On Demand Generation of Single Photons Locked to Rubidium

On Demand Generation of Single Photons Locked to Rubidium

Transitions

ULRIKA WENNBERG

KTH

SKOLAN FÖR TEKNIKVETENSKAP

Abstract

High-quality, single photon sources that can generate photons on-demand at a high repetition rate is one of the important fundamentals for various appli- cations within quantum information, such as fully secure quantum communi- cation. When using quantum communication one can mathematically prove that it is impossible to eavesdrop without destroying the information carrier.

Though, this is also the reason for why it is impossible to amplify the signal.

Hence, if the signal is not repeated, the losses will make it almost impossible to transfer the information over large distances.

One way to generate single photons is to use resonant excitation of a semi- conductor nanostructure, called quantum dot. When resonantly exciting a two-level system, re-excitation can degrade the purity of the single photons.

Therefore, we have performed two-photon resonant excitation of the biexci- tonic state of a gallium arsenide quantum dot. The re-excitation is such sys- tems are strongly suppressed by the cascaded emission scheme. The aim is to characterize semiconductor quantum dots that can generate single photons of high purity on demand ready for storage in a rubidium vapor quantum memory.

The characterization includes acquiring photoluminescence spectra to de- termine that we are exciting resonantly, performing Rabi oscillations to excite the system as efficiently as possible and a Stokes measurement to determine the polarization and linewidth of the components. The linewidth was also measured by utilizing a Fabry Pérot interferometer. The single photon purity was measured using a Hanbury Brown and Twiss-like setup, yielding a su- per high purity with g

⁽²⁾

(0) = (4.51 ± 0.6) · 10

⁻⁴

for the exciton of the first quantum dot. By exciting at different π-pulses, we saw that the purity of the single photons depends on the excitation power. Furthermore, we saw a strong cross correlation between the exciton and the biexciton verifying the cascaded emission scheme.

After the characterizations, we interfaced the single photons with an atomic vapor quantum memory. We were able to read a fraction of the single photons into the memory but were not able to retrieve them, most likely due to too little power of the read-out laser. Hence, the next step is to try storage again, but modifying by using a stronger laser power per pulse and a new rubidium cell.

In conclusion, we have generated and characterized single photons of high

purity generated on demand ready for storage in a rubidium atomic vapor quan-

tum memory. We have seen read-in of the single photons into the optical quan-

tum memory. The next step is to read-out the photons and characterize them

to make sure that the quantum properties are conserved.

Sammanfattning

Högkvalitativa singelfotonkällor som med hög repetitionshastighet kan gene- rera fotoner på begäran är en av de viktigaste byggstenarna inom flera olika tillämpningar inom kvantinformation, bland annat säker kvantkommunikation.

Fördelen med att använda kvantkommunikation istället för klassisk kommu- nikation är att det går att matematiskt bevisa att det är omöjligt att avlyss- na kommunikationen utan att förstöra informationsbärarna kallade kvantbitar eller qubit. Å andra sidan är det samma anledning som gör det omöjligt att förstärka signalen. Således måste signalen istället repetera, för att förebygga att förlusterna gör det nästintill omöjligt att överföra informationen över långa distancer.

Ett sätt att generera singelfotoner är att använda resonant excitation av en halvledarnanostruktur, kallad kvantprick. Eftersom återexitation av ett tvåni- våsystem kan försämra renheten hos de genererade singelfotonerna, använder vi oss i denna avhandling av ett trenivåsystem. Vårt trenivåsystem är en galliu- marsenidkvantprick där biexcitontillståndet exciteras genom tvåfotonresonans.

Återexcitation i systemet hämmas start av dess möjliga energitillstånd. Målet med avhandlingen är att karakterisera en singelfotonkälla som kan generera singelfotoner med hög renhet på begäran redo för lagring i ett kvantminne ba- serat på förångade rubidiumatomer.

Karaktäriseringen inkluderar att ta fotoluminescensspektra för att påvisa att vi använder resonant excitation, utföra Rabi-oscillationer för att excitera systemet så effektivt som möjligt samt en Stokes-mätning för att bestämma polariseringen av komponenterna såväl som deras linjebredder. Linjebredden mättes också med användning av en Fabry Pérot-interferometer. Renheten av singelfotoner mättes med hjälp av en Hanbury Brown och Twiss-liknande upp- ställning, vilket gav en väldigt hög renhet med g

⁽²⁾

(0) = (4.51 ± 0.6) · 10

⁻⁴

för excitonen hos den första kvantpricken. Genom att excitera med olika π- pulser såg vi att renheten hos de enskilda fotonerna beror på excitationseffek- ten. Dessutom såg vi en stark korrelation mellan excitonen och biexcitonen.

Efter karaktäriseringarna försökte vi lagra singelfotonerna i ett kvantminne baserat på förångade rubidium atomer. Vi såg lite av en inläsning men ingen utläsning, troligen på grund av för svag lasereffekt. Följaktligen skulle nästa steg vara ytterligare försök till lagring av singelfotonerna. För att göra detta krävs en laser med starkare lasereffekt per puls och en ny

⁸⁷

Rb-cell.

Sammanfattningsvis har vi i den här avhandlingen lyckats tillhandahålla

och karakterisera singelfotoner av hög renhet som genereras på begäran redo

för lagring i ett optiskt kvantminne baserat på förångade rubidium-atomer.

1 Introduction 1

2 Theoretical Background 3

2.1 Single Photon Emission . . . . 3

2.2 Second Order Intensity Correlation Function . . . . 3

2.2.1 Anti-bunched Light . . . . 5

2.3 Gallium Arsenide . . . . 6

2.4 Quantum Dots . . . . 6

2.5 Confined Electron Hole Pairs . . . . 8

2.5.1 Exciton . . . . 8

2.5.2 Biexciton . . . . 9

2.6 Two-photon Resonant Excitation . . . . 10

2.6.1 Rabi Oscillations . . . . 11

2.7 Polarization of Light . . . . 12

2.7.1 Stokes Measurement . . . . 13

2.7.2 Poincaré Sphere . . . . 14

2.8 Optical Quantum Memories . . . . 15

2.8.1 Importance of Noise Reduction . . . . 16

2.8.2 ORCA Protocol . . . . 16

3 Experimental Methods 18 3.1 PicoEmerald Laser . . . . 18

3.1.1 Slicing Laser beam . . . . 19

3.2 Experimental Setups . . . . 19

3.2.1 Cryogenic Confocal Micro-Photoluminescence Setup . 20 3.2.2 Transmission Spectrometer . . . . 20

3.2.3 Fabry Pérot Interferometer . . . . 22

3.2.4 Stokes Measurement . . . . 22

3.2.5 ORCA Quantum Memory . . . . 24

iii

4 Measurements 26 4.1 Characterization of the Quantum Dots . . . . 26 4.1.1 Photoluminescence Measurements . . . . 27 4.1.2 Rabi Oscillation Measurement . . . . 29 4.1.3 Measuring Linewidth Using Fabry Pérot Interferometer 33 4.1.4 Stokes Measurements to Obtain Polarization . . . . . 37 4.2 Measuring Purity of Single Photons . . . . 42 4.3 Quantum Memory . . . . 50

