ABSTRACT In this paper, we study new non‐Gaussian states known as superpositions of photon‐added and photon‐subtracted displaced Fock states (SPA‐PS‐DFSs). We express the SPA‐PS‐DFSs in terms of displaced Fock states (DFSs) and investigate their Wigner function and nonclassical properties. The obtained results of the Wigner function show that the superposition of photon addition and subtraction can enhance the non‐Gaussian and nonclassical properties of the SPA‐PS‐DFSs. Furthermore, the SPA‐PS‐DFSs exhibit nonclassical features, including higher‐order squeezing and higher‐order antibunching. Notably, these nonclassical characteristics are more enhanced than those of previous states generated solely by adding or subtracting photons to DFSs without superposition. These findings underscore the effectiveness of the superposition technique in enhancing the non‐Gaussian and nonclassical properties of the states.
ABSTRACT In this paper, we study new non‐Gaussian states known as superpositions of photon‐added and photon‐subtracted displaced Fock states (SPA‐PS‐DFSs). We express the SPA‐PS‐DFSs in terms of displaced Fock states (DFSs) and investigate their Wigner function and nonclassical properties. The obtained results of the Wigner function show that the superposition of photon addition and subtraction can enhance the non‐Gaussian and nonclassical properties of the SPA‐PS‐DFSs. Furthermore, the SPA‐PS‐DFSs exhibit nonclassical features, including higher‐order squeezing and higher‐order antibunching. Notably, these nonclassical characteristics are more enhanced than those of previous states generated solely by adding or subtracting photons to DFSs without superposition. These findings underscore the effectiveness of the superposition technique in enhancing the non‐Gaussian and nonclassical properties of the states.
Abstract Nonclassical properties of photon added and subtracted displaced Fock states are studied using various witnesses of lower‐ and higher‐order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower‐ and higher‐order antibunching and sub‐Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel parameter, zeros of Q function, Klyshko's criterion, and Agarwal–Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non‐Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.
Abstract In this paper, we aim to introduce a new state called photon-subtracted-then-added squeezing-enhanced coherent state (PSASECS) by multiple photon subtraction and then addition to a squeezing-enhanced coherent state. We investigate the non-Gaussianity and nonclassicality of this new state in detail, including its Wigner function, sub-Poissonian statistics, Q -function, squeezing, and antibunching properties. The obtained results indicate that these non-Gaussian and nonclassical characteristics have been enhanced by appropriately changing between photon subtraction l and photon addition k . Additionally, the non-Gaussianity and nonclassicality of PSASECS are enhanced compared to cases involving only the addition or subtraction of photons. This demonstrates the importance of subtracting and then adding photons to the squeezing-enhanced coherent state, and introducing a significant state for application in quantum optics, particularly in mitigating phase noise fluctuations in quantum devices.
Abstract Pair coherent states (PCSs) as a kind of two-mode non-Gaussian and nonclassical states were introduced and studied. Some nonclassical characteristics of them such as two-mode sum-squeezing, two-mode antibunching, and entanglement have been well investigated. In this paper, we focus on studying the superposition of photon addition and subtraction to the PCSs called superposition of photon-added and photon-subtracted pair coherent states (SPAPSPCSs). Our main purpose is to show that the non-Gaussian feature and all the above-mentioned nonclassical properties of the SPAPSPCSs can be enhanced compared with the photon-added-and-subtracted two modes pair coherent states (PAASTMPCSs) and the original PCSs. In general, we demonstrate that the SPAPSPCSs have more enhanced non-Gaussian character and nonclassical properties than the PCSs and the PAASTMPCSs by examining the negativity of the Wigner function. Specifically, we indicate that both the SPAPSPCSs and the PAASTMPCSs can exist in two-mode sum-squeezing while the original PCSs (without photon-addition and photon-subtraction) cannot, and the degree of squeezing is stronger in the SPAPSPCSs than in the PAASTMPCSs. The obtained results also indicate that the superposition of photon addition and subtraction of the SPAPSPCSs plays a vital role in enhancing the two-mode antibunching property and the entanglement degree compared with the PCSs and the PAASTMPCSs.
Abstract Non‐Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. Considering these facts, a quantitative analysis of the nonclassical and non‐Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures, namely entanglement potential, Wigner–Yanese skew information, Wigner logarithmic negativity, and relative entropy of non‐Gaussianity. It is observed that Fock parameter always increases the amount of nonclassicality and non‐Gaussianity, while photon addition is effective only for small values of the displacement parameter. Further, the nonclassical and non‐Gaussian effects decrease initially with an increase in the displacement parameter before increasing for the large displacement to saturate to the corresponding Fock state (equivalently displaced Fock state) value. Finally, dynamics of the Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.
Abstract Higher‐order nonclassical properties of r photon added and t photon subtracted qudit states (referred to as rPAQS and tPSQS, respectively) are investigated here to answer: How addition and subtraction of photon can be used to engineer higher‐order nonclassical properties of qudit states? To obtain the answer, higher‐order moment of relevant bosonic field operators is first obtained and subsequently used to study the higher‐order nonclassical properties (e.g., higher‐order antibunching, higher‐order squeezing, and higher‐order sub‐Poissonian photon statistics) of the corresponding states. These witnesses establish that rPAQS and tPSQS are highly nonclassical. To quantitatively establish this observation and to make a comparison between rPAQS and tPSQS, volumes of the negative part of Wigner function are computed. Finally, for the sake of verifiability of the obtained results, optical tomograms are also reported. Throughout the study, a particular type of qudit state named as a new generalized binomial state is used as an example.
Abstract In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f ‐deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude–squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.