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.
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.
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.
Most phenomena around us can be explained by classical optics since photons interact weakly with atoms. When the interaction is strong enough where one photon affects the properties of other photons, we go to the regime of quantum photon-photon nonlinear optics. The work in this thesis explores this regime of physics. This paves the path to exploring strongly interacting many-body physics with photons which is still a largely unexplored domain. The ability to control strongly interacting photons is also of central importance in quantum science and engineering. We use the approach of Electromagnetically Induced Transparency (EIT) in atomic ensembles to create strong interactions and demonstrate coherent control between single photons. Using EIT, we coherently map single photons onto the atoms which travel as coupled excitations of light and matter called dark-state polaritons. When the medium is optically dense, the polariton propagates as a massive particle with a velocity that is much smaller than the speed of light. These polaritons interact with each other via their atomic component. In this thesis, we show robust symmetry-protected collisions between photons that imprint a large phase of π/2 with little loss and extend the nature of photon-photon interactions to the repulsive regime, which are essential for quantum communication and metrology. We use the technique of photon blockade to make a fast optical detector of Rydberg states, directly demonstrating the use of quantum nonlinear optics for quantum computation. We also study the extensions of the attractive and repulsive photons for three particles shedding light into the formation of bound states and crystals of photons and paving the way to studying many-body physics of photons.
The recent rapid advancement in the ability to create and manipulate superconducting qubit systems has created an exciting opportunity to construct quantum materials from the ground up, artificial atom by atom. This thesis will explore the creation of a new architecture of quantum simulation in which we use the circuit quantum electrodynamics toolbox to build quantum topological materials that so far have proven difficult to understand with theory, simulate with computational methods, and realize/measure with other quantum systems. Specifically we design a two-dimensional material in which microwave photons living in a superconducting 3D microwave cavity lattice interact strongly with a time-reversal symmetry breaking magnetic field and with each other. This is the first photonic topological lattice platform compatible with strong interactions. The combination of these interactions will enable the study of fractional quantum Hall systems, where fractionally charged particles called anyons are theorized to exist. This thesis describes how to engineer a tunable, low loss microwave lattice, create a magnetic field for chargeless photons using ferrite crystals, and generate inter-particle interactions using Josephson junction transmon qubits.
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.
Although photons do no a ect each other in vacuum, interactions between individual photons could enable a wide variety of scienti c and engineering applications. Here we report on the creation of a quantum nonlinear medium with large photon-photon interactions at the single photon level. Our approach relies on Electromagnetically Induced Transparency (EIT) techniques, in which individual photons are coherently mapped onto strongly interacting Rydberg atoms. Under EIT conditions, photons traveling in the medium are best described as part-matter part-light quantum particles, called polaritons, which experience long-range interactions through the Rydberg blockade. In particular, we demonstrate coherent photon-photon interactions, akin to those associated with conventional massive particles, paving the way for novel photonics states and quantum simulation with light.
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.