5 Summary and Outlook 52

Bibliography 55

A Matlab Code used for Analysis 61

A.1 Error analysis . . . . 61

A.2 Calculating Second Order Intensity Correlation Function . . . 62

A.3 Analysis of Stokes Measurement . . . . 69

2.1 Hanbury Brown and Twiss-like setup . . . . 4 2.2 Scheme of the confined energy states in the potential of a quan-

tum dot . . . . 7 2.3 The exciton and biexciton as electronic states . . . . 9 2.4 Cascade scheme of the exciton and biexciton system excited

by two-photon resonant excitation . . . . 10 3.1 The setup used to slice the PicoEmerald laser to the desired

pulse length . . . . 19 3.2 Cryogenic setup including the excitation and detection paths . 21 3.3 Setup of the transmission spectrometer . . . . 21 3.4 Setup for measuring Stokes parameters . . . . 23 3.5 Setup of the optical quantum memory . . . . 25 4.1 Photoluminescence spectra of QD1 detecting through free space

and coupled into an optical fiber exciting at the π-pulse . . . . 27 4.2 Photoluminescence spectra of QD1 exciting at 6 µW . . . . 28 4.3 Photoluminescence spectra of QD1 exciting using a continu-

ous wave laser pulsed by the ModBox with a power of 2 µW . 29 4.4 Photoluminescence spectra of QD2 detecting through free space

and coupled into an optical fiber exciting at the π-pulse . . . . 29 4.5 Rabi osillations of QD1 with an excitation pulse length of 5 ps 30 4.6 Rabi osillations of QD2 with an excitation pulse length of 5 ps 31 4.7 Rabi osillations of QD2 with an excitation pulse length of 30 ps 31 4.8 Rabi osillations of QD2 two-photon resonantly excited by the

DL Pro pulsed by the ModBox . . . . 32 4.9 Measurement giving the relationship between the FSR in tem-

perature and the FSR in frequency . . . . 34 4.10 Measurement giving the relationship between the FSR in re-

sistance and the FSR in frequency . . . . 34

v

4.11 Linewidth of the exciton of QD1 using the Fabry Pérot inter- ferometer . . . . 35 4.12 Linewidth of the biexciton of QD1 using the Fabry Pérot in-

terferometer . . . . 36 4.13 Linewidth of the biexciton of QD2 using the Fabry Pérot in-

terferometer . . . . 36 4.14 Stokes parameters of QD1 presented pixel by pixel . . . . 38 4.15 Stokes parameters of QD2 presented pixel by pixel . . . . 39 4.16 Poincaré sphere showing the polarization of the exciton and

biexciton components of QD2 . . . . 42 4.17 Coincidence measurement of the exciton of QD1 . . . . 44 4.18 Coincidence measurement of the biexciton of QD1 . . . . 44 4.19 Coincidence measurement between the exciton and biexciton

of QD1 . . . . 45 4.20 Coincidence measurement of the biexciton of QD2 . . . . 46 4.21 Coincidence measurement of he biexciton of QD1 exciting

with the continuous wave laser pulsed by the ModBox . . . . . 46 4.22 Correlation measurement of the exciton of QD1 at different

π-pulses . . . 48 4.23 Correlation measurement of the biexciton of QD1 at different

π-pulses . . . 49

4.24 Read-in in quantum memory over 10 cycles . . . . 50

4.25 Read-in in quanutm memory over 30 cycles . . . . 51

4.1 Ratio of the biexciton-exciton emission from the differnet quan- tum dots . . . . 30 4.2 Measured g

⁽²⁾

(0) exciting at different π-pulses . . . 47

vii

87

Rb Rubidium. ii, 2, 17, 24, 25, 50, 51, 53 λ/2 Half Wave Plate. 22

λ/4 Quarter Wave Plate. 22 2D Two dimensional. 3 A Anti-diagonal. 12, 42 bcc Cody centered cubic. 6 BS Beam splitter. 21 CL Cylindrical lens. 19 D Diagonal. 12, 42

EIT Electromagnetically induced transparency. 15 EP1 Excitation path 1. 27, 28, 30, 52

EP2 Excitation path 2. 28–31, 50, 52 fcc Face centered cubic. 6

FLAME Fast ladder memory. 16 FSR Free spectral range. v, 33 FSR Free spectral range. 26, 34

FSS Fine structure splitting. 35, 37, 40, 41, 53

viii

FWHM Full width at half maximum. 12, 35, 36, 53 GaAs Galium Arsenide. 2–4, 6, 7, 11, 34, 37, 52 H Horizontal. 12, 34, 35, 40–42

L Left. 12, 40

LP Long pass filter. 25 M Mirror. 21

MM Magnetic mirror. 21

ModBox ModBox-PG-795nm-30ps. v, vi, 24, 27–29, 31, 32, 45, 50, 52 N Notch Filter. 21

ORCA Off-resonant cascade absorption. 2, 16, 17 PBS Polarizing beam splitter. 21

PIC Photonic intergrated circuits. 7 PL Photoluminescence. 40

PS Periscope. 24, 25 QD Quantum dot. 25

QD1 Quantum dot 1. v, vi, 26–30, 32, 33, 35–38, 41, 43–46, 48, 49, 52, 53 QD2 Quantum dot 2. v, vi, 26, 28–31, 35–38, 41, 42, 44, 46, 52, 53

qubit Quantum bit. 15 R Right. 12, 40

S1 Polarimeter position 1. 23 S2 Polarimeter position 2. 23 SM Spectrometer. 21

SNSPDs Superconducting nanowire single photon detectors. 20, 24, 33, 42

V Vertical. 12, 23, 34, 35, 40–42

Introduction

In 1984, Bennett and Brassard published a paper on how to create a fully se- cure communication channel based on quantum mechanical principles, which today is called the BB84 protocol [1]. It is based on quantum key distribu- tion and was the first quantum cryptography protocol. Bennett and Brassard explored the possibility to send information using photons as qubits in a quan- tum network, where the polarization of the photon is the information carrying part, and argue that it is impossible to be certain that the measured polariza- tion of the photon is the initial polarisation without knowing which basis to measure it in. Another important property in order to prohibit eavesdropping is the no-cloning theorem, which makes it impossible to measure the state of the qubit, reproduce it and then resend it in such a way that the interception is unnoticed [2]. Based on these two principles, the idea of secure quantum communication was born.

The problem with quantum networks using single photons as information carriers over a large spatial range is that the losses in optical fibers reduces the bandwidth significantly for secure communication. The total losses, from e.g.

absorption and depolarization, exhibit an exponential growth with the distance l between the sender and the receiver. Amplification in the same manner as used in classical optical communication is not possible, also in accordance with the no-cloning theorem. A possible solution is to introduce quantum re- peaters, creating several nodes between the sender and the receiver and then transmit the information using quantum entanglement [3, 4, 5, 6]. The idea of quantum repeaters is to divide the length l into N segments and use entangle- ment swapping to pass on the information. In each node, an entangled photon pair is created. The photons are sent to both adjacent nodes for all nodes inside the network, though the sender and receiver at the ends keeps one each. Each

1

node then receives two photons from both adjacent nodes, and performs a Bell measurement. By purifying at each segment, almost perfect entangled states can be achieved at the first and last nodes [7].

In 2001, Lloyd et al. published a quantum repeater protocol based on quan- tum teleportation between nodes in a network using Bell measurements [8].

