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Conference on Lasers and Electro-Optics

Adaptive control of quantum phase in Rydberg wave packets

T. C. Weinacht, P. H. Bucksbaum

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.We have devised and implemented a method to program quantum phase in Rydberg wave packets. Our method involves several recently developed techniques all acting in concert. Furthermore, the method is quite general: one need not even know the details of the atomic potential or the optical pulse shape in order to construct the desired phase function! This is because the method relies on adaptive feedback of direct phase information from the system. Below we give some details. A regenerative amplifier was seeded by 100-fs pulses from a Ti:sapphire oscillator.

DOI
10.1109/iqec.1998.680011

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•Jan 1, 2002•0 citations
Summary form only given.We have devised and implemented a method to program quantum phase in Rydberg wave packets. Our method involves several recently developed techniques all acting in concert. Furthermore, the method is quite general: one need not even know the details of the atomic potential or the optical pulse shape in order to construct the desired phase function! This is because the method relies on adaptive feedback of direct phase information from the system. Below we give some details. A regenerative amplifier was seeded by 100-fs pulses from a Ti:sapphire oscillator.
Summary form only given. Many realized or potential applications of optically driven ultrafast quantum dynamics require specially shaped quantum states, with the ability to detect these shapes and modify them using active feedback. We have developed methods to sculpt wave packets using shaped ultrafast optical pulses. We can also view these wave packets using quantum interference methods that have been adapted from holographic techniques used to characterize classical light. These quantum state holograms have been used as feedback to sculpt specific target shapes.
We have used amplified, programmable, shaped optical pulses to engineer Rydberg wave packets in cesium. Our apparatus employs a computer-controlled liquid-crystal pulse shaper which could control either the phase or the magnitude of the pulse's spectrum. The shaped optical field was analyzed via cross correlation and frequency-resolved optical gating. The wave-packet evolution was analyzed by monitoring temporal interference via the optical Ramsey method to obtain both auto- and cross-interferograms of the engineered wave packet.
Experimental and theoretical work is presented on the control of wave packet dynamics in atomic and molecular systems. Using sequences of phase-locked optical pulses, the link between optical phase and quantum mechanical phase is explored in the Na atom and Naj dimer, representing a step towards the logical engineering of quantum states in more complicated systems. A novel apparatus, constructed to study and control the vibrational dynamics of vibrational wave packets on the Na ionic potential surface, is described in chapter 3. Theoretical simulations for proposed experiment are presented in chapter 4. Control is achieved by exploiting the phase-evolution of the constituent vibrational quantum states within the wave packet superposition. The phase relationship and the accumulated phase difference between the various components of the wave packet is determined, and a sequence of phase-locked optical pulses is employed to selectively enhance or depopulate specific vibrational states, or sets of vibrational states. The quantum state composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multi-pulse response of the time-dependent vibrational state populations. In chapter 5, the quantum interference between Rydberg electron wave packets in the Na atom is investigated using pairs of phase-locked wave packets, allowing manipulation of the total orbital angular momentum of Na Rydberg atoms. Initially the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows specific angular momentum compositions within the resultant wave packet to be engineered. Experimentally, this final quantum state distribution is analysed in the frequency domain using state selective field ionisation, and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets.
We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the system into a desired state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.
We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the quantum system into a desired physical state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator (AOM) pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.
Quantum computation has experienced a steady growth in interest in recent years. With the rapid development of quantum technologies, the quantum mechanical nature of physical systems is becoming an increasingly important part of future industrial technology. The Rydberg atom is one of the best test tubes in which to attempt programmable coherent control because of our in-depth understanding of both atomic physics and ultrafast optics. We demonstrate the use of Rydberg atoms for processing quantum information and implementing quantum algorithms. We adopted N Rydberg energy levels of Cesium atom to store information. The phases of the energy states were each programmed and coherently evolve in time with the encoded information. A coherent manipulation then transferred the information contained in the phases to state amplitudes. The programming and the converting of the information in the data register were both performed by ultrafast optical pulses. We implemented an N-state Rydberg atom data register, with N = 6 and 8. Using half-cycle pulses (HCP), we devised methods which perform unitary operations on this data register. Application of the HCP, or terahertz short pulse, to wave packets prepared with one energy state phase-reversed with respect to the others yields a much simpler wave packet. This interaction forced multi-mode interference which constructively interfered only for the phase-flipped state. An impulsive model calculation as well as direct integration of the time-dependent Schrodinger equation showed good agreement with the experimental data. Related to the quantum algorithms, the pseudo-unitary operation implemented by the HCP had a similar structural form to the Grover's inversion-about-average operation. For the same reasons that lead to the Grover's quantum state amplification, the state amplitude of the energy state whose phase was reversed robbed atomic population from all other states. Our implementation of the Grover's inversion-about-average operation has accomplished most of Grover's search protocol. In order to improve upon our implementation and to attempt other quantum algorithms, we conclude that a sophisticated shaping of terahertz pulses is required.