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.
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.
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.
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 describe a technique for creating superpositions of degenerate quantum states, such as are needed for beam splitters used in matter-wave optics, by manipulating the timing of three orthogonally polarized laser beams through which moving atoms (or molecules) pass; motion across the laser beams produces pulses in the atomic rest frame. As illustrated with representative simulations for transitions in metastable neon, a single pass through three overlapping laser beams can produce superpositions (with preselected phase) of atomic beams differing by transverse momentum corresponding to the momentum of four photons. Like the two-photon momentum transfer of the tripod linkage pattern which it extends, the method relies on controlled adiabatic time evolution in the Hilbert subspace of two degenerate dark states. It is thus a generalization to multiple dark states (and larger transfers of linear momentum to the atomic beam) of the single dark state occurring with the stimulated Raman adiabatic passage (STIRAP) technique, and therefore it is potentially insensitive to decoherence due to spontaneous emission. By extending the tripod-linkage system to more numerous degenerate states, the technique not only increases the atomic beam deflections but, as we demonstrate, allows control over the superposition phase and amplitudes. LIke other techniques based on adiabatic time evolution, the technique is robust with respect to variations of the intensity, timing, and other characteristics of the laser fields. Unlike STIRAP, the same robust partial population transfer occurs for opposite timings of the pulse sequence, as is needed for such procedures as Hadamard gates.
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 consider an adiabatic population transfer process that resembles the well-established stimulated Raman adiabatic passage. In our system, the states have nonzero angular momentums J , therefore, the coupling laser fields induce transitions between the magnetic sublevels of the states. In particular, we discuss the possibility of creating coherent superposition states in a system with coupling pattern J = 0 ⇔ 1 and 1 ⇔ 2. Initially, the system is in the J = 0 state. We show that by, applying two delayed overlapping laser pulses, it is possible to create any final superposition state of the magnetic sublevels |2, −2⟩, |2, 0⟩, |2, +2⟩. Moreover, we find that the relative phases of the applied pulses influence not only the phases of the final superposition state but also the probability amplitudes. We show that if we fix the shape and the time delay between the pulses, the final state space can be entirely covered by varying the polarizations and relative phases of the two pulses. Performing numerical simulations we find that our transfer process is nearly adiabatic for the whole parameter set.
We propose a scheme for creating atomic coherent superposition states via the technique of stimulated Raman adiabatic passage in a $\ensuremath{\Lambda}$-type system where the final state has twofold levels. With the application of a control field, it is found that the presence of double dark states leads to two arbitrary coherent superposition states with equal amplitude but inverse relative phases, even though the condition of multiphoton resonance is not met. In particular, two orthogonal maximal coherent superposition states are created when the control field is resonant with the transition of the twofold levels. This scheme can also be extended to manifold $\ensuremath{\Lambda}$-type systems.