Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for...
Transcript of Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for...
![Page 1: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/1.jpg)
Hanbury Brown and Twiss effect for bosons and fermions
Chris WestbrookLaboratoire Charles Fabry, Palaiseau
DPP - fermions 2019, Lille 7 Feb 2019
1
Huntingdon and Broad Top Mountain RR
![Page 2: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/2.jpg)
Outline
Fluctuations:“Noise is the chief product and authenticating sign of civilization.” Ambrose Bierce
1. HB&T for light (stars & history)
2. HB&T for particles (atoms)
3. The Hong Ou Mandel effect
![Page 3: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/3.jpg)
Einstein, Sitz. Ber. Preuss. Ak., 1925, p. 18
Number fluctuations in an ideal quantum gas
δN2 = 〈N2〉 − 〈N〉2 = 〈N〉 + 〈N〉2 /z
z = (ΔpΔx/h)3 is the number of phase space cells in the volume.
〈N〉 “... if the molecules were independent”
〈N〉2 “... interference fluctuations” interferenzschwankungen
“… a mutual influence between molecules of a currently altogether puzzling nature.”eine gegenseitige Beeinflussung der Moleküle von vorläufig ganz rätselhafter Art
![Page 4: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/4.jpg)
Michelson: stellar interferometer
Fringe contrast indicates the spatial coherence of the source. When d is too big, fringes disappear:
θ ~ λ/dMichelson measured the angular diameters of 6 stars.
d
![Page 5: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/5.jpg)
Principle of stellar interferometry
5
For point sourceσ = l λ/ddisplace source by θ → fringe shift δ = l θ
θmax = s/L ~ λ/dIf the source is not monochromatic, fewer fringes
![Page 6: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/6.jpg)
Fringes from a real star
from the European Southern Observatory
![Page 7: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/7.jpg)
Hanbury Brown: intensity interferometry
The noise in two optical (or radio) telescopes should be correlated for sufficiently small separations d. Reminiscent of Michelson's interferometer to measure stellar diameters, but less sensitive to vibrations or atmospheric fluctuation.
Robert Hanbury Brown1916 - 2001
d
I1 I2
correlator C ~ 〈I1 I2〉
reflecting telescope
![Page 8: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/8.jpg)
The Hanbury Brown Twiss experiment (Nature, 1956)
“The experiment shows beyond question that the photons in the two coherent beams of light are correlated and that this correlation is preserved in the process of photoelectric emission.”
![Page 9: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/9.jpg)
Measurement of a stellar diameter (1957)
Independent photons from different points on a star “stick together” - photon bunching
Siriusθ = 3×10−8 radians
![Page 10: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/10.jpg)
Stellar interferometer in Australia 1960’s
Hanbury Brown’s group measured diameters of 32 stars
![Page 11: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/11.jpg)
(Classical) speckle interpretation
g(2)(Δx) = 〈I(x) I(x+Δx)〉 / 〈I〉2
large Δx → uncorrelated:
〈I1 I2〉 = 〈I1〉〈I2〉
Δx = 0:
〈I2〉 > 〈 I 〉2
thermal source (Einstein): 〈I2〉 = 2 〈 I 〉2
I(x)
x
s
L
lC = Lλ/s Δx
lC
g(2)
![Page 12: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/12.jpg)
Time dependent speckle
12
![Page 13: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/13.jpg)
Photon interpretation (Fano, Am. J. Phys. 1961)
Two “paths”
Amplitude:
Amplitude:
�1|a⇥�2|b⇥
�1|b⇥�2|a⇥
Interference:
+ for bosons, - for fermions.After summing over extended source, interference term survives if
ds / λL ≪ 1A simple classical effect corresponds to a subtle quantum one: photons are not independent.
P = |⇥1|a⇤⇥2|b⇤±⇥ 1|b⇤⇥2|a⇤|2
![Page 14: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/14.jpg)
What about a laser?
Coherence length is very long. Strong correlations?Some said “yes”
LASER Glauber, PRL 10, 84 (1963)
“The fact that photon correlations are enhanced by narrowing the spectral bandwidth has led to a prediction of large-scale correlations to be observed in the beam of an optical maser. We shall indicate that this prediction is misleading and follows from an inappropriate model of the maser beam.”
![Page 15: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/15.jpg)
Temporel correlations in a laser: measurement
Arecchi, Gatti, Sona, Phys. Lett. 1966Temporal fluctations are only due to shot noise.
g(2)(τ) = 1
laser
![Page 16: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/16.jpg)
Photon interpretation using quantized fields 1963
for thermal bosons:
Einstein formula recoveredFor a laser there is only one mode: no interference.For fermions, use anti-commutation: minus sign.
