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Acta Physica Sinica

QUANTUM JUMP AND CONTINUOUS MEASUREMENT IN MULTI-LEVEL ATOM

Yi-Xin Chen, SHANGGUAN WANGZUO, JI DA-REN, (1)浙江大学环境科学系,杭州 310028; (2)浙江大学浙江近代物理中心和物理系,杭州 310027

Published Jan 1, 1999• 0 citations
Publisher

Abstract

In this paper we investigate the quantum jump in a multi-level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi-level atom with incident resonant laser. It is proved that pure state analysis theory is no longer applicable to a multi-level atom system, so a mixed one is developed, concluding that the resetting density of a multi-level atom should be described by mixed state analysis theory. We also discuss the continuous quantum measurement along with quantum jumping in a multi-level atom.

DOI
10.7498/aps.48.775

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In this paper we investigate the quantum jump in a multi-level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi-level atom with incident resonant laser. It is proved that pure state analysis theory is no longer applicable to a multi-level atom system, so a mixed one is developed, concluding that the resetting density of a multi-level atom should be described by mixed state analysis theory. We also discuss the continuous quantum measurement along with quantum jumping in a multi-level atom.
Abstract In this paper we investigate the quantum jump in a multi level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi level atom with incident resonant laser.It is proved that pure state analysis theory is no longer applicable to a multi level atom system,so a mixed one is developed,concluding that the resetting density of a multi level atom should be described by mixed state analysis theory.We also discuss the continuous quantum measurement along with quantum jumping in a multi level atom.
Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.
Abstract A method is presented for transfer of a quantum state from one atom to another atom. In this method, we consider the interaction of a multi-mode cavity with a multi-level quantum system and adopt the multi-photon resonance theory for preparing an efficient quantum memory and a quantum network. From the use of effective two- and three-level Hamiltonians, the proper values for interaction times, coupling constants, and detunings are predicted. To examine the sensitivity of the quantum state transfer against decoherence processes, we introduce the quantum-jump approach. Proceeding with this approach leads to a description of the system via wavefunctions instead of density operators and provides simple effective differential equations for obtaining analytic expressions of the probability amplitudes.
In Chap. 17 we developed the quantum theory of the laser obtaining in particular expressions for the laser photon statistics and linewidth. In this chapter we discuss and amplify those results in terms of measurement theory. Section 18-1 provides an overview of measurement theory as it applies to the quantum electric field. The discussion leads naturally into a specific discussion of the measurement of photon statistics and the laser linewidth. In Sec. 18-2 a heuristic model of a photodetector is presented with reveals how the photo­ electron statistics resulting from incident radiation is related to the photon statistics of that radiation, t In Sec. 18-3 we discuss the laser linewidth with the use of a simple two level atom beam much like that of Sec. 16-1. Our present discussion utilizes the density matrix technique throughout rather than the density matrix-state vector combination of Sec. 16-1. The laser spectrum “seen” by the atomic beam has, in fact, the same Lorentzian profile given in Sec. 17-3. In Sec. 18-4 the laser linewidth is discussed in terms of a quantum version of the classical correlation function <£(* -f t )E(t)y. In spite of the fact that two time correlations are apparently required, we show that a single time and solutions to the density operator equation of motion are sufficient. This reduction is an example of the so-called Onsager regression hypothesis, which shows how to proceed from single-time to multitime correlation functions.
We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.
We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.