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arXiv:1607.03169 · Physical Review Letters

Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles

Tyler Keating, Charles H. Baldwin, Yuan‐Yu Jau, Jongmin Lee, Grant W. Biedermann, Ivan Deutsch

Published Nov 14, 2016• 27 citations
arXivHTMLPDF

Abstract

We study the production of arbitrary superpositions of Dicke states via optimal control. We show that N atomic hyperfine qubits, interacting symmetrically via the Rydberg blockade, are well described by the Jaynes-Cummings Hamiltonian and fully controllable by phase-modulated microwaves driving Rydberg-dressed states. With currently feasible parameters, it is possible to generate states of ∼ten hyperfine qubits in ∼1 μs, assuming a fast microwave phase switching time. The same control can be achieved with a "dressed-ground control" scheme, which reduces the demands for fast phase switching at the expense of increased total control time.

DOI
10.1103/physrevlett.117.213601

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We study the production of arbitrary superpositions of Dicke states via optimal control. We show that N atomic hyperfine qubits, interacting symmetrically via the Rydberg blockade, are well described by the Jaynes-Cummings Hamiltonian and fully controllable by phase-modulated microwaves driving Rydberg-dressed states. With currently feasible parameters, it is possible to generate states of ∼ten hyperfine qubits in ∼1 μs, assuming a fast microwave phase switching time. The same control can be achieved with a "dressed-ground control" scheme, which reduces the demands for fast phase switching at the expense of increased total control time.
We propose a protocol to realize arbitrary state synthesis and unitary operations on a qudit encoded in the collective dressed states of a Rydberg-blockaded array of three-level atoms. This system is isomorphic to the Jaynes-Cummings model and acts as a multilevel Rydberg superatom whose nonlinear spectrum can be precisely controlled through the parameters of the laser driving the intermediate-to-Rydberg transition. Control of the qudit state is possible through pulse sequences of the laser driving the ground-to-intermediate transition. The dimension of the qudit Hilbert space is scalable by adjusting the number of atoms involved in the Rydberg-blockaded array. We estimate the fidelity of our protocol for realizing arbitrary unitaries and discuss the influence of the finite lifetime of the Rydberg state. Our work paves the way for processing quantum information with Rydberg blockaded arrays of atoms as an alternative to atom qubit arrays.
We explore the feasibility of realizing Dicke states in qubit arrays with always-on isotropic Heisenberg coupling between adjacent qubits, assuming a single Zeeman-type control acting in the zzz direction on an actuator qubit. The Lie-algebraic criteria of controllability imply that such an array is not completely controllable, but satisfies the conditions for subspace controllability on any subspace with a fixed number of excitations. Therefore, a qubit array described by the model under consideration is state-to-state controllable for an arbitrary choice of initial and final states that have the same Hamming weight. This limited controllability is exploited here for the time-efficient dynamical generation of an aaa-excitation Dicke state ∣DaN⟩|D^{N}_{a}\rangle∣DaN​⟩ (a=1,2,…,N−1a=1,2,\ldots, N-1a=1,2,…,N−1) in a linear array with NNN qubits starting from a generic Hamming-weight-aaa product state. To dynamically generate the desired Dicke states -- including WWW states ∣WN⟩|W_{N}\rangle∣WN​⟩ as their special (a=1a=1a=1) case -- in the shortest possible time with a single local ZZZ control, we employ an optimal-control scheme based on the {\em dressed chopped random basis} (dCRAB) algorithm. We optimize the target-state fidelity over the expansion coefficients of smoothly-varying control fields in a truncated random Fourier basis; this is done by combining Nelder-Mead-type local optimizations with the multistart-based clustering algorithm that facilitates searches for global extrema. In this manner, we obtain the optimal control fields for Dicke-state preparation in arrays with up to 999 qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as O(N2.08)\mathcal{O}(N^{2.08})O(N2.08) for WWW states and O(N1.78)\mathcal{O}(N^{1.78})O(N1.78) for a=2a=2a=2 Dicke states.
Because of their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multiqubit Rydberg-blockade gates that involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multiqubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom Greenberger-Horne-Zeilinger state can be created using only three gates with an error of 5.8%.
