Coherent nonlinear optical spectroscopy of quantum dots Cameron Nelson Steel Group This work is funded by NSF-CPHOM

Old school atomic spectroscopy Figure from Annalen der Physik und der Chemie (Poggendorff), Vol. 110 (1860), pp (dated Heidelberg, 1860) Solar Spectrum

Semiconductor quantum dots: artificial atoms Hydrogen atom: Characteristic length is given by Bohr radius Dipole moment is big: strong coupling to light! Quantum Dot: Characteristic length is given by exciton Bohr radius: typically much larger than atomic Bohr radius. CB VB Quantized Energy Levels h e Exciton: Coulomb-bound electron-hole pair (quasiparticle) Can be grown epitaxially within a layer of semiconductor MBE

Nonlinear optical spectroscopy is necessary for a complete understanding of the resonant interaction of a laser field and quantum dot. The interaction between a laser field and a two-level system is extremely nonlinear. ON OFF Quantum Dot Exciton Quantum Harmonic Oscillator Compare to a harmonic oscillator, a linear system. Resonant excitation of a linear harmonic oscillator moves it to a higher energy state. This continues indefinitely. In a two-level system, you can only excite the system once. If you try to excite it again, you will drive it back down to the ground state (Rabi oscillations).

Applications of optically controlled quantum dots The laser field can be used to coherently control the quantum state of the quantum dot, resulting in a controllable qubit (on-off switch). Quantum Information Science JQI Website Quantum optics in solid state X. Xu, et al. Science 317, (2007). Quantum information processing X. Li, et al. Science 301, (2002). Coherent control of the quantum state N. H. Bonadeo, et al. Science 282, 5393 (1998). All-optical switching D.A.B. Miller Nat. Photonics. 4, 3 (2010).

The world is demanding more bandwidth, so data distributors will become more reliant on all-optical switching Worldwide data usage is increasing every year Image from Cisco Currently, most routing of information requires optical to electronic conversion to route signals. This is slow, and wasteful (electronics generate a lot of heat).

Quantum dot-based technology shows some promise for all-optical switching A small pulse of light can be used to switch the quantum state of a quantum dot, thereby allowing another light pulse to either pass or reflect. Image from NTT photonics This offers an extremely low power switch for controlling an information signal. (switching power ~attojoules) D.A.B. Miller Nat. Photonics. 4, 3 (2010). Chip-level interconnects also suffer from heat-related issues. All-optical switches may be a good future solution for replacing CMOS transistors.

Many quantum applications requiring multiple qubits will only be realized very far in the future. 1 qubit Even coupling together two quantum dot qubits for applications such as quantum computing is extremely complicated or requires very long integration times for experimental verification. Most importantly, the most well-studied materal for this application, InAs, requires cooling down to 4K to work properly!. The search is still on for new computer hardware…

Photoluminescence: useful for characterization of energy level structure of quantum dots Photoluminescence: Excite high energy charge carriers that decay nonradiatively to the lowest energy emitting state. The resulting spectrum is usually similar to the linear absorption spectrum of the lowest energy states in the system Photons Pump laser (PL) CB VB Emission Spectrometer D Camera Quantum Dot:

What I study: InGaN/GaN quantum dots for room temperature applications The main advantage of InGaN/GaN systems is a large exciton binding energy compared to other III-V material. This has allowed for quantum dot operation up to room temperature. The InGaN quantum dot is one of the only stable solid state systems that gives single photon emission behavior up to room temperature. This has immediate applications in quantum cryptography, for example. 50:50 beamsplitterExcitation Pulse Quantum Dot Luminescence D D Time-correlation Electronics Hanbury Brown-Twiss Experiment APD

What do you get from nonlinear absorption that you can’t from linear absorption? You can measure (among other things):  Dephasing and population decay rates of exciton  Inhomogeneous broadening in the system  Coupling between excited states CB VB Quantum Dot: Energy ω0ω0 ωLωL Gaussian Laser Absorption ω L – ω 0 Lorentzian (Homogeneously Broadened) γ is the dipole dephasing rate Laser Absorption ω L – ω 0 2γ2γ 1.67σ W

Theoretical description of measurements We utilize the density matrix equations of motion for a two-level system to describe the optical response of a quantum dot exciton. This theory is extremely well developed and has been used to successfully describe the nonlinear optical response of GaAs/InAs quantum dots. Most of the following can be found in standard textbooks:

Optical Bloch equations for a homogeneously broadened two-level system (Lorentzian absorption) |1> = |0> |2> = |X> δ ELEL E0E0 Maxwell-Bloch equation: relation between absorption and off-diagonal density matrix: Pure dephasing rate Density matrix equations of motion: Density matrix: ρ = |ψ><ψ|

From S. Rand, Lectures on Light The exciton transition energy often undergoes time-dependent fluctuations due to the solid state background (i.e. Stark shifts from surrounding charges). Image by S. Kelly, JQI Univ. of Maryland Quantum dot systems gain pure dephasing from environmental fluctuations. Fluctuation-dissipation theorem

