Interfacing single photons and condensed-matter systems
Interfacing single photons and condensed-matter systems A. Imamoglu Quantum Photonics Group, Department of Physics ETH‐Zürich
Outline • A two dimensional electron gas embedded in a microcavity at B=0: Fermi-edge polaritons? • Strong coupling of optical excitations out of quantum Hall ground states to a microcavity.
Outline • A two dimensional electron gas embedded in a microcavity at B=0: Fermi-edge polaritons? • Strong coupling of optical excitations out of quantum Hall ground states to a microcavity.
Motivation
• A new spectroscopic tool for studying condensed-matter; bulk properties, quantum quenches, etc. • A new paradigm for quantum optics with nonlinearities arising from correlations.
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
A bound electron‐hole pair free to move in 2D
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
A bound electron‐hole pair free to move in 2D
Undoped QW in a cavity: polaritons Strong‐coupling regime: two split harmonic oscillator modes for each in‐plane k (Bloch)
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
Undoped QW in a cavity: polaritons
2D electron gas
Fermi edge Singularity (FES)
Electrons at the Fermi‐ surface of the 2DEG screen out the (heavy) hole/impurity potential and in the process render the final state Fermi sea wave‐funtion orthogonal to the initial one: Power‐law tails
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
Undoped QW in a cavity: polaritons
2DEG
Fermi edge Singularity (FES)
Electrons at the Fermi‐ surface of the 2DEG screen out the (heavy) hole/impurity potential and in the process render the final state Fermi sea wave‐funtion orthogonal to the initial one: Power‐law tails
2DEG in a cavity: Fermi‐edge polaritons Theoretical prediction by Averkiev & Glazov (2007): ignores finite hole mass and assumes power law is not altered by the strong cavity coupling
Experiment: a gate-tunable 2DEG embedded in a DBR microcavity • The experiments are carried out in a fiber-coupled dil fridge at an electron temperature of T~200 mK Electron density is varied from 3x1010 to about 3x1011 covering the ranges kFaB < 1 & kFaB > 1
Density dependent optical spectrum • Low electron density: trions and excitons are simultaneously visible; PL from trion – the lowest energy excitation • Medium density: exciton disappeares. Trion aquires an asymmetric lineshape (FES). • High density; PL from the whole Fermi sea is visible. Asymmetric reflection/ absorption at the Fermi level
Low density limit: tuning the cavity through the QW resonances
High density limit: tuning the cavity through the Fermi edge The excess broadening of the cavity‐mode for Ecav > EF is consistent with per pass absorption of %
High electron density regime: cavity on resonance with the Fermi edge • As the temperature is lowered below 4K, a split resonance with large asymmetry and a sharp lower peak appears • The lower energy peak is ~lorentzian and is narrower than the cavity-mode. T = 4K
T = 0.2K
High electron density regime: cavity on resonance with the Fermi edge • As the temperature is lowered below 4K, a split resonance with large asymmetry and a sharp lower peak appears • The lower energy peak is ~lorentzian and is narrower than the cavity-mode. • «Best fit» with Glazov model yields an exponent of -0.7!
T = 0.2K
Fermi-edge polaritons • Dispersion relation could be measured using white-light reflection at a finite angle • The splitting g > κcav/2 – strong coupling!
Fermi‐edge polaritons as the denisty is increased above kFaB > 1
ne increased from 1x1011 (black) to 3x1011 (red)
Features and open questions • The role of hole-recoil: the disappearance of normal mode splitting with increasing electron density (kF)? • We expect recoil to change the low energy physics and to remove the enhancement of the optical coupling at the Fermi edge – why does the narrow lower-polariton peak survive? • Note: interesting physics takes place in the final state of the optical transition
Two-dimensional electron-gas (2DEG) in a perpendicular magnetic field • A Hall bar of size 1 mm and an optical excitation spot of 2 μm diameter, probing the bulk locally. Transport measurements
Landau levels in off‐resonant cavity reflection ν1 ν=1
Cavity
• Landau fan of singlet trion lines • Spin polarization at n=1 is visible • For B > 4 T, exciton line also appears
ν=1
Polariton modes for 2 > ν > 1 at B= 3T ν = 1
ν = 2
ν = 2
• • •
For ν > 2, we observe the uncoupled cavity reflection since all electronic transitions are Pauli‐blocked At ν = 2, a normal mode splitting appears At ν = 1, ‐ splitting is minimal whereas + splitting is maximal.
