Synthetic quantum materials offer an exciting opportunity to explore quantum many-body physics and novel states of matter under controlled conditions. In particular, they provide an avenue to exchange the short length scales and large energy scales of the solid state for an engineered system with better control over the system Hamiltonian, more accurate state preparation, and higher fidelity state readout. Here we propose a unique platform to study quantum phases of strongly interacting photons. We introduce ideas for controlling the dynamics of individual photons by manipulating the geometry of a multimode optical cavity, and combine them with recently established techniques to mediate strong interactions between photons using Rydberg atoms. We demonstrate that this approach gives rise to crystalline- and fractional quantum Hall- states of light, opening the door to studies of strongly correlated quantum many-body physics in a photonic material.
Synthetic quantum materials offer an exciting opportunity to explore quantum many-body physics and novel states of matter under controlled conditions. In particular, they provide an avenue to exchange the short length scales and large energy scales of the solid state for an engineered system with better control over the system Hamiltonian, more accurate state preparation, and higher fidelity state readout. Here we propose a unique platform to study quantum phases of strongly interacting photons. We introduce ideas for controlling the dynamics of individual photons by manipulating the geometry of a multimode optical cavity, and combine them with recently established techniques to mediate strong interactions between photons using Rydberg atoms. We demonstrate that this approach gives rise to crystalline- and fractional quantum Hall- states of light, opening the door to studies of strongly correlated quantum many-body physics in a photonic material.
Designing materials with specific properties has been a long-time goal of the physics community. Optical photons have recently emerged as a promising candidate for such metamaterials due to their fast dynamics and available manipulation toolkit. In conjunction with carefully engineered optical resonators, it is possible to precisely control the properties of individual photons through the resonator Hamiltonian. The only missing ingredient to photonic materials is strong photon-photon interactions. This thesis describes the characterization of cavity Rydberg polaritons and the emergence of strong interactions in such a system. Electromagnetically induced transparency (EIT) is used to create quasiparticles that inherit the properties of both photons and Rydberg atoms: fast dynamics and trapping from the photons and long-range dipole-dipole interactions from the Rydberg atoms. The emergent polaritonic properties are characterized and controlled through the dark-state rotation angle and agree very well with theoretical predictions. We then expand upon this understanding of polaritons by putting them inside a zerodimensional quantum dot. Confining the polaritons in such an object allows for strong interparticle interactions to manifest. We observe these interactions through the temporal auto-correlation intensity function g2(t) and verify the dimensionality of the quantum dot itself by measure the polariton Rabi oscillations. With the experimental demonstration of strong photonic interactions, a complete understanding of Rydberg atoms and polaritons is needed to allow for better control of the system. To this effect, the properties of Rydberg atoms are analytically and numerically understood and the full formalism needed to describe resonator Rydberg polaritons is developed, along with their interactions and various sources of decoherence. Furthermore, a renormalized effective field theory for single mode cavities is developed and tested against full numerical models, paving the way for the simulation of the physical phenomena of manybody states in multi-mode cavities. Strongly interacting cavity polaritons can be utilized in quantum gate and repeater protocols for quantum information processing. Furthermore, combining the experimental and theoretical work here with non-planar resonators presents a clear path to non-trivial topological synthetic materials and strongly correlated quantum states.
Understanding and manipulating quantum materials is a long-sought goal in both the condensed matter and cold atom communities. Photons have recently emerged as a good candidate for studying quantum many-body states due to their fast dynamics and convenient manipulation. Tremendous efforts have been made to engineer single particle Hamiltonian with non-trivial topology. Having individual photons to strongly collide with each other and form an entangled many-body state remained as a challenge in optical domain. ,In this thesis, I will first demonstrate how to engineer artificial magnetic field and non-trivial topology for microwave photons. In a classical lumped element circuit, we demonstrate the edge modes for microwave photons within the bulk band, and also show that these modes propagates with topological protection against the local lattice disorder. This work paves the way to synthesize correlated quantum materials in a lattice using microwave photons, combined with circuit QED technique. ,Recently, Rydberg-Rydberg interaction has been broadly used in cold atom experiment to generate long-range inter-particle coupling for quantum information processing and quantum material simulation. We combine this technique with cavity electromagnetically induced transparency and create a robust quasi-particle, cavity Rydberg polaritons, which harness the power from both cavity photons with exotic topology and Rydberg atoms with strong interactions. We first demonstrate the interaction in the single quanta level in a quantum dot with single cavity mode and further expand it into multi-mode regime with modulated atomic states.
