We propose the use of Rydberg interactions and ensembles of cold atoms in mixed state for the implementation of a protocol for deterministic quantum computation with one quantum bit that can be readily operated in high dimensional Hilbert spaces. We propose an experimental test for the scalability of the protocol and to study the physics of discord. Furthermore, we explore the possibility of extending to non-trivial unitaries, such as those associated to many-body physics. Finally develop a scheme to add control to cold atom unitaries in order to facilitate their implementation in our proposal.
We propose the use of Rydberg interactions and ensembles of cold atoms in mixed state for the implementation of a protocol for deterministic quantum computation with one quantum bit that can be readily operated in high dimensional Hilbert spaces. We propose an experimental test for the scalability of the protocol and to study the physics of discord. Furthermore, we explore the possibility of extending to non-trivial unitaries, such as those associated to many-body physics. Finally develop a scheme to add control to cold atom unitaries in order to facilitate their implementation in our proposal.
In this thesis, I describe a proposal for experiments with dense ensembles of ultracold Rubidium atoms optically excited to highlying electronic states known as Rydberg states. The proposed experiment is designed to implement a model of quantum computation known as deterministic quantum computation with one qubit (DQC1). My proposal is novel among other proposals for Rydberg atoms because it employs mixed states and could provide insights into the source of the enhancements of quantum technology over classical technology. I demonstrate that ultracold atoms and Rydberg interactions offer new perspectives for exploring the DQC1 model. This is mainly due to the large strength, long range and controllability of Rydberg interactions. My specific contributions include: a proposal that solves one of the main issues with implementing quantum logic gates between ensembles of atoms; numerical simulations of the proposed cold atom implementation of a DQC1 protocol; and the design and laboratory implementation of a high-performance optical system for imaging ultracold atoms. These contributions bring the experimental exploration of the DQC1 model closer to realisation.
In this work we report on the development progress of a cold atoms platform to demonstrate a model of quantum computation known as deterministic Quantum computing with One Clean Qubit (DQC1). This is a novel class of algorithms where interactions between qubits enable nonclassical correlations other than entanglement, namely discord. We aim to demonstrate the DQC1 protocol using a scheme in which the information processing is realized on cold neutral rubidium atoms through the cNOT gate based on a Rydberg blockade. The implementation of this protocol imposes very stringent requirements on the cloud of atoms: to realise the cNOT gate with high fidelity it is required that a full Rydberg blockade is operating throughout the extent of the ensemble. This means that a cloud of atoms needs to have a radius below approximately 5 μm (for Rydberg states of atoms n = 43). A dipole trap system was designed and implemented during the course of this PhD with the aim of satisfying these experimental constraints. In our setup, a vapour of 87Rb is first trapped in a Magneto-Optical Trap (MOT) and cooled to sub-Doppler temperatures. The atoms are then subsequently trapped in the dipole trap. Our dipole trapping setup is based on a high numerical aperture lens (NA=0.53) to achieve a sub-micron trapping potential and simultaneously observe trapped atoms with a micrometre resolution. According to the design and the optical tests, the system is capable of creating the trapping potential with about 1 μm waist and 4 μm Rayleigh length. The aim of this work was to examine and optimise experimental conditions under which the dipole trap should be operated, so that the sufficiently small trap for the DQC1 algorithm can be obtained in the future. For characterisation, a trap of a bigger volume (about 6 μm waist and 28 μm length) was setup instead of using the full capacity of the system. This enhanced the atom loading procedure and provided more convenient conditions for experiments. The temperature of atoms was typically around 250 μK, and the trap lifetime (2.5 s) was limited by the background collisions, which indicates that the vacuum was maintained on the expected level. The key findings of the thesis are that the properties of the atoms reservoir (MOT temperature and density), and the loading processes (intensity of MOT beams), need to be optimised to be able to load a micrometre size trap. These findings are instrumental for the future implementation of the DQC1 protocol and also have implications for other protocols founded on the use of a Rydberg blockade.
