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.
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.
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).
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.
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.
Coupling light to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of interacting quasiparticles, termed Rydberg polaritons. We derive a one-dimensional model describing the time evolution of these polaritons under paraxial propagation conditions. Specifically, we obtain a master equation governing the dynamics of Rydberg polaritons and identify conditions when it can essentially be described by an effective Hamiltonian of a single-species polariton. We verify this Hamiltonian by numerical two-excitation simulations. Under typical stationary EIT conditions it is impossible to reach the strongly interacting regime where long-range density-density correlations emerge. In contrast, by employing the time dependence of the control field the regime of strong interactions can be reached where the polaritons attain quasicrystalline order. We provide a physical explanation for the differences between stationary and time-dependent schemes.
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.
Electromagnetically-induced transparency (EIT) with Rydberg atoms enables strong interactions between atoms to be controlled and measured by pulses of light. Consequently, Rydberg dark polaritons are a promising platform for quantum simulations. Of particular interest are simulations of one-dimensional systems, known to exhibit unique properties compared to their higher-dimensional counterparts. One limitation of standard EIT is that reducing the polariton group velocity to bring the dark polaritons to rest also implies activating strong Rydberg interactions. To achieve independent control of polariton speed and interaction strength, we propose a stationary light-scheme to bring Rydberg polaritons to a stand-still. This allows them to remain primarily photonic and, therefore, non-interacting, before Rydberg interactions are turned on. Once activated, in the dilute regime and in the presence of strong transverse confinement, the strong polarizabilities of Rydberg atoms give rise to an effective contact interaction between polaritons. By tuning the various parameters of the stationary-light scheme, the effective one-dimensional scattering length may be adjusted to yield various kinds of physics, including the regime of a Tonks-Girardeau gas, when polaritons exhibit fermionic behavior. We outline a protocol to observe the resulting spatial correlations between neighboring polaritons.