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arXiv:0707.0063 · Bulletin of the American Physical Society

The STIRAP-based unitary decelerating and accelerating processes of a single free atom

Xijia Miao

Published Jul 1, 2007• 5 citations
arXivHTMLPDF

Abstract

A STIRAP-based unitary decelerating (accelerating) process consists of a train of the standard three-state STIRAP pulse sequences which may act as the basic unitary decelerating (accelerating) sequences. The present work is focused on investigating analytically and quantitatively how the momentum distribution of a momentum superposition state such as a momentum Gaussian wave-packet state of a single freely moving atom affects the STIRAP state transfer in these decelerating and accelerating processes. The complete STIRAP state transfer and the unitarity of these processes are stressed highly in the investigation. It has been shown that the momentum distribution has an important influence upon the STIRAP state-transfer efficiency. In the ideal adiabatic condition these unitary decelerating and accelerating processes for a freely moving atom are studied in detail, and it is shown that they can be used to manipulate and control in time and space the center-of-mass position and momentum of a Gaussian wave-packet motional state of a free atom. Two general (strict and accurate) adiabatic conditions for the basic STIRAP decelerating and accelerating processes are derived analytically. With the help of the STIRAP theory and the unitary quantum dynamics it confirms theoretically that the time- and space-compressing processes of the quantum control process (quant-ph/0607144) can be realized almost perfectly by the STIRAP-based unitary decelerating and accelerating processes in the ideal or nearly ideal adiabatic condition.

