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Three classes of quantum states are induced from coherent state (CS) based on three operations associated with the photon creation operator. One class is the famous photon-added coherent state (PACS) introduced by Agarwal and Tara (Phys. Rev. A 43, 492–497, 1991). The other two classes are the orthogonal states of the CS (Here we abbreviate them as OCS1 and OCS2). Indeed, the OCS1 is just the displacement Fock state, and the OCS2 is constructed by orthogonalizer proposed by Kim group (Phys. Rev. Lett. 116, 110501, 2016). In contrast to the original CS, the three induced states can exhibit their respective nonclassical properties. We study and compare some properties for these four quantum states (CS, PACS, OCS1, OCS2). The studied properties include the mean number of photons, the sub-Poissonian character, the squeezing effect in the field quadrature, and the quasi-probability distributions including the Husimi Q function and the Wigner function. Besides, their fidelities between each two of them are also discussed.

The nonclassical and non-Gaussian quantum states—photon-added two-mode squeezed coherent states have been theoretically introduced by adding multiple photons to each mode of the two-mode squeezed coherent states. Starting from the new expression of two-mode squeezing operator in entangled states representation, the normalization factor is obtained, which is directly related to bivariate Hermite polynomials. The sub-Poissonian photon statistics, cross-correlation between two modes, partial negative Wigner function are observed, which fully reflect the nonclassicality of the target states. The negative Wigner function often display non-Gaussian distribution meanwhile. The investigations may provide experimentalists with some better references in quantum engineering.

Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator Ml, m is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ|β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.

Different from the previous methods of obtaining optical tomography of quantum states, in this paper we use the Radon transform between the single- (two-)mode Wigner operator and the pure-state density operator |q〉 f,g f,g 〈q| (|η,τ 1,τ 2〉〈η,τ 1,τ 2|) to analytically obtain optical tomograms for single- (two-)mode squeezed chaotic fields, where the states |q〉 f,g (|η,τ 1,τ 2〉) refer to the newly introduced intermediate coordinate-momentum (entangled) states. More interestingly, we find that the tomograms of squeezed chaotic fields and those of coherent states are related by a integration. Thus, we establish a new convenient approach of obtaining tomograms for quantum states.

A new kind of bipartite coherent-entangled state (CES) is introduced in the two-mode Fock space which exhibits the properties of both coherent state and entangled state. The set of CESs make up a complete and partly nonorthogonal representation. A simple experimental scheme to produce the CES is proposed by using a beam splitter. Some applications of the CES are also presented in quantum optics.

Using the entangled state representation of Wigner operator and some formulae related to the two-variable Hermite polynomials, the Wigner function of the squeezed pair coherent state (SPCS) and its two marginal distributions are derived. Based on the entangled Husimi operator introduced by Fan et al. (Phys. Lett. A 358:203, 2006) and the Weyl ordering invariance under similar transformations, we also obtain the Husimi function of the SPCS and its marginal distribution functions. The comparison between the two quasibability functions shows that, for the same amount of information included in two functions, the solving process of the Husimi function is simpler than that of the Wigner function.

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the even and odd negative binomial states (NBSs) are obtained. We concentrate our analysis on the fact that the even and odd NBSs interpolate between the even and odd coherent states and the even and odd quasi-thermal states depending on the values of the parameters involved. Moreover, the tomograms of the even and odd NBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the Klauder-Perelomov coherent states (KP-CSs) for the pseudoharmonic oscillator (PHO) are obtained and the variations of the Wigner functions with the parameters k and z are discussed. Moreover, the tomograms of the KP-CSs for the PHO are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.