The implementation of this protocol is based on a few crucial components.

It is necessary to generate entangled photons on demand and to have a quan- tum memory where the photons can be stored for a sufficient amount of time.

The state of each segment can then be stored until the purification between all nodes is close to perfect. It is essential, since no quantum repeater protocol guarantees that all the entanglement swapping events works out nor even that all photons are transmitted at the same time [7].

There are multiple different sources that can create entangled photons, e.g.

cascade decay in atoms, cascade decay in semiconductor quantum dots (also known as artificial atoms) or parametric down conversion in non-linear crys- tals. In this thesis, we produce and characterize entangled photon pairs from GaAs quantum dots on demand. These photon pairs are entangled via the cas- cade recombination of the biexciton and exciton [9]. This correlation can be deduced from coincidence measurement between the biexciton and exciton.

The emission wavelength of the biexciton is tuned to match the D1 absorption

line in

⁸⁷

Rb. The idea is then to store the single photons in an off-resonant cas-

caded absorption (ORCA) memory. The wavelength can be tuned by applying

voltage to the piezo substrate that the sample with quantum dots are placed on

top of. In conclusion, the aim of this thesis is to generate single photons on

demand ready for storage in a

⁸⁷

Rb quantum memory.

Theoretical Background

2.1 Single Photon Emission

In order to utilize applications within photonic quantum technologies, single photon emission from dedicated sources is a necessity. Single photon emission can be characterized measuring anti-bunching using the second order intensity correlation function, the details of which are found in the next section.

There are many different types of single photon emitters. The first one to be discovered showing single photon emission in an isolated system was an atomic cascade in mercury atoms in 1974 [10] followed by resonance fluores- cence in sodium atoms [11]. Today, single photon emission has been achieved from multiple different sources, e.g. nitrogen vacancies [12, 13], quantum dots [14, 15], two-dimensional (2D) materials [16]. In this thesis, we focus on the gallium arsenide, (GaAs), quantum dot for single photon emission, due to it having previously shown high quality single photons generated on-demand yielding the as of yet highest measured single photon purity [15].

2.2 Second Order Intensity Correlation Func- tion

There are three different types of light sources; thermal light, coherent light and non-classical light. A thermal light source exhibits bunching, meaning that the photons are likely arrive close to other photons in time. For a co- herent light source, such as a laser, the photons are randomly distributed in time. Anti-bunching is a non-classical phenomena, where the photons are more likely to be arriving further apart in time. This means that we are more

3

BS

Correlator D

1

D

₂

Figure 2.1: Hanbury Brown and Twiss-like setup used in order to measure coincidences within a single beam.

likely to have a time delay between the photons, than two photons arriving at the same time [17].

To tell the different light sources apart, the second order intensity correla- tion function can be used. The second order intensity correlation function is defined as in Equation (2.1), where τ is the time delay between the photons and h· · ·i indicates taking the average of multiple photon coincidence events [18].

g

⁽²⁾

(τ ) = hI(t)I(t + τ )i

hI(t)ihI(t + τ )i (2.1)

In order to experimentally measure the correlation of light, a Hanbury Brown and Twiss-like setup may be used, see Figure (2.1). It utilizes a 50:50 beam splitter and two detectors. The beam splitter divides the beam into two equally distributed beams, before the photons hits either detectors. As a photon is hitting the detectors, an electric pulse is sent to a correlator which records the time delay between detection events on the two detectors D

¹

and D

²

[19].

By using the Hanbury Brown and Twiss-like setup, the second order in- tensity correlation function can be written in terms of registrated photons on the detectors as in Equation (2.2), where n

1

is the number of photons registred by the first detector D

¹

and n

²

the number of photons registred by the second detector D

2

[18].

g

⁽²⁾

(τ ) = hn

₁

(t)n

₂

(t + τ )i

hn

₁

(t)ihn

₂

(t + τ )i (2.2)

In this thesis, the focus will be on the anti-bunched light measured from

GaAs quantum dots.

2.2.1 Anti-bunched Light

To derive the second order intensity correlation function for non-classical light we will use the number state operator, which is defined by ˆ n = ˆ a

^†

a where ˆa ˆ

^†

is the creation operator and ˆ a is the annihilation operator. Using these operators and normal ordering we can rewrite Equation (2.2) to Equation (2.3).

g

⁽²⁾

(τ ) = hˆ a

^†₁

(t)ˆ a

^†₂

(t + τ )ˆ a

₂

(t + τ )ˆ a

₁

(t)i

hˆ a

^†₁

(t)ˆ a

₁

(t)ihˆ a

^†₂

(t + τ )ˆ a

₂

(t + τ )i (2.3) At the origin, where the time delay between start and stop is τ = 0, the dif- ference between a quantum, coherent and classical source is apparent. Hence, at zero time delay the expression can be simplified into Equation (2.4).

g

⁽²⁾

(0) = hˆ a

^†₁

a ˆ

^†₂

ˆ a

2

ˆ a

1

i

hˆ a

^†₁

a ˆ

1

ihˆ a

^†₂

ˆ a

2

i (2.4) Using that the probability of the light reaching the two different detectors is equally distributed, we can express the annihilation and creation operators in terms of the incident light field annihilation ˆ a

_I

and creation ˆ a

^†_I

operators using the relation in Equation (2.5).

ˆ

a

₁

= ˆ a

₂

= a ˆ

_I

√ 2 (2.5)

By letting our creation and annihilation operators act on input state ψ

I

before hitting the beam splitter, we obtain Equations (2.6-2.8).

hˆ a

^†₁

ˆ a

₁

i = hψ

I

|ˆ a

^†_I

ˆ a

I

|ψ

I

i

2 = hψ

I

|ˆ n

I

|ψ

I

i

2 (2.6)

hˆ a

^†₂

ˆ a

2

i = hψ

I

|ˆ a

^†_I

ˆ a

I

|ψ

I

i

2 = hψ

I

|ˆ n

I

|ψ

I

i

2 (2.7)

hˆ a

^†₁

a ˆ

^†₂

ˆ a

2

ˆ a

1

i = hψ

_I

|ˆ a

^†_I

ˆ a

^†_I

ˆ a

_I

ˆ a

_I

|ψ

_I

i

4 (2.8)

By evaluating the latter, we obtain Equation (2.9).