Abstract Photonic materials are an emerging platform to explore quantum matter (Carusotto and Ciuti 2013 Rev. Mod. Phys. 85 299; Sommer et al 2015 arXiv: 1506.00341 ) and quantum dynamics (Peyronel et al 2012 Nature 488 57). The development of Rydberg electromagnetically induced transparency (Weatherill et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 201002; Petrosyan et al 2011 Phys. Rev. Lett. 107 213601) provided a clear route to strong interactions between individual optical photons. In conjunction with carefully designed optical resonators, it is now possible to achieve extraordinary control of the properties of individual photons, introducing tunable gauge fields (Schine et al 2016 Nature 534 671) whilst imbuing the photons with mass and embedding them on curved spatial manifolds (Sommer et al 2016 New J. Phys. 18 035008). Building on work formalizing Rydberg mediated interactions between propagating photons (Gorshkov et al 2011 Phys. Rev. Lett. 107 133602; Gullans et al 2016 Phys. Rev. Lett. 117 113601), we develop a theory of interacting Rydberg polaritons in multimode optical resonators, where the strong interactions are married with tunable single particle properties to build and probe exotic matter. In the presence of strong coupling between the resonator field and a Rydberg-dressed atomic ensemble, a quasiparticle called the ‘cavity Rydberg polariton’ emerges. We investigate its properties, finding that it inherits both the fast dynamics of its photonic constituents and the strong interactions of its atomic constituents. We develop tools to properly renormalize the interactions when polaritons approach each other, and investigate the impact of atomic motion on the coherence of multi-mode polaritons, showing that most channels for atom-polariton cross-thermalization are strongly suppressed. Finally, we propose to harness the repeated diffraction and refocusing of the optical resonator to realize interactions which are local in momentum-space. This work points the way to efficient modeling of polaritonic quantum materials in properly renormalized strongly interacting effective theories, thereby enabling experimental studies of photonic fractional quantum Hall fluids and crystals (Sommer et al 2015 arXiv: 1506.00341 ; Umucalılar et al 2014 Phys. Rev. A 89 023803; Grusdt and Fleischhauer 2013 Phys. Rev. A 87 043628), plus photonic quantum information processors and repeaters (Jaksch et al 2000 Phys. Rev. Lett. 85 2208; Saffman et al 2010 Rev. Mod. Phys. 82 2313; Han et al 2010 Phys. Rev. A 81 , 052311).
Harnessing the interaction between light and matter at the quantum level has been a central theme in atomic physics and quantum optics, with applications from quantum computation to quantum metrology. Combining complex interactions with photonic synthetic materials provides an opportunity to investigate novel quantum phases and phenomena, establishing interesting connections to condensed matter physics. Here we explore many-body phenomena with a single artificial atom coupled to the many discrete modes of a photonic crystal. This experiment reaches the ultrastrong light-matter coupling regime using the circuit quantum electrodynamics paradigm, by galvanically coupling a highly nonlinear fluxonium qubit to a tight-binding lattice of microwave resonators. In this regime, the transport of a single photon becomes a many-body problem, owing to the strong participation of multi-photon bound states arising from interactions that break particle number conservation. Exploiting the effective photon-photon interactions mediated by the qubit, the transport of multiple photons leads to complex multimode dynamics that can be employed for generating a continuous reservoir of strongly-correlated photons, an important resource for quantum networks. This work opens exciting prospects for exploring nonlinear quantum optics at the single-photon level and stabilizing entangled many-body phases of light.
An exciting frontier in quantum information science is the creation and manipulation of \nbottom-up quantum systems that are built and controlled one by one. For the past 30 \nyears, we have witnessed signi cant progresses in harnessing strong atom- eld interactions \nfor critical applications in quantum computation, communication, simulation, and metrology. \nBy extension, we can envisage a quantum network consisting of material nodes coupled \ntogether with in nite-dimensional bosonic quantum channels. In this context, there \nhas been active research worldwide to achieve quantum optical circuits, for which single \natoms are wired by freely-propagating single photons through the circuit elements. For all \nthese systems, the system-size expansion with atoms and photons results in a fundamental \npathologic scaling that linearizes the very atom- eld interaction, and signi cantly limits \nthe degree of non-classicality and entanglement in analog atom- eld quantum systems for \natom number N 1. \nThe long-term motivation of this MSc thesis is (i) to discover new physical mechanisms \nthat extend the inherent scaling behavior of atom- eld interactions and (ii) to \ndevelop quantum optics toolkits that design dynamical gauge structures for the realization \nof lattice-gauge-theoretic quantum network and the synthesis of novel quantum optically \ngauged materials. The basic premise is to achieve the strong coupling regime for a quantum \nmany-body material system interacting with the quantized elds of an optical cavity. Our \nlaboratory e ort can be described as the march towards \\many-body QED," where optical \n elds acquire some properties of the material