For simplicity, we use two fields, E pump = E 1 and E probe = E 2. This gives a total of 8 terms. Optical Bloch equations for a two-level system with multiple laser fields There is no analytical steady-state solution for this problem. To understand it, perturbation theory has to be used. We are particularly interested in third order terms. k s = k µ - k ν + k σ δ s = δ µ - δ ν + δ σ

Isolating two nonlinear terms along the probe beam direction Sample C.W. Pump (ω 1 ) C.W. Probe (ω 2 ) Pump and probe are crossed at the center of the sample A detector can be aimed along the probe beam propagation direction. In this way, we can isolate the detection to nonlinear terms that propagate along the probe beam direction. Recall that the third order nonlinear density matrix element goes like: We therefore select k s = k µ - k ν + k σ = k 2 δ s = δ µ - δ ν + δ σ = δ 2 This requires μ = ν = 1, σ = 2 and μ = 1, ν = 2, σ = 1.

1. Population pulsation term: follows the probe frequency and has a FWHM ~γ 2 No pure dephasingSome dephasing 2. Saturation term: does not follow the probe term. Has a FWHM ~γ The nonlinear optical spectrum reveals both the pure dephasing rate and the exciton decay rate. This cannot be easily obtained using linear techniques. Γ deph = 0 Γ deph = 10 γ 2 Imaginary component of total nonlinear response Im(ρ 21 (3) ) δ2δ2 δ2δ2 1 2 γ2γ2

Note: the previous slides only applied to the case of homogeneous broadening. In general, the Bloch equations have to be modified to account for inhomogeneous broadening (Gaussian lines) properly. The final results are a lot more complicated, usually. Inhomogeneously broadened response Homogeneously broadened response

Nonlinear response of inhomogeneously broadened transitions: spectral hole burning The third order spectra look similar to the homogeneously broadened case, except the saturation term tracks with the pump laser. The nonlinear spectrum can be used to distinguish inhomogeneous and homogeneous broadening. Linear Absorption, Inhomogeneously Broadened Transition Nonlinear Absorption Pump Wavelength σ W = 20 γ 2 γ2γ2 γ2γ2 Γ= 0 γ 2 Γ= 3γ 2

Measuring nonlinear signals with differential transmission Sample C.W. Pump (ω 1 ) C.W. Probe (ω 2 ) Lock-in Amplifier Function Gen Optical Chopper Positive dT/T: Pump beam modifies sample absorption so that the probe beam absorbs less → saturation Negative dT/T: Pump beam modifies samples absorption so that the probe beam absorbs more The lowest order contribution comes from the third order nonlinear signal ~χ (3) |E pu | 2 |E pr | 2

Sample grown by Zetian Mi’s group at McGill University Our study: Coherent nonlinear optical spectrum of InGaN disks in GaN nanowires Current studies show evidence of a compact quantum dot in the center of the disk.

Disk-in-nanowires show single photon emission behavior, which allows for unique quantum applications. Quantum cryptography requires quantum key generation. For this, can use polarization of photons from a single quantum dot, for example. 1 μm single quantum dot A novel quantum key distributor can be made using a single electrically injected quantum disk LED Polarized Emission

Background states can cause a significant spectral diffusion (dephasing) for the InGaN exciton M. Holmes et al. Phys Rev. B (2015) Charges captured by traps may cause a Stark shift of the exciton resonance J.H. Rice et al. Appl. Phys. Lett. 84, 4110 (2004). The photoluminescence spectrum of a single InGaN quantum dot shows fluctuations in the transition energy over time. Stark Shifts from background states in InGaN dots-in-nanowires can cause extremely large optical linewidths. -Very small nonlinear signal InGaN materials are known to be very messy (lots of background disorder states)

Optical Setup

Preliminary sample data: bright PL from quantum confined excitons The PL data shows evidence for radiative recombination from quantum confined exciton states: there is no continuous blue shift as a function of excitation intensity, a signature of quantum confinement. Photoluminescence The PL originates from disks- in-nanowires with different diameters, and therefore different emission wavelengths. The broad emission comes from inhomogeneous broadening.

Nondegenerate nonlinear optical spectrum reveals evidence of saturation resonances with ~100 fs dephasing rates, this is at least 10,000x faster dephasing than similar QD systems. Ongoing work: Analyzing the full coherent nonlinear spectrum 10 K Exciton excited statesEmissive Exciton States

Coherent population pulsations of excitons reveal that excitons are stable up to room temperature Δ pu,pr (γ 2 units) Total nonlinear spectrum Pump-probe detuning (GHz) We observe strong coherent population pulsation resonances in the sample that reveal the population decay time (T 1 ) of the exciton states all the way up to room temperature. We find that the nonlinear signal is relatively robust against temperature, but fast dephasing is still present, likely due to very fast Stark shifting from background states.

Conclusions We observe coherent population pulsation resonances that allow us to extract fundamental decay parameters of the exciton states and to verify a low density of metastable trap states. For the first time, we show that the quantum dot exciton is likely homogeneously broadened, and the dipole dephasing rate is ~100 fs, probably due to background disorder states. Our results show that excitons can be stably excited up to room temperature,

InGaN is typically grown along polar axes, which leads to internal electric fields InGaN has a wurtzite crystal structure The internal electric fields changes the band diagram and pushes the electron and hole apart along the growth direction