ˆ

a

^†_I

ˆ a

^†_I

ˆ a

_I

ˆ a

_I

=ˆ a

^†_I

(ˆ a

_I

a ˆ

^†_I

− 1)ˆ a

_I

=ˆ a

^†_I

ˆ a

_I

a ˆ

^†_I

ˆ a

_I

− ˆ a

^†_I

ˆ a

_I

=ˆ n

_I

n ˆ

_I

− ˆ n

_I

=ˆ n

_I

(ˆ n

_I

− 1)

(2.9)

By plugging in the result from Equations (2.6, 2.7, 2.9) into Equation (2.4), we obtain Equation (2.10).

g

⁽²⁾

(0) = hψ

_I

|ˆ n

_I

(ˆ n

_I

− 1)|ψ

_I

i/4

(hψ

_I

|ˆ n

_I

|ψ

_I

i/2)

²

= hˆ n

_I

(ˆ n

_I

− 1)i

hˆ n

_I

i

²

(2.10) Using the photon number state |ni of the source as the input state, we obtain Equation (2.11) [18]. This means that the expected value for a perfect single photon source at τ = 0 is g

⁽²⁾

(0) = 0. The expected value for a perfect two photon source at τ = 0 is g

⁽²⁾

(0) = 1/2. This means that all sources that measures a g

⁽²⁾

(0) in the range between 0 ≤ g

⁽²⁾

(0) ≤ 1/2 indicates that the source is emitting single photons. Furthermore, it also is an indication of the quality of the single photon source, where a lower g

⁽²⁾

(0) value indicates a purer single photon source with less unwanted background emission.

g

⁽²⁾

(0) = n(n − 1)

n

²

(2.11)

2.3 Gallium Arsenide

Gallium arsenide is a III-V semiconductor with a direct band gap. It has a zinc-blend structure, meaning that it consists of two combined face centered cubic (fcc) lattices with a tetrahedral coordination with one of the basis atoms at (000) and the other one at (

¹₄¹₄¹₄

). Each atom has four nearest neighbors with a distance of

√ 3a/4, where a is the lattice constant, spread with an angle of 109.47°. Due to the fcc lattice structure in real space, GaAs has a body centered cubic (bcc) lattice stucture in the reciprocal space. In bulk GaAs, the direct band gap is found at the Γ valley of 1.42 eV. The lattice structure imposes that an intrinsic GaAs crystal has an isotropic thermal conductivity [20].

2.4 Quantum Dots

Quantum dots are zero dimensional particles commonly made from atoms

classified as II-VI, II-V or IV-VI semiconductors. These semiconductor quan-

tum dots are known for being bright emitters, i.e. have strong luminescence,

and a narrow emission spectrum [21]. In particular, a semiconductor quantum

dot has been proven to be a deterministic source of single photons with high

purity and near-unity indistinguishability with the possibility to generate sin-

gle photons on demand. Furthermore, quantum dots are scalable single photon

Figure 2.2: Scheme of the confined energy states in the potential of a quantum dot. The valence band contains the hole states and the conduction band con- tains the electron states. The lowest energy band is called the s-shell, followed by the p-shell and d-shell. Image courtesy of Klaus Jöns [22].

sources that can be incorporated in photonic integrated circuits (PIC). From strong quantum confinement, carrier localization and Pauli exclusion principle we obtain excitonic many-body states with optically bright exciton and biex- citon emission similar to the states in atoms. The discrete energy levels in a quantum dot is visualized in Figure (2.2), used with permission from Klaus Jöns adapted from Orieux et al. [22]. In particular, the discrete energy levels can be precisely engineered to emit certain wavelengths by adjusting the size.

Hence, quantum dots are sometimes referred to as artificial atoms [23].

The quantum dots used in this thesis are fabricated using local droplet etch-

ing in molecular beam epitaxy. This technique produces high quality nanos-

tructures with the possibility to specify structural and optical properties of the

quantum dot, such as specific emission wavelengths [24]. After fabrication,

the emission wavelength of the quantum dot can be tuned slightly by plac-

ing the sample on top of a piezo-electric substrate. By applying voltage over

the piezo-electric substrate, the quantum dot exhibits anisotropic biaxial strain

which tunes the wavelengths of (for example) the exciton emission line and

biexciton emission line of the quantum dot [25, 26]. The ability to tune the

emission wavelength very precisely opens up the possibility to tune the GaAs

quantum dot to for example an absorption line of rubidium in order to store

photons in a rubidium memory [26].

2.5 Confined Electron Hole Pairs

During optical excitation of a semiconductor, an electron is lifted from the valence band up to the conduction band. During this process an electrically positive quasi particle commonly denoted as a hole is created in the valence band. The hole and electron can form a bound state using the Coulomb inter- action between the positive and negative particles. This bound state is called exciton, and is an electrically neutral quasiparticle. Due to conservation of en- ergy the photon energy E

γ

required to create an exciton is given by Equation (2.12), where E

g

is the energy of the band gap and E

b

is the binding energy of the exciton.

E

_γ

= E

_g

− E

_b

(2.12)

There are two different subgroups of excitons, the Frenkel exciton and the Wannier-Mott exciton. The Frenkel exciton has a high binding energy and a small spatial extent in comparison to the lattice constant. It is tightly bound to a specific atom or molecule and can only move throughout a crystal by hopping inbetween different lattice sites. The Frenkel exciton is in general found in insulators or molecular crystals [27, 28, 29].

The Wannier-Mott exciton is typically found in semiconductors. It has a larger spatial extent where the exciton can span multiple units in the lattice, implying that the radius is much larger than the lattice constant. The bind- ing energy is small, it moves freely within the lattice and the total energy is independent of the specific position [30, 29].

2.5.1 Exciton

In this thesis we will refer to exciton as the event when one electron is excited to the first excitonic level and bound to the hole created in the valence band.

Due to the Pauli exclusion principle, each excitonic level has multiple possi- ble exciton spin configurations on the carriers, creating a multiplet of states within the excitonic level. The excitonic level can exhibit internal splittings, i.e. the different multiplets of states corresponds to different energy levels.

This is called fine structure splitting, which occurs due to broken symmetry of the confining potential. The fine structure splitting can be influenced by e.g.

electric fields, magnetic fields and strain in the material [31].

Electron Hole

|00i |01i |10i |11i

Figure 2.3: The system |00i refers to the ground state, when both electrons are in the valence band. In the systems |01i and |10i, one of the electrons is excited to the conduction band and then creating a bond to the hole created in the valence band. Both of |01i and |10i are excitonic states called an exciton.

When both of these excitons are created simultaneously, we obtain a biexciton visualized as |11i. The arrows represents the spin of the electron and hole respectively.

2.5.2 Biexciton

The exciton has two different states, where one has spin up and the other one

spin down. In accordance with the Pauli exclusion principle, these excitons

can be created simultaneously, due to the different spin configurations. This is

called a biexciton. Hence, the biexciton consists of two mutually coupled ex-

citons. The binding energy of the biexciton E

^b,XX

is given by Equation (2.13),

where E

X

is the ground-state energy of the exciton and E

XX

is the ground-

state energy of the biexciton. Furthermore, the binding energy of the biexciton

is inverse proportional to the radius of the quantum dot [32]. The extra bind-

ing energy of the biexciton appears due to not only Coulomb interaction within

the electron-hole pair, but also between the different excitonic states. This is

visualised in Figure (2.3), where |00i is the ground state, |01i and |10i are two

different excitonic states with orthogonal polarisation and |11 > is the biexci-

ton state [33]. In this thesis, we will refer to the |01i and |10i components as

the exciton (X in figures) and |11i as the biexciton (XX in figures) when the

two components can not be distinguished from one another.

E

_b,XX

= 2E

_X

− E

_XX

(2.13)

If the recombination of the biexciton and exciton occurs through a cascade recombination, the emitted photon pair is entangled through polarization. Due to the cascade recombination, the exciton and biexciton will exhibit bunching in a cross-correlation measurement [34].

