[pt] Estuda-se a relação de complementaridade entre a visibilidade e a distinguibilidade espectral dos pacotes de onda fotônicos deslocados em frequência em um interferômetro de Hong-Ou-Mandel. Uma definição experimental de K, o parâmetro de distinguibilidade, é proposta e testada para a desigualdade de complementaridade K2 mais V2 é menor ou igual à 1 quando um parâmetro de visibilidade consistente é definido. Os resultados mostram que a distinguibilidade espectral é, de fato, complementar à visibilidade e que o aspecto quântico do fenômeno de interferência de dois fótons pode ser examinado empregando estados coerentes atenuados. / [en] The complementarity relation between the visibility and the spectral distinguishability of frequencydisplaced photonic wave-packets in a Hong- Ou-Mandel interferometer is studied. An experimental definition of K, the distinguishability parameter, is proposed and tested for the K2 + V2 is less than or equal to 1 complementarity inequality when a consistent visibility parameter is defined. The results show that the spectral distinguishability is, indeed, complementary to the visibility and that the quantum aspect of the two-photon interference phenomenon can be examined by employing weak-coherent states.

In der vorliegenden Dissertation wird ein neues experimentelles Konzept zur Durchführung von Gravitationswellendetektion und Spektrometrie mit einem Hong-Ou-Mandel (HOM) Interferometer im Weltraum untersucht. Dabei wird das Rauschbudget des Instruments bewertet. Die grundlegenden experimentellen Anforderungen werden berechnet. Es wird gezeigt, dass die Leistung und Wellenlänge der verschränkten Photonenquelle, zusammen mit der Winkelgenauigkeit der Messung der Photonenpolarisationsdrehung, die Haupteinschränkungen bilden, um die Art der Gravitationswellenquellen zu bestimmen, die das Ziel von HOM - Gravitationswellenspektrometern sein würden. Die derzeit verfügbaren pW-Leistungen mit typischen Photonenfrequenzen in der Größenordnung von 1014 Hz (sichtbarer - UV-Anteil des optischen Spektrums) sind völlig ungeeignet, was die erforderliche Detektionszeit für eine der Gravitationswellenquellen betrifft, die derzeit von bodenund raumgestützten Gravitationswellendetektoren anvisiert werden. Der Betrieb des HOM-Interferometers als GW-Spektrometer wird mit einem numerischen Modell veranschaulicht, das die von LIGO am 14 September 2015 (GW150914-Ereignis) aufgezeichneten Gravitationswellendehnungsdaten verwendet. Unter der Annahme einer Winkelgenauigkeit von μrad für die Messung der Polarisationsdrehung von Photonen könnten diese Messungen nur mit Armlängen des HOM-Interferometers in der Größenordnung von 10.000 km (nur im Weltraum erreichbar, wenn wir keine optischen Kavitäten verwenden) und unter Verwendung von verschwänkten Photonenquellen von etwa 1 W Leistung durchgeführt werden, die verschränkte Photonen mit Wellenlängen im Radiowellenbereich des elektromagnetischen Spektrumserzeugen, (10 MHz), und unter Verwendung von Photodetektoren mit minimaler Detektionszeit für einzelne Photonen und minimaler detektierbarer Leistung, die weit von den Möglichkeiten der gegenwärtigen Photodetektortechnologie entfernt sind. Auch die erforderliche Präzision der Uhrensynchronisation, um die Koinzidenz- Zählgeschichte zu erfassen, ist noch ange nicht erreicht. Obwohl die Technologie zur Herstellung der erforderlichen verschränkten Photonenquellen, Photodetektoren und Uhrensynchronisationsgenauigkeit derzeit nicht verfügbar sind, diskutieren wir verschiedene Missionsszenarien zur Implementierung eines großarmigen HOMInterferometers.:Contents 1 Introduction 1 2 Gravitational waves and their measurement 7 2.1 Theory of general relativity in a nutshell . . . . . . . . . . . . . . . . 8 2.2 On the physical nature of gravitational waves . . . . . . . . . . . . . 13 2.2.1 Effect of gravitational waves on the test masses of a detector . 