Recent achievements in ultra-cold experiments have made quantum simulation of interacting many-body systems possible in a well controllable environment. Of many candidates as quantum simulators, Rydberg atoms have been extensively utilised due to its exaggerated and fascinating atomic properties. Example includes high susceptibility to electric fields and relatively long life time in comparison to atoms in low-lying states. The tunable interaction between Rydberg atoms have made them even more versatile in simulating quantum many-body systems, e.g. interacting spin-1/2 particles. We will start the thesis by reviewing these properties of Rydberg atoms and explain how they lead to the Rydberg lattice gases that of interest. Following the review of the essential knowledge of Rydberg atoms, we first study the ground states of interacting Rydberg lattice gases in both one-dimension and two-dimensions. The many-body system we are interested in is initially prepared in a Mott-insulator state, with each lattice site containing one atom that is laser coupled to its highly excited Rydberg state. The extremely huge van der Waals interactions between Rydberg atoms at close distance leads to an interesting Rydberg blockade effect. As we shall show, these strong interactions lead to rich phases and critical behaviours in the ground states of the many-body Hamiltonians that describes the systems. The aim of the first three chapters is to analyse these ground states in detail. Having investigated the static properties, we then move on to study the dynamical behaviour of a class of generic spin models which can in principal be realised by Rydberg lattice gases with tunable blockade radius. By deriving an effective master equation, and comparing it to the exact calculation, we will demonstrate how different pure initial states eventually evolve to the same equilibrium state and analysed in detail the time evolution and the steady state.
Recent achievements in ultra-cold experiments have made quantum simulation of interacting many-body systems possible in a well controllable environment. Of many candidates as quantum simulators, Rydberg atoms have been extensively utilised due to its exaggerated and fascinating atomic properties. Example includes high susceptibility to electric fields and relatively long life time in comparison to atoms in low-lying states. The tunable interaction between Rydberg atoms have made them even more versatile in simulating quantum many-body systems, e.g. interacting spin-1/2 particles. We will start the thesis by reviewing these properties of Rydberg atoms and explain how they lead to the Rydberg lattice gases that of interest. Following the review of the essential knowledge of Rydberg atoms, we first study the ground states of interacting Rydberg lattice gases in both one-dimension and two-dimensions. The many-body system we are interested in is initially prepared in a Mott-insulator state, with each lattice site containing one atom that is laser coupled to its highly excited Rydberg state. The extremely huge van der Waals interactions between Rydberg atoms at close distance leads to an interesting Rydberg blockade effect. As we shall show, these strong interactions lead to rich phases and critical behaviours in the ground states of the many-body Hamiltonians that describes the systems. The aim of the first three chapters is to analyse these ground states in detail. Having investigated the static properties, we then move on to study the dynamical behaviour of a class of generic spin models which can in principal be realised by Rydberg lattice gases with tunable blockade radius. By deriving an effective master equation, and comparing it to the exact calculation, we will demonstrate how different pure initial states eventually evolve to the same equilibrium state and analysed in detail the time evolution and the steady state.
Rydberg-dressed ground state atoms are atoms with an electron off-resonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydberg-dressed ground state atoms trapped in several multi-well potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and long-ranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multi-well potential traps. Generally, multi-well systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of long-range interaction on Rydberg-dressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of Bose-Einstein condensate. Then, the fundamentals of the interaction between two-level atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg- dressed atoms trapped in static, i.e., time-independent, multi-well potentials using a mean-field theoretical approach. I choose one-dimensional double- and triple-well in addition to a two-dimensional quadruple-well potentials. The time-dependent non-linear Gross-Pitaevskii equation is used to numerically explore the ensemble’s quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied long-range interaction shows that the behaviour of non-interacting Rydberg-dressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the non-linear interacting limit, such as macroscopic quantum self-trapping. After investigating an ensemble of interacting Rydberg-dressed atoms in static multi-well potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended Bose-Hubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging long-range interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydberg-dressed atoms. In the fourth chapter, the dynamics of Rydberg-dressed atoms trapped in a dynamical, i.e., time-dependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double- well potential. The analysis investigates an ensemble of contact-interacting atoms via the time-dependent non-linear GP equation.
