radiation-matter interaction · 2019-08-13 · radiation-matter interaction spontaneous emission...
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Radiation-matter interaction
Spontaneous emission control
• Drexhage’s experiment
• The Purcell effect
Optical antennas
• Radiation reaction in dipolar scatterers
• Decay-rate engineering with optical antennas
• Directionality control with optical antennas
• Overview: sub-wavelength vs. super-wavelength “antennas”
• Overview: optical antennas vs. RF antennas
The limits of our classical theory – from weak to strong coupling
The limits of our classical theory – single photon emission
www.photonics.ethz.ch 1
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EmitterTransition dipole moment:Wave function engineering by synthesizing molecules, and quantum dots
Chemistry, material science
EnvironmentLDOS: Electromagnetic mode engineering by shaping boundary conditions for Maxwell’s equations
Physics, electrical engineering
www.photonics.ethz.chantennaking.com, Wikimedia, emory.edu
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Decay-rate engineering
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Clean-up: LDOS and absorption
• The LDOS offers a handle to control spontaneous emission rate
• Does it offer a handle to control light absorption?
• Well, maybe under very special circumstance but in general:Don’t use LDOS when arguing about absorption.
• Get absorption rate via absorption cross section and intensity at absorber
www.photonics.ethz.ch 3
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Yagi-Uda antenna (1926)
• Single active element
• Field of active element polarizes passive elements
• Passive elements generate fields and polarize each other (self-consistent solution)
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Feed element
Passive directors
Passive reflectors
p=aE
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Yagi-Uda antenna
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Taminiau et al., 2008
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Optical antennas for directional photon emission
• Optical antennas allow control of directionality of light emission for quantum emitters
• Antenna is photonic environment that offers a large density of states with specific k-vector
www.photonics.ethz.ch 6
Driven elementPassive scatterers
emission
Scale down size, scale up frequency
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Yagi and Uda (1920s) Curto et al., Science 329, 930 (2010)
emission
Quantum emitter
Metal nanoparticles
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Antennas – resonators with engineered radiation loss
www.photonics.ethz.ch 7
In the µwave-regime:
Total internal reflection Metallic reflection
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From resonators to antennas
www.photonics.ethz.ch 8
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Near-field antennas• Sub-l-sized resonators• Naturally high radiation loss
Cavity-based antennas:• l-sized resonators• Deliberately introduced
radiation loss
Is this an antenna?
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From resonators to antennas
www.photonics.ethz.ch 9
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Is this an antenna?
Antennas are devices which mediate between far-field (=propagating) radiation and localized fields.Antennas boost light-matter interaction.Discuss antennas using LDOS.Do not discuss antennas in terms of Purcell factors (mode volume V not well defined).
Near-field antennas• Sub-l-sized resonators• Naturally high radiation loss
Cavity-based antennas:• l-sized resonators• Deliberately introduced
radiation loss
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Antennas – radio vs. optical
www.photonics.ethz.ch 10
Curto et al., Science 329, 930 (2010)
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Radio-antennas Optical antennas
Antenna theory: Maxwell Maxwell
Resonance mechanisms: Geometric resonances Geometric resonancesMaterial resonances
Sources: Classical current source Quantum emitter
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Antennas – radio vs. optical
www.photonics.ethz.ch 11
Curto et al., Science 329, 930 (2010)
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Radio-antennas Optical antennas
Antenna theory: Maxwell Maxwell
Resonance mechanisms: Geometric resonances Geometric resonancesMaterial resonances
Sources: Classical current source Quantum emitter
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Antennas – radio vs. optical
www.photonics.ethz.ch 12
Curto et al., Science 329, 930 (2010)
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• Nano-optics with optical antennas relies on classical antenna theory due to the scale invariance of Maxwell’s equations.
• Difference 1: Frequency dependence of the material constants.At radio frequencies we have practically perfect metals.At optical frequencies metals are imperfect and show material resonances.
• Difference 2: Emitters in the optical regime show quantum behavior.
Radio-antennas Optical antennas
Antenna theory: Maxwell Maxwell
Resonance mechanisms: Geometric resonances Geometric resonancesMaterial resonances
Sources: Classical current source Quantum emitter
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EmitterTransition dipole moment:Wave function engineering by synthesizing molecules, and quantum dots
Chemistry, material science
EnvironmentLDOS: Electromagnetic mode engineering by shaping boundary conditions for Maxwell’s equations
Physics, electrical engineering
www.photonics.ethz.chantennaking.com, Wikimedia, emory.edu
13
Decay-rate engineering
Where is the limit to this theory?
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Where is the limit of our formalism?
