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Zeitschrift für Naturforschung A

Flopping between Schrödinger's Cat States

Marco Frasca

Published Feb 1, 2001• 3 citations
Publisher

Abstract

Abstract We show that for an atom in a cavity in the strong coupling regime, flopping between Schrödinger cat states, devised as a superposition of displaced number states, can be accomplished. Beside, the Rabi frequency can be set to zero, so that population trapping or localization can be accomplished. These states could be proved to be useful for quantum computation

DOI
10.1515/zna-2001-0133

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Abstract We show that for an atom in a cavity in the strong coupling regime, flopping between Schrödinger cat states, devised as a superposition of displaced number states, can be accomplished. Beside, the Rabi frequency can be set to zero, so that population trapping or localization can be accomplished. These states could be proved to be useful for quantum computation
A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong coupling regime. It is shown that, in agreement with the recent results on Rabi flopping in a Josephson junction (Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, to appear in Phys. Rev. Lett.), the Rabi frequency is indeed proportional to first kind integer order Bessel functions in the limit of a large number of photons and the dressed states are Schr\\"odinger cat states. To approach this problem analytically use is made of the dual Dyson series and the rotating-wave approximation.
A Schrödinger-cat state is a coherent superposition of macroscopically distinguishable quantum states, in quantum optics usually realized as superposition of coherent states.Protocols to prepare photonic cats have been presented for atomic systems.Here we investigate in what manner and how well the preparation protocols can be transferred to a solid-state platform, namely, a semiconductor quantum-dot-cavity system.In quantum-dotcavity systems there are many disruptive influences like cavity losses, the radiative decay of the quantum dot, and the coupling to longitudinal acoustic phonons.We show that for one of the protocols these influences kill the quantum coherence between the states forming the cat, while for a second protocol a parameter regime can be identified where the essential characteristics of Schrödinger-cat states survive the environmental influences under conditions that can be realized with current equipment.
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.
We perform experiments with Rydberg atoms crossing one at a time a superconducting cavity containing a few microwave photons. The coupling between the atoms and the cavity field is either resonant or dispersive. In the resonant case, quantum Rabi oscillations induced by the vacuum or by a small coherent field are observed. These signals reveals in a striking way the quantization of the field. Quantum Rabi oscillations are also used to prepare Fock states of radiation, to transfer information or to produce entanglement between two successive atoms crossing the cavity. Dispersive atom–field coupling is used to prepare and probe coherent superpositions of field states with different phases (Schrödinger's cat states). The progressive decoherence of these states is observed. These experiments constitute fundamental tests of quantum theory and shed light on the transition from quantum to classical in mesoscopic systems.