Old quantum theory stated that the 2S and 2P states of hydrogen were degenerate. True to form, this was subsequently proven false by experiment. Lamb and Retherford measured a small splitting of the levels that is known today as the Lamb shift. It is the result of the emission and reabsorption of virtual photons by the electron ("self energy") in the atom. Thus, for a true picture of atomic energy states one must include the quantum theory of light and matter known by the moniker quantum electrodynamics or QED. Legend has it that the theoretical expression for the Lamb shift in hydrogen was formulated by Bethe whilst taking a train journey.
A false belief peddled when a student is introduced to quantum theory is that the hydrogen atom is the simpliest, and in fact only, multi-body system that can be sloved exactly. However, this is not the case: in many ways, the simpliest quantum system is muonium, the pairing of a positive muon with an electron. This is because both muon and electron are leptons, and when we enter the world of QED the physics of leptons is much better understood than that of hadrons, the family of particles to which the proton belongs. A simple example of the difference between leptons and hadrons is that leptons are essentially point like particles, where as hadrons have a finite (if small) size. When increasingly accurate determinations of the Lamb shift appeared, it soon became apparent that the size of the proton (which has still to be accurately determined) was embarassingly unknown.
In collaboration with the University of Heidelberg, we are conducting experiments to measure the 1S-2S transition in muonium, in an attempt to determine the Lamb shift of the transition (1S and 2S shifts together). We attempt to do this via 2 +1 Resonance Enhanced Multiphoton Ionisation (REMPI) of the atom via the 2S state. The muonium is stripped of the electron, and the muon decays to a positron, electron and neutrino. The decay products of the muon are detected in a Time Of Flight (TOF) analyser. The coincidence between the laser pulse and the detection of decay products indicates that the positrons and electrons are from the muonium 2S state. The muonium is produced using a pulsed muon source (50 Hz) at the ISIS facility at the Rutherford Appleton Laboratory (RAL). A fraction of these muons are stopped in a silicon dioxide powder target and forms muonium by electron capture. Around 80 atoms leave the surface per muon pulse. They interact with two conterpropagating laser beams, which allow Doppler free spectroscopy of the 1S-2S transition.
The 2S state of hydrogen has a forbidden one photon electric dipole transition to the ground state (essentally, two photon emission is necessary) and thus the 2S state is long lived and the two photon transition line is very narrow. However, the muonium atom has a lifetime of only a few microseconds (the decay time of the positive muon), so there is a fundamental limit on the accuracy of the shift. The lifetime of the muon is 2.2 microseconds, and since both the ground and excited states decay with this time constant, the fundamental linewidth is 145 kHz. Nevertheless, experiment has yet to approach the natural linewidth of muonium. In the 1991 experiment, 28 ns uv pulses were produced from seeded dye laser amplifier, that unfortunately possessed a large amount of chirp- dispersion of the output radiation wavelength. Because of instabilities in the dye flow, the chirp also varied from pulse to pulse. Finally, the short pulse length limited the frequency accuracy to at most 5MHz. The most recent determination of the 1S-2S transition frequency has an experimental uncertainty of 46 MHz. Our next experiment hopes to reduce this error by a factor of at least ten.
In order to improve the accuracy, the dye laser is replaced by a Ti:Sapphire solid state laser seeding an Alexandrite laser amplifier at 409 254 660 MHz. To lock the laser to an absolute frequency, we are developing at Oxford, in collaboration with the University of Novosibirsk, a new frequency standard based on hot iodine. The technique of Frequency Modulation spectroscopy is used to produce derivative-like hyperfine spectra suitable for locking. For more details, visit our laser spectroscopy page.
The Alexandrite ring amplifier produces 150-200 ns pulses, leaving a transform-limited pulse width of about 1 MHz. In addition, the chirp should be reproducable from pulse to pulse, and efforts are to be made to reduce this further. The output is frequency tripled to 1 227 760 GHz (around 244 nm) in LBO and BBO crystals. This radiation probes the cloud of transient muonium atoms formed just above the silicon dioxide target.
We have recently set up this experiment at RAL and performed a preliminary run. Several muonium "events" were recorded, but a final result will not be possible until the run is repeated next May.