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arXiv:2101.11232 · Physical Review A

Scalable W -type entanglement resource in neutral-atom arrays with Rydberg-dressed resonant dipole-dipole interaction

Vladimir M. Stojanović

Published Feb 9, 2021• 26 citations
arXivHTMLPDF

Abstract

While the Rydberg-blockade regime provides the natural setting for creating $W$-type entanglement with cold neutral atoms, it is demonstrated here that a scalable entanglement resource of this type can even be obtained under completely different physical circumstances. To be more precise, a special instance of twisted $W$ states---namely, $\ensuremath{\pi}$-twisted ones---can be engineered in one-dimensional arrays of cold neutral atoms with Rydberg-dressed resonant dipole-dipole interaction. In particular, it is shown here that this is possible even when a (dressed) Rydberg excitation is coupled to the motional degrees of freedom of atoms in their respective, nearly harmonic optical-dipole microtraps, which are quantized into dispersionless (zero-dimensional) bosons. For a specially chosen (``sweet-spot'') detuning of the off-resonant dressing lasers from the relevant internal atomic transitions, the desired $\ensuremath{\pi}$-twisted $W$ state of Rydberg-dressed qubits is the ground state of the effective excitation---boson Hamiltonian of the system in a broad window of the relevant parameters. Being at the same time separated from the other eigenstates by a gap equal to the single-boson energy, this $W$ state can be prepared using a Rabi-type driving protocol. The corresponding preparation times are independent of the system size and several orders of magnitude shorter than the effective lifetimes of the relevant atomic states.

DOI
10.1103/physreva.103.022410

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While the Rydberg-blockade regime provides the natural setting for creating WWW-type entanglement with cold neutral atoms, it is demonstrated here that a scalable entanglement resource of this type can even be obtained under completely different physical circumstances. To be more precise, a special instance of twisted WWW states---namely, \ensuremathπ\ensuremath{\pi}\ensuremathπ-twisted ones---can be engineered in one-dimensional arrays of cold neutral atoms with Rydberg-dressed resonant dipole-dipole interaction. In particular, it is shown here that this is possible even when a (dressed) Rydberg excitation is coupled to the motional degrees of freedom of atoms in their respective, nearly harmonic optical-dipole microtraps, which are quantized into dispersionless (zero-dimensional) bosons. For a specially chosen (``sweet-spot'') detuning of the off-resonant dressing lasers from the relevant internal atomic transitions, the desired \ensuremathπ\ensuremath{\pi}\ensuremathπ-twisted WWW state of Rydberg-dressed qubits is the ground state of the effective excitation---boson Hamiltonian of the system in a broad window of the relevant parameters. Being at the same time separated from the other eigenstates by a gap equal to the single-boson energy, this WWW state can be prepared using a Rabi-type driving protocol. The corresponding preparation times are independent of the system size and several orders of magnitude shorter than the effective lifetimes of the relevant atomic states.
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.
Motivated by the significantly improved scalability of optically trapped neutral-atom systems, extensive efforts have been devoted in recent years to quantum-state engineering in Rydberg-atom ensembles. Here we investigate the problem of engineering generalized (``twisted'') WWW states, as well as Greenberger-Horne-Zeilinger (GHZ) states, in the strongly interacting regime of a neutral-atom system. We assume that each atom in the envisioned system initially resides in its ground state and is subject to several external laser pulses that are close to being resonant with the same internal atomic transition. In particular, in the special case of a three-atom system (Rydberg-atom trimer) we determine configurations of field alignments and atomic positions that enable the realization of chiral WWW states---a special type of twisted three-qubit WWW states of interest for implementing noiseless-subsystem qubit encoding. Using chiral WWW states as an example we also address the problem of deterministically converting twisted WWW states into their GHZ counterparts in the same three-atom system, thus significantly generalizing recent works that involve only ordinary WWW states. We show that starting from twisted---rather than ordinary---WWW states is equivalent to renormalizing downward the relevant Rabi frequencies. While this leads to somewhat longer state-conversion times, we also demonstrate that those times are at least two orders of magnitude shorter than typical lifetimes of relevant Rydberg states.
We examine interactions between atoms continuously and coherently driven between the ground state and a Rydberg state, producing ``Rydberg-dressed atoms.'' Because of the large dipolar coupling between two Rydberg atoms, a small admixture of Rydberg character into a ground state can produce an atom with a dipole moment of a few debye, the appropriate size to observe interesting dipolar physics effects in cold atom systems. We have calculated the interaction energies for atoms that interact via the dipole-dipole interaction and find that because of blockade effects, the RRR dependent two-atom interaction terms are limited in size and can be RRR independent up until the dipolar energy is equal to the detuning. This produces RRR dependent interactions different from the expected 1/R31/{R}^{3}1/R3 dipolar form that have no direct analogy in condensed-matter physics and could lead to interesting quantum phases in trapped Rydberg systems.
Quantum Information Processing with Rydberg-Dressed Atoms• Ground state neutral atoms allow for precise and robust single-qubit control.(Check out Univeristy of Arizona's posters 38 and 41 for specific examples!)• Interactions between ground state neutrals are very weak, making it hard to create 2-qubit interactions.• By dressing ground state neutrals with Rydberg (large-n) states, we can access dipole-dipole interactions that are orders of magnitude stronger.• Specifically, we use weak, off-resonant coupling to the Rydberg state to mediate a strong two-qubit interaction via the Rydberg blockade.
We study the generation of metrologically useful entanglement in a three-level (spin-1) system naturally realized in arrays of dipole-interacting Rydberg atoms confined in optical tweezers. In the spin-quadrupolar operator basis, the interaction Hamiltonian decomposes into effective SU(2) subspaces, within which quench dynamics from product initial states generate scalable spin-nematic squeezing. For symmetric interactions, we identify a mapping to effective one-axis twisting within bright and dark manifolds and demonstrate that the squeezing parameter scales as ξ2∝N−2/3ξ^{2}\propto N^{-2/3}ξ2∝N−2/3 (ξ2∝N−0.5ξ^{2}\propto N^{-0.5}ξ2∝N−0.5) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches FQ∝N2F_Q\propto N^{2}FQ​∝N2. For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing ξ2∝N−0.7ξ^{2}\propto N^{-0.7}ξ2∝N−0.7 for all-to-all interactions and moderate squeezing for dipolar interactions in 2D. Our results constitute a first theoretical step beyond the well-studied qubit setting toward scalable entanglement generation in qudit systems with dipolar interactions, directly relevant to current Rydberg tweezer experiments.
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.