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Acta Physica Sinica (Overseas Edition)

Superposition of coherent states in Kerr medium

Wu Jin-wei, Guo Guang-Can

Published Oct 1, 1996• 2 citations
Publisher

Abstract

The evolution of the input coherent state in the Kerr medium is studied. Upon the derivation we know that the output state at time t which corresponds to a rational number is Schrodinger's cat state. Using Fourier integral of the evolution operator, we obtain the integral expression of the output state at time t which corresponds to an irrational number. It is a kind of one-dimensional continuous superposition of coherent states, not an ordinary Schrodinger's cat state.

DOI
10.1088/1004-423x/5/10/006

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The evolution of the input coherent state in the Kerr medium is studied. Upon the derivation we know that the output state at time t which corresponds to a rational number is Schrodinger's cat state. Using Fourier integral of the evolution operator, we obtain the integral expression of the output state at time t which corresponds to an irrational number. It is a kind of one-dimensional continuous superposition of coherent states, not an ordinary Schrodinger's cat state.
We study the evolution of a initially coherent state of an electromagnetic field propagating in a Kerr medium with saturable nonlinearity. By using the quantum phase distribution formalism, we analyse the dependence of the output signal phase configuration upon input field amplitude. We observe that the saturation of the nonlinear contribution of the refractive index of the propagation medium introduces interference effects that compromise the observation of macroscopically well distinguishable components of the output state. For input amplitudes much larger than a characteristic saturation amplitude the final state differs from the input state only by an overall phase shift. Possible relevance of the present results in the experimental search of Schrödinger cat-like states using semiconductor-doped glass optical fibres is discussed.
The phase properties of an initially coherent field propagating through a Kerr medium are examined using two different measures of phase uncertainty: (i) variance of periodic functions and (ii) the entropy. The variance of a periodic function of phase (with period 2\ensuremath{\pi}/m) is found to be minimized only at the times when the field evolves into a discrete superposition of n distinguishable coherent states (Schr\"odinger-cat states) where n is a factor of m. The phase entropy is found to be more sensitive, as it is minimized at the times when the field evolves into a superposition of an arbitrary number of distinguishable coherent states. The sum of the photon number and phase entropies is found to display behavior very similar to the Wehrl entropy for the evolving field, i.e., the sum is minimal at the times the cat states occur, and at these times it has a value that indicates the number of component coherent states in the cat states.
In this work we analyze the temporal dynamics of a system comprising an optical cavity filled with a nonlinear Kerr medium, whose frequency is allowed to change during time evolution. By exactly solving the corresponding time-dependent anharmonic-oscillator Hamiltonian, we demonstrate that squeezed coherent-state superpositions can be generated within the optical cavity. Moreover, we show that the squeezing degree of the produced states may be tuned by properly controlling the frequency shift of the cavity, a feature that might lead to interesting studies in the field of quantum state engineering.