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Two Quantum Photoemission and dc Photomixing in Sodium

Malvin Carl Teich

Published Feb 1, 1966• 1 citation
Publisher

Abstract

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.

DOI
10.5281/zenodo.15858945

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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.
Two-photon correlation measurement provides a promising way to experimentally demonstrate the statistical nature of a light source, which is very significant for the deep understanding of the photon-generating process and the diagnosing of the coherence property. Quantitatively two- photon correlation is described by second-order coherence. Usually the behavior of the second-order coherence against any of the parameters defining the phase volume is different for different photon statistics. The Poisson photon statistics for coherent light gives its second-order coherence as a flat response; The Bose-Einstein photon statistics for chaotic light gives its second-order coherence as a bunching effect; While the Sub-Poisson photon statistics for non-classical light gives its second-order coherence as an anti-bunching effect. Therefore the measurement of two-photon correlation is proved to be a good finger print to check whether light is in coherent state or incoherent state such as thermal state or non-classical state. Historically the measurement of two-photon correlation was first performed by Hanbury-Brown and Twiss (HBT) in 1956. They used a linear mixer to realize the correlation of the two currents from the photoelectric detectors illuminated by a stationary thermal light souece, a mercury arc, and the photo-bunching effect was first successfully observed in the visible region of 435.8 nm. HBT method is no doubt a good way to extract the small excess two-photon correlation for a stationary light because the background, that is the DC components, has been cut off automatically by the broad band amplifiers, which is in fact the key of the success of HBT experiment. However there exists a general problem, to which no attention has ever been paid, in measuring the two-photon correlation of non-stationary light such as synchrotron radiation (SR) by the HBT method. Here the "non-stationary" means a sense of classical mechanics that the observed intensity has some deterministic time structure. The systematic time structure of SR decided by the bunch distribution of the electric current in a storage ring will give rise to a large amount of unexpected accidental correlation, which in fact has nothing to do with the inherent photon statistics of light source and usually l000～l0000 times larger than the true two-photon correlation due to the short bunch separation length (2ns) and the short coherence time (～0.1ps) which is not comparable to the time resolution (1ns) of the measuring system. The existence of the accidental correlation would severely prevent us from observing the bunching effect of the true two-photon correlation. Therefore to suppress the much larger accidental correlation and to extract the small true two-photon correlation, a novel intensity interferometer has been developed for soft X-ray synchrotron radiation. This intensity interferometer consists of an optical vacuum chamber and an electric correlator. All the essential optical elements which includes a wire scanner, a precise diffraction slit, a grating monochromator with a coherence time modulator, a beam divider and two fast-response photon detectors (microchannel plates) are mounted in this high vacuum chamber. The electric correlator completes the multiplication of the two broad band electric currents coming from the photoelectric detectors. The basic idea to suppress the much larger accidental correlation is to modulate the coherence time by modulating the entrance slit width of the monochromator by a piezoclectric translator. The two sets of light intensity are simultaneously modulated too. When the frequency of modulation is f, the third harmonics 3f is detected with a loch-in amplifier because the 3f components include only the true two-photon correlation. Practically it is difficult to modulate with frequency f without any higher order harmonics distortion which might add some false 3f components. To overcome this difficulty we have used a sharp bandpass filter of l00～350 MHz in each branch of the correlator, which is lower than the RF frequency 500 MHz and much higher than 1.6 MHz, the revolution frequency of the stored beam of the 2.5 GeV storage ring. This new apparatus has been operated successfully in the measurement of the horizontal two-photon correlation for the first harmonic of undulator radiation with photon energy of 70 eV at the Photon Factory, KEK. By narrowing the precise slit width which correspondingly changes the spatial coherence of the incident SR, a bunching effect of the normalized excess two-photon correlation has been clearly observed. This explicit bunching effect implies that synchrotron radiation is chaotic radiation. Further investigation shows that although second-order coherence is completely determined by the first-order coherence for the case of chaotic light, the measured information from the light source is essentially different. The two-photon correlation of synchrotron radiation does not depend on the response time of the detectors but gives the information of instantaneous emittance of the stored beam with the time scale of coherence time τC. By fitting the experimental data, the horizontal instantaneous emittance of the stored beam is estimated to be 40nmrad. This intensity interferometer can be utilized to characterize the coherence properties of incomplete FELs, such as SASE, because if they are fully coherent light sources the normalized excess two-photon correlation would have a flat response, but not showing a photon-bunching effect.
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.
Two-time correlations in the emissions of photons by a single atom of sodium in the presence of a coherent exciting field near resonance have been investigated. In the experiment sodium atoms in an atomic beam are excited by a perpendicular light beam from a tunable dye laser, and they are prepared by optical pumping to behave as two-level quantum systems. The fluorescent light is collected by a microscope objective in a direction that is approximately orthogonal to both beams and imaged on two photomultipliers. Photoelectric pulse correlations are measured in the presence of exciting fields of various strengths and for various detunings from the atomic resonance, and are found to exhibit significant nonclassical features. The results show clearly that the emitted photons exhibit antibunching, in good quantitative agreement with the predictions of quantum electrodynamics.
We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.
The relation between the two-quantum photocounting distribution p(n, T) and the intensity fluctuations of the radiation incident on the detector is obtained and compared with the one-quantum results. The actual statistics are evaluated for several cases of interest, including a chaotic source, an amplitude-stabilized wave, and the output of a single-mode laser (Van der Pol oscillator). The two-quantum count rate 〈n〉/T is found to depend on the mean-square intensity of the radiation, in contrast to the one-quantum count rate which is proportional to the mean intensity. The effects of photon correlations in the radiation beam become apparent since the two-quantum distributions manifest a distinctly more positive second derivative than the corresponding one-quantum distributions. Both the low-and the high-count probabilities are therefore increased at the expense of counts near the mean. The quantum-theoretical treatment is found to be equivalent to the semiclassical treatment for density operators possessing a positive-definite weight function in the P-representation. Some possible experiments to verify the theory are discussed and shown to be feasible.
The signal-to-noise ratio (S/N) of the Brown–Twiss stellar intensity interferometer, in which the resolving time (τr) of the photodetectors is much longer than the coherence time of incident radiation (τc), is derived, especially for incident radiation with a very high effective temperature. The statistical properties of the wave amplitude of the incident radiation is assumed to be described by a gaussian distribution function. In order to evaluate the mean square error in the intensity-correlation measurement, the eighth-order moment of complex wave amplitudes is obtained by using the moment theorem for a gaussian random process. The mean square error of the high-intensity correlation experiment during a finite observation time (τ0) is determined chiefly by the random correlation of noise currents due to intensity fluctuations of the incident radiation. The S/N in the case of extremely high-intensity radiation, thus, is given by (τ0/τc)12∣γ12∣2, where γ12 is the complex degree of coherence between two observation points independent of the intensity of incident radiation. In the case of low-intensity radiation the mean square error of an intensity-correlation measurement is determined by the random correlation of shot noise in photoelectric currents. The S/N for low-intensity radiation, as originally discussed by Hanbury Brown and Twiss, is given by (τ0/τr)12∣γ12∣2ηnτc where n is the number of incident photons per second and η is the quantum efficiency of a photodetector. The S/N for the intermediate case is also discussed.