15 2.2.2 Estimation of gravitational wave’s amplitude . . . . . . . . . . 18 2.2.3 Gravitational radiation luminosity and cross section of the Hydrogen atom to GWs . . . . . . . . . . . . . . . . . . . . . 21 2.3 Measuring cosmic distances with GW astronomy . . . . . . . . . . . . 25 2.4 Influence of gravitational waves on photon’s polarization . . . . . . . 28 2.4.1 Effect of gravitational waves on the parallel transport of photon’s polarization four-vector - revisited . . . . . . . . . . . . 29 2.4.2 Effect of primordial gravitational waves on the polarization of the cosmic microwave background . . . . . . . . . . . . . . . 36 2.4.3 Gravitomagnetic Faraday effect . . . . . . . . . . . . . . . . . 40 2.5 Michelson type gravitational wave antennas . . . . . . . . . . . . . . 41 2.6 Rough estimation of the sensitivity and cross section of Michelson type detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3 Interaction of gravitational waves with Hong-Ou-Mandel interferometers 47 3.1 Fundamental nature of quantum entanglement in brief . . . . . . . . 47 3.2 Why a HOM interferometer to detect GWs? . . . . . . . . . . . . . . 50 3.3 Quantum mechanics of Hong-Ou-Mandel interferometers . . . . . . . 54 3.4 Principle of gravitational waves detection with a Hong-Ou-Mandel interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.5 Instrument noise budget . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.6 Basic experimental requirements for HOM based gravitational waves detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4 Gravitational waves spectrometry with a Hong Ou Mandel interferometer in space 77 4.1 Principles of gravitational waves spectrometry with a Hong-Ou-Mandel interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.2 Hong-Ou-Mandel spectrometer in geostationary orbit . . . . . . . . . 93 4.3 Hong-Ou-Mandel spectrometer scanner in space . . . . . . . . . . . . 95 5 HOMER mission scenarios for gravitational waves spectrometry - basic design requirements 97 5.1 HOMER mission design analysis . . . . . . . . . . . . . . . . . . . . . 98 5.1.1 HOMER GEO mission . . . . . . . . . . . . . . . . . . . . . . 99 5.1.2 HOMER ground-GEO mission . . . . . . . . . . . . . . . . . . 105 5.1.3 HOMER scanner mission . . . . . . . . . . . . . . . . . . . . . 106 5.2 Influence of earth gravitomagnetism on photon polarization . . . . . 106 5.3 Payload design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.4 Spacecraft design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.5 Summary of HOMER mission requirements . . . . . . . . . . . . . . 120 6 Outlook and conclusions 129 6.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.1.1 HOM gravitational wave detector with optical cavities . . . . 129 6.1.2 Bright entangled heralded photon sources . . . . . . . . . . . 130 6.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7 ANNEX: Detailed derivation of gravitational waves and gravitoelectric and gravitomagnetic fields 137 7.1 Weak gravitational fields . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.2 General relativity for the practical physicist . . . . . . . . . . . . . . 138 7.3 Gravitational wave equation . . . . . . . . . . . . . . . . . . . . . . . 144 7.4 Gravitoelectromagnetic split of spacetime . . . . . . . . . . . . . . . 145 7.4.1 Gravitational scalar potential . . . . . . . . . . . . . . . . . . 147 7.4.2 Gravitomagnetic vector potential . . . . . . . . . . . . . . . . 147 7.4.3 Space curvature . . . . . . . . . . . . . . . . . . . . . . . . . . 149 7.5 Maxwell-type gravitational equations . . . . . . . . . . . . . . . . . . 151 7.6 Gravitomagnetic waves . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.7 The equations of motion in the weak field approximation . . . . . . . 156 7.8 Production of gravitational radiation . . . . . . . . . . . . . . . . . . 160 Bibliography 163

