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arXiv:quant-ph/0312092 · Physical Review A

Mesoscopic superposition of states with sub-Planck structures in phase space

G. S. Agarwal, Pradyumna K. Pathak

Published Nov 11, 2004• 57 citations
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Abstract

We propose the cavity quantum electrodynamics method, using dispersive interaction between atoms and a high-quality cavity to realize the mesoscopic superposition of coherent states that would exhibit sub-Planck structures in phase space, i.e., the structures at a scale smaller than the Plank's constant $(\ensuremath{\hbar})$. These structures are direct signatures of quantum coherence and are formed as a result of interference between the two superposed cat states. In particular we focus on a superposition involving four coherent states. We show interferences in the conditional measurements involving two atoms.

DOI
10.1103/physreva.70.053813

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We propose the cavity quantum electrodynamics method, using dispersive interaction between atoms and a high-quality cavity to realize the mesoscopic superposition of coherent states that would exhibit sub-Planck structures in phase space, i.e., the structures at a scale smaller than the Plank's constant (\ensuremathℏ)(\ensuremath{\hbar})(\ensuremathℏ). These structures are direct signatures of quantum coherence and are formed as a result of interference between the two superposed cat states. In particular we focus on a superposition involving four coherent states. We show interferences in the conditional measurements involving two atoms.
We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopic-quantum-superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.
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We show that entanglement of two superposed coherent states produces sub-Planck structures in phase space. The origin of these structures depends entirely on entanglement, unlike those in Zurek [Nature (London) 412, 712 (2001)], where the effect of entanglement was not considered. The constituent states are sensitive enough to carry out the Heisenberg sensitive measurements. However, their usefulness is limited in providing high sensitivity in either the position (x)(x)(x) direction or in the momentum (p)(p)(p) direction of the phase-space. Interestingly, the entanglement causes the proposed states to be sensitive in both xxx and ppp directions. This state offers a better sensitivity compared to the single partite compass state in Zurek [Nature (London) 412, 712 (2001)] in carrying out precision measurements. It is also argued that such states are easy to create and are better suited for carrying out precision measurements.
We study mesoscopic superpositions of two component Bose-Einstein condensates. Atomic condensates, with long coherence times, are good systems in which to study such quantum phenomena. We show that the mesoscopic superposition states can be rapidly generated in which the atoms dispersively interact with the photon field in a cavity. We also discuss the production of compass states which are macroscopic quantum superposition states. The physical realization of mesoscopic states is important in studying decoherence and precision measurement.
We present several schemes for preparing and detecting coherent superpositions of classically distinct states of the electromagnetic field in one or two high-Q cavities. These proposals are based on two-atom correlation measurements, to be performed on circular Rydberg atoms interacting dispersively with the cavity fields. Changing the time interval between the two detected atoms allows a monitoring of the decay of quantum coherence due to dissipation. \textcopyright{} 1996 The American Physical Society.