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arXiv:0901.1274 · Physical Review A

Decoherence, environment-induced superselection, and classicality of a macroscopic quantum superposition generated by quantum cloning

F. De Martini, Fabio Sciarrino, Nicolò Spagnolo

Published May 6, 2009• 20 citations
arXivHTMLPDF

Abstract

The high resilience to decoherence shown by a recently discovered macroscopic quantum superposition (MQS) generated by a quantum-injected optical parametric amplifier and involving a number of photons in excess of $5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on $|\ensuremath{\alpha}⟩$ and N-photon maximally entangled states (NOON), in the perspective of the comprehensive theory of the subject by Zurek. In that perspective the concepts of ``pointer state'' and ``environment-induced superselection'' are applied to the new scheme.

DOI
10.1103/physreva.79.052305

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The high resilience to decoherence shown by a recently discovered macroscopic quantum superposition (MQS) generated by a quantum-injected optical parametric amplifier and involving a number of photons in excess of 5\ifmmode×\else\texttimes\fi1045\ifmmode\times\else\texttimes\fi{}{10}^{4}5\ifmmode×\else\texttimes\fi104 motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on ∣\ensuremathα⟩|\ensuremath{\alpha}⟩∣\ensuremathα⟩ and N-photon maximally entangled states (NOON), in the perspective of the comprehensive theory of the subject by Zurek. In that perspective the concepts of pointer state'' and environment-induced superselection'' are applied to the new scheme.
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) involving a number of photons in excess of 5 x 10^4 motivates the present theoretical and numerical investigation. The results are placed in close comparison with the properties of the well known MQS based on |alpha> states. The very critical decoherence properties of the latter MQS are found to be fully accounted for, in a direct a simple way, by a unique "universal" function: indeed a new property of the quantum "coherent states".
This work reports on an extended research endeavor focused on the theoretical and experimental realization of a macroscopic quantum superposition (MQS) made up of photons. This intriguing, fundamental quantum condition is at the core of a famous argument conceived by Schr\"odinger in 1935. The main experimental challenge to the actual realization of this object resides generally in unavoidable and uncontrolled interactions with the environment, i.e., ``decoherence,'' leading to the cancellation of any evidence of the quantum features associated with the macroscopic system. The present scheme is based on a nonlinear process, ``quantum-injected optical parametric amplification,''which, by a linearized cloning process maps the quantum coherence of a single-particle state, i.e., a microqubit, onto a macroqubit consisting of a large number MMM of photons in quantum superposition. Since the adopted scheme was found resilient to decoherence, a MQS demonstration was carried out experimentally at room temperature with $M\ensuremath{\ge}{10}^{4}$. The result led to an extended study of quantum cloning, quantum amplification, and quantum decoherence. The related theory is outlined and several experiments are reviewed, such as the test of the ``no-signaling theorem'' and the dynamical interaction of the photon MQS with a Bose-Einstein condensate. In addition, the consideration of the microqubit-macroqubit entanglement regime is extended to macroqubit-macroqubit conditions. The MQS interference patterns for large MMM are revealed in the experiment and bipartite microqubit-macroqubit entanglement was also demonstrated for a limited number of generated particles: $M\ensuremath{\precsim}12$. Finally, the perspectives opened by this new method for further studies on quantum foundations and quantum measurement are considered.
Recent experimental results demonstrated the generation of a macroscopic quantum superposition (MQS), involving a number of photons in excess of $5\ifmmode\times\else\texttimes\fi{}{10}^{4}$, which showed a high resilience to losses. In order to perform a complete analysis on the effects of decoherence on these multiphoton fields, obtained through the quantum injected optical parametric amplifier, we investigate theoretically the evolution of the Wigner functions associated to these states in lossy conditions. Recognizing the presence of negative regions in the WWW representation as an evidence of nonclassicality, we focus our analysis on this feature. A close comparison with the MQS based on coherent $|\ensuremath{\alpha}⟩$ states allows us to identify differences and analogies.
It is known that a macroscopic quantum superposition (MQS), when it is exposed to an environment, decoheres at a rate scaling with the separation of its component states in phase space. This is more or less consistent with the well-known proposition that a more macroscopic quantum state is reduced more quickly to a classical state in general. Effects of initial mixedness, however, on the subsequent decoherence of MQSs have been less known. We study the evolution of a highly mixed MQS interacting with an environment and compare it with that of a pure MQS having the same size as the central distance between its component states. Although the decoherence develops more rapidly for the mixed MQS in short times, its rate can be significantly suppressed after a certain time and becomes smaller than the decoherence rate of its corresponding pure MQS. In an optics experiment to generate a MQS, our result has the practical implication that nonclassicality of a MQS can still be observable in moderate times, even though a large amount of noise is added to the initial state.
In the present work we propose to realize a macroscopic light-matter entangled state, obtained by the interaction of a multiphoton quantum superposition with a BEC system. The multiphoton quantum state is generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair and interacts with a Mirror-BEC shaped as a Bragg interference structure. The overall process will realize an entangled macroscopic quantum superposition involving a "microscopic" single-photon state of polarization and the coherent "macroscopic" displacement of the BEC structure acting in space-like separated distant places. This hybrid photonic-atomic system could open new perspectives on the possibility of coupling the amplified radiation with an atomic ensemble, a Bose-Einstein condensate, in order to implement innovative quantum interface between light and matter.
We report the successful generation of an entangled multiparticle quantum superposition of pure photon states. They result from a multiple universal cloning of a single photon qubit by a high gain, quantum-injected parametric amplifier. The information preserving property of the process suggests for these states the name of ”multi-particle qubits”. They are ideal objects for investigating the emergence of the classical world in quantum systems with increasing complexity, the decoherence processes and may allow the practical implementation of the universal 2-qubit logic gates. Typeset using REVTEX 1 Since the golden years of quantum mechanics the interference of classically distinguishable quantum states, first epitomized by the famous ”Schroedinger-Cat ” apologue [1] has been the object of extensive theoretical studies and recognized as a major conceptual paradigm of Physics [2,3]. In modern times the sciences of quantum information (QI) and quantum computation deal precisely with collective processes involving a multiplicity of