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Quantum Magellan theorem(the simplest NO-GO Theorem for hidden variables)

Vladan Panković

Published Oct 13, 2009• 0 citations
OpenAlex

Abstract

In this work we theoretically consider possibilities of the detection of single photon quantum superposition if before detection by photo plate only one superposition arm can directly quantum dynamically interact with two-level quantum systems appropriate for corresponding non-disturbing stimulated emission or absorption. If photo plate is relatively close or if life time of the excited state is relatively large (so that there is no excited state decay before detection) this photo plate will effectively detect interference effects, i.e. superposition. (Exactly quantum dynamically here is an entangled state of the super-system, photon and two two-level systems. But it can be effectively consistently approximated by superposition of the photon only.) If photo plate is relatively distant or if life time of the excited state is relatively short (so that there is excited state decay and new spontaneously emitted photon appearance before detection) this photo plate will effectively detect interference effects (absence, i.e. superposition absence. (Exactly quantum dynamically here is an entangled state of the super-system, initial photon, two two-level systems and new photon. But it can be effectively consistently approximated by entangled state of super-system, initial photon and new photon, but not on the superposition of the initial photon only.) All this can be very interesting for discussion of the quantum detection, i.e. measurement procedure (as unique, Magellan straight| between Atlantic ocean of the classical macroscopic decoherent phenomena and Great, Pacific ocean of the microscopic quantum superposition (entanglement) phenomena).

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In this work we theoretically consider possibilities of the detection of single photon quantum superposition if before detection by photo plate only one superposition arm can directly quantum dynamically interact with two-level quantum systems appropriate for corresponding non-disturbing stimulated emission or absorption. If photo plate is relatively close or if life time of the excited state is relatively large (so that there is no excited state decay before detection) this photo plate will effectively detect interference effects, i.e. superposition. (Exactly quantum dynamically here is an entangled state of the super-system, photon and two two-level systems. But it can be effectively consistently approximated by superposition of the photon only.) If photo plate is relatively distant or if life time of the excited state is relatively short (so that there is excited state decay and new spontaneously emitted photon appearance before detection) this photo plate will effectively detect interference effects (absence, i.e. superposition absence. (Exactly quantum dynamically here is an entangled state of the super-system, initial photon, two two-level systems and new photon. But it can be effectively consistently approximated by entangled state of super-system, initial photon and new photon, but not on the superposition of the initial photon only.) All this can be very interesting for discussion of the quantum detection, i.e. measurement procedure (as unique, Magellan straight| between Atlantic ocean of the classical macroscopic decoherent phenomena and Great, Pacific ocean of the microscopic quantum superposition (entanglement) phenomena).
In this work we suggest a technically simple experimental realization of a continuous phase transition (with critical parameters determined by Heisenberg uncertainty relation), or, metaphorically speaking, Magellan strait, from the Great, Pacific ocean of the photon trajectories superposition detection into the Atlantic ocean of the photon trajectories statistical mixture detection in well-known experiment of the single photon interference (at double slit diaphragm or beam splitter). This phase transition or self-collapse can be considered as the spontaneous (non-dynamical) breaking (effective hiding) of the unitary symmetry (superposition) of quantum mechanical dynamics as an especial case of the general formalism of the spontaneous symmetry breaking. All this admits a consistent model of the detection or measurement procedure in the general case.
In this work we suggest a variant of the remarkable Wheeler's delayed choice gedanken experiment. In our experiment, single photon described by a superposition state with two terms dynamically interacts with an atom. Preparation of the atom in any of two excited states can be realized practically in the last moment before interaction. For atom in the first excited state there is practically none dynamical interaction between atom and photon so that the interference effects on the photon can be detected later by a photo plate. For atom in the second excited state dynamical interaction between photon and atom causes certainly the stimulated emission of a new photon that moves coherently with the first photon. Both photons do a super-system described by an entangled quantum state. But in this case photo plate, that realizes simultaneously sub-systemic measurement at any photon, does not detect interference effects. We suggest a simple explanation of given as well as original variant of the delayed choice experiment in full agreement with standard quantum mechanical formalism.
In this work we suggest a technically simple experimental realization of a continuous phase transition (with critical parameters determined by Heisenberg uncertainty relation), or, metaphorically speaking, Magellan strait, from the Great, Pacific ocean of the photon trajectories superposition detection into the Atlantic ocean of the photon trajectories statistical mixture detection in well-known experiment of the single photon interference (at double slit diaphragm or beam splitter). This phase transition or self-collapse can be considered as the spontaneous (non-dynamical) breaking (effective hiding) of the unitary symmetry (superposition) of quantum mechanical dynamics as an especial case of the general formalism of the spontaneous symmetry breaking. All this admits a consistent model of the detection or measurement procedure in the general case.
In this work we theoretically consider quantum Zeno effect for entangled (correlated) quantum states. (Our physical systems and calculations are simpler than it is case in remarkable work on entanglement protection via Zeno effect by Maniscalco et all. But Maniscalco et all and our final conclusions are the same.) Firstly, we demonstrate well-known quantum Zeno effect by frequent decay detection for single, simple, two-level quantum system, with stable, ground quantum state and one non-stable, excited quantum state which can decay, by photon emission, in the ground state. (In this case, by frequent decay detections, system stands in the excited state.) Further, we consider single photon with energy equivalent to energy difference between excited and ground energy level of mentioned system. After interaction with a half-silvered mirror, mentioned photon is in a quantum superposition of the reflected and transmitted quantum state or trajectory. Mentioned trajectories are directed toward two identical, but distant, mentioned simple two-level systems both of which are initially (before interaction with photon) in ground state. Immediately after interaction with photon (photon absorption) two two-level systems are described by entangled (correlated) quantum state ( (excited, ground) + (ground, excited) , symbolically). We prove that in this case, by frequent decay detections on both systems, mentioned two two-level systems are described by initial entangled (correlated) quantum state ( (excited, ground) +(ground, excited)).
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.
The dynamics of an exact two-photon Hamiltonian is used to study the time evolution of an initially disentangled pure state of the atom-field system as it goes through cycles of entanglement separated by instances of disentanglement. For specific initial states of the electromagnetic field, the output state is a pure quantum superposition of a squeezed vacuum state and an orthogonal, odd-photon-number state. The odd-photon-number state, which is not a squeezed state, exhibits both nonclassical sub-Poissonian and classical super-Poissonian photon statistics. In the latter case the quantum superposition resembles a macroscopic superposition state. Conditions are obtained on the atom-cavity interaction time for such states to represent the steady states in the injection in a high-QQQ cavity of a monoenergetic, low-density beam of three-level atoms in a coherent state.