Un phénomène d'intrication entre des photons a été observé dans les années 80 par l'équipe dirigée par Alain Aspect. Cette observation a permis de rendre compte du caractère non local de ce phénomène. Nous verrons comment transposer les expériences d'optique au domaine des atomes froids. Une étude nouvelle d'une source d'atomes corrélée (intriquée ?) en impulsion sera présentée et des expériences d'interférences multiples seront analysées. L'objectif final de notre étude est de montrer qu'un test de violation des inégalités de Bell avec des atomes corrélés en impulsion est possible. C'est une expérience de physique fondamentale qui, si elle réussit, ouvre une porte sur la mesure d'effets de la gravité sur l'intrication, un des grands enjeux de la physique actuelle. / It has been experimentally demonstrated in the 1980s by Alain Aspect that the polarization entanglement between two photons can exist and consequently that the locality is no longer valid in this type of experiment. In our experiments, we seek to highlight this kind of phenomenon on atoms. Measurements will focus on external variables such as speed and we will see what tools we need to achieve them. It is a fundamental physics experiment that, if successful, opens the door to measures of possible effects between gravity and entanglement.

Deux expériences d'Optique Atomique Quantique sont étudiées dans ce manuscrit : l'expérience Hong-Ou-Mandel atomique ainsi qu'une expérience préliminaire au test des inégalités de Bell sur la variable d'impulsion de deux atomes. Ces deux expériences permettent de révéler des comportements très particuliers de la matière. La première produit une interférence à deux particules et la seconde suggère l'intrication de deux atomes en impulsion. Ces deux aspects de la mécanique quantique sont non-intuitifs et surprenants. Pouvoir les réaliser avec quelques atomes dans des environnements contrôlés est nécessaire à la consolidation de nos connaissances des lois de la nature et tout particulièrement quand mécanique quantique et gravitation sont à l'oeuvre simultanément. / We report two Quantum Atom Optics experiments : the atomic Hong-Ou-Mandel experiment and preliminary results toward Bell's inequality test on momentum of two atoms. Both experiments reveal interesting behaviors of matter. The first one shows a 2-particle interference and the second one suggests entanglement momenta between two atoms. These aspects of quantum mechanics are really surprising and unintuitive. Realizing these experiments with a few atoms in a controlled environment are necessary to strengthen our understanding of the world, particularly when quantum mechanics and gravitation act simultaneously.

We study different phenomena associated with single-photon propagation in optical cavities coupled through optical fibers. We first address the issue of storing and delaying single-photon wavepackets in an array of microcavities. This has possible applications in developing reliable and efficient quantum repeaters that will be utilized in building long distance quantum networks. Second, we investigate a Hong-Ou-Mandel (HOM) type of interference between two photons that are produced in two coupled atom-cavity systems. The HOM effect in this setup can test the degree of indistinguishability between photons when they are stored inside cavities. This part of the dissertation also includes the study of entanglement between atoms, cavities and atom-cavity systems induced by the photons. Finally, we focus on single-photon interactions with a tiny movable mirror in the context of quantum optomechanics. We investigate how the mechanical motion of the mirror leaves its imprints on the optical spectrum of the photon This dissertation includes previously published and unpublished co-authored material. / 10000-01-01

Les boîtes quantiques sont des sources de photons uniques prometteuses pour les réseaux d’information quantique, qui peuvent être intégrées dans des circuits photoniques et s’appuyer sur des technologies de semi-conducteur éprouvées. Dans ce contexte, ce travail se concentre sur les propriétés d’indiscernabilité des photons émis par une boîte quantique semiconductrice sous excitation résonnante. Nous utilisons une configuration particulière où les boîtes sont insérées dans une microcavité planaire permettant de s’affranchir du fond de diffusion parasite du laser d’excitation et d’améliorer la collection du signal d’émission. Nous pouvons ainsi explorer un régime de très basse puissance, où les photons d’excitation sont diffusés élastiquement sur la transition fondamentale de la boîte quantique (régime de diffusion Rayleigh résonnante). Dans ce régime, la cohérence du laser d’excitation est transmise aux photons émis, faisant des boîtes quantiques une source de photons uniques avec une cohérence extrêmement longue.Les propriétés d’indiscernabilité sont étudiées en utilisant les interférences à deux photons (coalescence) dans un interféromètre de Hong–Ou–Mandel. Une étude expérimentale complète de l’indiscernabilité est présentée en fonction de la puissance d’excitation ainsi que du temps de cohérence du laser d’excitation. Elle montre en particulier l’effet de la diffusion élastique dans la limite de basse puissance d’excitation. Il apparaît qu’une nouvelle caractéristique quantitative doit être introduite afin d’estimer l’indiscernabilité en tant que phénomène temporel, un aspect particulièrement important lorsque les émetteurs sont des sources continues de photons. / Quantum dots are good candidates as single photon emitters for quantum information networks, facilitating their integration in photonic circuits based on well known semiconductor technology. In this context, this work focuses on the indistinguishability of the photons emitted by semiconductor quantum dots excited resonantly. We use a peculiar configuration where the quantumdots are embedded in a planar microcavity, allowing for better excitation and collection efficiencies. We are then able to investigate very low excitation power regimes, where the photons are elastically scattered by the fundamental transition of the quantum dot (Resonant Rayleigh Scattering). In this regime, the coherence of the excitation laser is imprinted on the emitted photons, making the quantum dot a source of single photons with a very long coherence.The indistinguishability is investigated by using a Hong–Ou–Mandel interferometer to perform two-photon interference. We carry out a comprehensive experimental study of the excitation power dependence of the indistinguishability as well as its dependence on the excitation laser coherence, which shows the important role of elastic scattering in the low excitation power limit. It appears that a new figure of merit needs to be introduced to assess the indistinguishability as a temporal phenomenon, an aspect which is particularly relevant when dealing with continuous-wave excitation.

