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Physical Review A

Coherence length of photons from a single quantum system

Fedor Jelezko, Andreas Volkmer, I. Popa, Karl K. Rebane, Jörg Wrachtrup

Published Apr 17, 2003• 45 citations
Publisher

Abstract

We present a methodology that allows recording the coherence length of photons emitted by a single quantum system in a solid. The feasibility of this approach is experimentally demonstrated by measuring the self-interference of photons from the zero-phonon line emission of a single nitrogen-vacancy defect in diamond at 1.6 K. The first-order correlation function has been recorded and analyzed in terms of a single exponential decay time. A coherence time of $\ensuremath{\sim}5\mathrm{ps}$ has been obtained, which is in good agreement with the corresponding spectral line width and demonstrates the feasibility of the Fourier-transform spectroscopy with single photons.

DOI
10.1103/physreva.67.041802

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We present a methodology that allows recording the coherence length of photons emitted by a single quantum system in a solid. The feasibility of this approach is experimentally demonstrated by measuring the self-interference of photons from the zero-phonon line emission of a single nitrogen-vacancy defect in diamond at 1.6 K. The first-order correlation function has been recorded and analyzed in terms of a single exponential decay time. A coherence time of \ensuremath∼5ps\ensuremath{\sim}5\mathrm{ps}\ensuremath∼5ps has been obtained, which is in good agreement with the corresponding spectral line width and demonstrates the feasibility of the Fourier-transform spectroscopy with single photons.
Photon interference among distant quantum emitters is a promising method to generate large scale quantum networks. Interference is best achieved when photons show long coherence times. For the nitrogen-vacancy defect center in diamond we measure the coherence times of photons via optically induced Rabi oscillations. Experiments reveal a close to Fourier-transform (i.e., lifetime) limited width of photons emitted even when averaged over minutes. The projected contrast of two-photon interference (0.8) is high enough to envisage applications in quantum information processing. We report 12 and 7.8 ns excited state lifetimes depending on the spin state of the defect.
Photon interference among distant quantum emitters is a promising method to generate large scale quantum networks. Interference is best achieved when photons show long coherence times. For the nitrogen-vacancy defect center in diamond we measure the coherence times of photons via optically induced Rabi oscillations. Experiments reveal a close to Fourier transform (i.e. lifetime) limited width of photons emitted even when averaged over minutes. The projected contrast of two-photon interference (0.8) is high enough to envisage the applications in quantum information processing. We report 12 and 7.8 ns excited state lifetime depending on the spin state of the defect.
Fourier transform spectroscopy with classical interferometry corresponds to the measurement of a single-photon intensity spectrum from the viewpoint of the particle nature of light. In contrast, the Fourier transform of two-photon quantum interference patterns provides the intensity spectrum of the two photons as a function of the sum or difference frequency of the constituent photons. This unique feature of quantum interferometric spectroscopy offers a different type of spectral information from the classical measurement and may prove useful for nonlinear spectroscopy with two-photon emission. Here, we report the first experimental demonstration of two-photon quantum interference of photon pairs emitted via biexcitons in the semiconductor CuCl. Besides applying Fourier transform to quantum interference patterns, we reconstruct the intensity spectrum of the biexciton luminescence in the two-photon sum or difference frequency. We discuss the connection between the reconstructed spectra and exciton states in CuCl as well as the capability of quantum interferometry in solid-state spectroscopy.
Spectral diffusion is the phenomenon of random jumps in the emission wavelength of narrow lines. This phenomenon is a major hurdle for applications of solid state quantum emitters like quantum dots, molecules, or diamond defect centers in an integrated quantum optical technology. Here, we provide further insight into the underlying processes of spectral diffusion of the zero-phonon line of single nitrogen vacancy centers in nano-size diamond by using a novel method based on photon correlation interferometry. The method works although the spectral diffusion rate is several orders of magnitude higher than the photon detection rate and thereby improves the time resolution of previous experiments with nano-size diamond by 6 orders of magnitude. We study the dependency of the spectral diffusion rate on the excitation power, temperature, and excitation wavelength under off-resonant excitation. Our results bring insight into the mechanism of spectral diffusion and suggest a strategy to increase the number of spectrally indistinguishable photons emitted by diamond nanocrystals.
Fourier transform spectroscopy with classical interferometry corresponds to the measurement of a single-photon intensity spectrum from the viewpoint of the particle nature of light. In contrast, the Fourier transform of two-photon quantum interference patterns provides the intensity spectrum of the two photons as a function of the sum- or difference frequency of the constituent photons. This unique feature of quantum interferometric spectroscopy offers a different type of spectral information from the classical measurement and may prove useful for nonlinear spectroscopy with two-photon emission. Here, we report the experimental demonstration of two-photon quantum interference of biphotons emitted via biexcitons in the semiconductor CuCl. Besides applying Fourier transform to quantum interference patterns, we reconstruct the intensity spectrum of the biexciton luminescence in the two-photon sum- or difference frequency. We discuss the connection between the reconstructed spectra and exciton states in CuCl as well as the capability of quantum interferometry in solid-state spectroscopy.
We examine the possibility of measuring the emission linewidth $2\ensuremath{\hbar}{\ensuremath{\Gamma}}_{2}$ of a single-photon source by Michelson interferometry. Such an emitter is characterized by a limited fluorescence intensity and, when embedded in a solid matrix, a large spectral diffusion. We show that fast spectral diffusion renders standard Fourier spectroscopy irrelevant. We then calculate the correlations of the intensities detected at the two interferometer outputs, point out the existence of two-photon interferences (coalescence) even for a non-single-mode emission, and show that the correlations are not affected by spectral diffusion at correlation times shorter than spectral dynamics. This yields two ways to measure the decoherence rate ${\ensuremath{\Gamma}}_{2}$: the recently proposed photon-correlation Fourier spectroscopy, and the study of the coalescence dip. We examine the feasibility and spectral resolution of each method, depending on spectral-diffusion characteristics, and show that both methods could be applied to typical nanometer-sized emitters such as colloidal quantum dots.