Polariton modes at ν = 1 (B=3T)
Spin polarization at ν=1 is not perfect: high temperature or heavy‐ light‐hole mixing?
Polariton modes at B=6T • ν = 1 spin polarization occurs over a very narrow gate voltage range • No feature at ν = 2/3 (spin polarization or depolarization) • A small feature at ν = ½ • The cavity is red‐detuned – hence the asymmetry of the polariton peak strengths.
Few-photon dependent reversible polariton splitting
Line cut at 4T without (red) and with (blue) a resonant laser.
Time‐resolved measurents: laser power on sample 60pW
• Controlling polariton splitting with single photons: strong photon‐photon interactions?
Features and open questions • Cavity-QED is a powerful spectroscopic tool for studying the bulk properties of both IQHE and FQHE states: -
-
The optically generated hole is delocalized over the entire excitation region. Spectroscopy using one photon at a time – photon absorption induced local heating can be minimized (signal = transmission/reflection of incident photons). Sensitivity of the polariton splitting to incompressibility of the ground-state?
• Novel platform for photon-photon interactions • Photon absorption induced quantum quench into or out of a state with topological order?
Versatile structure for cavity-QED (Reichel)
• Allows for coupling a wide range of emitters to a cavity with m size beam radius: - 2DEG, Graphene-like WSe2 (Kis group) • Tunable vacuum field strength and cavity lifetime
Transition metal dichalcogenides (TMDC) WSe2
m=+3/2 m=+1/2
m=‐3/2 m=‐1/2
m=+1/2 m=‐1/2
m=‐1/2 m=+1/2
Photoluminescence from a monolayer of WSe2 Degree of circular dichroism: ~ 50 – 60 %
quantum dot?
Measurement of the exciton magnetic moment: Faraday geometry ~ 2.5meV@ 8T g‐factor ~5 ‐linearly polarized excitation ‐detection in circular basis
Measurement of the exciton magnetic moment: Faraday geometry ~ 2.5meV@ 8T g‐factor ~5 ‐linearly polarized excitation ‐detection in circular basis
Voigt geometry Strongly anisotropic magnetic field response – consistent with the orbital contribution.
Thanks to • Stephan Smolka, Wolf Wuester, Werner Wegscheider • Ajit Srivastava, Meinrad Sidler, Andras Kis
Outline • A two dimensional electron gas embedded in a microcavity at B=0: Fermi-edge polaritons? • Strong coupling of optical excitations out of quantum Hall ground states to a microcavity.
Outline • A two dimensional electron gas embedded in a microcavity at B=0: Fermi-edge polaritons? • Strong coupling of optical excitations out of quantum Hall ground states to a microcavity.
Motivation
• A new spectroscopic tool for studying condensed-matter; bulk properties, quantum quenches, etc. • A new paradigm for quantum optics with nonlinearities arising from correlations.
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
A bound electron‐hole pair free to move in 2D
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
A bound electron‐hole pair free to move in 2D
Undoped QW in a cavity: polaritons Strong‐coupling regime: two split harmonic oscillator modes for each in‐plane k (Bloch)
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
Undoped QW in a cavity: polaritons
2D electron gas
Fermi edge Singularity (FES)
Electrons at the Fermi‐ surface of the 2DEG screen out the (heavy) hole/impurity potential and in the process render the final state Fermi sea wave‐funtion orthogonal to the initial one: Power‐law tails
Coupling optical excitations of 2D semiconductors to cavities Undoped QW
Exciton resonance
Undoped QW in a cavity: polaritons
2DEG
Fermi edge Singularity (FES)
Electrons at the Fermi‐ surface of the 2DEG screen out the (heavy) hole/impurity potential and in the process render the final state Fermi sea wave‐funtion orthogonal to the initial one: Power‐law tails
2DEG in a cavity: Fermi‐edge polaritons Theoretical prediction by Averkiev & Glazov (2007): ignores finite hole mass and assumes power law is not altered by the strong cavity coupling
Experiment: a gate-tunable 2DEG embedded in a DBR microcavity • The experiments are carried out in a fiber-coupled dil fridge at an electron temperature of T~200 mK Electron density is varied from 3x1010 to about 3x1011 covering the ranges kFaB < 1 & kFaB > 1
Density dependent optical spectrum • Low electron density: trions and excitons are simultaneously visible; PL from trion – the lowest energy excitation • Medium density: exciton disappeares. Trion aquires an asymmetric lineshape (FES). • High density; PL from the whole Fermi sea is visible. Asymmetric reflection/ absorption at the Fermi level
Low density limit: tuning the cavity through the QW resonances
High density limit: tuning the cavity through the Fermi edge The excess broadening of the cavity‐mode for Ecav > EF is consistent with per pass absorption of %
High electron density regime: cavity on resonance with the Fermi edge • As the temperature is lowered below 4K, a split resonance with large asymmetry and a sharp lower peak appears • The lower energy peak is ~lorentzian and is narrower than the cavity-mode. T = 4K
T = 0.2K
High electron density regime: cavity on resonance with the Fermi edge • As the temperature is lowered below 4K, a split resonance with large asymmetry and a sharp lower peak appears • The lower energy peak is ~lorentzian and is narrower than the cavity-mode. • «Best fit» with Glazov model yields an exponent of -0.7!
