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Physical Review A

Probing the quantum commutation rules through cavity QED

Qingqing Sun, M. Al-Amri, Muhammad Suhail Zubairy

Published Oct 1, 2008• 10 citations
Publisher

Abstract

We propose a cavity QED-based scheme to observe the noncommutativity between the creation and annihilation operators. By conditional measurement after the atom-field interaction in a cavity, it is possible to achieve a photon-added-then-subtracted state and a photon-subtracted-then-added state, which have different statistical properties. This scheme has the advantages of simple analytical results and much higher generation probabilities. We show that the ideal results of one-cycle photon addition and subtraction are approached in the short time limit. We also discuss the possible implementation scheme.

DOI
10.1103/physreva.78.043801

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We propose a cavity QED-based scheme to observe the noncommutativity between the creation and annihilation operators. By conditional measurement after the atom-field interaction in a cavity, it is possible to achieve a photon-added-then-subtracted state and a photon-subtracted-then-added state, which have different statistical properties. This scheme has the advantages of simple analytical results and much higher generation probabilities. We show that the ideal results of one-cycle photon addition and subtraction are approached in the short time limit. We also discuss the possible implementation scheme.
Theoretical analysis is given of an experimental scheme that can perform individual photon operations such as the photon annihilation operation a, creation operation a†, and commutation operation aa†−a†a, utilizing atom-cavity field interactions and conditional measurements. In order for the scheme to perform the desired photon operation, the atom-cavity field interaction times are generally required to be sufficiently short that photon annihilation and/or creation are dominated by the one-half Rabi cycle process. Such short interaction times, however, lead inevitably to a low success probability of the scheme. It is shown that this problem of low success probability can be overcome by preparing the cavity field in a superposition of a small number (two) of Fock states and choosing the interaction times appropriately.
We propose an experimental scheme to prove the photon commutation relation, [ a , a † ]=1. The scheme exploits interaction between a single-mode cavity field and three two-level atoms, two of which are prepared in an entangled state. The success of the scheme is subject to observation of the atoms in predetermined states after the interaction. We show, in particular, that a reasonably high success probability can be obtained with our scheme by preparing the cavity field in a superposition of two Fock states and choosing the interaction times appropriately.
A scheme for approximately and conditionally teleporting an unknown atomic state via two-photon interaction in cavity QED is proposed. It is the extension of the scheme of Ref. [11] [Phys. Rev. A 69 (2004) 064302], which is based on Jaynes–Cummings model in QED and where only a time point of system evolution and the corresponding fidelity implementing the teleportation are given. In our scheme, the two-photon interaction Jaynes–Cummings model is used to realize the approximate and conditional teleportation. Our scheme does not involve the Bell-state measurement and an additional atom, only requiring two atoms and one single-mode cavity. The fidelity of the scheme is higher than that of Ref. [11]. The scheme may be generalized to not only the teleportation of the state of a cavity mode to another mode by means of a single atom but also the teleportation of the state of a trapped ion.
A simple scheme is proposed to generate an nnn-qubit WWW state in cavity QED. Conditioned on no photon leakage from the cavity, the nnn-qubit WWW state can be generated by resonant interaction between atoms and the cavity if the cavity is initially prepared in the single-photon state and all the atoms are in the ground states. We check the time evolution of the system involving decay, and show that, since the required interaction time is very short, with present cavity QED techniques, the success probability of our scheme is almost unity.
The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.