2.6 Two-photon Resonant Excitation

Two-photon resonant excitation is when two photons are used in order to excite an electronic state. In order to excite the biexciton system using this technique, there are two crucial properties. First of all, due to the binding energy of the biexcition, the photons of the two-photon resonant excitation ω = c/λ is de- tuned from the exciton energy by ω

^X

= E

X

/~. Instead, the energy of two of these photons perfectly match the energy between the ground energy E

g

and the biexciton energy E

XX

given by Equation (2.14) such that 2ω

laser

= ω

₀

. Furthermore, it is important that we excite the system with linearly polarized light, which is a superposition of the circular polarization |σ

⁺

> and the or- thogonal circular polarization |σ

⁻

> [35].

ω

₀

= E

_XX

− E

_g

~ (2.14)

In Figure (2.4), the exciton-biexciton transitions are visualised together with the two-photon resonant excitation process, where λ is the wavelength of the excitation laser and E

b

is the binding energy of the biexciton.

|01i

|11i

|00i

|01i

E

_b

2λ

Figure 2.4: Cascade scheme of the exciton-biexciton system together with the

two-photon resonant excitation (red arrows).

2.6.1 Rabi Oscillations

Simply put, Rabi oscillations is a periodic change between absorption and stimulated emission. The oscillations appear with the frequency defined in Equation (2.15), called the Rabi frequency, where µ

¹²

is the dipole matrix el- ement associated with the transition between state 1 and state 2 and 

0

is the vacuum permittivity.

Ω

_R

=   

µ

₁₂



₀

~  

 (2.15)

The phenomena appears when the light field is strongly interacting with matter. In order to reach the high excitation powers needed to obtain Rabi os- cillations, pulsed lasers are commonly used, thereby giving a time-dependent light field. As the light field is time-dependent, the Rabi oscillations are also time-dependent. Therefore, the pulse area defined in Equation (2.16) is useful, where E is the electric field amplitude.

Θ =   

µ

₁₂

~

Z

+∞

−∞

E

₀

(t)dt  

 (2.16)

The effect is strongest during resonant excitation, i.e. when the photon energy of the exciting source ω matches the energy difference between the ground and excited state ω

⁰

. By excitation of an atomic system, the excited state will begin to be populated. At a certain excitation power, the population density of the excited state will reach its maximum. This point is called the π- pulse, since the excitation pulse has an area equal to π. If the power is increased even more, the upper state population is more and more likely to be depleted into the ground state. It reaches a minimum when the pulse area is equal to 2π, since the light field is depleting the excitation maximally. By increasing the power to a pulse area of 3π, the system has enough power to become excited, depleted and excited within the same excitation pulse [18].

In this thesis we will explore the Rabi oscillations of the exciton and biexci- ton cascade in a GaAs quantum dot while excited using two-photon resonance, which can be seen as a three-level system. For this system, Stufler et al. [35]

showed that the system effectively undergoes Rabi oscillations with an occu- pancy of the biexciton state N

XX

given by Equation (2.17), where h11| is the biexciton state, ψ is an eigenstate of the Hamiltonian of the system and Λ is a non-trivial function of the pulse shape.

N

_XX

= | h11|ψi |

²

= sin

²

 Λ(∞) 2



(2.17)

For a pulse area Θ satisfying Θ  τ

0

E

_BXX

/~, where τ

0

is the FWHM of the laser, E

^BXX

is the binding energy of the biexciton and ~ is the reduced Planck constant, the non-trivial function of the pulse shape can be approxi- mated by Equation (2.18) [35].

Λ(∞) ≈ 4~ · arccosh( p(2))

π

²

E

_BXX

τ

₀

Θ

²

(2.18) For a very large pulse area Θ  τ

0

E

_BXX

/~, we can neglect the single- exciton detuning. In these case, we obtain the alternative expression for the biexcitonic state occupation in Equation (2.19) regardless of the pulse shape.

N

_XX

≈ sin

²

 Θ 2p(2)



(2.19)

2.7 Polarization of Light

Light is an electromagnetic wave which has a corresponding electric field. The direction of the electric field is defined as the polarization of the light. If the electric field vector is constant, the light is linearly polarized. Linearly polar- ized light is commonly measured in the horizontal (H) and vertical (V) basis, where H and V are two orthogonal polarizations. If the vectors are tilted 45°, we use another linear basis with the diagonal (D) and antidiagonal (A) polar- ized light. The light field can also rotate during propagation. This is called elliptically polarized light. A special case of the elliptically polarized light is circularly polarized light. In this case, the electric field can be decomposed into two orthogonal linearly polarized light waves with mutual amplitude and a phase shift of 90°. When the light is rotating clockwise from the observer, it is called right circularly polarized light (R) denoted σ

⁺

and when it rotates counter clockwise it is called left circularly polarized light (L) denoted σ

⁻

. If the direction of the electric field is random, the light is unpolarized [18].

In general, it is equally likely to excite an electron with spin up m

^s

= +

¹₂

as an electron with spin down m

s

= −

¹₂

in the absence of a magnetic field and

when using linearly polarized light. However, by using circularly polarized

light, one can create a net spin of the electrons in the conduction band. This

occurs because circularly polarized light is photons carrying angular momen-

tum. This is called optical spin injection. Photons with an angular momentum

of +~ are right circularly polarized while photons with an angular momentum

of −~ are left circularly polarized [29].

In general, polarized light can be described using the two orthogonal and independent components E

^x

(z, t) and E

^y

(z, t) where the propagation is de- fined to be in z-direction without loss of generallity. These components can be written in accordance with Equations (2.20-2.21), where the maximum am- plitude of the electric field is given by E

0x

and E

0y

and the propagation is described by ωt − κz. The angular frequency ω, the wave number κ and the phase constants δ

^x

and δ

^y

are in general difficult to measure [36].

E

_x

(z, t) = E

_0x

cos(ωt − κz + δ

_x

) (2.20)

E

_y

(z, t) = E

_0y

cos(ωt − κz + δ

_y

) (2.21) By deriving and combining these equations, we obtain the polarization ellipse in Equation (2.22), which describes the polarization of the electric field [36].

E

_x

(z, t)

²

E

_0x²

+ E

_y

(z, t)

²

E

_0y²

− 2E

_x

(z, t)E

_y

(z, t) E

0x

E

0y

cos(δ

_y

−δ

_x

) = sin

²

(δ

_y

−δ

_x

) (2.22)

2.7.1 Stokes Measurement

The polarization ellipse can not be measured nor observed. Hence, we will transform it to the intensity domain by taking the time average of the polar- ization ellipse. This is defined by Equation (2.23), where i, j = x, y utilizing Einstein sum notation.

hE

_i

(z, t)E

_j

(z, t)i = lim

_{T →∞}

1 T

Z

T 0

E

_i

(z, t)E

_j

(z, t)dt (2.23) This leads to the definition of the Stokes parameters S

0

, S

1

, S

2

and S

3

. The parameters obey the constraint in Equation (2.24), which is an equality if and only if the light is fully polarized. The Stokes parameters are defined in accor- dance with Equation (2.25), which is called the Stokes vector. The parameter S

₀

describes the total intensity of the electric field, S

1

describes the intensity of the electric field in the horizontal and vertical basis, S

2

describes the in- tensity in the diagonal and antidiagonal basis and S

3

describes the intensity in the circular basis. These components are measureable, since they represent intensities [36].

