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Advances in Theoretical & Computational Physics

Generation of the GHZ and the W State in a Series of Rydberg Atoms Trapped in Optical Lattices

Published Jun 5, 2022• 0 citations
Publisher

Abstract

In this work, we present a quantum control methodology to create multi-particle entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). The methodology is demonstrated on a generation of the W and GHZ three-atomic states via the mechanism of two-photon passage using overlapping chirped pulses and the interplay of the chirp rate, the one-photon and two-photon detuning, the peak Rabi frequency and the strength of the Rydberg-Rydberg interactions. A chain of N alkali 87Rb atoms in an optical lattice interacting with two laser fields is modeled within a semi-classical theory. The strategy to create different classes of multiparticle entangled states was revealed through performed dressed state analysis

DOI
10.33140/atcp.05.03.01

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•Jan 1, 2019•0 citations
In this work, we present a quantum control methodology to create multi-particle entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). The methodology is demonstrated on a generation of the W and GHZ three-atomic states via the mechanism of two-photon passage using overlapping chirped pulses and the interplay of the chirp rate, the one-photon and two-photon detuning, the peak Rabi frequency and the strength of the Rydberg-Rydberg interactions. A chain of N alkali 87Rb atoms in an optical lattice interacting with two laser fields is modeled within a semi-classical theory. The strategy to create different classes of multiparticle entangled states was revealed through performed dressed state analysis
Entangled states are crucial for modern quantum enabled technology which makes their creation key for future developments. In this paper, a robust quantum control methodology is presented to create entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). It was developed from the analysis of a chain of alkali atoms $^{87}Rb $ interaction with laser pulses, which lead to the two-photon transitions from the ground to the Rydberg states with a predetermined magnetic quantum number. The methodology is based on the mechanism of two-photon adiabatic passage using overlapping chirped pulses and interplaying the Rabi frequency, the one-photon detuning, and the strength of the Rydberg-Rydberg interactions.
Quantum entanglement is a crucial resource in many quantum information and quantum communication tasks. In this work, we present a quantum control methodology to create entangled states of two basic classes, the W and the GHZ. A chain of 87 Rb atoms in an optical lattice is considered interacting with laser pulses to induce two-photon excitations to Rydberg states having a specific magnetic quantum number. Generation of the W and GHZ three-atomic states is demonstrated via the mechanism of the two-photon adiabatic passage in collective states implying the overlapping chirped pulses and the interplay of the Rabi frequency with the one-photon detuning and the strength of the Rydberg-Rydberg interactions. Copyright © VBRI Press.
Entangled states are crucial for modern quantum enabled technology which makes their creation key for future developments. In this paper, a robust quantum control methodology is presented to create entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). It was developed from the analysis of a chain of alkali atoms [Formula: see text] interaction with laser pulses, which leads to the two-photon transitions from the ground to the Rydberg states with a predetermined magnetic quantum number. The methodology is based on the mechanism of the two-photon excitation, adiabatic for the GHZ and non-adiabatic for the W state, induced by the overlapping chirped pulses and governed by the Rabi frequency, the one-photon detuning, and the strength of the Rydberg-Rydberg interactions.
Schemes for creation of NNN-particle entangled Greenberger-Horne-Zeilinger (GHZ) states are important for understanding multiparticle nonclassical correlations. Here, a theoretical scheme for creation of a multiparticle GHZ state implemented on a target ensemble of N, $\mathrm{\ensuremath{\Lambda}}$ 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 with high fidelity to the other ground state, depending on the state of the control atom. Measurement of the control atom in a specific basis after this conditional transfer facilitates one-step creation of an NNN-particle GHZ state. A thorough analysis of adiabatic conditions for this scheme and the influence of radiative decay from the excited Rydberg levels is presented. We show that this scheme is immune to the decay rate of the excited level in ensemble atoms and provides a robust way of creating GHZ states.
The field of quantum computation and communication has prospered over the last few decades because of multiple advances in our understanding of trapping and controlling physical quantum systems like neutral atoms, superconducting qubits, trapped ions, quantum dots etc. using light. A lot of research has gone into development of techniques which facilitate trapping and manipulation of ensembles of neutral atoms by studying how the atomic properties of the system respond to properties of light used to control them. In this dissertation we shall explore some applications of light-matter interactions in ensembles of lambda three level neutral atoms for the purpose of entanglement generation and distribution. The first part of this dissertation focuses on the study of a protocol that can be used to generate multi-particle entangled quantum states called the Greenberger-Horne-Zeilinger (GHZ) states in an ensemble of N neutral atoms. Schemes for creation of N particle entangled Greenberger-Horne-Zeilinger (GHZ) states are important for understanding multi-particle non-classical correlations. A theoretical protocol for creation of a multi-particle GHZ state implemented on a target ensemble of N, 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 with high fidelity to the other multi-particle ground state, depending on the state of the control atom. Measurement of the control atom in a specific basis after this conditional transfer facilitates one-step creation of a N particle GHZ state. A thorough analysis of adiabatic conditions associated with STIRAP for this scheme and the influence of radiative decay from the excited Rydberg levels is presented. The most important and novel feature of this scheme is that it is immune to the decay rate of the excited level in ensemble atoms and provides a robust way of creating GHZ states. In the second part of this dissertation, we study atomic ensemble based quantum interfaces used in quantum repeater protocols for entanglement distribution. Quantum interfaces provide a platform where in the flying photonic qubits used for information and entanglement transfer can interact with a physical system which stores, processes and releases this information back as photons. The Duan-Lukin-Cirac-Zoller (DLCZ) quantum repeater protocol, which was proposed to realize long distance quantum communication, requires usage of quantum memories or quantum interfaces. Atomic ensembles interacting with optical beams based on off-resonant Raman scattering serve as convenient on-demand quantum memories. Here a complete, free space, three-dimensional theory of the associated read and write process for this quantum memory is worked out with the aim of understanding intrinsic retrieval efficiency. We develop a formalism to calculate the transverse mode structure for the signal and the idler photons and use the formalism to study the intrinsic retrieval efficiency under various configurations. The effects of atomic density fluctuations and atomic motion are incorporated by numerically simulating this system for a range of realistic experimental parameters. Results describe the variation in the intrinsic retrieval efficiency as a function of the memory storage time for skewed beam configuration at a finite temperature, which provides valuable information for optimization of the retrieval efficiency in experiments.