Spectrum of photons generated in a one-dimensional cavity with oscillating boundary

David L. Feder, Adam G. D’Souza, Barry C. Sanders

Han Cai, Qichun Liu, Chang-Hao Zhao +3 more

We report the implementation of qubit–qubit coupling in a three-dimensional (3D) cavity, using the exchange of virtual photons, to realize logical operations. We measure single photon and multi-photon transitions in this qubit–qubit coupling system and obtain its energy avoided-crossing spectrum. With ac-Stark effect, fast control of the qubits is achieved to tune the effective coupling on and off and the state-swap gate S W A P is successfully constructed. Moreover, using two-photon transition between the ground state and doubly excited states, a kind of two-photon Rabi-like oscillation is observed. A quarter period of this oscillation corresponds to the logical gate b S W A P , which is used for generating Bell states. b S W A P and i S W A P are the foundations of future preparation of two-qubit Bell states and realization of CNOT gate.

A. I. Alekseev

Xiao-Ping Feng, Kikuo Ujihara

A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).

Liping Fu, Chang‐Kui Duan, Guang‐Can Guo

Mauro Antonio ANDREATA, Alexandre V. Dodonov, V. V. Dodonov +1 more

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ω3 = 3ω1, whose wall oscillates at the frequency ωw = 2ω1, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum ωn = nω1 where the distance between perfect mirrors oscillates at the frequencies ω1 and 2ω1. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.