S

₀²

≥ S

₁²

+ S

₂³

+ S

₃²

(2.24)

S = ˆ















 S

₀

S

₁

S

₂

S

3

















=

















E

_0x²

+ E

_0y²

E

_0x²

− E

_0y²

2E

_0x

E

_0y

cos(δ

_y

− δ

_x

) 2E

0x

E

0y

sin(δ

y

− δ

x

)

















(2.25)

By using the bases (H, V ), (D, A) and (R, L) we can rewrite this in ac- cordance with Equation (2.26).

S = ˆ

















I

_H

+ I

_V

I

_H

− I

_V

I

D

− I

A

I

_R

− I

_L

















(2.26)

If the light is non-elliptic, all different polarizations can be reached us- ing a half waveplate and a quarter waveplate. A half waveplate introduces a phase shift of half a wave, i.e. a phase shift of π while the quarter waveplate introduces a phase shift of π/2 [36].

2.7.2 Poincaré Sphere

The Poincaré vector ˆ s is defined by dividing the Stokes vector ˆ S by the first Stokes polarization parameter S

0

, see Equation (2.27) [37].

ˆ s = S ˆ

S

₀

=















 1 S

₁

/S

₀

S

2

/S

0

S

₃

/S

₀

















(2.27)

By using the Poincaré vector notation in Equation (2.24), we obtain Equa-

tion (2.28) which is an equality only when the light is fully polarized. In fact,

the equation represents nothing else than a sphere with radius r = 1 and cen-

ter in the origin (0, 0, 0) where all points corresponding to fully polarized light

will be found on the surface. Unpolarized light will be found in the origin and

partially polarized light will be found inside the sphere.

1 ≥  S

₁

S

₀



2

+  S

₂

S

₀



2

+  S

₃

S

₀



2

(2.28)

2.8 Optical Quantum Memories

The purpose of an optical quantum memory is to store quantum bit (qubit) strings with the possibility to release them on demand. A qubit is a basic unit of quantum information and has a coherent superposition of two states |0i and

|1i, which can be described using Equation (2.29), where α and β are constants satisfying Equation (2.30). Some examples of observables that can be used as information carrying states are polarization, photon-numbers, spin or time-bin encodings [38].

|φi = α |0i + β |1i (2.29)

|α|

²

+ |β|

²

= 1 (2.30)

A well-known example of an optical quantum memory is based on electro- magnetially induced transparency (EIT). It has a symmetry breaking λ-scheme and utilizes two different, co-propagating optical fields. One is a strong con- trol field used to induce a transparent window with a narrow spectral range within an absorption line of the medium, and the other one is the signal field carrying the quantum information. If the frequency difference of the fields is close to the two-photon resonance, the signal field undergoes a large normal dispersion leading to a group velocity that is reduced inversely proportionally to the intensity of the control field. This means that the light will be slowed down in the medium to a degree which adjusted by the control field intensity.

This causes the signal to be spatially compressed inside the cell while propa- gating. If the control field is turned off at this point, the signal is collectively absorbed such that all atoms are in a superposition state creating a magnon.

This magnon is also called a dark-state polariton which does not couple to the light field. As the control field is turned on again, the magnon is recoupled to the light field and the signal is retrieved [38].

The problem with an EIT quantum memory is that in room-temperature

operation noise from inherent strong atomic motion, decoherence, and back-

ground photons appears. One way to solve this is to implement noise-supp-

ression using a control field which affects the background photons and the

qubits differently [39]. Two other optical quantum memories that have been developed in order to solve this problem is the fast ladder memory (FLAME) [40] and the off-resonant cascaded absorption (ORCA) [41].

2.8.1 Importance of Noise Reduction

As described in the introduction, one wants to use photons as information car- riers in complex communication networks due to their property preserving nature when transmitted over a large spatial range. Due to the non-cloning theorem, the amplifiers in classical networks needs to be substituted with quan- tum repeaters. These repeaters needs to be noise free, in order to to keep the information intact [40].

The definition of a low-noise quantum memory is that both the mean of added photons and the variance of added photons by the quantum memory is low. Zero noise means that the signal is unchanged in the memory, i.e. the input and output are identical [41].

2.8.2 ORCA Protocol

In the ORCA memory protocol, the control field and the signal field are counter- propagating, as well as spatially and temporally overlapped inside a cell with atomic vapour. The protocol utilizes a three level atomic cascade configuration in order to store photons without degrading the quantum characteristics. The strong control field is far-detuned from the intermediate state leaving it off- resonance, but it can excite the system using two-photon resonance together with the much weaker signal field. Hence, the system is left in a collective atomic coherence when excited. This is called read-in. The read-out occurs on-demand by applying a second control pulse, re-mapping the atomic coher- ence causing re-emission of the signal field [41].

Noise is reduced in multiple different ways in the ORCA protocol. The

counter-propagation of the control and signal field leads to reduced motion-

induced dephasing in the atomic ensemble. By being able to choose the wave-

lengths of the signal and control field it is possible to detune the control field

from the populated transitions, eliminating scattering or fluorescence noise

from the control field. Furthermore, the electronic state configuration makes

sure no scattering process can populate the storage state. It is not even possible

to reach the storage state using thermal excitation at high temperatures. Hence,

there is no requirement of preparation prior to storage nor any contamination

of the recalled signal field. Last but not least, the external device efficiency is

approaching the internal memory efficiency using interference filters to sup- press control field leakage [41].

In this thesis, the idea is to use the emission from the biexciton of the

quantum dot as the signal field and interface it with a

⁸⁷

Rb ORCA optical

quantum memory.

Experimental Methods

This Chapter presents the methods used in the experiments. The PicoEmer- ald laser is presented in Section (3.1), along with the how to manipulate the pulse length and spectral bandwidth of the excitation pulse. In Section (3.2), the experimental setups is presented. This includes the excitation path to the cryostat with the quantum dots, the detection path to the spectrometer, the fiber coupled detection, the transmission spectrometer, the Fabry Pérot Interferom- eter, the setup for the Stokes measurement as well as the setup of the ORCA quantum memory.

3.1 PicoEmerald Laser

In this thesis we use a PicoEmerald laser from APE to excite the quantum dot during most of the measurements. It can emit short pulses with durations down to 2 ps with a pulse repetition rate of 320 MHz. It is a pair source creating a signal and an idler using non-linear effects. We use the signal output of the laser, which is tunable in the range of 700 nm-900 nm [42]. In this thesis, it is used at the two-photon resonant wavelength, see Section (2.6). The wave- length is given by Equation (3.1), where λ

L

is the laser wavelength, λ

X

is the emission wavelength of the exciton and λ

XX

is the emission wavelength of the biexciton. To obtain this result we have used the Einstein relation E = hc/λ, where h is the Planck constant and c is the velocity of light in vacuum. In practice this gives us a center wavelength of approximately 793.8 nm.

λ

_L

= 2 ·  1

λ

_X

+ 1 λ

_XX



⁻¹

(3.1)

18

3.1.1 Slicing Laser beam

The setup of the slicer is visualized in Figure (3.1). The beam enters the slicer and is focused onto a grating using a two lenses and a mirror. A curved mirror is directing the beam through a cylindrical lens (CL) onto another curved mir- ror. The beam is then directed through a slit which cuts, or slices, the spectral bandwidth of the beam.

