The fields of quantum simulation with cold atoms and quantum optics are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities , lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range –mediated by a quantized optical light field– were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms N\rightarrow \infty N → ∞ , (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field appears in combination with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.
The fields of quantum simulation with cold atoms and quantum optics are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities , lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range –mediated by a quantized optical light field– were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms N\rightarrow \infty N → ∞ , (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field appears in combination with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.
The fields of quantum simulation with cold atoms [1] and quantum optics [2] are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities [3, 4], lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range - mediated by a quantized optical light field-were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms N -> infinity, (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short-and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice [5] coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field appears in combination with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.
Present-day experiments have started to couple traditional simulations of ultracold atom experiments with quantum light-fields in cavities. This has provided a wealth of op- portunities to enlarge the number of interaction potentials: cavity mediated long-range interactions compete with kinetic energies, longitudinal fields, short-ranged collisional or magnetic spin-spin interactions. The intracavity many-body lattice models often have to be maintained far from equilibrium through the presence of external driving lasers that help to boost and engineer the various interaction potentials. The steady influx of energy is compensated by a steady stream of energy out of the atom-cavity system for example by photon losses or atomic spontaneous emission. Several experiments have demonstrated that such environments can give rise to new competing quantum phases. \nBut this long-standing ambition to push for models with tailorable interaction potentials can bring with it also considerable challenges in their theoretical description, since sponta- neous symmetry breaking transitions in many body lattice systems coupled to dynamical light-fields with single-photon character occur in the presence of drive and dissipation for the photonic force carriers. This clearly calls for model systems where the above men- tioned interplay of interactions, drive, dissipation and cooperative many-body behaviour can be theoretically studied to provide simple, experimentally verifiable predictions. \nThe Dicke model is, through its simplicity (an exactly solved ferromagnet with infinite range atom-atom interactions mediated by a single cavity mode), an exceptionally well- suited candidate. As the generic model for atom-light interactions, it has been experimen- tally realized in a variety of modern quantum optical systems, highlighting its relevance for present-day research. The Dicke model is also highly versatile itself. It has been extended into the dissipative realm, was promoted to account for multiple optical light modes and was used to describe multiple, coupled single-mode cavity structures. It was adapted to treat spin-selective coupling to a cavity to describe superradiance phase tran- sitions in multi-level atomic systems. Moreover, it was realised in electronic circuits where the dipole coupling of real atoms to single mode fields is replaced by a capacitive cou- pling of artificial atoms to a resonator mode. This illustrates that the Dicke model and its extended variants are ’future-proof’ and continue to be of relevance for fundamental light-matter interactions and for driven-dissipative phase transitions. \nIn this thesis, we investigate magnetic phase transitions in driven-dissipative atomic en- sembles interacting with quantum light. We present three research projects on variants of cooperative radiation of an ensemble of laser driven two-level atoms in a single mode optical cavity, as described by the Dicke model. \nThroughout the chapters 2,3 and 4 that contain the main body of research of this thesis, we investigate phase transitions between non-equilibrium stationary states in engineered quantum-optical systems each of which extends the conventional Dicke model physics. As a starting point, we map the quantum equations of motion onto a set of semiclassical nonlinear stochastic equations and analyse their stationary states and instabilities with master equations for atomic spin and photon mean-field amplitudes. These are used to obtain experimentally relevant parameters such as critical atom-light couplings for phase transitions, phase diagrams and properties of stationary non-equilibrium states in addition to cavity output spectra that identify the imprint of magnetic correlations in the light-field. \nIn chapter 2, we help resolve a discrepancy between earlier experimental investigations of the critical atom-light coupling strength for the superradiance transition in the Dicke model: higher external pumping strengths than theoretically predicted were needed to observe a coherent, superradiant state of the light field in an optical cavity. By including incoherent spontaneous emission of atomic excitations, we extend the dissipative Dicke model to a two loss channel variant containing both photon leakage and atomic decay that reproduces the experimentally observed critical atom-light coupling. \nRecent experiments have started to interface quantum many body lattice models with coherent cavity fields, thereby allowing to realize new quantum phases through competing atom-cavity and atom-atom interactions. In chapter 3, we consider a simplified model for such a set-up where a single quantized mode of the light-field interacts with an ensemble of Rydberg-dressed atoms inside a high finesse optical cavity. This model provides a base case for further studies of quantum magnets in optical cavities. At the heart of this model is a competition of short- (dipolar atom-atom) and long-range (atom-light) interactions at the Hamiltonian level in the presence of both spontaneous emission and photon leak- age through the cavity mirrors. We show that different magnetic phases can coexist with coherent atomic radiation and provide clear experimental signatures to identify the mag- netic structure and intra-cavity dynamics. We suggest an experimental level-scheme for a quantum optical implementation of our model. \nIn chapter 4 we consider a generic, collective decay for many-body excitations in the paradigmatic Dicke model. This extension drastically enriches the dynamics as it induces a bicritical point and a bistable regime dominated by true non-equilibrium fluctuations that induce a dissipative first-order phase transition that can only be resolved by including finite fluctuation corrections with the help of stochastic Langevin equations. We investigate the hysteretic response to time-dependent ramps of the atom-light coupling. Discontinuous first-order phase transitions where metastable states coexist in a hysteresis domain have been investigated in recent dissipative quantum-optical experiments. We review noise- activation far from thermal equilibrium in chapter 5.
Interacting ultracold atomic quantum gases provide an ideal test bed to study strongly correlated quantum matter. The interactions between atoms in such an ultracold quantum gas are typically short-ranged and well described by an effective contact potential. Introducing longer-range interactions promises the realization of novel quantum phases which are absent in systems with only short-range interactions. Trapped atoms, resonantly laser-coupled to highly excited, strongly interacting Rydberg states have been proposed as a versatile platform to realize such long-range interacting quantum matter. In a first experiment presented in this thesis, we combined the single-atom-sensitive local preparation and detection enabled by a quantum gas microscope to prepare and microscopically characterize an ensemble of rubidium-87 atoms trapped in an optical lattice in the regime of strong Rydberg blockade. There, we observe collectively enhanced optical coupling in an effective two-level system, the so-called “superatom”, and infer the presence of entanglement. Detuned optical coupling to Rydberg states, termed “Rydberg dressing”, has been proposed as an alternative approach to induce long-range interactions. Rather than directly exciting an atom to a Rydberg state, the properties of the latter are admixed to a ground state, which consequently acquires long-range interactions. In the context of this thesis, we have designed a laser system in the ultraviolet spectral range to admix Rydberg P-state character to the ground state of atoms in an optical lattice. In an emerging Ising quantum magnet, the presence of Rydberg-dressed interactions was demonstrated by an interferometric technique combined with spatially resolved spin correlation measurements. The theoretically predicted tunability of the isotropy and range of the interaction were confirmed experimentally. While these initial measurements exhibited unexpected dissipation, in a subsequent experiment in a one-dimensional spin chain this dissipation was overcome. We substantiated the improved coherence times by tracking the time evolution of the magnetization upon suddenly switching on interactions and observing coherent collapse and revival dynamics, one of the hallmarks of coherent quantum evolution. Our results establish Rydberg-dressed interactions in ultracold gases and pave the way to realize and study novel exotic quantum phases.
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.
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.
We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose–Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas-cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas-cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.