T = 0.2K
Fermi-edge polaritons • Dispersion relation could be measured using white-light reflection at a finite angle • The splitting g > κcav/2 – strong coupling!
Fermi‐edge polaritons as the denisty is increased above kFaB > 1
ne increased from 1x1011 (black) to 3x1011 (red)
Features and open questions • The role of hole-recoil: the disappearance of normal mode splitting with increasing electron density (kF)? • We expect recoil to change the low energy physics and to remove the enhancement of the optical coupling at the Fermi edge – why does the narrow lower-polariton peak survive? • Note: interesting physics takes place in the final state of the optical transition
Two-dimensional electron-gas (2DEG) in a perpendicular magnetic field • A Hall bar of size 1 mm and an optical excitation spot of 2 μm diameter, probing the bulk locally. Transport measurements
Landau levels in off‐resonant cavity reflection ν1 ν=1
Cavity
• Landau fan of singlet trion lines • Spin polarization at n=1 is visible • For B > 4 T, exciton line also appears
ν=1
Polariton modes for 2 > ν > 1 at B= 3T ν = 1
ν = 2
ν = 2
• • •
For ν > 2, we observe the uncoupled cavity reflection since all electronic transitions are Pauli‐blocked At ν = 2, a normal mode splitting appears At ν = 1, ‐ splitting is minimal whereas + splitting is maximal.
Polariton modes at ν = 1 (B=3T)
Spin polarization at ν=1 is not perfect: high temperature or heavy‐ light‐hole mixing?
Polariton modes at B=6T • ν = 1 spin polarization occurs over a very narrow gate voltage range • No feature at ν = 2/3 (spin polarization or depolarization) • A small feature at ν = ½ • The cavity is red‐detuned – hence the asymmetry of the polariton peak strengths.
Few-photon dependent reversible polariton splitting
Line cut at 4T without (red) and with (blue) a resonant laser.
Time‐resolved measurents: laser power on sample 60pW
• Controlling polariton splitting with single photons: strong photon‐photon interactions?
Features and open questions • Cavity-QED is a powerful spectroscopic tool for studying the bulk properties of both IQHE and FQHE states: -
-
The optically generated hole is delocalized over the entire excitation region. Spectroscopy using one photon at a time – photon absorption induced local heating can be minimized (signal = transmission/reflection of incident photons). Sensitivity of the polariton splitting to incompressibility of the ground-state?
• Novel platform for photon-photon interactions • Photon absorption induced quantum quench into or out of a state with topological order?
Versatile structure for cavity-QED (Reichel)
• Allows for coupling a wide range of emitters to a cavity with m size beam radius: - 2DEG, Graphene-like WSe2 (Kis group) • Tunable vacuum field strength and cavity lifetime
Transition metal dichalcogenides (TMDC) WSe2
m=+3/2 m=+1/2
m=‐3/2 m=‐1/2
m=+1/2 m=‐1/2
m=‐1/2 m=+1/2
Photoluminescence from a monolayer of WSe2 Degree of circular dichroism: ~ 50 – 60 %
quantum dot?
Measurement of the exciton magnetic moment: Faraday geometry ~ 2.5meV@ 8T g‐factor ~5 ‐linearly polarized excitation ‐detection in circular basis
Measurement of the exciton magnetic moment: Faraday geometry ~ 2.5meV@ 8T g‐factor ~5 ‐linearly polarized excitation ‐detection in circular basis
Voigt geometry Strongly anisotropic magnetic field response – consistent with the orbital contribution.
Thanks to • Stephan Smolka, Wolf Wuester, Werner Wegscheider • Ajit Srivastava, Meinrad Sidler, Andras Kis
