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arXiv:2008.03876 · New Journal of Physics

Enhancing photoelectric current by nonclassical light

Hai-Yan Yao, Sheng-Wen Li

Published Nov 23, 2020• 3 citations
arXivHTMLPDF

Abstract

Abstract We study the photoelectric current generated by a driving light with nonclassical photon statistics. Due to the nonclassical input photon statistics, it is no longer enough to treat the driving light as a planar wave as in classical physics. We make a quantum approach to study such problems, and find that: when the driving light starts from a coherent state as the initial state, our quantum treatment well returns the quasi-classical driving description; when the the driving light is a generic state with a certain P function, the full system dynamics can be reduced as the P function average of many ‘branches’—in each dynamics branch, the driving light starts from a coherent state, thus again the system dynamics can be obtained in the above quasi-classical way. Based on this quantum approach, it turns out the different photon statistics does make differences to the photoelectric current. Among all the classical light states with the same light intensity, we prove that the input light with Poisson statistics generates the largest photoelectric current, while a nonclassical sub-Poisson light could exceed this classical upper bound.

DOI
10.1088/1367-2630/abcce9

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Abstract We study the photoelectric current generated by a driving light with nonclassical photon statistics. Due to the nonclassical input photon statistics, it is no longer enough to treat the driving light as a planar wave as in classical physics. We make a quantum approach to study such problems, and find that: when the driving light starts from a coherent state as the initial state, our quantum treatment well returns the quasi-classical driving description; when the the driving light is a generic state with a certain P function, the full system dynamics can be reduced as the P function average of many ‘branches’—in each dynamics branch, the driving light starts from a coherent state, thus again the system dynamics can be obtained in the above quasi-classical way. Based on this quantum approach, it turns out the different photon statistics does make differences to the photoelectric current. Among all the classical light states with the same light intensity, we prove that the input light with Poisson statistics generates the largest photoelectric current, while a nonclassical sub-Poisson light could exceed this classical upper bound.
We study a three-level quantum refrigerator which is driven by a generic light state, even a nonclassical one. With the help of PPP function expansion of the driving light, we obtain the heat current generated by different types of light states. It turns out all different input light states give the same coefficient of performance for this refrigerator, while the cooling power depends not only on the light intensity but also the specific photon statistics of the driving light. Comparing the coherent light with the same intensity, the driving light with super(sub)-Poissonian photon statistics could raise a smaller (stronger) cooling power. We find that this is because the bunching photons would first excite the system but then successively induce the stimulated emission, which draws the refrigerator back to the starting state of the cooling process and thus decreases the cooling current generation. This mechanism provides a more delicate control method via the high order coherence of the input light.
Understanding quantum system dynamics driven by nonclassical light pulses is challenging, particularly for general light states with large photon numbers. Here we introduce an efficient framework that makes this task tractable. By introducing a pulse-shaped P-representation, the exact quantum evolution is decomposed into a mixture of many independent quasi-classical branches, each governed by a standard master equation with a classical pulse which can be solved efficiently. As an illustration, for a two-level system interacting with an exponential pulse, we first find out the exact analytical solutions to the Bloch equations in each quasi-classical branch, and then by taking proper P-function average over all branches, the full system dynamics driven by nonclassical light pulses is analytically obtained. For the one-photon and two-photon cases, our method well reproduces the previous exact results either analytically or numerically. Crucially, our approach scales efficiently to more complex light states (Fock, thermal, squeezed vacuum states) with large photon numbers (N∼100N\sim 100N∼100). We further provide a clear physical interpretation how the system dynamics is influenced through the high-order optical coherence of the nonclassical pulses. This work provides a unified and computationally efficient route and a useful starting point to explore more complex quantum dynamics driven by nonclassical light in quantum optics and quantum information processing.
