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Preparation and Coherent Control of a Rydberg Qutrit in an Ultra-Cold Atomic Ensemble

HUGHES, OLIVER,DAVID,WRONSKI

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

This thesis presents the preparation, coherent control and interferometric readout of a single qutrit encoded in a cold Rydberg ensemble. A single photon is stored as a collective Rydberg excitation and subsequently manipulated by applying microwave fields coupling different Rydberg levels, before being retrieved after a programmable delay. A time-resolved sequential readout protocol is developed to determine the qutrit state populations. Coherence of the qutrit is investigated using a Ramsey interferometer implemented between Rydberg states, with the resulting fringe pattern demonstrating phase control and multilevel coherence. Following a vacuum failure, the system was fully dismantled, cleaned and reassembled with a new 2D MOT cell. A programme of optimisation and characterisation was carried out using time-of-flight thermometry, spatially resolved absorption imaging and temperature based magnetic field compensation. Sub-Doppler cooling yields a minimum ensemble temperature of $T = 12.8 \pm 0.5~\mathrm {\mu K}$, and the highest measured optical depth is $\mathrm {OD} = 4.3 \pm 0.1$. This work establishes a robust and flexible platform for investigating high-dimensional quantum information protocols using collective Rydberg states and demonstrates the feasibility of fast, coherent control of single qutrits encoded in an atomic ensemble.

