Subtopics: Pump-probe spectroscopy, Transient four-wave-mixing, Multidimensional Fourier Transform Spectroscopy

Ultrashort optical pulses can be used to probe the dynamical processes that occur on timescales that are similar, or somewhat longer, than the duration of the pulses. In a simple picture, one can think of this ability as being similar to the use of a stroboscope to do “stop action photography“. In regular photography, the ability to generate a clear picture of a moving object is based on the speed of the camera’s shutter (okay, that is in the good old days when cameras had shutter, but the equivalent exists for digital cameras). When using a stroboscope, the camera’s shutter is left open and instead the duration of the light flash is the relevant time scale. So much faster objects, for example a speeding bullet, can be “stopped”. Ultrafast spectroscopy does not entail making pictures, as in this analogy, but rather measures the evolution of the optical properties of a sample as a function of the delay between two or more pulses that are incident on the sample.

Our group uses ultrafast spectroscopy to study dynamics processes in a range of system including atomic vapors and semiconductor nanostructures. In addition, we are actively developing new spectroscopic methods, mainly in the are of multidimensional Fourier-transform spectroscopy.

Pump-probe spectroscopy

One of the simpler forms of ultrafast spectroscopy is often known as “pump-probe” spectroscopy, although that is not a particularly good name as it could describe most types of time-domain spectroscopy. A better name is probably “transient absorption” spectroscopy.

In a pump-probe measurement, an initial pulse, the “pump” excites the sample. A second time delayed pulse, the “probe”, then measures the absorption of the sample. In a simple system, say an ensemble of identical two-level atoms, the pump will excite some of the atoms, which therefore cannot absorb another photon, and thus decrease the absorption of the probe pulse. In the time interval between the pump and the probe, some of the atoms can relax back to the grounds state, and thus the absorption will recover. Thus as the delay between the pump and the probe is increased, the absorption will return to its original value and the rate at which it does will be provide information about the relaxation from the upper state to the lower state of the atoms.

For systems that are more complicated than identical two-level systems, the probe may experience other processes than just a decrease in absorption. For example, there may be an increase in absorption if there are higher excited states, or there may be changes in the shape of the absorption profile due to many-body interactions. These processes can be observed by making additional measurements on the transmitted probe pulses, with the most common being to measure its spectrum. This technique is often called “spectrally-resolved transient absorption”.

Transient four-wave-mixing

Transient four-wave-mixing (TFWM) is a coherent spectroscopy. In TFWM, the excitation pulses interact in the sample to produce a coherent signal beam in a direction that is different from the excitation beams themselves. The simplest case is for two beams, with wave vectors k_a and k_b, interacting to produce a signal beam with wavevector k_s = 2k_b – k_a. Note that while there are only two incident excition pulses, the pulse in direction k_bacts twice, thus the four waves that mix are k_a, k_b, k_b and k_s. It is also common to use 3 pulses, in which case the signal is emitted in the direction k_s = – k_a + k_b + k_c. There are many possible geometries for the incident beams in the 3 pulse experiment.

TFWM signals are typically measured as function of the delay(s) between the incident pulses. In a two pulse experiment the signal will decay exponentially at the dephasing rate, which is the homogeneous linewidth. In a simple two-level system, the homogeneous linewidth determines the width of the absorption feature, and thus TFWM does not provide any additional information compared to a simple linear absorption spectrum. However, if the sample is actually an ensemble of two-level systems and they each have a slightly difference resonance frequency, which is known as inhomogeneous broadening, the linear absorption spectrum will primarily give information about the distribution of resonance frequencies, whereas the TFWM signal will still give information about the homogeneous linewidth. In this case, the TFWM signal will actually be a pulse, known as a “photon echo”. Inhomogeneous broadening occurs due to Doppler broadening in gas phase samples and due to structural fluctuations in nanostructures.

Multidimensional Fourier Transform Spectroscopy

Multidimensional Fourier Transform spectroscopy is an enhancement to TFWM where the signal field, not just the intensity, is measured for each delay between the excitation pulses and the delays are stable and precise. These enhancements allow the Fourier transform to be taken with respect to the time over which the signal is emitted and also with respect to the delay(s) between excitation pulses. The result is a spectrum as a function of multiple frequencies. The most common case is a two dimensional spectrum, where the two frequencies correspond to the delay between the first two pulses and the signal emission time.

Two-dimensionals spectroscopy has many ways. Just as for TFWM, it can determine the homogeneous linewidth even if inhomogeneous broadening is present. However, in addition, it can determine if/how the homogeneous linewidth varies within the inhomogeneous distribution. In addition, 2D spectroscopy can immediately determine if two resonance are coupled to one another, whereas that is not the case for a simple TFWM experiment.

Multidimensional Fourier transform methods were first developed in Nuclear Magnetic Resonance spectroscopy. Over the last 15 years, there has been extensive work on implementing these ideas in the IR through visible parts of the spectrum. Our group is active in developing methods that work in the near-IR and visible. Ourprimary method is based on actively stabilizing the delays between the pulses using an apparatus that has been dubbed the “JILA MONStr” where MONStr stands for “Multdimensional Optical Nonlinear Spectrometer”. This approach is proving popular and has been duplicated (or is being duplicate) several times worldwide. We are also currently developing a new method that uses photocurrent detection, rather than a coherent signal beam.