Slit

CL

Grating

Figure 3.1: The light is directed from the laser output into the slicer, where the beam is magnified before hitting a grating. It is then directed onto a slit, which adjusts the spectral bandwidth as well as the pulse length due to the uncertainty principle. CL: Cylindrical lens.

Slicing the spectral bandwidth of the beam increases the time duration of the pulse. This occurs due to the uncertainty principle, which can be writ- ten in terms of the root-mean-square width of the signal in time (∆t

rms

) and frequency (∆ν

rms

) according to Equation (3.2) [43].

1

2 ≤ ∆ν

_rms

∆t

_rms

(3.2)

3.2 Experimental Setups

In this thesis, we use multiple different optical setups to facilitate doing differ-

ent kinds of measurements. These can be combined by using fibers and fiber

couplers, such that it can easily be rearranged to fit different purposes. The ex- citation of the quantum dots is done by coupling a laser to the cryogenic setup.

The photoluminescence spectra are acquired using a spectrometer, see Subsec- tion (3.2.1). The photoluminescence can also be coupled into a fiber, which can either be directed to the spectrometer or to the transmission spectrometer.

The transmission spectrometer divides the photoluminescence spectrally, and makes it possible to detect signals with a spectral bandwidth of up to 20 GHz at a time. This signal can be either directly sent to the superconducting nanowire single photon detectors (SNSPDs) in order to measure the correlations and lifetime, or through the Fabry Perot interferometer and then to the SNSPDs in order to measure the linewidth.

3.2.1 Cryogenic Confocal Micro-Photoluminescence Setup

The cryogenic setup includes two excitation paths and two detection paths.

One of the excitation paths uses a magnetic mirror to direct the photolumines- cence to the spectrometer in free space, while the second path is coupling the photoluminescence into a fiber. This fiber can be connected to a fiber coupler directed to the spectrometer for alignment purposes, to the transmission spec- trometer, directly to the SNSPDs or to the quantum memory. The cryogenic setup is visualized in Figure (3.2).

The quantum dots are placed on a piezo stack inside a cryostat. A micro- scope is focusing the excitation laser beam onto the quantum dot, as well as collecting the emission from the quantum dot.

3.2.2 Transmission Spectrometer

The transmission spectrometer is utilized in order to distinguish the signal of

the biexciton or the exciton from the laser as well as emission from other quasi

particles before being led onto the SNSPDs. The signal is split spectrally using

a grating. The laser is blocked by an adjustable blade that can be put further

in or further away from the diffracted light path. The biexciton is led to one

fiber coupler and the exciton is led to another. The setup of the transmission

spectrometer is visualized in Figure (3.3).

N MM

PM

EP1 EP2

Excitation Detection

PBS

SM

M

BS

Figure 3.2: Cryogenic setup including the excitation and detection paths. BS:

Beam Splitter, M: Mirror, MM: Magnetic Mirror, N: Notch filter, PBS: Polar- izing Beam Splitter, SM: Spectrometer

Figure 3.3: The transmission spectrometer utilizes a curved mirror to expand

the beam, a greating to diffract the light before contracting the light by an-

other curved mirror. There are two different outputs which can be adjusted to

match and collect the emission from the exciton emission wavelength and the

biexciton emission wavelength.

3.2.3 Fabry Pérot Interferometer

A fiber Fabry Pérot interferometer from Micron Optics is used in order to mea- sure the linewidth of the photoluminescence from the exciton and the biexciton of the quantum dots. It has a free spectral range of 19.92 GHz and a bandwidth of 0.0248 GHz which gives a finesse of 804.

The quantum dots were excited from the top with the detection coupled into the fiber. The fiber was connected to the transmission spectrometer aligned for the exciton or the biexciton respectively. This signal was in turn sent through the Fabry Pérot interferometer which was tuned by changing the temperature

3.2.4 Stokes Measurement

In order to determine the polarization of the quantum dots, Stokes measure- ments where performed by using the setup visualized in Figure (3.4). For the measurement we used one polarizer and four waveplates: one motorized half waveplate (λ/2), one motorized quarter waveplate (λ/4), one normal λ/2 and one normal λ/4. A PAX5720IR1-T polarimeter from Thorlabs was used in order to measure the polarization of a DL Pro continuous wave laser from Toptica used to align the setup and precisely tune the waveplates. A pulsed PicoEmerald laser from A.P.E. was used in order to two-photon resonantly excite the quantum dot at 793.78 nm using a pulse length of 5 ps.

The continuous wave laser was attenuated using ND filters at the optical table where the laser is placed, before coupling it to the fiber directed to the spectrometer. The setup which should have been used during the Stokes mea- surement is presented in Figure (3.4), where the faded parts are utilized for calibration but removed when the actual measurement is performed. The setup actually used was missing the vertical polarizer before the spectrometer. How- ever, the experiment could not be remade due to limited lab access caused by the Covid-19 pandemic.

To perform the Stokes measurement, the procedure was as follows: First,

the polarimeter was put in the position S

¹

. A polarizer was put in front of

the fiber coupled output of the laser and rotated such that the laser was ver-

tically polarized. The half waveplate and the quarter waveplate was put in

front of the polarimeter and turned to desired angles, such that the polarime-

ter shows desired polarization. During the first measurement it was turned to

V -polarization. The polarimeter was then put in the S

2

position. A motor-

ized quarter waveplate and a motorized half waveplate was put in front the

polarimeter and the angles was changed such that the light is V -polarized be-

fore going into the spectrometer. This is done in order to achieve the same

V

S2 PBS

M

Excitation

BS

S1

Detection

Figure 3.4: The Stokes measurements was performed on the Cryogenic setup with some additions, where the semitransparent parts are utilized for calibra- tion only. The non-stationary waveplates are the ones closest to the cryostat.

The polarimeter is put in place S

¹

in order to measure which polarization the vertical polarization is transformed into using these waveplates. The polarime- ter is then put in position S

2

to use the stationary waveplates in order to trans- form the light back to V polarization, since this is the polarization measured best by the spectrometer. The non-stationary waveplates are then removed before three spectra integrated over 0.1 s are recorded. A polarizer set to V should is placed before the spectrometer, such that only the desired compo- nent is measured. S1 Polarimeter position 1. S2: Polarimeter position 2. V:

Vertical polarizer.

efficiency from the spectrometer for all polarizations. The polarimeter and the first set of waveplates where then removed from the path, and a magnetic mir- ror put in such that the photoluminescence emission from the quantum dot is directed through the motorized waveplates into the spectrometer.

For measuring the other polarizations, the magnetic mirror was removed and the waveplates put back into the alignment together with the polarimeter in the S

¹

position. The waveplates was turned such that the laser was H- polarized. The polarimeter was again put in the S

2

position of the setup and the motorized waveplates turned such that the light was turned to V -polarization before entering the spectrometer.

3.2.5 ORCA Quantum Memory

The aim of the ORCA quantum memory is to store the single photons gen- erated through the two-photon resonant excitation of the quantum dot. The single photons are sent through the transmission spectrometer, where the emis- sion from the biexciton is filtered out and coupled into a fiber leading to the quantum memory setup, visualized in Figure (3.5). In this experiment, either a 80 MHz or the 320 MHz PicoEmerald from APE was used as control field.

