Non-gaussian Squeezed States And Their Nonclassical Effects

Nonclassicality of optical fields has been a topic of great interest in quantum optics and quan-tum information. Usually, the nonclassicality manifests itself in specific properties of quantumstatistics, such as the anti-bunching, sub-Poissonian photon statistics, squeezing in one of thequadratures of the field, partial negative Wigner distributions, etc. Among them, the Wigner func-tion is a quasi-probability distribution function, whose value can be positive or negative. For thequasi-classical state (such as a typical coherent state), its Wigner function is always non-negative.Thus, the partial negativity of Wigner functions is indeed a good indication of the highly non-classical character of quantum states. In order to obtain new and non-classical quantum states,many researchers have proposed a variety of schemes. The basic approach for constructing non-classical quantum states is making use of the principle of superposition in quantum mechanics,for example, some superposition states of Fock states, coherent states, squeezed states, displacedFock states and so on. Another approach is that acting an operator on a reference state, for exam-ple, the usual squeezed state can be generated by operating the squeezing operator on a coherentstate. In recent years, it is found that subtracting photons from or adding photons to quantumstates can obtain some non-classical states such as photon-added coherent states. In fact, thesestates mentioned above are not involved in the Gaussian quantum states. The so-called Gaussianquantum state is defined as a state with a Gaussian Wigner function. With the development ofexperimental techniques, experimental and theoretical physicists are trying to use non-Gaussianstate as the source of information. The most notable example is certainly their applications for anoptical quantum computer, alongside their employment for improving teleportation, cloning, andstorage. Squeezing is a main resource for various important protocols in quantum information. Inparticular, non-Gaussian squeezed states with strongly nonclassical properties, such as negativityof the quasi-probability phase space distributions and entanglement, may constitute powerful re-sources for the efficient implementation of quantum communication and computation. Therefore,some theoretical and experimental efforts have been made towards engineering and controllinghighly nonclassical, non-Gaussian squeezed states of optical fields. In this thesis, some new non-Gaussian squeezed states, exhibiting non-classical features, have been obtained from Gaussiansqueezed ones after operating non-Gaussian operation. This thesis is organized as follows:In Chap.1, we briefly introduce some basis theories of quantum optics. To begin with, the technique of integration within ordered product of operators (IWOP), first proposed by Prof. FanHong-yi, is briefly reviewed, and based on this technique fundamental quantum states in quantummechanics are derived from new point of view. Finally, we introduce some nonclassical criteri-ons for optical states, such as the sub-Poissonian photon statistics, quadrature squeezing, partialnegative Wigner distribution and so on.In Chap.2, based on the more general squeezing operator introduced by Mandel and Wolf, weintroduce a new two-parameter generalized squeezing operator V (r, κ), which conducts rotated-squeezing effect. Then a squeezing-enhanced thermal state is obtained by the new-type squeezingoperator V (λ, r) operating on a thermal state. We introduce the Fresnel operator for convertinga kind of time-dependent Hamiltonian into the standard harmonic oscillator Hamiltonian. TheFresnel operator with the parameters A, B, C, D corresponds to classical optical Fresnel transfor-mation, these parameters are the solution to a set of coupled partial differential equations set up inthe above mentioned converting process.In Chap.3, we study the photon-number distributions of a general Gaussian states, especiallythe displaced squeezed states, and further investigate how the phase angel in the state affects thephoton-number distributions. By applying photon subtraction and addition, we first introducethe photon subtracted displaced squeezed thermal states and the photon added one, their photon-number distributions are also obtained. Our results show that these photon-number distributions areall periodic function of the compound angle θ/2with a period π. Compared with the displacedsqueezed state, all peaks of the photon-number distributions of both non-Gaussian squeezed statesmove to the larger photon number and photon-number distributions become more flat and wide.Our results indicate that generating new photon-number-controllable nonclassical states from asqueezed light with coherent component is effective by multiple-photon subtraction or additionwhen θ/2=π/2.In Chap.4, we study phase-sensitive nonclassical properties of photon subtracted or addeddisplaced squeezed thermal states. And we evaluate whether the non-Gaussianity of our seed statesis connected to these nonclassical properties. We find that the Mandel Q parameter, the quadraturesqueezing, the negative volume of the Wigner function and the fidelity between both seed statesand displaced squeezed thermal states are all periodic functions of θ/2with a period π. Inaddition, our results indicate that, for both seed states, non-Gaussianity and nonclassicality havesimilar behavior. Thus, the non-Gaussianity induced by photon-subtraction or-addition operationis essentially nonclassical.In Chap.5, we study nonclassical properties of the optical field when photon subtraction-addition coherent operation ta+ra (|t|2+|r|2=1) acts on a squeezed thermal state, andinvestigate the decoherence of the seed state in amplitude-damping channel is studied by the timeevolution of the Wigner function. We proved that applying coherent operation ta+ra to the squeezed vacuum state has the same impact as adding a single-photon to(or subtracting a single-photon from) it (the seed state is a squeezed single photon one). Comparing with the squeezedthermal state, the degree of squeezing of the seed state becomes weaker. However, for smallsqueezing amount, the the seed state can show sub-Poissonian statistics. Based on the time evo-lution of the Wigner function, the length of time that this nonclassical field preserves its partialnegativity of the Wigner function can be modulated by r, and increases with r.