WWW- and Dicke-state engineering using optimal global control in nearest-neighbor coupled ring-shaped qubit arrays
Motivated by a compelling need for time-efficient and robust schemes for quantum-state engineering in systems of neutral atoms in optical tweezers, we consider a ring-shaped array of qubits with nearest-neighbor Ising-type (zzzzzz) coupling and transverse (xxx and yyy) global control fields. This system to a large extent mimics -- outside of the Rydberg-blockade regime -- a circular array of neutral atoms interacting through van-der-Waals type interaction. We investigate the preparation of WWW and Dicke states in this system starting from the default initial state ∣00…0⟩|00\ldots 0\rangle∣00…0⟩ using two different optimal-control approaches: (i) NMR-like pulse sequence, which consists of instantaneous (delta-shaped) control- and Ising-interaction pulses, and (ii) time-dependent control scheme, which entails shaped control pulses in the presence of always-on Ising interaction between adjacent qubits. By making use of the underlying dihedral symmetry of this system -- which allows one to use a symmetry-adapted computational basis with O(2N/N)\mathcal{O}(2^N / N)O(2N/N) states in an NNN-qubit system -- and utilizing advanced global-optimization methods, we find optimal sequences of pulses for realizing WWW and Dicke states within both approaches. In addition, we demonstrate robustness of these sequences against unavoidable control errors. Finally, using typical values of parameters in realistic Rydberg-atom systems, we show that our control schemes enable the preparation of the desired multiqubit states on time scales much shorter than the relevant coherence times of those systems.
The ability to engineer and control quantum states of many-body systems is a central challenge in quantum information science. For a register of NNN qubits, the full Hilbert space dimension grows exponentially as 2N2^N2N, rendering generic state preparation and control infeasible without exploiting structure or symmetry. A particularly important and physically motivated restriction is to the fully symmetric subspace, spanned by the Dicke states, which are simultaneous eigenstates of collective spin J=N/2J=N/2J=N/2. Ensembles of Rydberg atoms interacting via electric dipoles in two-dimensional tweezer arrays form a promising platform for achieving such control. However, the finite range of dipole-dipole interactions poses a challenge to generating and controlling the Dicke manifold because the Hamiltonian incurs leakage from the computational subspace. To counteract this leakage, we perform quantum optimal control algorithms on a truncated Hilbert space according to our newly developed method of ``irrep distillation'' (IRD), which captures the process by which the symmetric subspace couples to leakage error-spaces, using only linear-scaling Hilbert dimension. We implement gradient ascent pulse engineering (GrAPE) on control schemes with little or no local addressing, to generate resourceful states like Greenberger-Horne-Zeilinger, Dicke, and extremal quantum states. We benchmark each scheme of IRD-GrAPE for its quantum speed limit (QSL), as well as exactly testing pulse fidelities on small system sizes and predicting fidelities using higher-order IRD on larger systems.
We demonstrate a Rydberg-dressed ground-state blockade that provides a strong tunable interaction energy (~1 MHz), nearly 4 orders of magnitude larger than that in ultra cold collisions, between spins of individually trapped cesium atoms.With this interaction we directly produce Bell-state entanglement between two atoms with a fidelity ≥ 81(2)%, excluding atom loss events, and ≥ 60(3)% when loss is included [1].Our method is based on a Rydberg-dressed spin-flip blockade which allows single-step, direct entanglement of long-lived ground (clock) states.For the Bell-state entanglement generation, the probability remains entirely in the Rydbergdressed ground state, freeing the approach from the experimental burden of coherently exciting optical transitions to and from the Rydberg states.In principle Rydberg-dressed atoms are more insensitive to various decoherence mechanisms and lead to a better quantum control fidelity [2].In addition, we observed Jaynes-Cummings (JC) ladder and its nonlinearity of a Rydbergdressed atomic system.This nonlinearity induced by the Rydberg-dressed spin-flip blockade and the symmetric coupling between a Rydberg atom and atomic ensembles in the ground state, and this differentiates single and two microwave photon excitations from Rydberg-dressed state atoms.