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Physical Review A

Superposition of states by adiabatic passage in N -pod systems

M. Amniat-Talab, M. Saadati-Niari, S. Guérin, Rahim Naderali

Published Jan 21, 2011• 24 citations
Publisher

Abstract

We study the stimulated Raman adiabatic passage technique in an $N$-pod system driven by $N$ pulsed fields when $N\ensuremath{-}2$ and $N\ensuremath{-}1$ pulses not connected to the initial state have the same shape. We show that, for properly timed pulses, robust population transfer from an initial ground state to an arbitrary coherent superposition of the ground states can be achieved in a single step. The case of $N\ensuremath{-}2$ pulses of the same shape involves a geometric phase of the same type as the one appearing in tripod systems.

DOI
10.1103/physreva.83.013817

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We study the stimulated Raman adiabatic passage technique in an NNN-pod system driven by NNN pulsed fields when N\ensuremath−2N\ensuremath{-}2N\ensuremath−2 and N\ensuremath−1N\ensuremath{-}1N\ensuremath−1 pulses not connected to the initial state have the same shape. We show that, for properly timed pulses, robust population transfer from an initial ground state to an arbitrary coherent superposition of the ground states can be achieved in a single step. The case of N\ensuremath−2N\ensuremath{-}2N\ensuremath−2 pulses of the same shape involves a geometric phase of the same type as the one appearing in tripod systems.
The technique of stimulated Raman shortcut to adiabatic passage (STIRSAP) is implemented to chainwise and N-pod systems. In chainwise systems, for large detuning conditions, the population of the middle states can be suppressed during the time evolution of the system and therefore, the Hamiltonian of an N-state system is reduced to an effective two-level system, using adiabatic elimination technique. Applying the STIRSAP method in two-level systems, the modified Rabi frequencies for fast population transfer are achieved. For N + 1-pod systems, assuming that N Stokes pulses have the same time dependence, we reduce the Hamiltonian of the original system to a three-state system. For both resonance and detuning conditions, we can reduce the three-state Hamiltonian to an effective two-state one. Using the STIRSAP technique, robust population transfer can be achieved from an initial ground state to an arbitrary coherent superposition of all ground states.
We study a train of coincident pulses technique in an N-pod system driven by N pulsed fields, when all of the pulses have the same shape and are on exact resonance. We show that the solution of an N-pod system composed of N degenerate ground states and one upper excited state can be reduced using the Morris–Shore transformation to the solution of a three-state system involving an initial superposition of M ground states, the excited state and superposition of remaining ground states. We use reduced three-state propagator to create any preselected coherent superposition of states by a train of coincident pulses. A proper pulse train is used to connect any two preselected superposition states of an N-pod system. Other advantages of this method are exact analytic solution and enhancement to the robustness of system against deviation from exact pulse areas with increasing the number of coincident pulses.
We present a general and versatile technique of population transfer based on parallel adiabatic passage by femtosecond shaped pulses. Their amplitude and phase are specifically designed to optimize the adiabatic passage corresponding to parallel eigenvalues at all times. We show that this technique allows the robust adiabatic population transfer in a Raman system with the total pulse area as low as $3\ensuremath{\pi}$, corresponding to a fluence of one order of magnitude below the conventional stimulated Raman adiabatic passage process. This process of short duration, typically picosecond and subpicosecond, is easily implementable with the modern pulse shaper technology and opens the possibility of ultrafast robust population transfer with interesting applications in quantum information processing.
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.
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 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.