Pump-Probe Experiments with a Single Molecule: ac-Stark Effect and Nonlinear Optical Response

Abstract

We have measured the ac-Stark effect on single terrylene molecules in p-terphenyl crystals at superfluid helium temperatures.With the pump beam far enough from resonance, the molecular transition shifts as expected, i.e. , proportional to the pump intensity and to the inverse pump detuning.Experiments closer to resonance with stronger beams show Autler-Townes-like structures that can be well reproduced by means of Bloch equations with two intense laser fields. These experiments are a demonstration of nonlinear optical effects with the localized electronic states of a single molecule trapped in a solid. PACS numbers: 42.50.Hz, 33.80.b, 78.55.Kz Quantum optics, the study of the interaction of simple quantum systems with coherent light, has long been a testing ground for basic quantum mechanics. The many concepts it has bred may become crucial to the working of future nanoelectronic devices at the molecular scale. This remote aim requires experimental tests of the validity of quantum concepts in complex systems such as are found in condensed matter. Many of the quantum optical experiments done to date were performed on atoms or ions in vapors, beams, or traps. Atoms have the advantage of being simple, isolated from outside perturbations, and fairly well understood theoretically. Nonlinear spectroscopy [1] and, more recently, laser cooling [2] developed largely thanks to atoms. Here, we consider a particular class of experiments, those where two laser beams (a pump and a probe) act simultaneously on a quantum system. Several experiments in atomic physics fall into this category. For instance, in sub-Doppler spectroscopy, a strong pump beam "tags" atoms by saturating one of their transitions, while the probe beam reads the absorption change. More generally, a strong pump beam, by coupling two resonant levels, "dresses" atoms with laser photons, leading to changes in the response of the dressed atom to a probe beam [3] that appear as shifts of the levels and changes of their relaxation rates. For a slightly detuned pump, the transition of the dressed atom is shifted in proportion with pump intensity, and multiphoton resonances appear, which may exhibit gain for the probe beam [4]. For a resonant pump, transitions between dressed atom levels lead to three components in the emission spectrum [5] (the Mollow triplet), while the probe absorption spectrum shows a complex shape with amplification at strong pump saturation. The absorption spectrum from the excited state to a third level shows a splitting known as the Autler-Townes effect. The shift of atomic levels under pump light, often called light shift, can be interpreted as an ac-Stark effect, where the quadratic effect of the relatively weak pump laser field is amplified by near resonance with the transition. While being perhaps the simplest manifestation of the dressing of atoms by laser photons, the light shift is the cornerstone of powerful laser-cooling methods [2] and of proposed nondestructive quantum measurements of photons [6]. For all their importance as model...

Efficient coupling of photons to a single molecule and the observation of its resonance fluorescence

“…1c. By using the common start-stop scheme [23], we recorded the intensity correlation function g (2) (τ ) [15] …”

“…Single dye molecules embedded in solids have been shown to behave as quantum mechanical two-level systems at cryogenic temperatures, exhibiting phenomena such as antibunching [1], AC Stark shift [2] and various nonlinear effects [3] known from atoms. The pioneering detection of single molecules was achieved via absorption spectroscopy assisted by a double lock-in method [4].…”

“…In the weak excitation regime, the effect of a plane-wave illumination on a molecule with a transition between levels |1 and |2 at wavelength λ 21 can be formulated as I d = (1 − σ/F )I e . Here I d is the detected intensity of the excitation beam after having encountered the emitter, σ = 3λ 2 21 /2π is the absorption cross section of the transition, and F and I e are the area and intensity of the excitation beam, respectively. The experimental realization of this simple scenario is challenging because the effect of a single molecule has to be registered on top of the noise associated with a considerable laser power and scattering background.…”

Blinking molecules: Determination of photophysical parameters from the intensity correlation function

“…With the results of Table I, one now could calculate A (14) - (16). However, numerically it is better to insert the expressions for T L , T (i) D and p i into Eq.…”

“…In the presence of metastable triplet levels the molecule can exhibit light and dark periods in its fluorescence ("blinking") [5,6], just as ions in the V or Λ configuration [7,8,9,10,11,12,13,14]. Spectroscopy of single molecules is of fundamental importance both for basic quantum mechanical aspects like antibunching, quantum jumps or the dynamical Stark effect [5,15,16], as well as for applications in chemical and biophysics, cf. e.g.…”