![Page 1: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/1.jpg)
Quantum Optics with Propagating Microwaves in Superconducting Circuits II
2015 AMO Summer School
Io-Chun, Hoi
![Page 2: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/2.jpg)
Quantum applications
• The single-photon router
• The cross-Kerr phase shift
• The photon-number filter
• The quantum spectrum analyzer
• Photon mediated interactions
Quantum network
Outline
Io-Chun Hoi
![Page 3: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/3.jpg)
Resonant scattering in 1D waveguide
Io-Chun Hoi
![Page 4: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/4.jpg)
Fully coherent: no transmission, perfect reflection.
Io-Chun Hoi
Relaxation dominated by transmission line.O. Astafiev, et al. 327, 840 Science (2010) IoChun, Hoi et al. PRL 107, 073601 (2011)
λ >> d λ ∼ cm d ∼ μm Size of “atom”
Wavelength of EM field
Point like atom/dipole!
Al
Al
2nm
Fig. from E. Olsson & S. M. Nik
JJ
D.E. Chang et al. Nature Physics 3, 807(2007)
Resonant scattering in 1D waveguide
![Page 5: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/5.jpg)
Saturation of transmission
Nonlinear nature of the atom!
Io-Chun Hoi
![Page 6: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/6.jpg)
Io-Chun Hoi
T
[dBm] Pc
ωp /2π[GHz]
A. A. Abdumalikov, Jr et al. PRL 104, 193601 (2010)
![Page 7: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/7.jpg)
Io-Chun Hoi
![Page 8: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/8.jpg)
1(R) 2(T)
Probe input Control
1 2
I.-C. Hoi et al. PRL 107, 073601 (2011)
Io-Chun Hoi
By turning on or off the control tone, we can decide which port the input photons go to.
![Page 9: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/9.jpg)
Off
On
Off
PP ,PC
time
Io-Chun Hoi
![Page 10: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/10.jpg)
1.0
0.8
0.6
0.4
0.2
3.53.02.52.01.5μs
1.0
0.8
0.6
0.4
0.2
Io-Chun Hoi
![Page 11: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/11.jpg)
T
1.0
0.8
0.6
0.4
0.2
3.53.02.52.01.5μs
1.0
0.8
0.6
0.4
0.2
Io-Chun Hoi
![Page 12: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/12.jpg)
Io-Chun Hoi
![Page 13: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/13.jpg)
Io-Chun Hoi
![Page 14: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/14.jpg)
0
1
2
ωp
0
1
2
ωp
ωc
I
I
Q
Q
ΔϕP
Io-Chun Hoi
![Page 15: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/15.jpg)
0
1
2
ωp
0
1
2
ωp
ωc
I
I
Q
Q
ΔϕP
Io-Chun Hoi
1.0
0.9
0.8
0.7
0.6
0.5
0.4
-30-20-10
01020
7.47.27.06.8
ϕ p
ωp /2π [GHz]
[Deg.]
t p
( on )
t p
( off )
Δϕ p
![Page 16: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/16.jpg)
[GHz]ωp /2π
ωpωc
time
Device 1
Δϕ p
[Deg.]
NC � 0.3-4
-2
0
2
4
7.357.307.257.207.15
-140 dBm -127 dBm -117 dBm
Io-Chun Hoi
![Page 17: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/17.jpg)
-30
-25
-20
-15
-10
-5
01.00.80.60.40.20.0
Δϕ p
Device 1Device 2
Nc
[Deg.]
I.-C. Hoi et al.
Io-Chun Hoi
![Page 18: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/18.jpg)
-30
-25
-20
-15
-10
-5
01.00.80.60.40.20.0
Δϕ p
Device 1Device 2
Nc
[Deg.]
I.-C. Hoi et al.
N. Matsuda, et al. (
Io-Chun Hoi
V. Venkataraman, et al. (
Kerr medium
0
1
2
ωp
ωc
δω P
![Page 19: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/19.jpg)
rP , 2
rC , 2
Nc
Device 2
r P,2
r C,2
,
1.0
0.8
0.6
0.4
0.2
0.01.00.80.60.40.20.0
Io-Chun Hoi
0
1
2NC
NP
![Page 20: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/20.jpg)
Io-Chun Hoi
![Page 21: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/21.jpg)
![Page 22: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/22.jpg)
What is the photon statistics of the scattered field?
Io-Chun Hoi Io-Chun Hoi
![Page 23: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/23.jpg)
Io-Chun Hoi
Intensity-Intensity Correlation
Single photon source Beam splitter
Source
Second-order
correlation function
HBT measurement
Hanbury Brown-TwissNature 177, 27 (1956)
Source
![Page 24: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/24.jpg)
Coherent
state
ESONN 2010 lecture
Photon statistics from second order correlation function
Io-Chun Hoi
![Page 25: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/25.jpg)
Io-Chun Hoi
Photon number filter
Poisson probability distibution
![Page 26: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/26.jpg)
Io-Chun Hoi Io-Chun Hoi
Photon number filter
Antibunching!Bunching!
Poisson probability distibution
![Page 27: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/27.jpg)
Noise temperature of detection chain is about 7K
Noise of two amplifier is uncorrelated.