E = E+ + E�
E+ =�
�
⇥�⇤
2⇥0Ve�i�ta�
⇥I(t)I(t⇥)⇤ = ⇥E�(t)E+(t)E�(t⇥)E+(t⇥)⇤= ⇥E�(t)E�(t⇥)E+(t⇥)E+(t)⇤ + �(t � t⇥)⇥E�(t)E+(t)⇤
Roy Glauber Les Houches, 1965 Quantum Electronics p. 65-185
shot noise
�a†i a†j akal⇥ = �a†i ai⇥�a†kak⇥(�i,k�j,l + �i,l�j,k)
joint, 2 photon detection prob.
![Page 17: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/17.jpg)
Summary of (temporal) coherence
17
Interference contrast
Not true for a laser nor for "non-classical" light sources Before HBT and lasers, g(2) was ignored
![Page 18: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/18.jpg)
Experiments with (cold atoms)
18
Why? ! Advances in quantum optics, awareness of
quantum and classical coherence theory
! Possibility to study bosons and fermions
! With our without interactions (non-linearities)
! Cold atoms and BEC's provide long coherence times
! Distinction between temporal and spatial coherence is blurred
![Page 19: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/19.jpg)
Experiments with atoms
![Page 20: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/20.jpg)
Metastable helium and 3D detection
11S0
23S1 (He*)
20 eV
• detection by µ-channel plate (He* has 20 eV)
• single atom detection 25% quantum efficiency
• ~ 200 µm horizonta res. 105 detectors in //
• ~ 20 µm vertical res.• ~ 200 ns deadtime
![Page 21: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/21.jpg)
A “time of flight” observation
typically 105 atomstime of flight ~ 300 mswidth of TOF ~ 10 mswe record x,y,t for every detected atom
trap
detector
![Page 22: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/22.jpg)
Atoms dropped onto detector
n(pz) arrival time distribution integrated over detector, summed ~1000 times
ms3 2 03 1 03 0 02 9 0
0
1 0
2 0
3 0
4 0
0
5
1 0
1 5
2 0
0-5 1 05-1 0ms
a)
b) *1 0 3 pairs per 5 0 µs bin
*1 0 3 atoms per 1 0 0 µs bin
G(2)(p-p′) number of pairs within a small volume (500×500×150 µm3)
![Page 23: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/23.jpg)
Normalized correlation functions
g(2)(p-pʹ) of a thermal bose gas
in detector plane vertical
M. Schellekens et al. Science, 310, 648 (2005) T. Jeltes et al. Nature 445, 402 (2007)
comparison of a bose gas, a BEC and a fermi gas
![Page 24: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/24.jpg)
Higher order (bosons)
An ~ n!Dall et al. Nature Phys. 2013, DOI: 10.1038/NPHYS2632
![Page 25: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/25.jpg)
In situ imaging the quantum gas microscope
25
Mazurenko et alNature (2017). DOI: 10.1038/nature22362
![Page 26: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/26.jpg)
More general 2 particle interference
source
HBT: green and purple "histories" interfere to give a detected pair. Thermal source
![Page 27: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/27.jpg)
single particlessingle particle
source
No coincidences (obvious, but difficult in practice)
2 single particle sources
Coincidence?
![Page 28: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/28.jpg)
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
28
![Page 29: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/29.jpg)
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.
29
![Page 30: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/30.jpg)
G(2)cd = 〈ncnd〉 = 0independent of relative phase; no classical waves either
§ 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 )
2 boson fields at a beam splitter
1 particle at each input → 4 QM amplitudes:
both transmitted
both reflected
d
ca
b
30
![Page 31: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/31.jpg)
Experimental sequence
beam splitter use Bragg diffraction
t = 0 pair creation
t1 mirror exchanges ka and kb t1 = 500 µs
t2 beam splitter mixes 2 modes
atoms fall to detector
31
![Page 32: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/32.jpg)
HOM correlation
τ (µ 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 for each point
lack of 100% contrast due to extra particles
Lopes et al., Nature 520, 66 (2015)32
![Page 33: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/33.jpg)
2 fermi fields at a beam splitter
1 particle at each input → 4 QM amplitudes:
both transmitted
both reflected
d
ca
b
33
�� �⟩��� = �† �† �� � = ���† + �† -�† + �† �� �
= ��
-�†� + �†� + �† �† -�† �† �� �
= �� �⟩���
the interference effect is absent (less dramatic)
![Page 34: Huntingdon and Broad Top Mountain RR Hanbury Brown and ......Hanbury Brown and Twiss effect for bosons and fermions Chris Westbrook Laboratoire Charles Fabry, Palaiseau DPP - fermions](https://reader033.fdocuments.net/reader033/viewer/2022052815/60a714bfb268547c63231a99/html5/thumbnails/34.jpg)
Thanks
34