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Physica Scripta

Digital adiabatic passage in multi-state systems

N Irani, M. Saadati-Niari, M. Amniat-Talab

Published Sep 12, 2019• 6 citations
Publisher

Abstract

Abstract Digital adiabatic passage in multi-pod and multi-lambda systems is investigated. We show that using digital variation of control fields, one can create a coherent superposition of ground states in multi-state systems. In order to design the propagator at every step, the multi-state systems are simplified to a three-state system using Morris-Shore transformation. In this method, the number of steps is arbitrary and by increasing the number of steps the population of excited states decreases to negligible small values. Sensitivity of the final fidelity with respect to exact value of t max decreases by increasing the number of steps.

DOI
10.1088/1402-4896/ab4411

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Abstract Digital adiabatic passage in multi-pod and multi-lambda systems is investigated. We show that using digital variation of control fields, one can create a coherent superposition of ground states in multi-state systems. In order to design the propagator at every step, the multi-state systems are simplified to a three-state system using Morris-Shore transformation. In this method, the number of steps is arbitrary and by increasing the number of steps the population of excited states decreases to negligible small values. Sensitivity of the final fidelity with respect to exact value of t max decreases by increasing the number of steps.
We extend the shortcut to the adiabatic passage method, proposed by Chen et al. [Phys. Rev. Lett. 105, 123003 (2010)], to the creation of an arbitrary coherent superposition of states in a multi-level system.We consider a multi-state system composed of an initial ground state, an excited state and an arbitrary number of final states.In this method, the initial state is linked to the excited state using a pump laser pulse and final states are coupled to the excited state using the Stokes laser pulses.Furthermore, the initial state is coupled to the final states using additional laser fields.We show that the problem can be reduced to the solution of a three-state loop system involving an initial ground state, an excited state and a superposition of final states.This decomposition allows to create an arbitrary coherent superposition of states using the shortcut to the adiabatic passage method.When compared to other strategies, this method provides a fast and robust approach to the coherent superposition of states.
Descriptions of coherent excitation of multi-state quantum systems model changes through coupled ordinary differential equations that become more cumbersome as the number of involved quantum states increases. It is always useful to find simplifications of the equations, ideally involving exact analytic solutions. The ultimate simplification is to a set of independent pairs of quantum states. Such sets of independent two-state linkages occur naturally when we describe the excitation between two sets of degenerate Zeeman sublevels by a field that is linearly or circularly polarized. The Morris–Shore (MS) transformation, a Hilbert-space coordinate change, generalizes this procedure to replace the description of an elaborate linkage pattern of an -state Hamiltonian in the rotating-wave approximation by a set of independent two-state systems – a basis of paired bright states and excited states supplemented with dark states and spectator states. The three-state lambda-linkage found in stimulated Raman transitions is a simple example. Both bright and dark states have found application in various procedures for manipulating quantum states, either to achieve population transfer between states or to create coherent superpositions; the dark and spectator states coincide with particular dressed (or adiabatic) states. The present review describes the MS transformation, noting its historical background, and discusses examples of its use.
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.
Abstract The treatment of time-dependent dynamics of quantum systems involving multiple states poses considerable technical challenges. One of the most efficient approaches in treating such systems is the Morris–Shore (MS) transformation which decomposes the multistate dynamics to a set of independent systems of simpler interaction pattern and uncoupled spectator states. The standard MS transformation imposes restrictions on the time dependence of the external fields addressing the states, as it requires that both Rabi frequencies have the same time profile. In this work we treat the case of the time-dependent MS transformation, which opens prospects for a variety of physically interesting processes wherein the fields may have different time dependences. We explore the adiabatic and the double-adiabatic limit, in which we demonstrate population transfer between the MS states that results in population transfer from one set of states onto another. We demonstrate the generation of superposition states between the MS states by the techniques of half adiabatic passage and fractional stimulated Raman adiabatic passage, which translate to superpositions of all the states of the involved levels.
Abstract The generation of arbitrary preselected coherent superposition of states in multi-state systems using adiabatic pulses split by a phase jump has been investigated. We consider a linkage pattern that includes a ground state and N excited states so that the ground state is coupled to the excited states using N pulses with a chirped detuning. In this scheme, time-dependent Rabi frequencies and detuning are used in two steps, and in each step, it is assumed that the Rabi frequencies have the same time dependence. Also, the Rabi frequencies in the second step have a phase jump compared to the first step, and the amount of this phase jump is the same for all pulses. It is shown that by properly adjusting the amount of phase jump in the second step and also the maximum value of Rabi frequencies in both steps, an arbitrary coherent superposition of all states can be created. In this study, the maximum values of Rabi frequencies and detuning are considered to be large enough to establish the adiabatic passage condition, and it is numerically shown that this scheme is insensitive to the change of the maximum value of Rabi frequencies and detuning.
We study the stimulated Raman adiabatic passage technique in an NNN-pod system driven by NNN 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.