interactions that constrain their dynamical \nprocesses, as with quantum eld theories. While such an e ort currently do not exist elsewhere, \nwe are convicted that our work will become an essential endeavor to enable cavity \nquantum electrodynamics (QED) in the bona- de regime of quantum many-body physics \nin this entanglement frontier. \nIn this context, I describe an example in Chapter 2 that utilizes strong RydbergRydberg \ninteractions to design dynamical gauge structures for the quantum square ice \nmodels. Quantum \nuctuations driven by cavity-mediated in nite-range interaction stabilize \nthe quantum-gauged system into a long-range entangled quantum spin liquid that may \nbe detected through the time-ordered photoelectric statistics for photons leaking out of the \ncavity. Fractionalized \\spinon" and \\vison" excitations can be manipulated for topological \nquantum computation, and the emergent photons of arti cial QED in our lattice gauge \ntheoretic system can be directly measured and studied. \nThe laboratory challenge towards strongly coupled cavity Rydberg polaritons encompasses \nthree daunting research milestones that push the technological boundaries beyond of the state-of-the-arts. In Chapter 3, I discuss our extreme-high-vacuum chamber (XHV) \ncluster system that allows the world's lowest operating vacuum environment P ' 10 \nTorr for an ultracold AMO experiment with long background-limited trap lifetimes. In \nChapter 4, I discuss our ultrastable laser systems stabilized to the ultra-low-expansion \noptical cavities. Coupled with a scalable eld-programmable-gate-array (FPGA) digitalanalog \ncontrol system, we can manipulate arbitrarily the phase-amplitude relationship of \nseveral dozens of laser elds across 300 nm to 1550 nm at mHz precision. In Chapter 5, \nwe discuss the quantum trajectory simulations for manipulating the external degrees of \nfreedom of ultracold atoms with external laser elds. Electrically tunable liquid crystal \nlens creates a dynamically tunable optical trap to move the ultracold atomic gases over \nlong distance within the ultra-high-vacuum (UHV) chamber system. \nIn Chapter 6, I discuss our collaborative development of two science cavity platforms \n{ the \\Rydberg" quantum dot and the many-body QED platforms. An important development \nwas the research into new high-index IBS materials, where we have utilized our \nlow-loss optical mirrors for extending the world's highest cavity nesse F 500k! We discuss \nthe unique challenges of implementing optical cavity QED for Rydberg atoms, which \nrequired tremendous degrees of electromagnetic shielding and eld control. Single-crystal \nSapphire structure, along with Angstrom-level diamond-turned Ti blade electrodes, is utilized \nfor the eld compensation and extinction by > 60 dB. Single-crystal PZTs on silica \nV-grooves are utilized for the stabilization of the optical cavity with length uncertainty less \nthan 1=100 of a single nucleon, along with extreme level of vibration isolation in a XHV \nenvironment. The capability to perform in-situ RF plasma cleaning allows the regeneration \nof optical mirrors when coated with a few Cs atoms. Lastly but not the least, we combine \nsingle-atom resolution quantum gas microscopy technique with superpixel holographic algorithm \nto project arbitrary real-time recon gurable di raction-limited optical potential \nlandscapes for the preparation of low-entropy atom arrays.
Synthetic materials made of engineered quasiparticles are a powerful platform for studying manybody physics and strongly correlated systems due to their bottom-up approach to Hamiltonian modeling. Photonic quasiparticles called polaritons are particularly appealing since they inherit fast dynamics from light and strong interaction from matter. This thesis describes the experimental demonstration of cavity Rydberg polaritons, which are composite particles arising from the hybridization of an optical cavity with Rydberg EIT, as well as the tools for probing and stabilizing the cavity. ,We first describe the design, construction, and testing of a four-mirror Fabry-Perot cavity, whose small waist size on the order of 10 microns is comparable to the Rydberg blockade radius. By achieving strong coupling between the cavity photon and an atomic ensemble undergoing electromagnetically induced transparency (EIT), we observe the emergence of the dark-state polariton and characterize its single-body properties as well as the single-quantum nonlinearity.,We then describe the implementation of a holographic spatial light modulator for exciting different transverse modes of the cavity, an essential tool for studying polariton-polariton scattering. For compensating optical aberrations, we employ a digital micromirror device (DMD), combining beam shaping with adaptive optics to produce diffraction-limited light. We quantitatively measure the purity of the DMD-produced Hermite-Gauss modes and confirm up to 99.2% efficiency. One application of the technique is to create Laguerre-Gauss modes, which have been used to probe synthetic Landau levels for photons in a twisted, nonplanar cavity.,Finally, we describe the implementation of an FPGA-based FIR filter for stabilizing the cavity. We digitally cancel the acoustical resonances of the feedback-controlled mechanical system, thereby demonstrating an order-of-magnitude enhancement in the feedback bandwidth from 200 Hz to more than 2 kHz. Harnessing the massive processing power of a state-of-the-art FPGA, we present a novel, low-latency digital architecture for loop-shaping, with applications in atomic physics and beyond.