In transient spectroscopy, the time-resolution is usually limited by the pulse width or the risetime of light sources or equivalent perturbers. In the extremely short time region, however, its improvement by shortening the pulse width is not an easy way even with the recent development of femtosecond pulse technique. We propose here a new method of transient spectroscopy were the time resolution is not limited by the light duration tp but limited only by the correlation time τc of light sources, being generally much shorter than tp. A temporally incoherent light has a short τc corresponding to the reciprocal bandwidth, and appears like a single pulse of duration τc in the auto-correlation measurement. This kind of light is therefore expected to play essentially the same role as a short pulse in nonlinear spectroscopy utilizing the auto-correlation technique. We present here a basic theory and an experiment which confirm this idea.
A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}$ which are originated from a single beam at frequency $\ensuremath{\omega}$ but have mutual time delay $\ensuremath{\tau}$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{3}=2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ at $\ensuremath{\omega}$ is calculated as a function of $\ensuremath{\tau}$. Even with the light having a much longer duration than both
T1 (the longitudinal relaxation time) and
T2 (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\ensuremath{\tau}$, represents a decay profile determined mainly by
T2 for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\ensuremath{\tau}}_{c}$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the
T1 effect. However, it does not cause a significant error in the determination of
T2. Moreover, as $\frac{{T}_{2}}{{T}_{1}}\ensuremath{\rightarrow}0$, the trace becomes a single-exponential decay curve determined only by
T2. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\ensuremath{\tau}}_{c}$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.
It has been recently pointed out that incoherent light can be used to generate coherent optical transients and that there are decided advantages in using such broad-band non-laser source to achieve very high time resolution {1,2}. When a light pulse and its time-delayed replica interact with a sample to produce the non-linear optical response, the ultimate time resolution should identify with the correlation time τC of the light field rather than with the pulse duration τL. The situation where τC ≪ τL is easily obtained with broad-band incoherent light sources. Time resolution in the femtosecond range is then attainable using nanosecond light pulses. This has been recently demonstrated through the observation of the relaxation of photon echoes in Nd3+-doped silicate glass {1,2}. In these cases, attention is focused on the measurement of fast homogeneous decay rates and the inhomogeneous broadening ΩD is assumed to be much larger than the spectral width of the excitation light.
Until now all reported studies of transient spectroscopy with incoherent light, including photon echo and pump-probe spectroscopy, were concerned with two-level systems where quasi-monochromatic light of only one frequency couples the two levels.[1-4] However, there exist various coherent transient phenomena where light of two or more frequencies are concerned, and time resolution of the transient spectroscopies using these phenomena are also expected to be limited not by the duration of used light pulses but by the correlation time of the radiation fields.[5]
Measurements of the relaxation times T1 and T2 of a two-level system by nonlinear transient spectroscopic methods are discussed, where delayed incident pulses are assumed to have correlation times much shorter than T1 or T2 but varied widths. In particular, a delayed degenerate four-wave mixing (photon echoe) and apump-and-probe type transmission measurement with incoherent long pulses are considered in detail, and a principle of their use for ultrafast spectroscopy is clarified. If the field is steady and T1>>T2, the time resolutionof T2measurement by the delayed four-wave mixlng is determined by the field correlation, therefore by the spectral width of the incident light irrespective of the pulse width. The time resoution of the T1 measurement by the pump-and-probe method is determined by the intensity correlation of the incident light, whereasthe one by the delayed four-wave mixing by a higher order correlation.
We present a fully quantum theory of time-resolved transient absorption spectroscopy, providing a general framework for describing the linear response of a nonequilibrium target to quantum probe fields beyond the semiclassical approximation. We elucidate how quantum correlations between probe-field frequency modes couple to coherences in the target and derive a simple expression for computing the resulting spectroscopic signals. We identify conditions under which quantum light can modify transient absorption spectra beyond the limits achievable with classical fields. Our work establishes a theoretical foundation for exploiting quantum light in ultrafast spectroscopy and suggests new routes for resolving dynamics in matter on timescales shorter than the duration of the probe pulse.
Over the past few years, dramatic advances in short pulse technology have pushed studies of dynamical processes to ever shorter time scales. Unfortunately, short pulse technology remains beyond the means of many investigators. A simple and clever alternative approach to achieving high temporal resolution was recently proposed by several groups1−4. In this approach, time resolution is limited only by the coherence time of the excitation light, rather than by its duration. Since laser light of short coherence time (i.e. large bandwidth) is much more easily generated than the corresponding short pulse, this result is of great importance.