* Corresponding author. Fax: #41-1-632-1021. E-mail address: donley@phys.chem.ethz.ch (E.A. Donley) Journal of Luminescence 87}89 (2000) 109}114 Invited Paper Zero}phonon lines of single molecules in polyethylene down to millikelvin temperatures Elizabeth A. Donley*, Sybrand Bonsma, Viktor Palm, Valeria Burzomato, Urs P. Wild, Taras Plakhotnik Physical Chemistry Laboratory, Swiss Federal Institute of Technology, ETH-Zentrum, CH-8092, Zu ( rich, Switzerland Abstract Linewidth distributions for single terrylene molecules in polyethylene have been measured in the temperature range from 30 mK to 1.83 K. The temperature dependence of the average linewidth is best described by a linear relationship over the full temperature range. At 30 mK, the linewidth distribution has a full-width at half-maximum of &18.6 MHz and an average linewidth of 42.8(6) MHz.  2000 Elsevier Science B.V. All rights reserved. Keywords: Single-molecule spectroscopy; Linewidth distributions; Natural linewidth 1. Introduction In this work, the spectra of single terrylene molecules in polyethylene (PE) have been measured with a He/He dilution refrigerator between 30 mK and 1.83 K to deter- mine the temperature dependence of the average linewidth and to measure the lifetime-limited linewidth distribution, which corresponds to the linewidth distribu- tion at ¹"0 K. A distribution of lifetime-limited linewidths might indicate a distribution of e!ective transition dipole moments,   , or of non-radiative re- laxation rates. A distribution for   was deduced from a correlation between the linewidth and the line areas that we observed for terrylene in polyvinylbutyral [1]. Consistent with this, we also recently observed a Gaus- sian distribution of lifetime-limited linewidths with a full-width at half-maximum (FWHM) of 4.3(13) MHz for terrylene in naphthalene [2]. Since PE is more dis- ordered than naphthalene, one would expect to observe a broader distribution of lifetime-limited linewidths in PE. The importance of the low temperature becomes clear when the linewidth is written as   (¹)"  #  (¹), (1) where   is the lifetime-limited contribution, which in- cludes contributions from radiative and non-radiative transitions from the excited to the ground state, and ¹ is the temperature. The physical origin of the dephasing term   (¹) depends on the host and the temperature. In amorphous systems at low temperature, dephasing from tunneling two-level systems (TTLS) dominates [3,4]. In crystals, there is usually no dephasing from TTLS, but there can be dephasing from local vibrations. In both cases, lim    "0 [5]. An additional source of broadening of single-molecule (SM) spectra is power broadening, a consideration of which is important for the interpretation of the data. The frequency-dependent emission rate for a SM may be written as [6] R" 2  ¹  ¹  /¹  1#[(!  )¹  ]#4  ¹  ¹  K , (2) where   "  ) E  /2 is the Rabi frequency, ¹  is the lifetime, ¹  "2/  is the dephasing time, ¹  is the radiative lifetime, and K is a constant depending on 0022-2313/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 2 4 0 - 9