The advances in laser cooling and trapping techniques allow samples of ultra-cold atoms to be created and controlled for the study of quantum physics. In this thesis, we focus on using ensembles of cold atoms to investigate novel quantum effects and their applications in quantum optics. Realization of a scalable intercontinental quantum system, e.g. a global quantum internet, relies on quantum memories with long lifetimes on the order of seconds. We have reduced the differential light shifts of the atomic ground states to a sub-Hz level and achieved a lifetime of 16 seconds. Achieving fast and efficient quantum operations, on the other hand, requires strongly-interacting systems. We explore highly excited Rydberg atoms towards this goal and demonstrate Rydberg excitation blockade, many-body Rabi oscillations, trapping of Rydberg atoms, deterministic single photon source, and atom-photon entanglement. Finally, we integrate the two essential capabilities for quantum information processing, fast quantum state generation and long-term storage, by simultaneously exploiting Rydberg levels for interactions and ground atomic levels for the storage of quantum state. Our work advances the control of coherence properties and interactions in cold atomic ensembles to a new level and opens new opportunities for studies of complex quantum systems.
In any physical platform, two ingredients are essential for quantum information processing: single-qubit control, and entangling interactions between qubits. Neutral atoms can be individually controlled with high fidelity and are resilient to environmental noise, making them attractive candidates for implementing quantum information protocols. However, achieving strong interactions remains a major obstacle. One way to increase the interaction strength between neutral atoms is to excite them into high-lying Rydberg states, which exhibit large electric dipole moments (and by extension, strong electric dipole-dipole interactions). By slowly ramping up the Rydberg level coupling in a system, one can "dress'' the atomic ground states with some Rydberg character; this maps the Rydberg dipole interaction to an effective interaction between ground states. Such Rydberg-dressed interaction is the focus of this dissertation. After describing the physics of the Rydberg-dressed interaction, we propose three protocols that demonstrate its versatility and provide a framework for considering some of the details of realistic implementation. In all three cases, Rydberg dressing --- along with some form of single-atom control --- is used to generate highly entangled states of interest. Our first proposal relates to the adiabatic model of quantum computing, in which solutions to problems are encoded in the ground states of carefully engineered Hamiltonians. The Rydberg-dressed interaction can provide nonlinear Hamiltonian terms, allowing us to encode NP-hard and other interesting problems. We model this protocol in the presence of decoherence, and find that computational fidelities of ~0.98 for four atoms should be possible with currently realistic experimental parameters. Our second proposal is also related to quantum computing, this time in the circuit model. The Rydberg-dressed interaction can be used to generate a controlled-NOT logic gate which, when interwoven with single-qubit gates, can perform universal quantum computation. Experimentally, noise due to atomic thermal motion has been a primary limitation on the fidelities of these gates. We show that a Doppler-free setup, with counterpropagating lasers, effectively suppresses this type of noise, allowing simulated fidelities of up to ~0.998 per gate. Such strong suppression is only possible because the Doppler-free configuration can harness the natural robustness of adiabatic dressing; other gate schemes using, e.g., resonant pulses, do not exhibit the same degree of improvement. Finally, we consider exploiting the many-body character of the Rydberg-dressed interaction to generate collective entanglement in mesoscopic ensembles of neutral atoms. An atomic ensemble uniformly illuminated by a single Rydberg-exciting laser is isomorphic to the well-known Jaynes-Cummings model. In addition to adapting generic Jaynes-Cummings entanglement protocols developed in other platforms, one can apply microwaves to drive entanglement in a way that is unique to the atomic platform. We prove that by allowing the microwave phase to vary in time, one can generate arbitrary symmetric states of the ensemble. While this method compares favorably with other entanglement protocols in many ways, the required frequency of phase switching presents a fundamental limitation on its effectiveness. To mitigate this, we propose a variant scheme in which parameters are chosen to only allow excitations within the system's dressed-ground subspace; this effectively cuts phase switching demands in half. All three protocols serve to illustrate the power of the Rydberg-dressed interaction and suggest directions for future study.
We propose a simple interaction protocol to be implemented on a scalable quantum network, in which the quantum nodes consist of qubit systems confined in cavities. The nodes are deterministically coupled by transmission and reflection of a single photon, which is disentangled from the qubits at the end of the coupling operation. This single photon can generate an entangling controlled-phase gate between any selected number of qubits in the network. Our multiqubit gate reaches a much higher fidelity compared to schemes concatenating one-qubit and two-qubit gates; thus it forms an efficient basis for universal quantum computing distributed over multiple processor units. In our analysis we consider atomic qubits coupled to optical photons, while the scheme can be readily generalized to other architectures, such as superconducting qubit nodes coupled by microwave photons.
Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.