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NATO ASI series. Series B : Physics

Quantum Superpositions: Squeezing and Dissipations

A. Vidiella-Barranco, Vladimír Bužek, P. L. Knight, W. K. Lai

Published Jan 1, 1992• 2 citations
Publisher
DOI
10.1007/978-1-4615-3386-3_18

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In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
Quantum oscillators with nonlinear driving and dissipative terms have gained significant attention due to their ability to stabilize cat states for universal quantum computation. Recently, superconducting circuits have been employed to realize such long-lived qubits stored in coherent states. We present a generalization of these oscillators, which are not limited to coherent states. The key ingredient lies in the presence of different nonlinearities in driving and dissipation, beyond the quadratic one. Through an extensive analysis of the asymptotic dynamical features for different nonlinearities, we identify the conditions for the storage and retrieval of quantum states, such as squeezed states, in both coherent and incoherent superpositions. We explore their applications in quantum computing, where squeezing prolongs the lifetime of memory storage for qubits encoded in the superposition of two symmetric squeezed states, and in quantum associative memory, which has so far been limited to the storage of classical patterns.