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Physical Review B

Quantum theory of entangled-photon photoemission

Francesco Lissandrin, Bahaa E. A. Saleh, Alexander V. Sergienko, Malvin Carl Teich

Published Apr 27, 2004• 28 citations
Publisher

Abstract

A quantum theory of two-photon volume photoemission from metals and semiconductors is developed when the incident source of light comprises collinear down-converted entangled-photon pairs with entanglement time ${T}_{e}.$ Despite the fact that the process involves the absorption of pairs of photons, the entangled-photon photocurrent varies linearly with the incident photon flux density. This is a consequence of the fact that the presence of one photon of an entangled-photon pair signals the presence of the other; it is in sharp contrast with the quadratic dependence of the classical two-photon photocurrent on incident photon flux density. Calculations are carried out for sodium metal (Na) and for ${\mathrm{K}}_{2}\mathrm{CsSb},$ a bialkali-antimonide semiconductor material often used as a cathode in photomultiplier tubes. The photocurrent is found to vary inversely with entanglement time although nonmonotonic behavior emerges over certain ranges of ${T}_{e}.$ Entangled-photon photoemission may well be useful for enhancing the range of two-photon photoemission spectroscopy and might find particular use in the investigation of surface and image states of various materials.

DOI
10.1103/physrevb.69.165317

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A quantum theory of two-photon volume photoemission from metals and semiconductors is developed when the incident source of light comprises collinear down-converted entangled-photon pairs with entanglement time Te.{T}_{e}.Te​. Despite the fact that the process involves the absorption of pairs of photons, the entangled-photon photocurrent varies linearly with the incident photon flux density. This is a consequence of the fact that the presence of one photon of an entangled-photon pair signals the presence of the other; it is in sharp contrast with the quadratic dependence of the classical two-photon photocurrent on incident photon flux density. Calculations are carried out for sodium metal (Na) and for K2CsSb,{\mathrm{K}}_{2}\mathrm{CsSb},K2​CsSb, a bialkali-antimonide semiconductor material often used as a cathode in photomultiplier tubes. The photocurrent is found to vary inversely with entanglement time although nonmonotonic behavior emerges over certain ranges of Te.{T}_{e}.Te​. Entangled-photon photoemission may well be useful for enhancing the range of two-photon photoemission spectroscopy and might find particular use in the investigation of surface and image states of various materials.
The phenomena of subthreshold photoemission and absorption under coherent and entangled-photon-pair illumination are reviewed, and the generation and properties of entangled-photon pairs are surveyed. Three prominent forms of subthreshold photoemission are examined: one-photon Fermi-tail photoemission (FTP), two-photon photoemission (TPP), and entangled-two-photon photoemission (ETPP). Experimental methods for measuring subthreshold photocurrents and photoelectron count rates are discussed, along with strategies for enhancing selected contributions. Experimental observations of FTP from a CsK2_22​Sb photocathode in a photomultiplier tube (PMT), under both coherent and entangled-photon-pair illumination, are reviewed, and the role of FTP as a noise source in two-photon measurements is elucidated. TPP from Na and CsK2_22​Sb photocathodes in a PMT under classical-light illumination is considered, as are TPP and ETPP from a CsK2_22​Sb photocathode in a channel photomultiplier (CPM) under coherent and entangled-photon-pair illumination. The observation of ETPP is facilitated by the use of a CPM, which suppresses FTP, and by low-intensity illumination, which minimizes TPP. Quantum models of TPP and ETPP accord well with experiment. Entangled-two-photon absorption (ETPA) is analyzed, as are its applications in entangled-two-photon fluorescence microscopy (ETPFM) and entangled-two-photon spectroscopy (ETPS). The three principal forms of subthreshold absorption parallel those of subthreshold photoemission: singleton-induced Boltzmann-tail absorption; cousin-induced/singleton-pair-induced two-photon absorption; and twin-induced ETPA. Heuristic particle and fully quantum models of these processes are compared, and experimental studies of ETPA and ETPFM, together with methods for enhancing their observability, are summarized.
Two-photon volume photoelectric emission from sodium metal has been observed. The two-quantum yield for the process, Λ(λ ,T), was found to be Λ(8450 Å, 300 K) = 8 x 10-16 I0 A/W, where I0 is the intensity of the incident radiation in W/cm2. A theoretical model for the process, in which the interaction arises from direct interband transitions, gives a double-quantum yield that is in good agreement with the observed value above. By illuminating the sodium surface with two superimposed laser beams that were obtained from the same source, two-photon DC photomixing has also been observed. With the laser operating well above threshold, the DC photomixing current iT(2) was found to respond as iT(2) ∝ (I1 + I2)2 , where I1 and I2 are the intensities of the individual beams. This result is discussed in terms of quantum-mechanical coherence theory. Using results recently derived by Titulaer and Glauber, it is shown that one double-quantum detector may be used as a self-integrating Hanbury Brown─Twiss type experiment. The two-quantum current induced by a thermal source of intensity I0 is shown to be twice as large as the two-quantum current induced by a single-mode laser of the same intensity. Because this effect arises from photon correlations, a similar result should also hold for other two-quantum processes. Other experiments are proposed in which the double-quantum photoelectric effect may be used to provide information about higher-order correlation functions of the radiation field. Finally, a simple method of work function estimation is discussed, in which only one (single-quantum) photocurrent measurement is necessary. The method requires the incident photon energy to be less than the work function of the material under investigation, and relies on the rapid decrease of the density of states above the Fermi level.
