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Journal of Modern Optics

Superposition of states in multi-lambda systems via generalized pulse area method

M. Amniat-Talab, M. Saadati-Niari

Published Jan 21, 2014• 10 citations
Publisher

Abstract

This paper presents an exact analytic solution for creation of any preselected coherent superposition of states in multi-lambda quantum systems by a train of coincident pulses. We show that the solution of a multi-lambda system composed of degenerate ground states, excited states, and a single initial state can be reduced by using Morris–Shore transformation to the solution of a three-state system. In this method, all of the pump and Stokes pulses have the same time dependence and the ratio of the pump pulses can be used to control the probability amplitudes of the ground states in the coherent superposition of states. Effect of spontaneous emission is efficiently suppressed by employing a train of coincident pulses. This technique resembles the technique of generalized -pulses with minimal pulse areas which is easy to reach experimentally.

DOI
10.1080/09500340.2013.877164

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This paper presents an exact analytic solution for creation of any preselected coherent superposition of states in multi-lambda quantum systems by a train of coincident pulses. We show that the solution of a multi-lambda system composed of degenerate ground states, excited states, and a single initial state can be reduced by using Morris–Shore transformation to the solution of a three-state system. In this method, all of the pump and Stokes pulses have the same time dependence and the ratio of the pump pulses can be used to control the probability amplitudes of the ground states in the coherent superposition of states. Effect of spontaneous emission is efficiently suppressed by employing a train of coincident pulses. This technique resembles the technique of generalized -pulses with minimal pulse areas which is easy to reach experimentally.
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 We present an analytically exactly solvable N -pod quantum model, in which the coupling has a hyperbolic-tangent temporal shape and the frequency detuning is constant. The solution is derived by using the Morris–Shore transformation to reduce the N -pod system to a -like one and then to a two state system and a set of decoupled states in two steps. In this work, we use the propagator for a reduced two state system and the inverse transformation to achieve the reduced three state propagator. It is shown that any preselected coherent superposition of all N ground states can be obtained from an initial superposition of M ground states in the presence of detuning. We use a train of tanh coincident pulses and we show that the effect of spontaneous emission is efficiently suppressed by increasing the number of pulses. Besides, we explore that a coherent superposition of ground states from the initial excited state can be implemented using tanh pulses.
We show that the solution of a multistate system composed of NNN degenerate lower (ground) states and one upper (excited) state can be reduced by using the Morris-Shore transformation to the solution of a two-state system involving only the excited state and a (bright) superposition of ground states. In addition, there are $N\ensuremath{-}1$ dark states composed of ground states. We use this decomposition to derive analytical solutions for degenerate extensions of the most popular exactly soluble models: the resonance solution, the Rabi, Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models. We suggest various applications of the multistate solutions, for example, as tools for creating multistate coherent superpositions by generalized resonant $\ensuremath{\pi}$ pulses. We show that such generalized $\ensuremath{\pi}$ pulses can occur even when the upper state is far off resonance, at specific detunings, which makes it possible to operate in the degenerate ground-state manifold without populating the (possibly lossy) upper state, even transiently.
In this paper, an exact analytical solution is presented for achieving coherent population transfer and creating arbitrary coherent superposition states in a five-state chainwise system by a train of coincident pulses. We show that the solution of a five-state chainwise system can be reduced to an equivalent three-state Λ-type one with the simplest resonant coupling under the assumption of adiabatic elimination together with a requirement of the relation among the four coincident pulses. In this method, the four coincident pulses at each step all have the same time dependence, but with specific magnitudes. The results show that, by using a train of appropriately coincident pulses, this technique not only enables complete population transfer, but also creates any desired coherent superposition between the initial and final states, while the population in all intermediate states is effectively suppressed. Furthermore, this technique can also exhibit a one-way population transfer behavior. The results are of potential interest in applications where high-fidelity multi-state quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, nuclear coherent population transfer, and light transfer in waveguide arrays.
Abstract Nuclear-state population transfer in the multi-lambda systems with N = 5 that interact with four x-ray laser pulses are investigated theoretically. By using the coincident pulses and stimulated Raman adiabatic passage (STIRAP) techniques, the population transfer from one initially populated ground state to an arbitrary coherent superposition of other ground states. Since the frequency of currently available x-ray lasers is lower than the gamma rays, in this method, x-ray laser pulses with different frequencies are interacting with the accelerated nuclei. We employ the Morris-Shore transformation to reduce the five-states system to two separate three-state and two-state linkage. The required laser intensities were calculated, which satisfy the conditions of coincident pulses and multi-lambda STIRAP techniques. Considering the spontaneous emission from excited states, the master equation has to be used for numerical study, and it is shown that an arbitrary superposition of final ground states can be obtained. Also, it is observed that by increasing the number of coincident pulses, the population of ground states gets closer to the ideal situation.
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.