There are a few issues your question brings up. First, the idea that species evolve from simple to complex is actually not a prediction or inevitable consequence of evolution by natural selection. The terms "simple" and "complex" themselves are ill-defined. For instance, if you defined "complex" to be size of the genome, the most complex organism found to date is probably a flowering plant from Japan. This idea of arranging organisms from simple to complex hearkens back to a pre-Darwinian idea of the Great Chain of Being.
You may be thinking that since multicellular life, for example, evolved from single-celled organisms, mutlticellular life is more complex than single celled life. The fallacy is that modern single celled organisms also evolved from the same single-celled ancestor. In no evolutionary sense is modern multicellular life more evolved than modern single celled organisms. You can, of course, defined notions of complexity to make multicellular life more complex than single celled life, but such definitions have no evolutionary significance.
We can, of course, say that organisms evolved from earlier organisms. So the second issue your question brings up is have scientists seen large evolutionary changes in a laboratory setting. The example you bring up is whether we could observe the evolution of photosynthesis in a lab.
The short answer is no. We would not expect traits which took millions of years to evolve to evolve in a lab in a shorter amount of time. In the case of photosynthesis, we may not even have a good idea what selective pressures were involved early in the evolution of cyanobacteria. Such traits do not usually evolve in their totality in one step. Instead there are many steps along the way, each of which may be selected for in particular environments for different reasons. Even if we had millions of years and a very large lab, we may not know of these early selective pressures to successfully recreate the evolution of a particular trait. (There's actually a bit more depth here which I am glossing over. Since the variation in the population is different, the same series of selective pressures won't necessarily yield the same outcome. When traits evolve through convergent evolution, which is what you are suggesting, they virtually always have different genetic bases and underlying biochemistry. But a digression into this is probably a distraction from the central point.)
So, you may reasonably ask, if we can not directly observe the evolution of these major traits in a lab, how do we know that they evolved? There are multiple lines of evidence:
- We can see smaller changes occur in shorter periods of time, so it seems likely that the same process creates larger changes in longer periods of time.
- For many large traits, we see evidence of common ancestry and the same underlying biology being used for different purposes.
- For some traits, we have the evolutionary history of that trait and can identify the sequence of events which brought that trait about (the best evidence generally comes from skeletal traits, where there's preservation).
- More speculative evolutionary histories can still be examined through genetic techniques such as molecular clocks, which can indicate when species diverged from a common ancestor.