Agarwal and Tara, in 1991 introduced a new class of states defined as m times application of creation operator to Coherent States known as Excited Coherent States (ECS) or Photon Added Coherent States (PACS). They are neither completely quantum nor completely classical. Here we present and develop these Excited Coherent Sates from a basic and more approachable Wave-function approach. We have derived the ECS wave function as a blend of Coherent States and Fock States and thus established them as a result of Quantum fluctuations (represented by Fock states) on Coherent States. We further derived and analyzed basic relations such as wave packet width and uncertainty relation in a more generalized form and presented their development with time. Another important property of ECS is Quadrature Squeezing. Here we also present a general analysis of squeezing in ECS and derived conditions on parameters for squeezing.
Agarwal and Tara, in 1991 introduced a new class of states defined as m times application of creation operator to Coherent States known as Excited Coherent States (ECS) or Photon Added Coherent States (PACS). They are neither completely quantum nor completely classical. Here we present and develop these Excited Coherent Sates from a basic and more approachable Wave-function approach. We have derived the ECS wave function as a blend of Coherent States and Fock States and thus established them as a result of Quantum fluctuations (represented by Fock states) on Coherent States. We further derived and analyzed basic relations such as wave packet width and uncertainty relation in a more generalized form and presented their development with time. Another important property of ECS is Quadrature Squeezing. Here we also present a general analysis of squeezing in ECS and derived conditions on parameters for squeezing.
A new scheme is proposed to design excited coherent states. where the states β,α denote the Glauber two variable minimum uncertainty coherent states, which minimize minimum uncertainty conditions while carrier nonclassical properties too and n is an integer. They are converted into the Agarwal's type of the photon added coherent states, arbitrary Fock states and the Glauber two variable coherent states, respectively depending on which of the parameters $\b{eta}$,α and n equal to zero. It has been shown that the resolution of identity condition is realized with respect to an appropriate measure on the complex plane, too. We have compared our results with the similar quantum states of Agarwal's type and seen that in our case amount of quantum fluctuations are much controllable. Moreover, we have also more flexibility to establish and set-out of their features. Also, there is a discussion on the statistical properties, can unveil (non-)classical properties of these states. For instance their Poissonian statistics are significant similar to what we saw earlier in the Glauber two variable coherent states. Interestingly, depending on the particular choice of the parameters of the above scenarios, we are able to determine the status of compliance with squeezing properties in field quadratures. The last stage is devoted to some theoretical framework to generate them in cavities.
State [Formula: see text] and state [Formula: see text] are same to state [Formula: see text], which is called as multi-photon-addition amplified coherent state (MPAACS) by us. Here, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are photon number operator, creation operator, coherent state, gain factor, and an integer, respectively. We study mathematical and physical properties for these MPAACSs, including normalization, photon component analysis, Wigner function, effective gain, quadrature squeezing, and equivalent input noise. Actually, the MPAACS, which contains more nonclassicality, is an amplified version of photon-added coherent state (PACS) introduced by Agarwal and Tara [Phys. Rev. A 43, 492 (1991)]. Our work provides theoretical references for implementing amplifiers for light fields.
Othman and Yevick [Int. J. Theor. Phys. 57, 2293 (2018)] introduced a new class of states defined as “near” coherent states attached to the simple harmonic oscillator. Such states can be expressed as superposition of a standard coherent state and a derivative state, which are neither completely quantum nor completely classical. Here, we introduce photon-added (-depleted) near coherent states [PA(D)NCS] through “m” times application of creation (annihilation) operators â†(â) to the near coherent state. A general analysis of nonclassical properties of the PA(D)NCS, such as sub-Poissonian statistics and squeezing effect, is given analytically and numerically in the context of the conventional quantum optics. We also derive the Wigner distribution function of the PA(D)NCS over phase space which may bear negative values, which is a good indication of their nonclassical properties. Finally, an experimental procedure for generating the PA(D)NCSs is established.
This chapter presents some basic aspects of coherent and squeezed states. Certain superpositions of energy Eigen functions of linear harmonic oscillators are called coherent states because they are of significance in optics for the representation of coherent light waves. The chapter obtains the Heisenberg uncertainty relation for the harmonic oscillator states and shows that it is a minimum for ground state. It defines coherent states and shows that they are the minimum uncertainty product states. Coherent states were constructed for many interesting potentials including infinite well and Poschl-Teller potentials and Morse potential. A particular quantum state of a spin system which most closely resembles a classical spin is termed as a spin coherent state. Use of squeezed states in quantum cryptography, quantum distribution of keys, extended coherence time, quantum engineering, teleportation, optics, detection of gravitational waves, quantum metrology and laser interferometers have been analyzed.
Abstract Photon-added coherent states (PACS) represent a critical bridge between classical coherent states and quantum Fock states, exhibiting non-classical properties such as squeezing and sub-Poissonian statistics. In this work, we investigate the entanglement properties of quasi-Bell states constructed from photon-added coherent states, with a focus on the concurrence and entanglement of formation under varying photon excitation numbers m and coherent state amplitudes |α|. By leveraging the mathematical framework of Glauber’s coherent states and Laguerre polynomial normalization, we derive analytical expressions for the overlap between |α, m⟩ and | − α, m⟩, and analyze their suitability for qubit encoding. Our results reveal that for |α| ≥ 2, these states approximate orthogonal logical qubits, while smaller amplitudes exhibit m-dependent entanglement degradation. Numerical simulations demonstrate that entanglement of formation E12 approaches unity for large |α|, independent of m, but diminishes with increasing m in the weak-field regime (|α|2 < 1.5). These findings advance the understanding of photon-added states in quantum information protocols, offering insights into decoherence mitigation and resource-efficient qubit design.
The addition of a photon into the same mode as a coherent state produces a nonclassical state that has interesting features, including quadrature squeezing and a sub-Poissonian photon-number distribution. The squeezed nature of photon-added coherent (PAC) states potentially offers an advantage in quantum sensing applications. Previous theoretical works have employed a single-mode treatment of PAC states. Here, we use a continuous-mode approach that allows us to model PAC state pulses. We study the properties of a single-photon and coherent-state wave packet superimposed with variable temporal and spectral overlap. We show that, even without perfect overlap, the state exhibits a sub-Poissonian number distribution, second-order quantum correlations, and quadrature squeezing for a weak coherent state. We also include propagation loss in waveguides and study how the fidelity and other properties of PAC state pulses are affected.