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Physical Review A

Preparation of macroscopic superpositions in many-atom systems

J. I. Cirac, P. Zoller

Published Oct 1, 1994• 199 citations
Publisher

Abstract

We propose a technique to prepare two or more atoms in certain entangled states, based on the interaction of the atoms with a cavity mode. After the atomic state is prepared, the cavity mode is left in the vacuum state, so dissipation does not affect the generated entangled states. These states could be used for improved tests that challenge local realistic theories, and to examine related phenomena, which, thus far, have been realized only with photons.

DOI
10.1103/physreva.50.r2799

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•Jan 1, 2015•0 citations
We propose a technique to prepare two or more atoms in certain entangled states, based on the interaction of the atoms with a cavity mode. After the atomic state is prepared, the cavity mode is left in the vacuum state, so dissipation does not affect the generated entangled states. These states could be used for improved tests that challenge local realistic theories, and to examine related phenomena, which, thus far, have been realized only with photons.
Highly entangled states of more than one quantum system are necessary for tests of local hidden-variable theories and of quantum mechanics itself. We show how to produce field states, which are located in several cavities and are highly entangled, by sending apropriately prepared atoms through the cavities. We discuss both a two-cavity and a three-cavity state in which either each cavity is in a one-photon number state or each is in the vacuum state. Finally, a test of quantum mechanics using the two-cavity state is presented.
A scheme for remote preparation of a two-atom entangled state is presented, which is based on the simultaneous nonresonant interaction of atoms with a single-mode cavity field. In view of the fact that two-particle entanglement is more easily generated than three-particle entanglement, the scheme prepares a two-atom entangled state via two pairs of two-atom entangled state as the quantum channel. Let two identical atoms Alice possesses interact with a single-mode cavity field simultaneously. Alice knows the state she wants to prepare. She selects a proper interaction time, measures the states of the atoms she possesses, and informs Bob of her measurement through a classical channel. Bob introduces an identical auxiliary atom and a single-mode cavity field in vacuum state to achieve the scheme. The scheme is insensitive to the cavity field states and cavity decay. The preparation can be achieved in a simple way. Based on current cavity quantum electrodynamics technique, the scheme can be realized experimentally.
I propose a method to prepare four atoms in an entangled state of the type discussed by Greenberger, Horne, and Zeilinger [in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989), p. 107]. The method involves two micromaser cavities, each supporting two modes initially prepared in a nonlocalized two-photon state by an atom undergoing a two-photon transition. Subsequently, two atoms pass through each cavity, becoming entangled in a Greenberger-Horne-Zeilinger state leaving the cavities in the vacuum. \textcopyright{} 1996 The American Physical Society.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
Quantum entanglement and quantum superposition are fundamental properties of quantum mechanics, which underline quantum information and quantum computation. Preparing quantum states in the macroscopic level is both conceptually interesting for extending quantum physics to a broader sense and fundamentally important for testing the validity of quantum mechanics. In this dissertation, schemes of preparing macroscopic entanglement and macroscopic superposition states in cavity optomechanics are studied using the unitary evolution method in the nonlinear regime or Lyapunov equation in the linearized regime. Quantum entanglement and quantum superposition states can be realized using experimentally feasible parameters with the proposals in this dissertation.\nFirstly, a scheme of entangling two movable end mirrors in a Fabry-Perot cavity that are coupled to a common single photon superposition state is studied. It is shown that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.\nSecondly, a scheme of entangling two movable end mirrors, that are coupled to two-mode entangled fields generated from a correlated-emission laser is investigated. By tuning the input driving laser frequencies at the Stokes sidebands of the cavity, the radiation-pressure coupling can be linearized as an effective beam-splitter-like interaction. Hence entanglement can be transferred from the two-mode fields to the two mechanical mirrors. Macroscopic entanglement between macroscopic mirrors persists at temperature ~ 1K.\nThirdly, a scheme of creating macroscopic quantum superpositions of a mechanical mirror via periodically flipping a photonic qubit is proposed. Quantum superposition states of a mechanical mirror can be obtained via the nonlinear radiation coupling with a single-photon superposition state. However, the difference between two superposed mechanical states is very small due to the weak single-photon coupling rate available in experiment. By periodically flipping the photonic qubit state, the difference can be magnified. It is shown in detail that this scheme is experimentally feasible under current technology.