We study the effect of electron-electron correlations on the quantum state of the light emitted from high-harmonic generation (HHG). The quantum state of the emitted light is obtained by using a fully quantum mechanical description of both the optical modes as well as the electronic system. This is different from the usual semiclassical description of HHG, which only treats the electronic target system quantum mechanically. Using the generic Fermi-Hubbard model, the strength of the electron-electron correlation can be treated as a parameter enabling us to investigate the two limiting cases of a completely uncorrelated phase and a correlated Mott-insulating phase. In the completely uncorrelated phase, the model reduces to a single-band tight-binding model in which only intraband currents contribute to the spectrum. In this limit, we analytically find that the emitted light is in a classical coherent state. In the Mott-insulating phase, a consideration of the photon statistics and squeezing of the emitted photonic state shows that the inter-Hubbard-subband current generates nonclassical light. In this sense, we show that electron-electron correlation can induce the generation of nonclassical states of light.
In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by applying numerical methods including those of Hamiltonian diagonalization and global characteristics. We show explicitly that the harmonic generations can indeed serve as a source of nonclassical light. Then, we demonstrate that the quasi-stationary sub-Poissonian light can be generated in these quantum processes under conditions corresponding to the so-called no-energy-transfer regime known in classical nonlinear optics. By applying method of classical trajectories, we demonstrate that the analytical predictions of the Fano factors are in good agreement with the quantum results. On comparing second and higher harmonic generations in the no-energy-transfer regime, we show that the highest noise reduction is achieved in third-harmonic generation with the Fano-factor of the third harmonic equal to 13/16.
The generation of higher-order harmonic radiation originating from the interaction of intense laser pulses with matter is typically described semiclassically: While the electronic structure and dynamics of matter is described quantum mechanically, the intense light field is described classically---and accordingly the generated harmonic radiation. However, pioneering experiments on quantum optical properties of high-order harmonic generation (HHG) in atomic gases from the group of P. Tzallas [I. Gonoskov et al., Sci. Rep. 6, 32821 (2016) and N. Tsatrafyllis et al., Nat. Commun. 8, 15170 (2017)], and theoretical investigations from the group of M. Lewenstein [M. Lewenstein et al., Nat. Phys. 17, 1104 (2021) and P. Stammer et al., Phys. Rev. Lett. 128, 123603 (2022)] have impressively demonstrated that light's quantum properties are observable in the strong-field realm. In this paper, we develop a quantum optical description of HHG in a bulk semiconductor originating from the nonlinear Bloch current. This mechanism of HHG, known as the intraband current, constitutes the major contribution to the emission spectrum for harmonic with energies of quanta roughly below the bandgap. Under certain approximations, employing a quantum description of both light and matter, we obtain analytical solutions, which allow us to analyze the classical and quantum optical characteristics of the fundamental mode of light and the harmonic modes. We find intricate but sufficiently mild modifications of the photon statistics of the fundamental mode and coherent displacements depending on the parameters of the driving laser field. Similar to high-harmonic generation in atoms, the fundamental and emitted harmonic field modes are entangled. Moreover, our analytical model predicts parameter ranges where these quantum optical properties will be most pronounced, allowing protocols for quantum information processing with high photon numbers over a large range of frequencies.
In recent years, strong-field processes such as high-order harmonic generation (HHG) and above-threshold ionization driven by nonclassical states of light have become an increasingly popular field of study. The theoretical modeling of these processes often applies an approximate phase-space expansion of the nonclassical driving field in terms of coherent states, which has been shown to accurately predict the harmonic spectrum. However, its accuracy for the computation of quantum optical observables like the degree of squeezing and photon statistics has not been thoroughly considered. In this work, we introduce this approximative phase-space description and discuss its accuracy, and we find that it mischaracterizes the quantum optical properties of the driving laser by making it an incoherent mixture of classical states. We further show that this error in the driving field description maps onto the light emitted from HHG, as neither sub-Poissonian photon statistics nor quadrature squeezing below vacuum fluctuations can be captured by the approximative phase-space description. Lastly, to benchmark the approximative phase-space description, we consider the quantum HHG from a one-band model, which yields an exact analytical solution. Using the approximative phase-space representation with this specific model, we find a small quantitative error in the quadrature variance of the emitted field that scales with pulse duration and emitter density. Our results show that using this approximative phase-space description can mischaracterize quantum optical observables. Attributing physical meaning to such results should therefore be accompanied by a quantitative analysis of the error.