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IEEE/LEOS Summer Topical Meetings

Many-Body Physics with Spin States of Rydberg Atoms

Svetlana Malinovskaya, Elliot Pachniak

Published Jul 1, 2018• 0 citations
Publisher

Abstract

Rydberg atoms with very high principal quantum numbers trapped in a optical trap are used to study the collective spin properties of ultracold atomic systems. The interaction Hamil-tonian of collective spin states of ultracold Rydberg atoms were explored in diatomic and tri-atomic chains. Quantum control methodology is presented to design many-body spin states using laser pulses and a magnetic field. A two-photon ladder type configuration is implemented, which is advantageous due to the combined action of the one-photon and two-photon detunings as control parameters. Many-body spin states are designed consisting of an ensemble of spins encoded in sublevels of Rydberg states and coupled via the van der Waals interactions [1].

DOI
10.1109/phosst.2018.8456783

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arXiv:1102.2150•Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 2011•6 citations
Rydberg atoms with very high principal quantum numbers trapped in a optical trap are used to study the collective spin properties of ultracold atomic systems. The interaction Hamil-tonian of collective spin states of ultracold Rydberg atoms were explored in diatomic and tri-atomic chains. Quantum control methodology is presented to design many-body spin states using laser pulses and a magnetic field. A two-photon ladder type configuration is implemented, which is advantageous due to the combined action of the one-photon and two-photon detunings as control parameters. Many-body spin states are designed consisting of an ensemble of spins encoded in sublevels of Rydberg states and coupled via the van der Waals interactions [1].
This thesis explores the implementation of a spin-1/2 system to realise quantum simulation of Heisenberg XX and XXZ models. The spins are mapped onto two high-lying atomic levels, so-called Rydberg states, in an ultracold sample of 87Rb and coupled by a microwave field. Efficient synthesis and control of the driving field has been introduced in the setup in order to probe the spin dynamics with NMR sequences. Two- and three-photon excitation schemes are implemented to prepare the Rydberg spins. In order to spatially resolve the Rydberg excitation dynamics, a new imaging technique is employed, which uses the depletion of absorption in presence of Rydberg atoms to detect their distribution in the atomic cloud, revealing the emergence of spatial order of the Rydberg excitations due to strong van der Waals interactions. To benchmark the validity of this platform, the coherence of the spin ensemble is measured by Ramsey techniques in the low-density regime, where the single-spin dynamics accurately describes the observations. Despite the black-body redistribution of Rydberg spins setting a limit for the T2* time of the spin system, the coherence is measured to persist over long timescales on the order of 130 μs. Thus, scaling up the density of spins, first signatures of dipolar many-body effects for |nS⟩ − |nP⟩ (XX) and |nS⟩ − |(n + 1)S⟩ (XXZ) spin combinations have been observed.
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.
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.
The creation of collective many-body quantum states from a two-dimensional lattice gas of atoms is studied. Our approach relies on the van der Waals interaction that is present between alkali metal atoms which are laser excited to high-lying Rydberg s-states. We focus on a regime in which the laser driving is strong compared to the interaction between Rydberg atoms. Here energetically low-lying many-particle states can be calculated approximately from a quadratic Hamiltonian. The potential usefulness of these states as a resource for the creation of deterministic single-photon sources is illustrated. The properties of these photon states are determined from the interplay between the particular geometry of the lattice and the interatomic spacing.