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Acta Physica Sinica (Overseas Edition)

Preparation of nonclassical states of a cavity field based on a nonlinear Jaynes-Cummings model

Wei Wei, Guo Guang-Can

Published Mar 1, 1998• 5 citations
Publisher

Abstract

It is proven in this paper that some kinds of nonclassical quantum states of the cavity field, such as Schrödinger cat state (amplitude cat or phase cat), sub-Poissonian photon distribution and Fock state, etc., can be generated by conditional measurements on atoms in the two-photon Jaynes-Cummings model with a Kerr-like medium. The nonlinear constant plays the key modulation role in the preparation of the quantum states, which gives a new controllable parameter for further experimental researches in this field.

DOI
10.1088/1004-423x/7/3/003

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It is proven in this paper that some kinds of nonclassical quantum states of the cavity field, such as Schrödinger cat state (amplitude cat or phase cat), sub-Poissonian photon distribution and Fock state, etc., can be generated by conditional measurements on atoms in the two-photon Jaynes-Cummings model with a Kerr-like medium. The nonlinear constant plays the key modulation role in the preparation of the quantum states, which gives a new controllable parameter for further experimental researches in this field.
We study the following situation: A two-level atom interacts according to the Jaynes–Cummings model with a quantized cavity field prepared in a coherent state by a classical source. The atom is selectively ionized after exiting the cavity, and it is found that the field states are highly dependent, for a given interaction time, on the outcome of the measurement and are dramatically different from those in the case of no selective measurement. First we show how to obtain a bifurcated Poisson distribution for which the probability of finding the photon number at the center of the initial Poisson distribution vanishes. Then we study the generation of sub-Poissonian states and show that the cavity field can approach a number state with a sequence of properly prepared and measured atoms.
The interaction of a cavity field with an entangled state of atoms is studied according to the nonlinear Jaynes-Cummings model. It is shown that the properties of the cavity field depend on not only the interaction time but also the nonlinear constant. After detecting an atom of the entangled state, the cavity field will be entangled with another atom even it is far away from the cavity. It is proved that the nonclassical properties of the field state are dramatically different from those in the case of no selective measurement.
A simple scheme is presented that allows the generation and detection of nonclassical states of the electromagnetic (em) field with controllable (predetermined) photon-number and phase distributions. It is based on the two-photon resonant interaction of a single em field mode in a high-Q cavity with initially excited atoms crossing the cavity sequentially (one at a time). The sequence duration should be much shorter than the cavity-mode lifetime. Nonclassical states of the field are generated conditionally, by selecting only those sequences wherein each atom is measured to be in the excited state after the interaction. The field distribution resulting from a sequence of N such measurements is peaked about 2N positions in the phase plane, which evolve sinusoidally as a function of the atomic transit times and are therefore simply controlled. When these peaks are chosen not to overlap, the field state constitutes a generalized Schr\"odinger cat. By choosing them to overlap, we can make parts of the field distribution strongly interfere, giving rise to decimation of the photon-number distribution. In particular, this process can prepare Fock states with controlled photon numbers. The generated phase distribution can be detected by monitoring the pattern of revivals in the excitation of a ``probe'' atom.
In this thesis we investigate the possibilities to create non-classical states by using light-matter interactions. Our basic approach to describe these interactions is the Jaynes-Cummings model. It describes interactions between a two-level atom and a quantized field in a lossless cavity (ultra high Q quality factor). The model can be easily generalized to describe multi-level atoms, Stark shifts, Kerr interactions, micromasers, etc. We use some of these generalizations in our study. Our main interest is in the production of Schrodinger cat states, that is, the coherent superposition of two or more classical macroscopic states; and the production of sub-Poissonian photostatistics. First of all, we use the simple Jaynes-Cummings model to investigate the interaction of coherent states with two-level atoms, and compare it to the case of interaction with a statistical mixture to show that we can discern between the two. We investigate as well the interaction of two level atoms and squeezed light, where we show that these states have a strong coherent character. However, the model itself is very simple, and as we have said before, some generalizations are necessary if we are to describe more realistically the atom field interactions. In particular, we use a phenomenological Hamiltonian, which incorporates Stark shifts in the atomic levels due to the electric field in the cavity, and show that some experimental results concerning the lineshapes in micromasers may be explained by such effects. Another step is to allow the atoms to enter and leave the cavity, which leads us to investigate a micromaser system. Within this structure, we allow for one- and two-photon transitions. In the latter case, it is shown that sub-Poissonian fields (by using special atom-field interaction times) and multi Schrodinger cat states (by measuring the state of the atoms as they leave the cavity) can be generated.
An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.