Covariance
Io-Chun Hoi
Hanbury Brown-Twiss measurement of output state
-30dB-30dB
-10dB
-20dB
-10dB
-20dB
DC Block
BPF
LPF
RT
4.2 K
1 K
50 mK
“Atom”Cc
Amplifier
ωp 1 2
∼
1
3 4
2
Commercial ”beam splitter”
![Page 28: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/28.jpg)
Io-Chun Hoi
![Page 29: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/29.jpg)
Io-Chun Hoi
2.42.22.01.81.61.41.21.0
-128 -124 -120
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
-150 -100 -50 0 50 100 150
P -129 dBm -128 dBm -127 dBm -125 dBm
g2 (0)
[dBm]
g2 (τ )
P
τ [ ]ns
![Page 30: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/30.jpg)
Io-Chun Hoi
I.-C. Hoi et al.
![Page 31: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/31.jpg)
Io-Chun Hoi
![Page 32: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/32.jpg)
Io-Chun Hoi
![Page 33: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/33.jpg)
a)
Vr
Vin
320 um320 um
b)L
Io-Chun Hoi
Single ion: J. Eschner Nature, 413, 495 (2001)
Mirror shapes the modes of the vacuum that couple to atom.
Reflection coefficient:
p
50mK
![Page 34: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/34.jpg)
6.0
5.8
5.6
5.4
5.2
5.0
4.8-0.2 -0.1 0.0 0.1 0.2
1.0
0.9
0.8
0.7
0.6
0.5
1.2
1.0
0.8
0.6
0.4
0.25.555.545.535.52
4.884.864.844.824.80
1.2 MHz 11.8 MHz
/Φ0Φ
[GHz]ωp /2π
p|r |
[GHz]ωp /2π
Γ1 /2π
p|r |
Changing the spontaneous emission rate
Experimental data Weak drive:
Io-Chun Hoi
![Page 35: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/35.jpg)
6.0
5.8
5.6
5.4
5.2
5.0
4.8-0.2 -0.1 0.0 0.1 0.2
1.0
0.9
0.8
0.7
0.6
0.5
1.2
1.0
0.8
0.6
0.4
0.25.555.545.535.52
4.884.864.844.824.80
1.2 MHz 11.8 MHz
/Φ0Φ
[GHz]ωp /2π
p|r |
[GHz]ωp /2π
Γ1 /2π
p|r |
Changing the spontaneous emission rate
Experimental data Weak drive:
Io-Chun Hoi
Atom decoupled from vacuum fluctuations at node.
![Page 36: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/36.jpg)
6.0
5.8
5.6
5.4
5.2
5.0
4.8-0.2 -0.1 0.0 0.1 0.2
1.0
0.9
0.8
0.7
0.6
0.5
1.2
1.0
0.8
0.6
0.4
0.25.555.545.535.52
4.884.864.844.824.80
1.2 MHz 11.8 MHz
/Φ0Φ
[GHz]ωp /2π
p|r |
[GHz]ωp /2π
Γ1 /2π
p|r |
Changing the spontaneous emission rate
Experimental data Weak drive:
Io-Chun Hoi
Atom decoupled from vacuum fluctuations at node.
![Page 37: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/37.jpg)
Io-Chun Hoi
: relaxation rate of bare atom : phase difference between scattered field from the same atom
Spontaneous emission rate as a function of normalized distance
12
10
8
6
4
2
0
0.540.520.500.480.460.44
[MHz]
L /
Γ /2πΓ1 /2π
φ
![Page 38: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/38.jpg)
Io-Chun Hoi
Probing quantum vacuum fluctuations from spontaneous emission rate
k: coupling constant
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.560.520.480.44
Theory Data
2.0
1.5
1.0
0.5
0.0
0.70.60.50.40.3
Theory Data
[ ]S Mirrorless
vacuumωah
Antinode vacuum
Node vacuum
L/L/
[ ]Sωah
![Page 39: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/39.jpg)
Io-Chun Hoi
![Page 40: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/40.jpg)
Fully coherent: no transmission, perfect reflection.
Io-Chun Hoi
![Page 41: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/41.jpg)
Io-Chun Hoi
![Page 42: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/42.jpg)
Io-Chun Hoi
![Page 43: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/43.jpg)
Io-Chun Hoi
Double-peak split by 15MHz exchange interaction J, mediated by virtual photons.
![Page 44: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/44.jpg)
The photon-number filter ( )
The cross-Kerr phase shift ( )
The single-photon router ( )
The quantum spectrum analyzer (Probing fluctuation)
Summary I
Io-Chun Hoi
![Page 45: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/45.jpg)
Io-Chun Hoi
![Page 46: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/46.jpg)
Io-Chun Hoi
![Page 47: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/47.jpg)
Io-Chun Hoi
R.W. Andrews, et al. Nature Physics 10, 321 (2014) Y. Kubo et al. PRL 105, 140502 (2010)
![Page 48: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/48.jpg)
Conclusion
Io-Chun Hoi
![Page 49: Quantum Optics with Propagating Microwaves in ...lbwang/AMO2015/Hoi2.pdf · 2 ω p 0 1 2 ω p ω c I I Q Q Δϕ P . ( 0 ./ #*0*)F #*0*) $)0 . 1*) 7$ 0#. F' 7 ' 0*( Io-Chun Hoi 1.0](https://reader034.vdocuments.us/reader034/viewer/2022052017/6030abc0a34ec73e3767a14d/html5/thumbnails/49.jpg)
Acknowledgements
Io-Chun Hoi