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This thesis presents the preparation, coherent control and interferometric readout of a single qutrit encoded in a cold Rydberg ensemble. A single photon is stored as a collective Rydberg excitation and subsequently manipulated by applying microwave fields coupling different Rydberg levels, before being retrieved after a programmable delay. A time-resolved sequential readout protocol is developed to determine the qutrit state populations. Coherence of the qutrit is investigated using a Ramsey interferometer implemented between Rydberg states, with the resulting fringe pattern demonstrating phase control and multilevel coherence. Following a vacuum failure, the system was fully dismantled, cleaned and reassembled with a new 2D MOT cell. A programme of optimisation and characterisation was carried out using time-of-flight thermometry, spatially resolved absorption imaging and temperature based magnetic field compensation. Sub-Doppler cooling yields a minimum ensemble temperature of T=12.8±0.5 μKT = 12.8 \pm 0.5~\mathrm {\mu K}T=12.8±0.5 μK, and the highest measured optical depth is OD=4.3±0.1\mathrm {OD} = 4.3 \pm 0.1OD=4.3±0.1. This work establishes a robust and flexible platform for investigating high-dimensional quantum information protocols using collective Rydberg states and demonstrates the feasibility of fast, coherent control of single qutrits encoded in an atomic ensemble.
Qutrit with highly efficient algorithms and security is imperative in quantum information processing. Here, we demonstrate for the first time the coherent creation, control, and readout of a single photonic qutrit in a cold Rydberg ensemble. In each measurement, an optical photon is stored as a Rydberg polariton through electromagnetically induced transparency. Employing two microwave fields, the polariton is driven into an arbitrary superposition of three collective states, each encoded in a Rydberg state. The collective state is mapped into a photonic time-bin qutrit with the microwave field and read out sequentially. The complete sequence, including preparation, control, and readout, is less than 1.8 µ s , which mitigates decoherence significantly. We measure the coherence of the qutrit with nondestructive Ramsey interferometry, which is preferable for quantum information processing, and find good quantitative agreement with the theoretical model. The ability to write, process, and read out the single photonic qutrit on microsecond timescales with microwave-coupled Rydberg states demonstrates the coherent connectivity among the high Hilbert space of the qutrit. Our study is an important step in exploring qutrit-based quantum information processes and quantum simulation of topological physics with microwave-coupled Rydberg atom ensembles.
This thesis proposes a means of implementing quantum information processing using photonic qubits as information carriers. Electromagnetically-induced transparency (\textsmaller{EIT}) is used to store information encoded in photons into Rydberg excitations in a cloud of cold atoms, where strong dipole-dipole interactions induce interactions between qubits. After a storage time, information is mapped back into photons collectively emitted from the cloud again via \textsmaller{EIT}. A new experimental apparatus is built to implement non-linear Rydberg quantum optics. A high repetition rate is achieved owing to a \textsmaller{2D-MOT} atom source, and high optical resolution for trapping and probing microscopic atomic ensembles is achieved by the use of aspheric lenses inside the vacuum chamber. A new, high resolution computer control scheme is implemented. This thesis demonstrates that, during the holding time, multiple collective Rydberg excitations at a controlled separation interact with each other to imprint a non-uniform phase gradient resulting in anti-correlation of photon emission. Interactions are observed at up to 151515 times the wavelength of the photonic qubits. These long range interactions offer a promising approach to scaling all-optical quantum computing. Applying resonant microwave fields during the storage time is demonstrated to offer a competitive method of performing sensitive microwave electrometry. A sensitivity of $12 \pm 7 \uV \percm \perRHz$ is found at a frequency of $7.7\GHz$. The high sensitivity is shown to arise from remnant, Rydberg excitations providing an additional source of atom loss from the atomic ensemble, leading to a suppression of photon storage and retrieval efficiency. An additional stage of microwave driving to sanitise the atomic ensemble for recycling is shown to successfully suppress the atom-loss mechanism. The use of successive microwave pulses is shown to provide a feasible approach to interfacing microwave and optical quantum information processing systems. Information encoded as the presence or absence of a microwave field is translated into information encoded as early or late retrieval of single photons, demonstrating proof of principle for an approach to implementing a proposal for an all-optical controlled-zzz gate. Externally driven microwave fields are used to provide rapid, low-loss modulation of the signal retrieved from an atomic ensemble, demonstrating the proof of principle of implementing a probabilistic single photon source that can intensity modulate with low-loss at frequencies of at least $27\MHz$, with evidence that modulation may be achievable at rates in excess of $500\MHz$.
We demonstrate a collectively encoded qubit based on a single Rydberg excitation stored in an ensemble of N entangled atoms. Qubit rotations are performed by applying microwave fields that drive excitations between Rydberg states. Coherent readout is performed by mapping the excitation into a single photon. Ramsey interferometry is used to probe the coherence of the qubit, as well as to test the robustness to external perturbations. We show that qubit coherence is preserved even as we lose atoms from the polariton mode, preserving Ramsey fringe visibility. We show that dephasing due to electric field noise scales as the fourth power of field amplitude. These results show that robust quantum information processing can be achieved via collective encoding using Rydberg polaritons, and hence this system could provide an attractive alternative coding strategy for quantum computation and networking.
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.
Advances in the coherent control of Rydberg atoms have led to an explosion in their use in a wide range of topics, including quantum computation, simulation, sensing, and networking. More specifically, Rydberg-coupled ensembles of atoms interfaced with a single mode of light have enabled studies of fundamental light-matter interactions at the single-photon level and have emerged as a promising platform to realize scalable quantum networking nodes. In the first part of this thesis, we utilize Rydberg blockade to generate large ensembles that host a single Rydberg excitation and use the collective state as a resource to efficiently generate single photons. We further investigate the shelving of the collective Rydberg excitations to the ground-state manifold, where we observe an order of magnitude increase in the coherence time of the excitation. In the latter half of the thesis, we use near-resonant microwave fields to generate microwave-dressed Rydberg states, where we utilize the degrees of freedom of the microwave field to tune the strength, form, and angular dependence of the dipole-dipole interactions. To this end, we develop a robust and highly tunable microwave polarization control system. We use a set of in-vacuum electrodes as microwave antennas. We measure the microwave polarizations produced by each source at the positions of the atoms using a Rydberg EIT-based polarimetry technique. By characterizing the three imperfect sources, we find the control settings necessary to produce \sigma_-, \pi, and \sigma_+ polarized microwaves with >99 % fidelity. We extend our purification techniques to frequencies away from Rydberg resonances by utilizing an auxiliary microwave field, generating two-photon microwave resonances. The high-fidelity microwave polarizations are used to resonantly admix opposite-parity Rydberg states, generating dressed states with dipole-dipole interactions that are longer range and stronger than the bare van der Waals interactions. To characterize the strength of the interactions, we measure the photon-number statistics of the light generated by the ensemble of atoms. By varying the cloud length relative to the blockade radii, we demonstrate a clear enhancement of the interaction strength due to microwave dressing. Our platform enables further engineering of interactions by exploiting the polarization and frequency degrees of freedom of the microwave fields, opening pathways for new quantum control strategies in many different experimental platforms.
We demonstrate a new approach for fast preparation, manipulation, and collective readout of an atomic Rydberg-state qubit. By making use of Rydberg blockade inside a small atomic ensemble, we prepare a single qubit within $3\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$ with a success probability of ${F}_{p}=0.93\ifmmode\pm\else\textpm\fi{}0.02$, rotate it, and read out its state in $6\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$ with a single-shot fidelity of ${F}_{d}=0.92\ifmmode\pm\else\textpm\fi{}0.04$. The ensemble-assisted detection is 103{10}^{3}103 times faster than imaging of a single atom with the same optical resolution, and enables fast repeated nondestructive measurement. We observe qubit coherence times of $15\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$, much longer than the $\ensuremath{\pi}$ rotation time of 90 ns. Potential applications ranging from faster quantum information processing in atom arrays to efficient implementation of quantum error correction are discussed.