Coherent superpositions of states in coupled Hilbert-space using step by step Morris–Shore transformation

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.

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“…θ j and θ j are time independent mixing angles to design the elements of T M and T N−M matrices, respectively. Taking pulse amplitudes as [27]…”

Section: Reducing Of N-pod System To a Three-state λ-Like Systemmentioning

confidence: 99%

“…T M and T N−M are respectively M-dimensional and N − M-dimensional matrices. T M can be obtained by the following matrix [27]:…”

Section: Reducing Of N-pod System To a Three-state λ-Like Systemmentioning

confidence: 99%

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

2018

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“…The method used in Ref. [32] is employed for the N -pod system and coupled Hilbert space in [33,34], respectively. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In order to use the zero-area pulse technique in the mentioned complex systems, the system must first be converted to an equivalent two-state system. For simplification of the system, we have used step-by-step Morris-Shore (MS) [50][51][52] transformation as the complex system is reduced to a two-level system and several uncoupled states [34]. Moreover, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Coherent superposition of states in degenerate systems using zero-area pulses

Saadati-Niari,

Amiri

2024

Rev. Mex. Fís.

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The coherent superposition of states in degenerate quantum systems is investigated using detuned laser pulses in which the Rabi frequencies are time-dependent, and the pulse area is zero. In this study, a quantum system with an arbitrary number of degenerate states in the ground set as well as an arbitrary number of degenerate states in the exciting set is considered. We assume that all states in the ground set are coupled to the excited states using laser pulses such that the pulse area of Rabi frequency is zero, and all of them have the same time dependence. It is also assumed that all laser pulses are in a non-resonant condition with Bohr transitions, and all detunings are the same. We will show that by applying the appropriate temporal dependence for the pulses and the appropriate rate for the detunings, the population can be transferred from an arbitrary superposition from the ground states to a desired superposition from the excited states.

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“…Rangelov and Vitanov [17] proposed another technique for producing complete population transfer in threestate Λ-like systems by a train of coincident pulse pairs, in which for large number of pulse pairs the maximum population in the middle state is reduced to a negligible small value. Recently, the proposed technique in [17] has been extended to multi-state systems [18][19][20], nuclear state population transfer [21,22] and hyperbolic-tangent pulses [23]. Vatikus and Greentree [24] proposed another scheme of adiabatic passage, with a stepwise change of the fields, named digital adiabatic passage (DAP).…”

Section: Introductionmentioning

confidence: 99%

Digital adiabatic passage in multi-state systems

2020

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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.

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Coherent superpositions of states in coupled Hilbert-space using step by step Morris–Shore transformation

Cited by 8 publications

References 40 publications

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

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

Coherent superposition of states in degenerate systems using zero-area pulses

Digital adiabatic passage in multi-state systems

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