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Laser Physics Letters

Coherent superposition of states in N -pod systems by hyperbolic-tangent coincident pulses

S. Mirza-Zadeh, M. Saadati-Niari, M. Amniat-Talab

Published Jul 26, 2018• 8 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/aacfaa

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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 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.
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 present an analytically exactly solvable two-state quantum model, in which the coupling has a hyperbolic-tangent temporal shape and the frequency detuning is constant. The exact solution is expressed in terms of associated Legendre functions. An interesting feature of this model is that the excitation probability does not vanish, except for zero pulse area or zero detuning; this feature is attributed to the asymmetric pulse shape. Two limiting cases are considered. When the coupling rises very slowly, it is nearly linear and the tanh model reduces to the shark model introduced earlier. When the coupling rises very quickly, the tanh model reduces to the Rabi model, which assumes a rectangular pulse shape and hence a sudden switch on. Because of its practical significance, we have elaborated the asymptotics of the solution in the Rabi limit, and we have derived the next terms in the asymptotic expansion, which deliver the corrections to the amplitude and the phase of the Rabi oscillations due to the finite rise time of the coupling.
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.
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 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.