The application of quantum states of light such as entangled photons, for example, created by parametric down conversion, has experienced tremendous progress in the almost 40 years since their first experimental realization. Initially, they were employed in the investigation of the foundations of quantum physics, such as the violation of Bell's inequalities and studies of quantum entanglement. They later emerged as basic platforms for quantum communication protocols and, in the recent experiments on single-photon interactions, in photonic quantum computation. These applications aim at the controlled manipulation of the photonic degrees of freedom, and therefore rely on simple models of matter, where the analysis is simpler. Furthermore, quantum imaging with entangled light can achieve enhanced resolution, and quantum metrology can overcome the shot noise limit for classical light. This Account focuses on an entirely different emerging class of applications using quantum light as a powerful spectroscopic tool to reveal novel information about complex molecules. These applications utilize two appealing properties of quantum light: its distinct intensity fluctuations and its nonclassical bandwidth properties. These give rise to new and surprising behavior of nonlinear optical signals. Nonclassical intensity fluctuations can enhance nonlinear optical signals relative to linear absorption. For instance, the two-photon absorption of entangled photon pairs scales linearly (rather than quadratically) in the photon flux, just like a single photon absorption. This enables nonlinear quantum spectroscopy of photosensitive, for example, biological, samples at low light intensities. We will discuss how the two-photon absorption cross section becomes a function of the photonic quantum state, which can be manipulated by properties of the entangled photon pairs. In addition, the quantum correlations in entangled photon states further influence the nonlinear signals in a variety of ways. Apart from affecting the signal's scaling with intensity, they also constitute an entirely new approach to shaping and controlling excitation pathways in molecular aggregates in a way that cannot be achieved with shaped classical pulses. This is because between the two absorption events in entangled two-photon absorption, the light and material system are entangled. Classical constraints for the simultaneous time and frequency resolution can thus be circumvented, since the two are not Fourier conjugates. Here we review the simplest manifestation of quantum light spectroscopy, two-photon absorption spectroscopy with entangled photons. This will allow us to discuss exemplarily the impact of quantum properties of light on a nonlinear optical signal and explore the opportunities for future applications.
Even though the quantized interaction between light and matter in the photoelectric effect is considered one of the cornerstones in the development of quantum mechanics, it was long thought impossible to directly observe the quantized nature of light itself. The advent of light-intensity autocorrelation techniques in the 1950s, first developed to study the size of stars, changed little in this perception, until true single-photon correlation spectroscopy from trapped ions was proven to be possible in the late 1970s: Photons from a single quantum emitter tend to arrive in bunches, but each light quantum is spaced apart in time—it is antibunched. Initially considered only as the workhorse of atomic quantum optics, over the past two decades, photon correlation techniques have become a standard in fields as diverse as quantum-information processing, biological imaging, polymer physics, and materials science, in general. The technique is particularly useful for probing materials that are specifically designed to emit or absorb light in optoelectronic devices, such as light-emitting diodes, solar cells, or lasers. The central question in such studies is how large a mesoscopic piece of material can become and still behave as an atom-like source of single photons. What interactions may arise between multiple excitations within a material, and what sort of dark states may give rise to intermittency in the stream of photons? We review the many different classes of optoelectronic materials for which photon-correlation spectroscopy has proven to offer useful insight into excited-state dynamics, ranging from molecular, over semiconductor to metallic nanostructures. The technique is particularly suited to probing mesoscopic aggregates of organic semiconductors since each single molecule acts as a quantum emitter itself.
The rate of absorption of entangled photon pairs is linear in the photon-flux density. We demonstrate that the two-photon absorption cross section is a nonmonotonic function of the entanglement time; it vanishes for certain energy-level configurations and values of the entanglement time. This entanglement-induced two-photon transparency arises from the coherent summation of transition-amplitude contributions over the finite entanglement time. As an example, the entangled two-photon cross section for the $1S\ensuremath{-}2S$ electronic transition in atomic hydrogen is obtained.