[pt] No presente trabalho, demonstramos o uso de fibras de cristais fotônicos (PCF) em diferentes configurações para sensoriamento. Investigamos o uso de fibras PCF com alta birrefringência para sensoriamento de pressão hidrostática e deformação, explorando a baixa dependência térmica. Onde a interferência entre os modos que se propagam em uma fibra birrefringente é analisada. Monitoramos o deslocamento do padrão de interferência do espectro de reflexão, com a variação da pressão ou deformação aplicada à fibra. Demonstramos uma técnica de criar cavidades Fabry-Perot dentro de uma fibra óptica, bem como uma técnica para controlar seu comprimento, e consequentemente, o período das franjas no padrão de interferência no espectro de reflexão. O interferômetro Fabry-Perot (FPI) investigado, possuí um altíssimo contraste nas franjas do padrão de interferência, acima dos 30 dB, sendo no momento, o recorde para o valor do contraste das franjas para FPI silica-ar. O dispositivo foi investigado quanto à resposta a deformação. Um robusto encapsulamento foi feito, possibilitando investigar a resposta do dispositivo à vibração externa. Um estudo da relação da sensibilidade com o comprimento do FPI é também investigado. Construímos um outro interferômetro a partir de um pedaço de fibra PCF e de duas regiões de colapso de suas micro-estruturas. Estas regiões permitem a excitação e recombinação dos modos da fibra. Um dos modos que participa da interferência, é o modo de casca da fibra PCF, o qual é sensível a mudança de índice de refração do meio. O dispositivo apresenta contraste acima dos 40 dB, e é investigado quanto à resposta as mudanças de índices de refração do meio externo em contato com a fibra. Com a mesma montagem, funcionalizamos um pedaço de 2,0 cm de PCF para monitoramento de respiração humana. A partir disso, desenvolvemos um dispositivo capaz de monitorar a respiração do ser humano. / [en] In this work, we have demonstrated the use of Photonic Crystal Fiber (PCF), in different configurations, for sensing applications. The high birefringence and low temperature dependence characteristics of the PCF were explored for sensing hydrostatic pressure and deformation in a reflection configuration. Sensing was based on the analysis of the interference patterns between the modes that propagate in the birefringent fiber under the variation of pressure and deformation applied to the fiber. We have also demonstrated a technique to manufacture a Fabry-Perot Interferometer (FPI) cavity within an optical fiber with control of the cavity length and thus the control of the period of the fringes in the interference pattern. The Fabry-Perot Interferometer investigated presented a very high fringe contrast, above 30 dB, and showed a record value of the contrast of the fringes for FPI silica-air. The FPI device integrated within the fiber was tested as a strain sensor and also as a device to monitor vibration. A study of the relative sensitivity of the length of the FPI was also investigated. Another interferometer was built from a piece of standard fiber and a PCF with two regions of collapsed microstructures. These regions allowed the excitation and recombination of the fiber modes. This device was tested as a refractive index sensor, presenting a fringe contrast above 40 dB. An application of this device was the development of a humid sensor to monitor human breathing.

This portfolio of work contributes to the remit of the National Physical Laboratory (NPL) to develop the underpinning expertise and tools for validating nascent and future optical quantum technologies based on the discrete and quantum properties of photons. This requirement overlaps with the requirement to provide validation for devices operating in the photon-counting regime. A common theme running through the portfolio is photon pairs generated through spontaneous parametric downconversion (SPDC). A Hong-Ou-Mandel (HOM) interferometer sourced with visible wavelength photon pairs from an SPDC process in beta-barium borate (BBO) was designed, built and characterised. The visibility of the HOM interference is dependent on the indistinguishability of the interfering photons, but is also influenced by imperfections of the interferometer; therefore an investigation was carried out to quantify the effects of the interferometer imperfections on the measured visibility so that the true photon indistinguishability could be measured with a quantified uncertainty. A bright source of correlated pair photons in the telecoms band based upon a pump enhanced SPDC process in periodically-poled potassium titanyl phosphate (PPKTP) was designed, built and characterised. From the characterisation measurements the source brightness was estimated to be 6.2×10⁴ pairs/ s/ mw pump. The photon pairs were further characterised through their incorporation as a source in a HOM interference experiment. The developed correlated photon pair source was at the heart of a novel scheme for the generation of polarisation entangled photon pairs, for which the design, build and characterisation work is presented. The source was demonstrated to produce two of the four maximally entangled Bell states with quantum interference visibilities of around 0.95. The generated states were also shown to break a form of Bell's inequality by around six standard deviations. The polarisation entangled photon pair source was originally built at the University of St Andrews and was later transferred to the NPL where it will extend NPL's capabilities to this key spectral region. Finally a study was carried out to investigate the possibility of a wavelength tuneable device for the absolute measurement of single photon detector quantum efficiencies based upon an established SPDC technique.

Spontaneous parametric down conversion (SPDC) is used to generate quantum entangled photons through a non-linear crystal. The entanglement of photons is demonstrated by observing the effects of indistinguishability on photons, first through time and energy, then by polarization. The Hong-Ou-Mandel (HOM) effect was also demonstrated. A theoretical derivation of the effect of a non 50/50 beam splitter (BS) is also investigated. The energy of the photons was changed by varying the temperature of the crystal whilst the time difference was changed by varying the relative position of two mirrors. Results showed a clear effect from indistinguishability on both energy and time.