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arXiv:1601.07282 · Journal of Physics B Atomic Molecular and Optical Physics

Simulated quantum process tomography of quantum gates with Rydberg superatoms

Ilya I. Beterov, M Saffman, E A Yakshina, D B Tretyakov, V M Entin, G N Hamzina, I. I. Ryabtsev

Published May 16, 2016• 27 citations
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Abstract

Abstract We have numerically simulated quantum tomography of single-qubit and two-qubit quantum gates with qubits represented by mesoscopic ensembles containing random numbers of atoms. Such ensembles of strongly interacting atoms in the regime of Rydberg blockade are known as Rydberg superatoms. The stimulated Raman adiabatic passage (STIRAP) in the regime of Rydberg blockade is used for determining Rydberg excitation in the ensemble, required for the storage of quantum information in the collective state of the atomic ensemble and implementation of two-qubit gates. The optimized shapes of the STIRAP pulses are used to achieve high fidelity of the population transfer. Our simulations confirm the validity and high fidelity of single-qubit and two-qubit gates with Rydberg superatoms.

DOI
10.1088/0953-4075/49/11/114007

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Abstract We have numerically simulated quantum tomography of single-qubit and two-qubit quantum gates with qubits represented by mesoscopic ensembles containing random numbers of atoms. Such ensembles of strongly interacting atoms in the regime of Rydberg blockade are known as Rydberg superatoms. The stimulated Raman adiabatic passage (STIRAP) in the regime of Rydberg blockade is used for determining Rydberg excitation in the ensemble, required for the storage of quantum information in the collective state of the atomic ensemble and implementation of two-qubit gates. The optimized shapes of the STIRAP pulses are used to achieve high fidelity of the population transfer. Our simulations confirm the validity and high fidelity of single-qubit and two-qubit gates with Rydberg superatoms.
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 have studied the regimes of deterministic single-atom Rydberg excitation in the conditions of Rydberg blockade and the methods of compensation for the dynamic phase of the wave function during the adiabatic passage. Using these methods, we have proposed schemes of single-qubit and two-qubit quantum states with mesoscopic atomic ensembles containing a random number of atoms, considred as quibits. The double adiabatic passage of the Förster resonance for two interacting atoms with a deterministic phase shift can be used for the implementation of two-qubit gates with reduced sensitivity of the gate fidelity to the fluctuations of the interatomic distance.
Abstract We review methods for coherently controlling Rydberg quantum states of atomic ensembles using adiabatic rapid passage and stimulated Raman adiabatic passage. These methods are commonly used for population inversion in simple two-level and three-level systems. We show that adiabatic techniques allow us to control population and phase dynamics of complex entangled states of mesoscopic atomic ensembles for quantum information processing with Rydberg atoms. We also propose several schemes of single-qubit and two-qubit gates based on adiabatic passage, Rydberg blockade and Förster resonances in Rydberg atoms.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes, which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.
Ensembles of atoms interacting via their Rydberg levels, known as "superatoms" for their ability to encode qubits and to emit single photons, attract increasing attention as building blocks for quantum network nodes. Assessing their performance requires an accurate, physically informative and numerically scalable description of interactions in a large and disordered ensemble. We derive such a description from first principles and successfully test it against brute-force numerics and experimental data. This model proves essential to make quantitative predictions about gate fidelities or photon emission efficiencies, and to guide experiments towards large-scale superatom-based systems.
Owing to the unique physical characteristics of Rydberg atoms, which play an important role in quantum information and quantum computation, the theoretical and applied research of Rydberg atoms have become the hot spots of scientific research in recent years. With the large polarizability of Rydberg atoms, even a small electric field could cause a considerable electric dipole moment, resulting in a strong dipole-dipole interaction between Rydberg atoms. The multiple excitations of the Rydberg states are strongly inhibited because of the strong dipole interaction between atoms within a mesoscopic interaction (blockade) region. We call this phenomenon the dipole blockade effect. The dipole blockade effect makes it possible to build single-photon quantum devices, implement quantum gates, generate quantum entanglement, and simulate many-body quantum problems, etc. A Rydberg atomic ensemble in the same blockade region can be regarded as a superatom. In the same way, if these atoms trapped in two optical dipole traps, each sub-ensemble can be considered as a sub-superatom which is closely related to the superatom. According to the fact that two Rydberg sub-superatoms can be strongly correlated due to sharing no more than one excited Rydberg atom, we study correlated collective excitation and quantum entanglement between two Rydberg sub-superatoms in a steady state. With the superatom model, the problem of exponentially increasing system size with the number of atoms can be circumvented to a certain extent in studying many-body physics. By solving the two-body Lindblad’s master equation accurately, we obtain the analytical expressions for the collective excitation probabilities of the two sub-superatoms, and the concurrence measuring the bipartite entanglement between them. Our results show that they are all sensitive to the number of atoms in each Rydberg superatom: the bigger (including more atoms) the Rydberg superatom, the higher the collective Rydberg excitation probability is. And that the maximally entangled state can only be obtained with two equal-sized Rydberg superatoms. When this condition is fulfilled, the mesoscopic entanglement can be generated by adding the number of atoms in each Rydberg superatom. This may provide an attractive platform for studying the quantum-classical correspondence and have potential promising applications in quantum information processing.