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Physical Review A

Adiabatic creation of coherent superposition states in atomic beams

Razmik G. Unanyan, Monika E. Pietrzyk, Bruce W. Shore, Klaas Bergmann

Published Nov 11, 2004• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.70.053404

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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 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^{3}{P}_{0}3P0​ state are transferred to a superposition of the metastable 3P2^{3}{P}_{2}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.
We discuss the properties of a simple and robust scheme for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states - fractional stimulated Raman adiabatic passage (fractional STIRAP) - first proposed by Marte et al (1991 Phys. Rev. A 44 R4118). As in STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, here the two pulses terminate simultaneously, while maintaining a constant ratio of amplitudes. We extend earlier research and suggest a realization of this scheme with two smoothly varying delayed laser pulses (which can be derived from a single laser), the parameters of the created superposition being controlled by the polarization of the delayed pulse. Furthermore, we provide simple analytic estimates of the robustness of this process against variations in the laser intensity, laser frequency and pulse delay. Finally, we discuss an extension to multistate systems which provides a possibility for creating coherent superpositions of more than two states.
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=2J=2J=2, starting from J=0J=0J=0. We offer an interpretation, from three different perspectives, of the subsequent characterization procedure.
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{J}_{g}=0Jg​=0, Je=1{J}_{e}=1Je​=1, and Jf=2{J}_{f}=2Jf​=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{M}_{f}Mf​ sublevels $({M}_{f}=\ensuremath{-}2,\ensuremath{-}1,0,+1,+2)$ of the Jf=2{J}_{f}=2Jf​=2 level with 100% efficiency in the adiabatic limit. The populations and the phases of the Mf{M}_{f}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{M}_{f}Mf​ states, that is, to reach any point in the Hilbert space of the Jf=2{J}_{f}=2Jf​=2 manifold, and the corresponding recipes for choosing the laser polarizations are presented.
We discuss a simple scheme for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states. The technique, which we call fractional stimulated Raman adiabatic passage ({\it f-STIRAP}), is based upon (incomplete) adiabatic population transfer between an initial state ψ1ψ_1ψ1​ and state ψ3ψ_3ψ3​ through an intermediate state ψ2ψ_2ψ2​. As in STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, the two pulses terminate simultaneously while maintaining a constant ratio of amplitudes. The independence of f-STIRAP from details of pulse shape and pulse area makes it the analog of conventional STIRAP in the creation of coherent superpositions of states. We suggest a smooth realization of f-STIRAP which requires only two laser pulses (which can be derived from a single laser) and at the same time ensures the automatic fulfillment of the asymptotic conditions at early and late times. Furthermore, we provide simple analytic estimates of the robustness of f-STIRAP against variations in the pulse intensity, the pulse delay, and the intermediate-state detuning, and discuss its possible extension to multistate systems.
Coherent manipulation of quantum states is of crucial importance in accurate control of a quantum system. A fundamental goal is coherently transferring the population of a desired state with near-unit fidelity. For this purpose, we theoretically demonstrate a novel coherent double-stimulated Raman adiabatic passage (STIRAP) in a three-level Λ-type system for realizing the switch of unequal initial preparations on two ground states. This operation uses a single optical pulse sequence accomplishing both bright-STIRAP and dark-STIRAP processes, in which the intermediate-level detuning and the pulse delay must be given an optimal adjustment. Besides, owing to the imperfection of double-STIRAP transition, the sensitivity of the switch fidelity with respect to the spontaneous loss from the intermediate state, to the pulse amplitude and to the population difference, is also discussed. This work suggests a simple and experimentally feasible all-optical approach to switch a superposition quantum state, serving as one-step closer to the goal of coherent manipulation of quantum systems.