DOI
10.48550/arxiv.0707.0063

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arXiv:1601.06058•Nature Communications•Aug 11, 2016•233 citations
A STIRAP-based unitary decelerating (accelerating) process consists of a train of the standard three-state STIRAP pulse sequences which may act as the basic unitary decelerating (accelerating) sequences. The present work is focused on investigating analytically and quantitatively how the momentum distribution of a momentum superposition state such as a momentum Gaussian wave-packet state of a single freely moving atom affects the STIRAP state transfer in these decelerating and accelerating processes. The complete STIRAP state transfer and the unitarity of these processes are stressed highly in the investigation. It has been shown that the momentum distribution has an important influence upon the STIRAP state-transfer efficiency. In the ideal adiabatic condition these unitary decelerating and accelerating processes for a freely moving atom are studied in detail, and it is shown that they can be used to manipulate and control in time and space the center-of-mass position and momentum of a Gaussian wave-packet motional state of a free atom. Two general (strict and accurate) adiabatic conditions for the basic STIRAP decelerating and accelerating processes are derived analytically. With the help of the STIRAP theory and the unitary quantum dynamics it confirms theoretically that the time- and space-compressing processes of the quantum control process (quant-ph/0607144) can be realized almost perfectly by the STIRAP-based unitary decelerating and accelerating processes in the ideal or nearly ideal adiabatic condition.
The paper first discusses theoretically the off-resonance selective excitation method that is dependent on the atomic internal states and used to generate approximately a standard coherent state of harmonic oscillator. The coherent average method then is proposed to construct the state-selective trigger pulse. A state-selective trigger pulse can keep Gaussian shape unchanged but change in an internal-state-dependent form the center-of-mass position and/or momentum of an atomic Gaussian wave-packet motional state. A Gaussian wave-packet state is one of the simplest wave-packet states that can be easily manipulated and controlled in time and space. The paper also investigates how to manipulate in time and space an atomic Gaussian wave-packet motional state by a generalized quadratic potential field. A general quadratic Hamiltonian can affect not only the center-of-mass position and momentum but also the complex linewidth of a Gaussian wave-packet motional state while keep Gaussian shape of the motional state unchanged. It is shown that generally quadratic terms of a quadratic Hamiltonian can control directly the complex linewidth, while linear terms of a quadratic Hamiltonian can affect only the center-of-mass position and momentum of a Gaussian wave-packet motional state.
The problem of the coherent control of atomic states, preparation of atoms in a stable superposition state, and atomic population transfer has attracted much attention in the last decade. One of the main motivations is associated with the rapid development of the field of quantum computing. One of the key problems of quantum information processing is the construction of given coherent superposition atomic states in a macroscopic volume. Stimulated Raman adiabatic passage (STIRAP) [1] is considered to be the most common method for atomic population transfer in quantum systems. Being analyzed in detail on various quantum systems from both theoretical and experimental points of view, this method is widely adopted for the implementation of tools as optical devices for atomic beams, control of chemical reactions, high-precision magnetometry, atom cooling, etc. Meanwhile, an alternative method for population transfer, based on the intuitive pulse sequence with large one-photon detunings was demonstrated in [2]. In contrast with the STIRAP method, where the population transfer is realized via a dark state, the population transfer for the intuitive pulse sequence is obtained via a bright state. The authors of [2] called the atomic population transfer of this kind b-STIRAP. A detailed theoretical analysis of the b-STIRAP process in media with equal oscillator strength on adjacent transitions was performed in [3]. However, it is well-known that an oscillator strengths ratio different from unity can considerably impact on the coherent processes in Λ-media (see e.g. [4]). In the present work an analytical and numerical analysis of the b-STIRAP process in a medium with unequal oscillator strengths is performed. It is shown that the length of population transfer can be considerably increased by an appropriate choice of the dipole transitions. 1. N.V.Vitanov, B.W.Shore,K.Bergman, Adv. Atom.,Mol, Optical Physics, 46, 55-190, (2001). 2. J.Klein, F.Beil, Th.Halfmann, , Phys.Rev.Lett. 99,113003 (2007) 3. G.G. Grigoryan, G. Nikoghosyan, T. Halfmann, Y.T. Pashayan-Leroy, C. Leroy, S.Guerin, Phys.Rev. A 80, 033402 (2009) 4. G.G.Grigoryan, Y.Pashayan, Propagation of pulses in a three-level medium at exact two-photon resonance. Phys.Rev. A 64, 013816, 2001
The rovibrational dynamics of stimulated Raman adiabatic passage (STIRAP) through permanent dipole moment transitions are investigated theoretically using a time-dependent quantum wave packet method for the ground electronic state of an HF molecule. The two basic STIRAP processes, $\ensuremath{\Lambda}$ and ladder systems, are simulated. The calculated results show that nearly 100100%100 of the population can be transferred to the target state. Besides the interested transitions, the pulses can induce other transitions which affect the dynamics of STIRAP. The final populations of the initial and target states depend on delay time.
This work theoretically investigates possibilities of using the Stimulated Raman Adiabatic Passage (STIRAP) and its variants to control a coherent superposition of quantum states. We present a generalization of the so-called fractional STIRAP (f-STIRAP), demonstrating precise control over the mixing ratio of quantum states in the wave packet. In contrast to conventional f-STIRAP, designed to drive a system from an eigenstate into a coherent superposition, our scheme enables arbitrary control over the composition of an already existing superposition state. We demonstrate that an approximate version of this technique -- where analytically designed laser pulses with composite envelopes are replaced by simple Gaussian pulses -- achieves comparable performance in controlling the dynamics of the wave packet. A limiting case of this scheme, utilizing two pulses with identical Gaussian envelopes and tuned delay and relative phase, is also explored, revealing experimentally accessible pathways for manipulating quantum coherence. We apply our developed techniques to control the ultrafast charge migration in the spin-orbit split ground electronic states of xenon cation via intermediate valence- and core-excited states. Finally, we propose concrete experimental realizations of the developed control schemes in combination with attosecond transient absorption spectroscopy as a method to probe the system.
The tomography of a single quantum particle (i.e., a quantum wave packet) in an accelerated frame is studied. We write the Schrödinger equation in a moving reference frame in which acceleration is uniform in space and an arbitrary function of time. Then, we reduce such a problem to the study of spatiotemporal evolution of the wave packet in an inertial frame in the presence of a homogeneous force field but with an arbitrary time dependence. We demonstrate the existence of a Gaussian wave packet solution, for which the position and momentum uncertainties are unaffected by the uniform force field. This implies that, similar to in the case of a force-free motion, the uncertainty product is unaffected by acceleration. In addition, according to the Ehrenfest theorem, the wave packet centroid moves according to classic Newton's law of a particle experiencing the effects of uniform acceleration. Furthermore, as in free motion, the wave packet exhibits a diffraction spread in the configuration space but not in momentum space. Then, using Radon transform, we determine the quantum tomogram of the Gaussian state evolution in the accelerated frame. Finally, we characterize the wave packet evolution in the accelerated frame in terms of optical and simplectic tomogram evolution in the related tomographic space.
Accurate control of a quantum system is a fundamental requirement in many areas of modern science ranging from quantum information processing to high-precision measurements. A significantly important goal in quantum control is preparing a desired state as fast as possible, with sufficiently high fidelity allowed by available resources and experimental constraints. Stimulated Raman adiabatic passage (STIRAP) is a robust way to realize high-fidelity state transfer but it requires a sufficiently long operation time to satisfy the adiabatic criteria. Here we theoretically propose and then experimentally demonstrate a shortcut-to-adiabatic protocol to speed-up the STIRAP. By modifying the shapes of the Raman pulses, we experimentally realize a fast and high-fidelity stimulated Raman shortcut-to-adiabatic passage that is robust against control parameter variations. The all-optical, robust and fast protocol demonstrated here provides an efficient and practical way to control quantum systems.