When storing, the quantum dot was excited by the DCL Pro pulsed by the Mod- Box. The modbox was locked to the control field laser in order to temporally overlap the signals inside the

⁸⁷

Rb-cell.

When using the 80 MHz laser, the laser was coupled into the setup using a periscope (PS). A Mach-Zehnder interferometer is used as a delay line, split- ting the laser into one write pulse and one read pulse. The length d of the delay line determines the storage time t, using the relation t = d/c· where c is the speed of light. When using the 320 MHz laser, a fiber coupler was put into the setup after the delay line. The first pulse was used as a write pulse and the next three pulses as a read pulses. In this case, the delay is corresponding to the pulse frequency, i.e. τ = (320 MHz)

⁻¹

= 3.125 ns.

The control laser hits the

⁸⁷

Rb-cell from the right. The signal from the

biexciton is spatially and temporally overlapped with the laser, entering the

memory from the opposite direction. The idea is that a strong write pulse

together with the biexciton signal is exciting the three level system through

two-photon resonant excitation. The read pulse releases the single photon by

depletion of the system. For more theory on how the storage works, see Sec-

tion (2.8.2). The stored single photons are then directed to the detection fiber

leading to the SNSPDs.

QD

320 MHz

80 MHz

Shutter LP

Delay line

PS Detection

Rb cell

Figure 3.5: Schematic setup of the quantum memory. Two different lasers can

be used in as control field. The 80 MHz laser was brought onto the table using a

periscope while the 320 MHz laser was entering through a fiber coupler placed

after the delay line. LP: Long pass filter. PS: Periscope. QD: Quantum dot

signal. Rb cell: Cell with

⁸⁷

Rb vapour.

Measurements

In the following chapter the measurements with the corresponding results are presented. In Section (4.1), different characteristics of the quantum dot are analyzed. This includes photoluminescence from the quantum dot, the Rabi oscillations that appears when the exciting power is varied, a more precise measurement of the linewidth of the quantum dot emission using a Fabry Pérot interferometer and a Stokes measurement to determine the polarization of the exciton and biexciton. The Fabry Pérot interferometer also includes a measurement which determines the free spectral range (FSR) of the interfer- ometer. This is followed by Section (4.2), in which the purity of the single photons are measured at different excitation pulse lengths using a correlation measurement. Finally, the measurement on the quantum memory is presented in Section (4.3).

Throughout this section, the quantum dots will be referred to as QD1 and QD2 respectively, where QD1 is the one measured first and QD2 is the one measured afterwards.

4.1 Characterization of the Quantum Dots

In order to characterize the quantum dots we utilize a few different methods.

By acquiring photoluminescence spectra we are able to determine that we are exciting the quantum dot, the emission lines of the exciton and the biexciton of the quantum dots as well as how much of the light we couple into the detection fiber. The Rabi oscillations let us find the π-pulse, where we have the most efficient emission. By using the Fabry Pérot interferometer we can very pre- cisely measure the linewidth of the quantum dot. We can also see how the fine structure components behave. From the Stokes measurement we can obtain

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the polarization of the quantum dots, and by plotting them pixel by pixel we want to exploit a possible fine structure splitting.

4.1.1 Photoluminescence Measurements

In order to measure the photoluminescence the dot was excited by the Pi- coEmerald laser with a repetition rate of 320 MHz in all cases except for in Figure (4.3), where it was excited by a DL Pro laser from Toptica pulsed by a ModBox-PG-795nm-30ps (ModBox) with a repetition rate of 80 MHz. The ModBox-PG-795nm-30ps is an electro optical modulator from the company iXblue Photonics used to generate optical pulses of a continuous wave input laser. The detection was done using the spectrometer, either by directing the emission through free space directly into the spectrometer or by coupling the emission into the detection fiber directed to the spectrometer. Also, a second excitation path was installed in order to achieve more efficient excitation of the quantum dot. The spectra shown here is a mean of three integrations using an integration time of 0.1 s.

In Figure (4.1), the photoluminescence from QD1 is visualized when ex- citing at the π-pulse (10 µW, see Section (4.1.2)) and detecting through free space versus coupling into the fiber. From the fitted curve we obtain a stan- dard deviation. By summing the counts over three standard deviations of each peak, we obtain that (45 ± 6)% of the emission from the exciton and (46 ± 4)%

of the biexciton emission is coupled into the fiber.

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Figure 4.1: Left: Photoluminescence spectrum of QD1 measured through free space. Right: Photoluminescence spectrum of QD1 coupled into a fiber di- rected to the spectrometer. The coupling efficiency is approximately 45 %.

The quantum dot is excited by EP1, see Figure (3.2).

The second excitation path was introduced in order to obtain more effi- cient excitation. A photoluminescence spectra acquired through free space is visualized in Figure (4.2). The excitation power was 6 µW.

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0 0.2 0.4 0.6 0.8 1

Figure 4.2: The photoluminescence from the exciton and biexciton of QD1 is measured through free space when excited using EP2. By changing the excitation path we were able to excite more efficiently, described in Section (4.1.2).

In Figure (4.3), two photoluminescence spectra acquired through free space when exciting with pulses produced by the modbox is visualised. The spec- trum was acquired when exciting through two-photon resonance at 2 µW. In the first plot a background appears. In the second plot this is removed, by filtering the DL Pro with an etalon before pulsing the laser using the ModBox.

The photoluminescence from QD2 is visualized in Figure (4.4) when ex- citing at the π-pulse (8.5 µW, see Section (4.1.2)) and detecting through free space versus coupling into the fiber. Utilizing the same method as previously, we obtain that (49 ± 1)% of the emission from the exciton and (47 ± 1)% of the biexciton emission is coupled into the fiber.

In Figures (4.1) and (4.4), it appears that the photoluminescence ratios of

the biexciton and exiton are different for QD1 and QD2 (or using EP1 and

EP2). However, the ratios of the exciton and biexciton emission are very simi-

lar for all four plots. In Table (4.1), the ratio of the biexciton emission and the

exciton emission are presented, where it is shown that the ratios are approxi-

mately the same. The reason for why the ratio appears to be different is most

likely due to the fact that the emission is hitting the CCD of the spectrometer

a bit differently, such that the maximum in Figure (4.4) is split between two

different pixels.

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0.2 0.4 0.6 0.8 1

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Figure 4.3: Left: When exciting QD1 with the DL Pro pulsed by the ModBox, a noisy background appears. Right: When an etalon is inserted before the DL Pro is pulsed by the ModBox, the noise disappears.

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0.2 0.4 0.6 0.8 1

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Figure 4.4: Left: Photoluminescence spectrum of QD2 measured through free space. Right: Photoluminescence spectrum of QD2 coupled into a fiber di- rected to the spectrometer. The coupling efficiency is approximately 47 %.

Both spectra show QD2 when excited by EP2, see Figure (3.2).

4.1.2 Rabi Oscillation Measurement

During the Rabi oscillation measurement, the quantum dot was excited using

the PicoEmerald laser with a repetition rate of 320 MHz in all cases except for

the last one, where it was excited by a DL Pro laser pulsed by a ModBox-PG-

795nm-30ps (ModBox) with a repetition rate of 80 MHz. The detection was

made using the spectrometer through free space. The integration time for each