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Strongly interacting many-body systems in cold atomic gases

Jens Honer

Published Jan 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.18419/opus-5100

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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.
This thesis investigates the effects of strong Rydberg-Rydberg interactions in the presence of three-level coherent phenomena such as electromagnetically induced transparency (EIT), Autler-Townes splitting (ATS) and coherent population trapping (CPT). As a result of their remarkable properties, highly excited Rydberg atoms have great potential for applications in diverse areas. The interaction-induced dipole blockade between the Rydberg atoms has been proposed as a fundamental tool in quantum information processing with neutral atoms. Yet, they require an increasing level of understanding and control. A many-body theory is developed for the Rydberg excitation dynamics in various atomic systems with different densities and velocity distributions such as for atoms in a vapour cell, ultracold atoms in magneto-optical and optical dipole traps, or a system of optical lattices or dipole trap arrays. The systems were investigated by solving the optical Bloch equations numerically for a two-photon ladder excitation scheme, taking into consideration various experimentally relevant conditions for the emergence of the effects of Rydberg-Rydberg interactions. The lineshape properties of the EIT/ATS/CPT spectra are observed and reviewed while the physical arguments for how the lineshape properties change as a function of various parameters are provided. To account for the differing atomic distributions in the atomic systems, a many-body model based on Monte-Carlo simulation is developed to describe the optical response of the multiatoms systems to two-photon excitation laser lights in the regimes of EIT, ATS and CPT and strong atomic interactions. The study of the lineshape properties allows one to understand possible ways to detect the emergence of interaction-induced excitation suppression, asymmetry, line shift and excitation "antiblockade" enhancement effects. Besides these, the main result of this study is the demonstration that the linewidth properties of the Rydberg EIT/ATS/CPT spectra can reveal collective many-body behaviour associated with the creation of many-body entangled states. The linewidth properties provide compelling evidence of the creation of collective states by confirming the predicted dependence of the generalised Rabi frequency on the square root of the number of atoms in the mesoscopic ensemble. This study could help to quantify and control the conditions necessary for creating many-body entanglement within atomic ensembles. The thesis also describes the step towards experimentally investigating the response of an atomic system to excitation lasers and studying the excitation dynamics of interacting atoms in such systems. Significant work was done to set up the two-photon excitation system for preparing atoms in high-lying Rydberg states and performing Rydberg-based vapour cell experiments. Qualitative analysis of the Rydberg states transparency features allows to obtain laser parameters such as the laser linewidths and Rabi frequencies that are used in the theoretical model to create the similarity between the experimental and theoretical parameters. Further works were carried out towards realising the building blocks for experimentally investigating the interactions between Rydberg atoms in ultracold atom systems. This is by setting-up a trapping system capable of producing a highly dense ultracold atom ensemble within a magneto-optical trap, cold enough to serve as a reservoir from which the optical dipole trap can be loaded efficiently. The optical dipole trap is designed and set up to achieve a micron-size trapping potential capable of producing a sub-micron sized atomic cloud, with a controllable number of atoms, where a full blockade effect can be achieved and exploited to implement a qubit system for quantum gate operations.
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 developments in the study of ultracold Rydberg gases demand an advanced level of experimental sophistication, in which high atomic and optical densities must be combined with excellent control of external fields and sensitive Rydberg atom detection. We describe a tailored experimental system used to produce and study Rydberg-interacting atoms excited from dense ultracold atomic gases. The experiment has been optimized for fast duty cycles using a high flux cold atom source and a three beam optical dipole trap. The latter enables tuning of the atomic density and temperature over several orders of magnitude, all the way to the Bose-Einstein condensation transition. An electrode structure surrounding the atoms allows for precise control over electric fields and single-particle sensitive field ionization detection of Rydberg atoms. We review two experiments which highlight the influence of strong Rydberg-Rydberg interactions on different many-body systems. First, the Rydberg blockade effect is used to pre-structure an atomic gas prior to its spontaneous evolution into an ultracold plasma. Second, hybrid states of photons and atoms called dark-state polaritons are studied. By looking at the statistical distribution of Rydberg excited atoms we reveal correlations between dark-state polaritons. These experiments will ultimately provide a deeper understanding of many-body phenomena in strongly-interacting regimes, including the study of strongly-coupled plasmas and interfaces between atoms and light at the quantum level.
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.
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.
This thesis presents several experiments investigating the regimes of behaviour of a proto-typical open quantum many-body system far away from equilibrium. The experimental platform is based on ultracold atoms laser-excited to Rydberg states, which we engineer to emulate a strongly interacting, driven-dissipative quantum spin system. The high degree of control over the relevant microscopic processes and their parameters, as well as the ability to widely tune interaction and driving strengths provides the means to address fundamental questions on how different regimes of dynamical behaviour emerge in complex open quantum systems and how they can be characterised. \n \nIn the first part, we discuss how control over the relevant properties of Rydberg spin systems, like temperature, density, long evolution times, strong interactions, tunable driving, and dissipation can be achieved. We introduce the new experimental apparatus developed during this thesis, which combines both single-photon and two-photon Rydberg excitation schemes with high atom densities and long excitation times using an optical dipole trap. Additionally, we investigate theoretically how long coherence times exceeding motional timescales combined with strong many-body interactions can be achieved in such a system. We identify an optimal parameter regime for two-photon excitation where such conditions can be generated with coherence times and interaction strengths comparable to what is achievable for single-photon excitation. \n \nIn the second part we explore the macroscopic non-equilibrium behaviour of our system and devise suitable observables for characterising different regimes of behaviour. We discover that the slow atom loss inherent to our system provides a convenient observable for the many-body state of the system. Focussing on evolution times where the effect of the atom loss on the evolution is small, we discover that the rate of atom loss exhibits powerlaw scaling with the driving strength over several orders of magnitude. The measured scaling exponents reveal the non-equilibrium phase structure of the many-body system and allow us to distinguish dissipation-dominated, paramagnetic and critical regimes, as well as an instability. In the observed critical regime, collectively enhanced driving dominates over dissipation, leading to scaling associated to the critical point of the non-dissipative equilibrium Rydberg spin system. Based on the known microscopic processes of our system, we perform classical many-body rate equation simulations, which agree well with the observed phase structure as well as the position and associated scaling exponents of the individual regimes. These findings open up new means to study and classify out of equilibrium systems based on slow particle loss and powerlaw scaling. \n \nIn the last part of this thesis we reveal a second type of criticality in our system, which is genuinely non-equilibrium in character and arises from an absorbing state phase transition. The critical state of this phase transition dominates the system evolution at late times where particle loss is no longer negligible. We identify self-organisation as the mechanism driving the system to this critical state, which we observe through powerlaw scaling of the non-equilibrium steady-state. These experiments establish Rydberg atoms as a well controlled platform for implementing and exploring models of absorbing state phase transitions and self-organised criticality with unprecedented access to the underlying microscopic properties of the system.