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Physical Review A

Phase-conjugate picture of a wave-packet interference design for arbitrary target states

Xin Chen, John A. Yeazell

Published May 1, 1999• 5 citations
Publisher

Abstract

Target states are specifically desired states of systems that allow the control of processes or the investigation of unique phenomena. A time-domain scheme for the excitation of such states by the interference of multiple wave packets is developed. The scheme leads to analytical results for the optical field required to excite an arbitrary target state. The scheme suggests a clear physical picture for the design process that is applicable to many systems. The design has strong similarities to the phase-conjugation process in optics. A strong point of the scheme is that it picks a simple set of solutions from the infinite number of possible solutions for a particular target state. This characteristic may be attributed to the choice of a classical wave-packet basis as the appropriate basis for this time-domain scheme. We show that a small number of pulses are sufficient to produce a wide range of target states (both classical and nonclassical target states are designed).

DOI
10.1103/physreva.59.3782

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Target states are specifically desired states of systems that allow the control of processes or the investigation of unique phenomena. A time-domain scheme for the excitation of such states by the interference of multiple wave packets is developed. The scheme leads to analytical results for the optical field required to excite an arbitrary target state. The scheme suggests a clear physical picture for the design process that is applicable to many systems. The design has strong similarities to the phase-conjugation process in optics. A strong point of the scheme is that it picks a simple set of solutions from the infinite number of possible solutions for a particular target state. This characteristic may be attributed to the choice of a classical wave-packet basis as the appropriate basis for this time-domain scheme. We show that a small number of pulses are sufficient to produce a wide range of target states (both classical and nonclassical target states are designed).
A general analytical formalism is described for the design of the excitation pulse (in the weak-field limit) that will excite a specified target wave packet. These analytical formulas (accurate to third order in the phase) provide multiple solutions for a class of target wave packets and provide a basis for choosing between these solutions. In addition, the possibility of independent compensation of the second- and third-order phase terms offers flexibility in the creation of exotic wave packets. A concrete design example is given for the generation of a well-localized Rydberg atomic wave packet at a specific target time.
Summary form only given. Design and excitation of novel quantum states and the measurement of those states is driven by both fundamental and technological goals. For example, the study of Schrodinger cat states touches upon the basic measurement hypotheses of quantum mechanics while the establishment of particular coherent superposition states is the starting point for the process of coherent control or for quantum information applications. The goals of the design research range from the manipulation of reaction pathways to the creation of novel states for the exploration of aspects of measurement theory. In addition to its fundamental interest the accurate measurement of both amplitude and phase of a wave function plays a key roles in the area of coherent control. The seminal work by Risken and Vogel (1989) reopened the modern discussion of the reconstruction problem that was first broached by Pauli. Since their work, reconstruction techniques have been developed for a variety of systems including the optical field in atomic systems. The measurement scheme used in the paper employs a noninterferometric technique. The subject of the measurement is a designed Rydberg wave packet in an atomic system. However, the noninterferometric character of the technique suggests that this technique may have wide applicability.
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.
By combining the theories of optimal control and coherent control, we derive an analytical formulation to evaluate the optimal 1-photon and n -photon fields together with their relative phase and intensity in the optimal “1 + n ”-coherent control scheme. The optimal coherent control exploits tailored light pulses to produce the best overlap with a predefined nuclear target in an electronically degenerate region. It also exploits explicitly the quantum interference between two optimal excitation pathways to achieve the product electronic selectivity. Numerical demonstrations are carried out to selectively control a minimum-uncertainty outgoing wave packet target in a molecular system. The electronically degenerate byproduct is shown to be completely discriminated against via the destructive interference between two optimal excitation pathways. The target considered in this paper would neither be achievable via the conventional continuous-wave coherent control nor via a single optimal control pathway in the weak response regime. Proposed is also a time-dependent excitation frequency degeneracy condition that incorporates the evolution of carrier frequencies in the optimal coherent control with tailored light fields.
We present a theoretical investigation of optical phase conjugation by use of nearly degenerate four-wave mixing in a two-level atomic system. The description is based on the semiclassical dressed-state approach, which offers a very transparent picture of the physics involved in the nonlinear process. The theory provides an explanation in terms of a quantum interference between two channels for the strong reduction of the optical phase-conjugate yield when the pump fields are tuned to the atomic resonance. In addition, the model predicts an efficient generation of the optical phase conjugate if the system is prepared in a pure dressed state.