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arXiv:quant-ph/0310005 · Journal of Optics B Quantum and Semiclassical Optics

Minimum decoherence cat-like states in Gaussian noisy channels

Alessio Serafini, Silvio De Siena, Fabrizio Illuminati, Matteo G. A. Paris

Published May 29, 2004• 55 citations
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Abstract

We address the evolution of cat-like states in general Gaussian noisy channels, by considering superpositions of coherent and squeezed-coherent states coupled to an arbitrarily squeezed bath. The phase space dynamics is solved and decoherence is studied keeping track of the purity of the evolving state. The influence of the choice of the state and channel parameters on purity is discussed and optimal working regimes that minimize the decoherence rate are determined. In particular, we show that squeezing the bath to protect a non squeezed cat state against decoherence is equivalent to orthogonally squeezing the initial cat state while letting the bath be phase insensitive.

DOI
10.1088/1464-4266/6/6/019

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We address the evolution of cat-like states in general Gaussian noisy channels, by considering superpositions of coherent and squeezed-coherent states coupled to an arbitrarily squeezed bath. The phase space dynamics is solved and decoherence is studied keeping track of the purity of the evolving state. The influence of the choice of the state and channel parameters on purity is discussed and optimal working regimes that minimize the decoherence rate are determined. In particular, we show that squeezing the bath to protect a non squeezed cat state against decoherence is equivalent to orthogonally squeezing the initial cat state while letting the bath be phase insensitive.
Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.
We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate quadratures is necessary and sufficient to determine the purity at any time. The statistical reliability and the range of applicability of the proposed measurement scheme are tested by means of Monte Carlo simulated experiments. We then consider the dynamics of purity in noisy channels. We derive an evolution equation for the purity of general Gaussian states both in thermal and in squeezed thermal baths. We show that purity is maximized at any given time for an initial coherent state evolving in a thermal bath, or for an initial squeezed state evolving in a squeezed thermal bath whose asymptotic squeezing is orthogonal to that of the input state.
We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.
We consider unitary evolution of finite bipartite quantum systems and study time dependence of purity for initial cat states -- coherent superpositions of Gaussian wave-packets. We derive explicit formula for purity in systems with nonzero time averaged coupling, a typical situation for systems where an uncoupled part of the Hamiltonian is Liouville integrable. Previous analytical studies have been limited to harmonic oscillator systems but with our theory we are able to derive analytical results for general integrable systems. Two regimes are clearly identified, at short times purity decays due to decoherence whereas at longer times it decays because of relaxation.
We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate of decoherence is quantified by relating it to the decay rates of various, complementary measures of the quantum nature of a state, such as the purity, some non-classicality indicators in phase space, and, for two-mode states, entanglement measures and total correlations between the modes. Different sets of physically relevant initial configurations are considered, including one- and two-mode Gaussian states, number states, and coherent superpositions. Our analysis shows that, generally, the use of initially squeezed configurations does not help to preserve the coherence of Gaussian states, whereas it can be effective in protecting coherent superpositions of both number states and Gaussian wavepackets.