1 + k2
Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013
lowest energy band
Pair production: 4 wave mixing in a latticedynamical instability: 2 k0 → k1 + k2
Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013
lowest energy band
Pair production: 4 wave mixing in a latticedynamical instability: 2 k0 → k1 + k2
Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013
lowest energy band
Bragg diffraction: mirror and beam splitter
kBragg-1𝜃
Angle 𝜃 adjusted so that kBragg = k2 - k1
100 µs pulse : mirror 50 µs pulse : 50-50 beam splitter
k1 k2
Experimental sequence
zx
y
45 c
m
a
timeposi
tion
zt1 t2 t3
b
a
b
a
b
c
d
a
b
c
d
c
t1 pair creation
t2 mirror exchanges ka and kb t2-t1 = 500 µs
t3 beam splitter mixes 2 modes
atoms fall to detector
Detected
atomnum
ber
Detected atom number
a
0.00
0.04
0.08
0.12b
0.00
0.04
0.08
0.12c
6.0 7.0 8.0
-2.0 0.0 2.0
0.00 0.02 0.04 0.06
-2.0 0.0 2.0vx (cm/s)
v z (cm
/s)
7.0
9.0
11.0
13.0
vx (cm/s)
vz (cm/s)
Filtering
small slice of the velocity distribution isolates one mode
0.8 atoms/mode0.2 detected
vb
va
HOM correlation
W (P s)
0.00
0.02
0.04
0.06
0.08
150
G(2) cd
900750600450300
G(2)cd = 〈ncnd〉0.06 coincidences per shot
50% contrast
delay: 𝜏 = t3-t2
n.b. t2-t1 = 500 µs~10 hrs of data for each point
Lopes et al. arXiv:1501.03065
observed contrast is mostly due to multiple atoms
Other, non-optical experiments
AtomsKaufmann et al., Science 345, 306 (2014).
ElectronsBocquillon et al., Science 339, 1054 (2013).Dubois et al., Nature 502, 659 (2013).
PlasmonsFakonas et al., Nature Photonics 8, 317 (2014).Di Martino et al., Phys. Rev. Appl. 1, 034004 (2014)
MicrowavesLang et al., Nature Phys, 9, 345 (2013).
2 particle interference in a double well
Kaufmann et al., Science 345, 306 (2014)
Future
Bell’s inequalities without spin degrees of freedom |k1,q1〉 + |k2,q2〉 Lewis-Swann and Kheruntsyan 1411.0191Need to increase the repetition rate with low pair production (D. Clément: He* BEC in 7 s)
with photons:Rarity and Tapster PRL 1990
Multiparticle interference with spins
2 mode squeezed state in the spin sector
B. Lücke, et al « Twin Matter Waves for Interferometry Beyond the Classical Limit », Science, 334, p. 773-776 (2011).
Photonic version, Spasibko et al. NJ Phys 2014
Do it in momentum space?
Merci
Merci
Two obvious causes for G(2) ≠ 0:
1. Lack of indistinguishibility i.e. imperfect spatial overlap2. Occasional presence of more than 1 particle
n.b. G(2)aa = 〈a†a†aa〉 = 0 for the |1,1〉 state
We find Vmax = 0.6 ± 0.1.
Data consistent with “perfect indistinguishibility” but extra particles in the state.
Interference contrast
HOM “peak”?
〈ncnd〉
〈nc2〉
0.0
0.5
1.0
1.5
2.0
2.5
200 400 600 800
g(2
)cd
⌧(µs)
Mean count rates
W (Ps)150 900750600450300
0.08
0.06
0.04
0.02
0.00
0.16
0.20
0.24
0.16
0.20
0.24
��n c!
��n d!
c
b
a
� n c!
. �
n d! G(2) cd
〈nc〉, 〈nd〉
... are roughly constant
Variation of contrast with filter widthV
a b
'�v z (cm/s) '�v ŏ� (cm/s)0.2 0.4 0.6 0.8 1.0 0.4 0.5 0.6 0.7 0.8
0.0
0.4
0.8
Variance in the number difference
V =h(N1 �N2)2i � hN1 �N2i2
hN1 +N2i
N1, N2 ~ 100
Vmin ~ 0.75
4 wave mixing in a (moving) optical lattice
Energy and quasi-momentum conservation2k0 = k1+k2
2E0 = E1+E2
Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013
Interactions produce a dynamical instability for large k0
A few characteristics
Final momenta can be chosen with k0
Turning lattice off stops interaction → atom number can be controlled
Including mean field
Bonneau et al. PRA 2013
Populations
beam bP0 = 0.9P1 = 0.090P2 = 0.005
beam aP0 = 0.82P1 = 0.16P2 = 0.021
measured
we infer 〈n〉 ≈ 0.5 - 0.8 depending on assumptions
A two mode squeezed state
Two mode squeezed state:
y\ = 1cosh r
S Htanh rLn n, n^Xn\ = sinh2 r
In our experiment Xn\ ª 0.7 Æ r ª 0.76. Probabilities for 0, 1 or 2 particles:
P0 ª 0.6P1 ª 0.24P2 ª 0.10
Correlated atom pairs
Correlation function for back to back pairsg(2)(p, –p+Δp)
0.05 krec
Jaskula et al. PRL 2010
Microchannel Plate
Single atom detectionq.e. ~ 25%
Detector photos
Delay lines MCP + Delay lines
8 cm
Four wave mixing of free atoms
a.k.a. “a collision”
H = � a1a2a†3a
†4 + h.c.
energy and momentum conservation:
k1 + k2 = k3 + k4
E1 + E2 = E3 + E4
restricts atoms to a spherical shell Perrin et al. PRL 2007
Detection MCP and delay line
hole separation: 24 µmspatial resolution ~250 µm5×104 detectors in // q. e. for He* ~ 25%
must be careful about saturation
time differences give the position on MCPrecord x, y, t for each atomreconstruct momentum distribution
! 4 wave mixing, seen in 3D
! 4 wave mixing, seen in 3D
Other methodswhy look for alternatives?small occupation per mode (0.1 - 0.01)not easily controlled
relaxation of transverse excitations in BEC Bücker et al. Nat Phys (2011)
modulation of speed of soundparametric downconversion of phonons (DCE)Jaskula et al. PRL (2012)
Wave particle duality
If we look for an anti-correlation, we find one〈ncnd〉 = 0 :Particle interpretation
single photon at a beam splitter (Grangier et al., EPL 1986)
If we look for interference, we find it:Wave interpretation
HOM is more subtle because neither interpretation works.
Interference fringes from single photons
(Grangier et al., EPL 1986)
Photon pairs
ω1, k1
ω2, k2
parametric downconversion:
H ~ b a1†a2† + h.c.
4 wave mixing:
H ~ b1 b2 a1†a2† + h.c.
A. Migdall, NIST
These processes have led to Bell’s inequality violations, squeezing, improvements in interferometry ...
Hong Ou Mandel effect
Start with 1 photon in each input → 4 QM amplitudes:
|2,0〉 + |0,2〉 1st two amplitudes cancel, leaving:
average number in one output port 〈N〉 = 1variance v = 〈N2〉 -〈N〉2 = 1 v = 1/2 without interference
both transmitted
both reflected
normalized variance V = v/v = 2
Laser trap and detector
position at detector gives initial velocity
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