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Physica Scripta

Coherent superposition of states in multi-state systems using adiabatic pulses split by a phase jump

Tohid Faraji, M. Amniat-Talab, M. Saadati-Niari

Published Aug 23, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad7335

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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 propose a technique for the accurate, flexible, and robust generation of arbitrary preselected coherent superpositions of two quantum states. It uses a sequence of two adiabatic pulses split by a phase jump serving as a control parameter. Each pulse has a chirped detuning, which induces a half crossing, and acts approximately as a half-$\ensuremath{\pi}$ pulse in the adiabatic regime. The phase jump is imprinted onto the population ratio of the created superposition state. Of the various possible relations between the two pulses, we select the case when the Rabi frequency and the detuning of the second pulse are mirror images of those of the first pulse, and the two detunings have opposite signs. Then the mixing angle of the created superposition state depends on the phase jump only. For other arrangements, the superposition mixing angle is shifted by the dynamic phases of the propagators, which makes these cases suitable for state tomography. This sandwich setup comes along with the advantage that it reduces the error $\ensuremath{\epsilon}$ of each individual pulse down to $4{\ensuremath{\epsilon}}^{2}$ overall. Therefore, the proposed technique combines the benefits of robustness stemming from adiabatic evolution with accuracy generated by the twin-pulse error suppression, and flexibility of the created superposition state controlled by the value of the phase jump $\ensuremath{\phi}$. In addition to the general analysis, we present a simple exactly soluble trigonometric model in order to illustrate the proposed technique. In this model, when the pulse area AAA increases, the nonadiabatic oscillations are damped as ${A}^{\ensuremath{-}1}$ for a single pulse and ${A}^{\ensuremath{-}2}$ for the two-pulse sequence. Finally, the proposed technique is iteratively extended to sequences of N=2nN={2}^{n}N=2n pulses by concatenating half-$\ensuremath{\pi}$ sequences and splitting them by a phase jump, thereby further reducing the nonadiabatic error $\ensuremath{\epsilon}$ to ${(2\ensuremath{\epsilon})}^{N}$. This makes the proposed technique suitable for generating high-fidelity quantum rotation gates even when starting with errant pulses.
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.
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.
The common objective of the application of adiabatic techniques in the field of quantum control is to transfer a quantum system from one discrete energy state to another. These techniques feature both high efficiency and insensitivity to variations in the experimental parameters, e.g., variations in the driving field amplitude, duration, frequency, and shape, as well as fluctuations in the environment. Here we explore the potential of adiabatic techniques for creating arbitrary predefined coherent superpositions of two quantum states. We show that an equally weighted coherent superposition can be created by temporal variation of the ratio between the Rabi frequency $\mathrm{\ensuremath{\Omega}}(t)$ and the detuning $\mathrm{\ensuremath{\Delta}}(t)$ from 0 to $\ensuremath{\infty}$ (case 1) or vice versa (case 2), as it is readily deduced from the explicit adiabatic solution for the Bloch vector. We infer important differences between cases 1 and 2 in the composition of the created coherent superposition: The latter depends on the dynamical phase of the process in case 2, while it does not depend on this phase in case 1. Furthermore, an arbitrary coherent superposition of unequal weights can be created by using asymptotic ratios of $\mathrm{\ensuremath{\Omega}}(t)/\mathrm{\ensuremath{\Delta}}(t)$ different from 0 and $\ensuremath{\infty}$. We supplement the general adiabatic solution with analytic solutions for three exactly soluble models: two trigonometric models and the hyperbolic Demkov-Kunike model. They allow us not only to demonstrate the general predictions in specific cases but also to derive the nonadiabatic corrections to the adiabatic solutions.
We propose a scheme for coherent control of population transfer and arbitrary superpositions of quantum states by a single-chirped laser pulse in a Λ-type excited-doublet four-level system. It is shown that selective, efficient, and robust population transfer from the initial state to the target states (excited or ground) can be achieved via chirped adiabatic passage when the pulse bandwidth is smaller than about 1/10 of the energy separations between the excited-doublet levels and between the ground states. Moreover, arbitrary coherent superpositions between the excited-doublet states, or between the higher ground state and either of the excited-doublet states, can be created by appropriately tuning the chirp rate and detuning the laser field. The proposed flexible method of coherent control of population transfer and arbitrary superpositions between the initially unpopulated states requires only a single pulse, and is robust against variations in the laser parameters, which has potential applications in quantum information processing.
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.