量子微波光子学

G0
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 10/1
Parametric Amplification/Oscillation
p Γa da √ ′ A′ , = igαb − a + γa Ain + γa dt 2 q db Γb √ ∗ ′ B′, = igα a − b + γb Bin + γb dt 2 √ Aout = γa a − Ain , √ Bout = γb b − Bin . Effective microwave resonator temperature ∝ b† b
Electro-Optic Modulation
´ ` ǫ = ǫ0 1 + χ(1) + χ(2) E + χ(3) : EE + . . . Optical: transparent between 350nm-5µm
χ(2) (Pockels): ∆φ(V ) ∝ V : e.g., lithium niobate (LiNbO3 )
Coupling Strength
g 2 Npump , G= γa γb
ωa n3 r g=η 2d
r
ωb . 2C
(17)
Ilchenko et al., JOSAB 20, 333 (2003) (γa ≈ 2π × 90 MHz, γb ≈ 2π × 50 MHz, d ≈ 150µm):
intrinsic Q ∼ 106 resonator at 1.55µm [Ilchenko et al., JOSAB 20, 333 (2003)] 10dB squeezing [Vahlbruch et al. PRL 100, 033602 (2008)] Microwave: intrinsic ǫl ≈ 28, ǫt ≈ 45, Q ≈ 2.3 × 103 at 9GHz, 300K [Bourreau et al., EL 22, 399 (1986)], loss should decrease with temp. Cu half-wave resonator: Q ≈ 100 at 9GHz, 300K [Ilchenko et al.] 26.5GHz EOM with Nb electrode on LiNbO3 at 4.2K [Yoshida et al., IEEE TMTT 47, 1201 (1999)]
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 3/16
Three-Wave Mixing
P (N L) ∝ χ(2) : EE, ωmicro + ωopt = Ωopt
20
10
0
−10 0
0.2
0.4
G0
0.6
0.8
1
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 13/1
p da Γa √ ∗ ′ A′ , = igαb − a + γa Ain + γa dt 2 q db Γb √ ∗ ′ B′, = igαa − b + γb Bin + γb dt 2 √ Aout = γa a − Ain , √ Bout = γb b − Bin .
(10)
(11) (12) (13)
Device Geometry
Cohen et al. (USC), “High-Q microphotonic electro-optic modulator,” SolidState Electronics 45, 1557 (2001)
Mahapatra and Robinson, “Integrated-optic ring resonators made by proton exchange in lithium niobate,” Appl. Opt. 24, 2285 (1985).
g ≈ 20 Hz,
G ≈ 2 × 10−5 at 2 mW pump
(18)
g can be improved by ∼ 101 − 102 , γb reduced by ∼ 103 using superconducting microwave resonator
Quantum Microwave Photonics:
2
Department of Physics
National University of Singapore
http://mankei.tsang.googlepages.com/
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 1/16
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators
Mankei Tsang
eletmk@nus.edu.sg
1
Department of Electrical and Computer Engineering
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 11/1
Parametric Amplification/Oscillation
Optical/microwave photons ↔ microwave/RF phonons:
O’Connell et al., Nature 464, 697 (2010)
optical photons ↔ microwave/RF photons:
Kippenberg and ence 321,
Up-conversion
Down-conversion
Parametric amplification
Spontaneous parametric down conversion
Spatial mode matching
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 4/16
r in BaTiO3 and KTN is higher than LiNbO3 by 101 − 102
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 9/16
Plots
R(0)/η
1.2
4G0 /(1 + G0 )2
1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5
Resonant Enhancement
How to enhance desired processes and suppress parasitic ones?
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 5/16
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 12/1
Plots
R(0)/η (dB)
30
10 log10 4G0 /(1–G0 )2
Ilchenko et al. (JPL), “Whispering-gallery-mode electrooptic modulator and photonic microwave receiver,” J. Opt. Soc. Am. B 20, 333 (2003), r = 2.4 mm, d = 150 µm, half-wave 9 GHz resonator
“ ” p † † HI ≈ g Npump a b + ab ,
g 2 Npump G≡ Γa Γb
(14) (15) (16)
Oscillation : G ≥ 1, Spontaneous Down Conversion/Entangled Photons : G ≪ 1
Double-sideband pumping: backaction-evading microwave quadrature measurement χ(3) (Kerr): φ(V ) ∝ V 2 , backaction-evading microwave energy measurement
Vahala, 1172
Sci(2008)
Tsang, Phys. Rev. A 81, 063837 (2010); e-print arXiv:1108.1829 (2011) Eichenfield et al., Nature 462, 78 (2009) Teufel et al., Nature 464, 697 (2010)
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 7/16
Laser Cooling and Noiseless Frequency Conversion
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 6/16
Analogy with Cavity Optomechanics
Hybrid Quantum Systems
Quantum Microwave Photonics:
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 2/16
“ ” p † † HI ≈ g Npump a b + ab r 3 ωb ωa n r , g=η 2d 2C g 2 Npump G≡ Γa Γb Cooling : G ≫ 1 Conversion : G = 1
Quantum Microwave Photonics:
(5)
(6)
(7) (8) (9)
Quantum Microwave Photonics:
(1)
(2) (3) பைடு நூலகம்4)
Coupling quantum microwave circuits to quantum optics via cavity electro-optic modulators – p. 8/16
Laser Cooling and Noiseless Frequency Conversion