The remarkable progress in control over cold atomic gases has led to a point where people are no longer satisfied with merely studying these systems, but rather put them to use to understand complex quantum many-body systems. The basis of this development is a deep understanding of the interaction between atoms, and how to exploit those in order to engineer interesting and novel quantum-systems. The aim of this particular thesis is to contribute to this third quantum revolution [1] and hence help to understand the inner workings of complex many-body systems. We present a method to control the shape and character of the interaction between cold atoms based on dressing the atomic ground-state with a Rydberg-state. The latter induces a van der Waals interaction between all the atoms in the ensemble, and allows for control via the coupling light-field. We find that with increasing atom densities the ensemble shows a direct transition into a collective regime that preempts the onset of three-body interactions associated with a break-down of the first Born-approximation. The reason for this intriguing behavior is the strong interaction between Rydberg atoms that gives rise to the blockade-mechanism, and prevents the simultaneous excitation to the Rydberg-state for spatially close atoms. The non-trivial behavior of the interaction-potential within the collective regime yields a novel tool for shaping the interaction between ground-state atoms beyond s-wave scattering. We study this collective regime and the resulting interaction-potential between the atoms within a variational/mean-field approach, and discuss its effects on a trapped Bose-Einstein condensate. Artificial atoms show remarkable properties, that are often superior to real atoms. In particular, since they are built out of many constituents, such systems often exhibit an enhanced coupling to the light-field as well as strong optical non-linearities even for small light-fields. On the other hand, noise in quantum-mechanical systems can not only destroy coherence, but rather can be used in order to robustly drive a system into an interesting state. We study the effect of a controlled dephasing onto an artificial atom in the context of an ensemble of atoms coherently coupled to a Rydberg state and demonstrate that such an enhanced artificial atom allows for the deterministic absorption of a single photon from an arbitrary incoming probe field. Such behavior yields a unique tool in light-matter interaction, and opens the path to realise quantum-networks or to fabricate novel quantum-devices. Here, we discuss the applicability of this single-photon absorber as a single-photon transistor, a high fidelity n-photon counter, and a device that allows for the deterministic creation of non-classical states of light via photon-subtraction. A non-trivial topological order of quantum-states leads to conservation of certain properties and, hence, increases their robustness against external perturbations. This can even stabilize quantum-states against local fluctuations. The latter usually corrupts the coherence within a macroscopic object and thereby prevents quantum-phenomena to occur in our macroscopic world. As an example of such a topological state, we study the behavior of vortex-excitations in a two-dimensional superfluid confined to a periodic potential, as can be realised within a cold atomic gas in an optical lattice. For large superfluid filling factors and strong interactions, the healing-length and, accordingly, the vortex core is much smaller than the lattice spacing. As a result, vortices are confined to the plaquettes of the lattice, and can be described in the framework of an effective tight-binding Hamiltonian. Via a first-principle calculation based on coherent-state path-integrals we derive the microscopic parameters of this model and provide an analytic expression for the vortex mass. Moreover, we show that such a quantum vortex is not obliged to follow the superfluid flow, but rather exhibits Bloch-oscillations perpendicular to it, which is a telltale sign for quantum interference of this macroscopic many-body excitation. Recently, Jonathan Simon et al. [2] performed a major step towards simulating quantum many-body systems in cold atomic gases by simulating the paramagnet-antiferro-magnet transition of a one-dimensional Ising-model. Fundamental excitations in the phase with broken translational symmetry are domain-walls carrying fractional statistics. The question is, whether experimentally accessible single-particle excitations, which correspond to two closely-bound domain-walls, decay into fractional excitations or remain closely-bound. By use of perturbation theory, we derive an analytic model for the time-evolution of these fractional excitations in the framework of a tilted Bose-Hubbard model, and demonstrate the existence of a repulsively bound state above a critical center-of-mass momentum. The validity of the perturbative approach is confirmed by the use of t-DMRG simulations. Together with the recent demonstration of single-site addressing and readout in optical lattices, these findings open the path for experimental observation of fractional excitations within cold atomic gases.
