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Journal of the Korean Physical Society

Planet versions of the state of Schrödinger’s cat prepared by using quantum measurements

Yong-Yi Huang

Published Apr 1, 2016• 1 citation
Publisher

Abstract

A classical charged particle travels along a circular orbit and interacts with a silver atom in its ground state fixed at the center of the circle through Biot-Savart coupling. We find that if the silver atom initially lies in a spin superposition state of valence electron, in the co-rotating frame of reference the projected measurements of the spin of silver’s valence electron along the z direction determine the rotational direction, and the projected measurements of that spin along the x or the y direction yield planet versions of the state of Schrödinger’s cat.

DOI
10.3938/jkps.68.944

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A classical charged particle travels along a circular orbit and interacts with a silver atom in its ground state fixed at the center of the circle through Biot-Savart coupling. We find that if the silver atom initially lies in a spin superposition state of valence electron, in the co-rotating frame of reference the projected measurements of the spin of silver’s valence electron along the z direction determine the rotational direction, and the projected measurements of that spin along the x or the y direction yield planet versions of the state of Schrödinger’s cat.
A classical charged particle moves along a straight line and interacts with a silver atom in its ground state fixed at the origin of coordinates through Biot-Savart coupling. If the silver atom initially lies in a spin superposition state of valence electron, in the co-moving reference frame the projected measurements of the spin of silver’s valence electron along the z direction determine the moving direction of the charged particle. The projected measurements of that spin along the x or the y direction yield straight line motion versions of Schrödinger’s cat state for the charged particle. When the spin coherence state of the silver atom suffers from its environment decoherence, as long as the silver atom’s spin is entangled with the trajectories of the moving charged particle, the measurements on the silver atom’s spin also yield the partial superpositions of different trajectories of the moving charged particle. It is possible to control mechanical motion up to quantum level by the means of quantum measurements.
A single circular Rydberg atom is used to prepare in a high quality superconducting cavity a "Schrödinger cat" state, quantum superposition of two coherent fields with different classical phases. A second atom probes the cavity state after a tunable delay. The decay of the quantum correlations between the two atoms reveals the evolution of the field state from an initial quantum superposition into a mere statistical mixture. The time scale of this decay decreases when the separation between the two components increases. This is the first experimental observation of the dynamics of decoherence, lying at the heart of the quantum measurement process.
An atomic electron is prepared in a state closely analogous to Schr\"odinger's coherent superposition of ``live cat'' and ``dead cat.'' The electronic state is a coherent superposition of two spatially localized wave packets separated by approximately $0.4\ensuremath{\mu}\mathrm{m}$ at the opposite extremes of a Kepler orbit. State-selective ionization is used to verify that only every other atomic level is populated in the ``cat state,'' and a Ramsey fringe measurement is used to verify the coherence of the superposition.
A single circular Rydberg atom is used to prepare in a high quality superconducting cavity a “Schrödinger cat” state, quantum superposition of two coherent fields with different classical phases. A second atom probes the cavity state after a tunable delay. The decay of the quantum correlations between the two atoms reveals the evolution of the field state from an initial quantum superposition into a mere statistical mixture. The time scale of this decay decreases when the separation between the two components increases. This is the first experimental observation of the dynamics of decoherence, lying at the heart of the quantum measurement process.
A "Schrodinger cat"-like state of matter was generated at the single atom level. A trapped 9Be+ ion was laser-cooled to the zero-point energy and then prepared in a superposition of spatially separated coherent harmonic oscillator states. This state was created by application of a sequence of laser pulses, which entangles internal (electronic) and external (motional) states of the ion. The Schrodinger cat superposition was verified by detection of the quantum mechanical interference between the localized wave packets. This mesoscopic system may provide insight into the fuzzy boundary between the classical and quantum worlds by allowing controlled studies of quantum measurement and quantum decoherence.
Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous “Schroedinger cat” state. The recent progress shows an increase in the number of components and the number of modes involved. Our work gives a theoretical treatment of multicomponent two-mode Schroedinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. After performing a symmetric (Loewdin) orthogonalization of the sets of coherent states in both modes we obtain the Schmidt decomposition of the two-mode state, and therefore an analytic expression for its entanglement. We show that the states obtained by splitting a RICS are generalizations of Bell states of two qubits to the case of N -level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that an exact probabilistic teleportation of arbitrary superposition of coherent states on the circle is possible with such a state used as shared resource.