• Emitter decay rate
• Cavity decay rate
• Emitter-cavity coupling rate:
www.photonics.ethz.ch 14
holds in the limit:
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The weak-coupling limit
www.photonics.ethz.ch 15
holds in the limit:
• This limit is called “weak-coupling regime”
• Classical model assumes monochromatic source
• Fermi’s Golden Rule assumes weak coupling (perturbation theory)
• Strong-coupling regime: deviation from exponential decay, cyclic energy exchange between emitter and cavity (Rabi oscillations)
See lecture on Quantum Optics
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The second-order correlation function
• Beam of light impinging on a 50/50 beamsplitter (BS)
• Record intensity I(t) in each arm after BS
• Calculate normalized cross correlation between signals I1 and I2
www.photonics.ethz.ch 16
50/50 beamsplitterI1(t)
I2(t)
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The classical case
• Beam of light impinging on a 50/50 beamsplitter (BS)
• Record intensity I(t) in each arm after BS
• For a classical field I1(t) = I2(t), so g(2) is intensity autocorrelation
www.photonics.ethz.ch 17
50/50 beamsplitterI1(t)
I2(t)
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Intensity autocorrelation - the classical case
• Beam of light impinging on a 50/50 beamsplitter (BS)
• Record intensity I(t) in each arm after BS
• For a classical field I1(t) = I2(t), so g(2) is intensity autocorrelation
• For long delay times
• correlation at zero delay
• global maximum at zero delay
www.photonics.ethz.ch 18
50/50 beamsplitterI1(t)
I2(t)1
t
HW2
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Intensity autocorrelation - the coherent case
• Perfectly monochromatic field
• Intensity is therefore
www.photonics.ethz.ch 19
50/50 beamsplitterI1(t)
I2(t)1
t
laser
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Intensity autocorrelation - the chaotic case
• Collection of sources
• Random phase
• Gaussian distribution of emission frequencies
www.photonics.ethz.ch 20
50/50 beamsplitterI1(t)
I2(t)1
t
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Intensity autocorrelation – counting photons
• ni(t) is the number of photons on detector i at time t
• Interpret g(2)(t) as the probability of detecting a photon on detector 2 at t= t given that a photon was detected on detector 1 at t=0.
www.photonics.ethz.ch 21
50/50 beamsplitterI1(t)
I2(t)
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Counting photons – coherent case
• ni(t) is the number of photons on detector i at time t
• Interpret g(2)(t) as the probability of detecting a photon on detector 2 at t= t given that a photon was detected on detector 1 at t=0
• g(2)(t) = 1 means that photons arrive with Poissonian distribution
www.photonics.ethz.ch 22
50/50 beamsplitterI1(t)
I2(t)1
t
laser
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Counting photons – chaotic case
• ni(t) is the number of photons on detector i at time t
• Interpret g(2)(t) as the probability of detecting a photon on detector 2 at t= t given that a photon was detected on detector 1 at t=0
• g(2)(t=0) > 0 means that photons tend to arrive in bunches
www.photonics.ethz.ch 23
50/50 beamsplitterI1(t)
I2(t)1
t
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Counting photons – a single quantum emitter
• Assume source is a single emitter
• Single emitter can only emit one photon at a time
• If there is a photon on D1 there cannot be a photon on D2 antibunching
• Photon antibunching is at odds with classical electromagnetism
• g(2)(t=0) = 0 is the signature of a single photon source
• What determines the rise time of g(2)(t)?
www.photonics.ethz.ch 24
50/50 beamsplitter
1
I1(t)
I2(t)
t
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Intensity correlation – counting single photons
• How do you know your emitter is a single photon source? For n emitters:
• How does the lifetime show up in the correlation function?Rise time is lifetime in the case of weak pumping.
www.photonics.ethz.ch 25
50/50 beamsplitterI1(t)
I2(t)
Beveratos, PhD thesis, Univ. Paris Sud (2002)
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Intensity correlation – summary
• Second-order correlation function measures temporal intensity correlation
• Bunching: photons tend to “arrive together”, classically allowed/expected
• Antibunching: photons tend to “arrive alone”, classically forbidden
www.photonics.ethz.ch 26
50/50 beamsplitterI1(t)
I2(t)
t
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Summary – light matter interaction
Quantum emitters are probes for their electromagnetic environment.
www.photonics.ethz.ch 27
Curto et al., Science 329, 930 (2010)
Kühn et al., PRL 97, 017402 (2006)
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Quantum emission can be tailored via the emitter’s electromagnetic environment.
Radiation carries information about• The emitter• The emitter’s environment• The emitter-environment interaction
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Summary – light matter interaction
Quantum emitters are probes for their electromagnetic environment.
www.photonics.ethz.ch 28
Curto et al., Science 329, 930 (2010)
Kühn et al., PRL 97, 017402 (2006)
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Quantum emission can be tailored via the emitter’s electromagnetic environment.
10 eV1 eV100 meV
kT Ry
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