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arXiv:2010.11846 · Physical Review A

Photon-added coherent states using the continuous-mode formalism

Jason Francis, Mark Tame

Published Oct 14, 2020• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.043709

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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.
The nonclassical properties of the hybrid coherent state (HCS), which is the superposition state of the coherent state and photon-added coherent (PAC) state, is investigated analytically. We evaluated the photon number statistics, the Wigner-Yanase skew information, the Mandel Q factor and the quadrature squeezing of the HCS to quantify its nonclassicality. This superposition state exhibits more nonclassical properties than the PAC state and even the superposition state of coherent state and single-photon-added coherent (SPAC) state. We reported that the addition of more photons to the PAC state part of the HCS generally quantifies more nonclassicalities. The nonclassical properties of the HCS also depend on the amplitudes of coherent state and the PAC state in the HCS.
Multi-photon-added cat states are constructed by repeatedly applying the creation operator to a cat state. We study in detail their photon-number distribution, QQQ parameter, squeezing properties, and Wigner function. We show that photon addition induces a πππ phase shift in the original parity configuration whenever an odd number of photons is added, reflected as swapped vanishing probabilities and phase space displacements at the origin. Remarkably, the same process drives these states into a sub-Poissonian regime regardless of the relative phase between their coherent state components, making them valuable resources for quantum imaging, at the cost of losing quadrature squeezing, but gaining amplitude-squared one. We also discuss how these states can be generated using existing hardware.
We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a qqq-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher-order quadrature squeezing, namely, the Hillery type and the Hong-Mandel type, and second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. Also, we compare the behavior of different types of quadrature and photon number squeezing of our system with those of the ordinary harmonic oscillator by considering the same set of parameters.
In this paper, we construct the m-photon-added and m-photon-subtracted coherent states on a sphere. These states are shown to satisfy the usual conditions of continuity in the label, normalizability, and the resolution of identity. The preparation of the constructed states, as the states of the radiation field, is considered. We examine and analyze the nonclassical properties of these states, including the photon mean number, Mandel parameter, and quadrature squeezing. We find that these states are sub-Poissonian in nature, whereas the degree of squeezing is reduced (enhanced) by increasing m for the photon-added (photon-subtracted) coherent states on a sphere. The results also exhibit that the curvature of the sphere contributes to the enhancement of nonclassical behavior of the photon-added and photon-subtracted coherent states on the sphere.
In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f -deformed creation operator A = f ( n ) a † on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f -deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.
The concept of a photon added two-mode Schrödinger cat state in which both modes are independent is introduced, and their nonclassical properties and entanglement are studied. The introduced states emerge as eigenstates of f 1 f 2 a 1 a 2 , where f 1 , f 2 are nonlinear functions of the number operator, and a 1 , a 2 are annihilation operators. We study the evolution of these states under canonical transformation using the parity operator for the case of standard coherent states of the harmonic oscillator. The nonclassical properties of these states are evaluated especially by considering sub-Poissonian photon statistics and photon number distribution. Interestingly, the addition of photons leads to shifting the region in which photon number distribution shows oscillatory behavior. In addition, the entanglement of introduced states is quantitatively analyzed using concurrence. We observe that the state approaches maximum entanglement more rapidly after the addition of photons.