We demonstrate experimental techniques for creating and measuring a coherent superposition of two degenerate atomic states with equal amplitudes in metastable neon. Starting from state (3)P(0), we create adiabatically a coherent superposition of the magnetic sublevels M=+/-1 of the state (3)P(2) using a tripod stimulated Raman adiabatic passage scheme. The measurement is based on the coupling of the levels (3)P(2)<-->(3)P(1) by a linearly polarized laser, followed by the detection of the population in the (3)P(2)(M=+/-2) states as a function of the polarization angle of that laser.
A technique for creation of well-defined preselected coherent superpositions of multiple quantum states is proposed. It is based on an extension of the technique of stimulated Raman adiabatic passage (STIRAP) to degenerate levels. As an example, the nine-state system composed of the magnetic sublevels of three levels with angular momenta
Jg=0,
Je=1, and
Jf=2 is studied in detail. Starting from the $\ensuremath{\mid}{J}_{g}=0,{M}_{g}=0⟩$ state, STIRAP can create an arbitrary preselected coherent superposition between the five
Mf sublevels $({M}_{f}=\ensuremath{-}2,\ensuremath{-}1,0,+1,+2)$ of the
Jf=2 level with 100% efficiency in the adiabatic limit. The populations and the phases of the
Mf states in this superposition are determined entirely by the polarizations of the two laser fields. It is shown that this technique allows one to create any superposition of the five
Mf states, that is, to reach any point in the Hilbert space of the
Jf=2 manifold, and the corresponding recipes for choosing the laser polarizations are presented.
We present the theory for a technique, based on multistate variants of the stimulated Raman adiabatic passage (STIRAP) process, that allows efficient and robust preparation of a preselected superposition of two or three degenerate states (magnetic sublevels of an atom) and the measurement of their relative amplitudes and phases. Because the preparation utilizes adiabatic passage it is robust against small fluctuations of the Rabi frequencies and temporal shapes of the coupling fields. We here describe and, in the following companion paper we demonstrate, an approach to the experimental characterization of the superposition state, i.e., the measurement of the relative phases and the ratios of amplitudes of the components. That technique, termed phase-to-population mapping, is applicable to the characterization of a stream of identically prepared atoms and is based on laser-induced fluorescence after the atoms have undergone optical pumping cycles induced by an additional laser. The optical pumping process maps the phase into populations of a subset of levels by means of a filtering laser field, and is robust against variations in the intensity and detuning of that field. We describe four linkage patterns appropriate to the creation of superpositions of two or three degenerate states of angular momentum
J=2, starting from
J=0. We offer an interpretation, from three different perspectives, of the subsequent characterization procedure.
We propose and analyze a scheme for creation of coherent superposition of meta-stable states in a multilevel atom. The scheme is based on interaction of a frequency modulated (chirped) laser pulse and a pulse of a constant carrier frequency with the atom having two meta-stable (ground) states and multiple excited states. The negligible excitation of the atoms is a priority in the proposed scheme to eliminate the de-coherence processes caused by the decay of the excited states. The scheme is applied to create coherent superposition of magnetic sublevels of ground states of the 87Rb atom taking into account all allowed electric-dipole transitions between magnetic sublevels of the 5 2S1/2 - 52P3/2 transition (D2 line). In addition to the theoretical analysis we consider possible experimental realizations of the proposed coherence creation scheme and discuss their feasibilities and constraints. We concentrate on a detection of the superposition state in the Faraday-rotation experiment. Such detection reduces technical laser noise background and offers high sensitivity of the coherence detection. Moreover, it allows extra control of the atomic sample and the interaction dynamics by external magnetic field.
We present experimental demonstrations of a technique, based on multistate variants of the stimulated Raman adiabatic passage (STIRAP) process, that allows efficient and robust preparation of a preselected superposition of two or three degenerate states (magnetic sublevels of an atom) and the measurement of their relative amplitudes and phases. The experiments verify theoretical results described in the preceding paper. We perform our experiments with neon atoms in a supersonic beam: atoms in the metastable
3P0 state are transferred to a superposition of the metastable
3P2 magnetic sublevels, using four different linkage patterns. Because the preparation utilizes adiabatic passage, it is robust against small fluctuations of the Rabi frequencies and temporal shape of the coupling fields. The relative phases and the amplitude ratios of the components of the prepared superpositions are experimentally analyzed using a technique termed phase-to-population mapping. Phase-to-population mapping is based on laser-induced fluorescence after the atoms have undergone optical pumping cycles induced by an additional laser. The optical pumping process maps the superposition phases into populations of a subset of levels by means of a filtering laser field, and is robust against variations in the intensity and detuning of that field.
The elaborate linkage pattern of the interaction Hamiltonian descriptive of pulsed laser interaction of elliptically polarized light with a degenerate two-level system can, for coherent excitation, be reduced to sets of independent pairs of coupled two-state equations by means of the Morris-Shore transformation [Phys. Rev. A 27, 906 (1983)]. By extending the earlier defining work, which dealt only with time-independent interactions, to consider various pulse shapes, one can obtain exact analytic solutions to various multilevel linkages. We use these to find the conditions on the interaction parameters (e.g., the ellipticity) leading to various population transfer schemes, for example, to achieve either population inversion or orientation. We illustrate these with the M and W linkages amongst magnetic sublevels of
J=1 or
J=2 excited by elliptically polarized light.