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arXiv:0811.1155 · Physical Review Letters

Mesoscopic Rydberg Gate Based on Electromagnetically Induced Transparency

Markus Müller, Igor Lesanovsky, Hendrik Weimer, Hans Peter Büchler, P. Zoller

Published Apr 28, 2009• 293 citations
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Abstract

We demonstrate theoretically a parallelized C-NOT gate which allows us to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering electromagnetically induced transparency. By this we can robustly implement a conditional transfer of all ensemble atoms between two logical states, depending on the state of the control atom. We outline a many-body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.

DOI
10.1103/physrevlett.102.170502

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We demonstrate theoretically a parallelized C-NOT gate which allows us to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering electromagnetically induced transparency. By this we can robustly implement a conditional transfer of all ensemble atoms between two logical states, depending on the state of the control atom. We outline a many-body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.
We propose a scheme to achieve a parallelized controlled-NOT (c-not) gate based on electromagnetically induced transparency (EIT) and cavity-assisted photon scattering. By using the flying photon as the control bit, we can implement a conditional transfer between two logical states of an atom trapped in the cavity with high fidelity and on a microsecond time scale. Thanks to the fact that the photon is well suited for scalable quantum computation, a quantum c-not gate between the single-photon pulses and the nonlocal gate on remote atoms are obtained by reflecting the photon pulse from an optical cavity with a single-trapped atom. Our protocol is robust for spontaneous emission and works quite well in the bad-cavity limit, which makes it more applicable in the laboratory with current experimental techniques.
Neutral atoms provide an excellent resource for quantum information processing, combining the long atomic coherence times of the hyperfine ground-state with strong dipole-dipole interactions of highly excited Rydberg states for generating deterministic entanglement between qubits separated by < 10 µm [1]. Scalable long-range interactions can be obtained by coupling the atomic array to a superconducting microwave cavity enabling hybrid quantum information processing where the cavity-mediated entanglement allows atoms to be coupled over cm length scales. We present the first steps towards such an experiment incorporating high fidelity readout using an sCMOS camera [2] and the ability to drive fast, optically addressable rotations of the hyperfine-encoded qubits to the Rydberg state. Using our sub-kHz cavitystabilised laser system [3] we demonstrate coherent control of single Rydberg atoms, performing Ramsey spectroscopy to determine coherence time and to generate entanglement between a pair of atoms separated by 6 µm. Combining this excitation scheme with our ground-state Raman lasers we show progress towards the implementation of a mesoscopic Rydberg gate based on electromagnetically induced transparency (EIT) offering robust entanglement of multi-atom ensembles [4].
We demonstrate a native CNOT gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit CNOT^{k} gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of F_{CNOT}^{cor}=0.82(6), and prepare an entangled Bell state with F_{Bell}^{cor}=0.66(5), limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.
The interaction between Rydberg states of neutral atoms is strong and long-range, making it appealing to put it to use in the context of quantum technologies. Recently, first applications of this idea have been reported in the fields of quantum computation1 and quantum simulation2–4. Furthermore, electromagnetically induced transparency allows one to map these Rydberg interactions to light5–15. Here we exploit this mapping and the resulting interaction between photons to realize a photon–photon quantum gate16,17, demonstrating the potential of Rydberg systems as a platform also for quantum communication and quantum networking18. We measure a controlled-NOT truth table with a fidelity of 70(8)% and an entangling-gate fidelity of 63.7(4.5)%, both post-selected upon detection of a control and a target photon. The level of control reached here is an encouraging step towards exploring novel many-body states of photons or for future applications in quantum communication and quantum networking18. Strong and long-range interactions between Rydberg states of neutral atoms can be mapped to light via electromagnetically induced transparency, realizing a photon–photon quantum gate for quantum communications and networking.
Rydberg atoms based mesoscopic CNOTN\text{CNOT}^{\text{N}}CNOTN gate using STIRAP
Schemes for implementation of CNOT gates in atomic ensembles are important for realization of quantum computing. Here, a theoretical scheme for a CNOTN\text{CNOT}^{\text{N}}CNOTN gate implemented on a target ensemble of N, Λ\LambdaΛ three-level Rydberg atoms and a single Rydberg atom as a control using Stimulated Raman Adiabatic Passage (STIRAP) is presented. We work in the Rydberg blockade regime for the ensemble atoms induced due to excitation of the control atom to a high lying Rydberg level. It is shown that using STIRAP, atoms from one ground state of the ensemble can be adiabatically transferred to the other ground state, depending on the state of the control atom, with high fidelity. A thorough analysis of adiabatic conditions for this scheme and the influence of radiative decay from the excited Rydberg levels is provided. We show that the CNOTN\text{CNOT}^{\text{N}}CNOTN process is immune to the decay rate of the excited level in ensemble atoms.
We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single-qubit and two-qubit quantum gates can achieve high fidelities around or above 99.999.9%99.9 in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.9899.98%99.98 for single ensemble qubit gate and 99.9499.94%99.94 for two-qubit gate even when the Rabi frequency of the gate laser acquires 1010%10 fluctuations. We also find that the optimized scheme can also reduce errors caused by higher order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows another route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.