Quantum computation with trapped ions in strongly detuned optical cavity

We propose a scheme to implement quantum phase gate for two Λ ions trapped in optical cavity. It is shown that quantum phase gate can be implemented by applying a laser addressing to a single ions in strongly detuned optical cavity. We further demonstrate that geometric quantum phase gate can be implemented by introducing a auxiliary ground state. In recent years, it is realized that quantum computer can provide more powerful computational ability than a classical one[1, 2]. This discovery motivated intensive research into apparatus which can be used to perform quantum logic operation on single or multiple qubits. To bulid a real quantum computer, we need to find quantum system, which have little decoherence and easy way for coherent operation. Several possible physical implementation have been suggested, including the Cavity QED[3], trapped ion system[4] and NMR system[5] and solid state system using nuclear spins[6], quantum dots[7] and Josephson Junction[8]. The ion trap quantum computation, first proposed by Cirac and Zoller[9], and demonstrated experimentally shortly afterward[10], is a promising candidate for realizing a small scale of quantum computation. They offer the possibility in principle to store string of ions, cool them almost to zero temperature and address them individually with laser field. The original idea of Cirac and Zoller uses the collective spatial vibrations for communication between ions, and it requires that the system is restricted to the joint motional ground state of the ions. For two ions, this has recently been accomplished[11]]. Any heating (i.e. excitation by external fields) will diminish the accuracy of a logic gate, thus leading to unreliable performance of the quantum computer as a whole, and may be making the implement of even simple algorithms impossible. Eliminating all of the possible cause of heating is a very demanding task. Several schemes[12, 13, 14, 15, 16] have been proposed to address the problem. Recently approaches have been proposed which employs ions trapped in an optical cavity. It has been shown that cavity decay can be used to create entan-glement implement quantum computation between ions in cavity[17]. More recently, a scheme is proposed to implement quantum information processing with ions trapped in strongly detuned optical cavity[18]. All these scheme require that laser fields addressing different ions was will matched in amplitude and phase. In this paper, we propose 1