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Physical Review A

Generation of nonclassical light by dissipative two-photon processes

L. Gilles, B. M. Garraway, P. L. Knight

Published Apr 1, 1994• 122 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.49.2785

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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.
It has recently been shown that multiphoton absorption in cavities containing an emitter and a nonlinear mirror or a two photon absorber can be used to create antibunched photons (i.e. nonclassical light). We investigate the generation of nonclassical photon states using nonlinear laser cavities where the excitation has been modified so that it consists of short current pulses. The light fields in the studied setups are ideally formed of superpositions of zero photon and one photon states. Our goal is to study and develop single photon sources which are needed e.g. in quantum information processing and quantum computing, and fundamental quantum optical experiments. We investigate the effect of exciting the photon emitter with time dependent current pulses to provide single-photon-on-demand sources. We maximize the probability of the single photon state by optimizing the strengths of linear losses, nonlinear absorption, photon emission, and the length of the current injection pulse into the amplifier. Furthermore, we analyze the output photon statistics and waiting times using Monte Carlo simulations. This type of a setup is technologically attractive since it potentially provides room temperature realization of photon antibunching with essentially standard optoelectronic materials and processing techniques.
We study the formation of mixtures of superposition states of the coherent states \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}\ensuremath{\alpha}〉, also known as Schr\"odinger-cat states, from a competitive process involving a two-photon parametric process and two-photon absorption. Using the fact that photons are created or destroyed in pairs, we deduce the long-time steady-state form of the density operator. We numerically study the evolution at all times and show that generally the field is in a mixed state. We also examine nonclassical properties of the field such as squeezing and sub-Poissonian statistics, and also the evolution of the Q function.
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.
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.
In this paper, we investigate the distribution statistics of photons in a single mode radiation field subjected to two-photon absorption (TPA) and the factors that contribute to squeezing and antibunching of photons, leading to the generation of nonclassical light. TPA is a nonlinear optical phenomenon in which the atoms interact with the light field by absorbing two photons simultaneously. The motivation to study TPA is the recent intense activity on nanocrystallites/quantum dots. Further, it is the only nonlinear optical phenomenon that can be analytically studied. The simultaneous occurrence of squeezing and antibunching is studied with small initial photon numbers by solving the master equation for TPA of a single mode radiation directly by numerical integration, without going through analytical procedure. The results are compared with those of analytical/numerical procedures available. Further, the discussion on the parameters of squeezing and antibunching for short-time (ST) as well as long-time is done comprehensively in the present work by taking up the ST approximation and summation of ST (SST) procedure along with the exact numerical method.