While dissipative Rydberg gases exhibit unique possibilities to tune dissipation and interaction properties, very little is known about the quantum many-body physics of such long-range interacting open quantum systems. We theoretically analyze the steady state of a van der Waals interacting Rydberg gas in an optical lattice based on a variational treatment that also includes long-range correlations necessary to describe the physics of the Rydberg blockade, i.e., the inhibition of neighboring Rydberg excitations by strong interactions. In contrast to the ground state phase diagram, we find that the steady state undergoes a single first order phase transition from a blockaded Rydberg gas to a facilitation phase where the blockade is lifted. The first order line terminates in a critical point when including sufficiently strong dephasing, enabling a highly promising route to study dissipative criticality in these systems. In some regimes, we also find good quantitative agreement of the phase boundaries with previously employed short-range models, however, with the actual steady states exhibiting strikingly different behavior.
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.
Rydberg atoms are often proposed as the basis of quantum computing and quantum information protocols. One of the central reasons for this is that they provide a strong and long-ranged interaction that can be coherently switched on and off. This thesis details two techniques which use the exaggerated properties of Rydberg atoms to manipulate both the quantum state of the atom itself and that of the external light field.\n\nThe first proposal initially focuses on the creation of many-body quantum states from two-level atoms trapped in a two-dimensional lattice. This approach uses the van der Waals interaction present between alkali metal atoms in highly excited Rydberg s-states. The approximate solution of the corresponding Hamiltonian is detailed in the regime where the laser driving is the largest energy scale of the system. The states which are most likely achieved using an oscillating laser detuning are then determined. These states are then taken as the basis for the creation of deterministic single-photons, whose properties are shown to rely on the interplay between interatomic spacing and the geometry of the lattice.\n\nThe second technique described uses the coupling between a Rydberg atom and a moving electron to manipulate the atomic state. In this system, the atom is initially excited to a Rydberg s-state and trapped at a finite distance from an electron waveguide. Two analytical methods are used to show that the final state of the atom depends strongly on the direction and modulus of the electron momentum. A complementary numerical simulation shows that the atoms may be left in a polarised state, suggesting the possibility of using this setup to ‘switch on’ permanent electric dipoles in the atoms. This investigation leads naturally to a system where multiple interacting atoms are trapped close to the waveguide, allowing various many-body states to be accessed.
The work presented in this dissertation concerns dynamics of Rydberg atom lattices in the presence of noise and dissipation. Rydberg atoms possess a number of exaggerated properties, such as a strong van der Waals interaction. The interplay of that interaction, coherent driving and decoherence leads to intriguing non-equilibrium phenomena. Here, we study the non-equilibrium physics of driven atom lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we compare between global and local noise and explore their effect on the number of excitations and the full counting statistics. We find that both types of noise give rise to a characteristic distribution of the Rydberg excitation number. The main method employed is the Langevin equation but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power-law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations. In contrast to nearest-neighbour models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. Yet, for finite laser detunings, we show that Rydberg atom lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic phase. We identify the advantages of Monte Carlo rate equations over mean field predictions. Having studied the dynamics of Rydberg atom lattices, we study an application of the strong interactions in such systems for quantum information processing. We investigate the coherent exchange of a single photon between a superconducting microwave cavity and a lattice of strongly interacting Rydberg atoms in the presence of local electric field fluctuations plaguing the cavity surface. We show that despite the increased sensitivity of Rydberg states to electric fields, as compared to ground state atoms, the Rydberg dipole-dipole interaction can be used to protect the system against the dephasing induced by the local noise. Using 1/f and laser phase noise models, we show that compared to the case with non-interacting atoms, our system exhibits longer coherence lifetimes and larger retrieval efficiency of the photon after storing into the atoms.