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Journal of Modern Optics

Superposition states of light in a three-photon absorbing dissipative medium

S. T. Gevorgyan, Min Xiao, V. O. Chaltykyan

Published Jul 2, 2008• 3 citations
Publisher

Abstract

We consider the process of simultaneous absorption of three photons in a medium in the presence of weak one-photon absorption. We show that in such a system stationary three-component superposition states of light may be formed in the range of small values of state amplitude (weak perturbation). This circumstance is associated with the fact that in this range of interaction the field spends more time in one of the three types of superposition states of light (constituting an ensemble of quantum trajectories of the system) than in two other types. We also show that in the range of large values of state amplitude it is possible to obtain three types of non-stationary superposition states of light. By using numerical simulation of quantum trajectories of the system we study the dynamics of the quantum entropy of the field. We calculate the Wigner functions of the field states. We also obtain analytical results for the density matrix of the steady state of the system.

DOI
10.1080/09500340801891991

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We consider the process of simultaneous absorption of three photons in a medium in the presence of weak one-photon absorption. We show that in such a system stationary three-component superposition states of light may be formed in the range of small values of state amplitude (weak perturbation). This circumstance is associated with the fact that in this range of interaction the field spends more time in one of the three types of superposition states of light (constituting an ensemble of quantum trajectories of the system) than in two other types. We also show that in the range of large values of state amplitude it is possible to obtain three types of non-stationary superposition states of light. By using numerical simulation of quantum trajectories of the system we study the dynamics of the quantum entropy of the field. We calculate the Wigner functions of the field states. We also obtain analytical results for the density matrix of the steady state of the system.
The process of the simultaneous absorption of three photons in a medium possessing weak one-photon absorption is analyzed. The mode experiencing absorption is perturbed externally via a three-photon parametric process. It is shown that a steady-state, three-component superposition state of light can exist in this system in the range where the amplitude of the state is small (small perturbations of the system). The latter condition is due to the fact that, in this range of interactions, the field spends significantly more time in one of three types of superposition states of light that form an ensemble of quantum trajectories of the system than in the other two.
The process of simultaneous absorption of two photons in a medium in the presence of a weak one-photon absorption is considered. The medium is perturbed from outside in a two-photon parametric manner. The formation of a stationary even-parity superposition state of light in such a medium is shown to be possible in the region of small amplitudes of the state (weak perturbations of the system). This is associated with the fact that, in this region of interaction, the field spends considerably more time in the even superposition state than in the odd state. It is shown that a nonstationary superposition state of light with a large amplitude of the state (large photon numbers) can be obtained for interaction times that are longer than the most probable time of the first two-photon quantum jump of the field state and shorter than the most probable time of the first one-photon jump of the field state. The dynamics of formation of the quantum entropy of the field is studied by numerical simulation of quantum trajectories of the system. The Wigner functions of the state of the field are calculated. Analytical results are obtained for the density matrix of the stationary state of the system in the presence of a weak one-photon absorption.
The process of simultaneous absorption of three photons in a medium subjected to a three-photon parametric perturbation is considered. It is shown that in such a medium one can observe the formation of the radiation field states, which are the quantum superposition of three coherent components. One-photon and twophoton absorption processes in the medium also destroy the interference between the components of the superposition state. The states being formed are investigated in both the temporal development (numerically) and the stationary limit (numerically and analytically); the Wigner functions, as well as the quantum entropy, are calculated for a whole series of initial states. It is shown that depending on the initial state of the radiation field, the interference between the three-component superposition states being formed can lead, for example, to the almost total localization of the system in a two-component state or to the destruction of the interference between different coherent components.
For the process of three-photon absorption in the case of a cubic parametric perturbation a possibility to obtain quantum superposition states of three coherent components is shown. The one-photon and two-photon absorption processes are shown to destroy the interference between the state components: the quantum superposition state decays into the classical mixture of its components. It is shown that the interference between different three-component coherent superposition states formed in the system can, depending on the initial state of the field, result in almost full localization of the optical system in a two-component state, or in destruction of the interference between different coherent components. The Wigner functions and quantum entropy of the system are calculated for a variety of initial states.
Nonclassical states of light may be generated by processes involving the creation or annihilation of photons in pairs. A quadratic coupling, characteristic of a parametric amplifier, generates a squeezed vacuum from a normal vacuum, and a two-photon absorber can also generate a squeezed state (though not a minimum-uncertainty state) even though it is a purely dissipative process. We consider here the simultaneous action of a quadratic pump on a two-photon absorber and demonstrate how superpositions of distinct coherent states may be generated by their combined effects. We use standard master equations to describe the time development, employing split operators and direct numerical integrations to determine the field density-matrix elements and quasiprobabilities. The purities of the nonclassical states are determined by evaluating the field entropy. Provided one-photon dissipative processes may be ignored, a pure superposition state is formed in the steady state. This superposition is destroyed if one-photon loss processes are important.
We investigate the dynamical evolution of nonclassical states of light undergoing a two-photon absorption process. We consider two distinct cases of initial states, a squeezed coherent state and an eigenstate of the two-photon annihilation operator (a superposition of macroscopically distinct coherent states). We analyze the fluctuations in the photon-number operator and in the quadrature components of the field. Whereas one-photon linear damping rapidly destroys quantum features such as squeezing, we demonstrate that substantial coherence is retained when such light interacts with a two-photon-absorbing reservoir. This surviving coherence is responsible for the preservation of squeezing in the steady state despite the effect of dissipation. We relate the origin of squeezing of initially unsqueezed light interacting with two-photon absorbers with the squeezing generated by simple superposition states of light.