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arXiv:quant-ph/0205118 · Physical Review A

Entanglement generation by adiabatic navigation in the space of symmetric multiparticle states

Razmik G. Unanyan, Michael Fleischhauer, Nikolay V. Vitanov, Klaas Bergmann

Published Oct 1, 2002• 32 citations

Abstract

We propose a technique for robust and efficient navigation in the Hilbert space of entangled symmetric states of a multiparticle system with externally controllable linear and nonlinear collective interactions. A linearly changing external field applied along the quantization axis creates a network of well separated level crossings in the energy diagram of the collective states.One or more transverse pulsed fields applied at the times of specific level crossings induce adiabatic passage between these states. By choosing the timing of the pulsed field appropriately, one can transfer an initial product state of all N spins into (i) any symmetric state with n spin excitations and (ii) the N-particle analog of the Greenberger-Horne-Zeilinger state. This technique, unlike techniques using pulses of specific area, does not require precise knowledge of the number of particles and is robust against variations in the interaction parameters. We discuss potential applications in two-component Bose condensates and ion-trap systems.

DOI: 10.1103/physreva.66.042101

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We consider systems of two and three qubits, mutually coupled by Heisenberg-type exchange interaction and interacting with external laser fields. We show that these systems allow one to create maximally entangled Bell states, as well as three-qubit Greenberger-Horne-Zeilinger and

W

states. In particular, we point out that some of the target states are the eigenstates of the initial bare system. Due to this, one can create entangled states by means of pulse area and adiabatic techniques, when starting from a separable (nonentangled) ground state. On the other hand, for target states, not present initially in the eigensystem of the model, we apply the robust stimulated Raman adiabatic passage and $\ensuremath{\pi}$ pulse techniques, that create desired coherent superpositions of nonentangled eigenstates.

We propose an efficient method to generate multiparticle entangled states of nitrogen-vacancy (NV) centers in a spin-mechanical system, where the spins interact through a collective coupling of the Lipkin-Meshkov-Glick (LMG) type. We show that through adiabatic transitions in the ground state of the LMG Hamiltonian, the Greenberger-Horne-Zeilinger (GHZ)-type or the W-type entangled states of the NV spins can be generated with this hybrid system from an initial product state. Because of adiabaticity, this scheme is robust against practical noise and experimental imperfection, and may be useful for quantum information processing.

We propose to apply stimulated adiabatic passage to transfer atoms from their ground state into Rydberg excited states. Atoms a few micrometers apart experience a dipole-dipole interaction among Rydberg states that is strong enough to shift the atomic resonance and inhibit excitation of more than a single atom. We show that the adiabatic passage in the presence of this interaction between two atoms leads to robust creation of maximally entangled states and to two-bit quantum gates. For many atoms, the excitation blockade leads to an effective implementation of collective-spin and Jaynes-Cummings-like Hamiltonians, and we show that the adiabatic passage can be used to generate collective J_{x}=0 eigenstates and Greenberger-Horne-Zeilinger states of tens of atoms.

We derive a technique of robust and efficient adiabatic passage for a driven nonlinear quantum system, describing the transfer to a molecular Bose-Einstein condensate from an atomic one by external fields. The pulse ingredients are obtained by tracking the dynamics derived from a Hamiltonian formulation, in the adiabatic limit. This leads to a nonsymmetric and nonmonotonic chirp. The efficiency of the method is demonstrated in terms of classical phase space, more specifically with the underlying fixed points and separatrices. We also prove the crucial property that this nonlinear system does not have any solution leading exactly to a complete transfer. It can only be reached asymptotically for an infinite pulse area.

We describe a novel technique for preparing the multiparticle W class states,which are based on adiabatic passage induced a suitably crafted time-dependent external field.We have derived the interaction Hamiltonian,and the adiabatic and diabatic evolution conditions of driving the system of n-spin-12 particles from initial unentangled state to the W class state.In addition,we show the diagram of the energies evolution and the populations of target state of transferring the system of three spin-12 particles from initial unentangled state to target entangled state of Wtype.

We propose a technique for the creation of maximally entangled symmetric Dicke states in an ion trap using adiabatic passage, which requires only a pair of chirped pulses from a single laser and is applicable to any number of ions and excitations. By utilizing a particular factorization of the Hilbert space for multilevel ladders we show that the problem can be reduced to ``bow-tie''-configuration energy-level crossings. This technique is naturally robust against fluctuations in the laser intensity and the chirp rate. Even when realistic heating rates are considered, we estimate that the overall fidelity should remain high (e.g., 98% for a ten-ion Dicke state), which represents a significant improvement over traditional approaches.